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31st Mechanisms and Robotics Conference

2007;():3-11. doi:10.1115/DETC2007-34191.

A compliant mechanism transmits motion and force by deformation of its flexible members. It has no relative moving parts and thus involves no wear, lubrication, noise, and backlash. Compliant mechanisms aims to maximize flexibility while maintaining sufficient stiffness so that satisfactory output motion can be achieved. When designing compliant mechanisms, the resulting shapes sometimes lead to rigid-body type linkages where compliance and rotation is lumped at a few flexural pivots. These flexural pivots are prone to stress concentration and thus limit compliant mechanisms to applications that only require small-deflected motion. To overcome this problem, a systematic design method is presented to synthesize the shape of a compliant mechanism so that compliance is distributed more uniformly over the mechanism. With a selected topology and load conditions, this method characterizes the free geometric shape of a compliant segment by its rotation and thickness functions. These two are referred as intrinsic functions and they describe the shape continuously within the segment so there is no abrupt change in geometry. Optimization problems can be conveniently formulated with cusps and intersecting loops naturally circumvented. To facilitate the optimization process, a numerical algorithm based on the generalized shooting method will be presented to solve for the deflected shape. Illustrative examples will demonstrate that through the proposed design method, compliant mechanisms with distributed compliance will lessen stress concentration so they can be more robust and have larger deflected range. It is expected that the method can be applied to design compliant mechanisms that have a wide variety of applications from precision instruments to biomedical devices.

Commentary by Dr. Valentin Fuster
2007;():13-23. doi:10.1115/DETC2007-34249.

This paper presents a closed-form analysis of a series of planar tensegrity structures to determine all possible equilibrium configurations for each device when no external forces or moments are applied. The equilibrium position is determined by identifying the configurations at which the potential energy stored in the springs is a minimum. The degree of complexity associated with the solution was far greater than expected. For a two-spring system, a 28th degree polynomial expressed in terms of the length of one of the springs is developed where this polynomial identifies the cases where the change in potential energy with respect to an infinitesimal change in the spring length is zero. Three and four spring systems are also analyzed. These more complex systems were solved using the Continuation Method. Numerical examples are presented.

Commentary by Dr. Valentin Fuster
2007;():25-32. doi:10.1115/DETC2007-34428.

An approach to design compliant mechanisms starting from rigid-body solution is presented in this work. However, instead of starting the optimization with a topology of fully populated rectangular grid of finite elements, the method begins with a design region that the links of the corresponding rigid-body mechanism (RBM) are likely to occupy as the mechanism traverses the intended task. The aim is to reduce the complexity of topology optimization by reducing the number of design variables. Several space reduction ideas and associated objective criteria are presented. A tabu-gradient algorithm is developed and adapted to solve the optimization problem. Several examples are given to demonstrate the proposed method.

Commentary by Dr. Valentin Fuster
2007;():33-45. doi:10.1115/DETC2007-34437.

A novel method is proposed in this paper to address the cutting-edge problem of topology optimization of distributed compliant mechanisms, which requires the design to possess both large output displacements and evenly distributed compliance simultaneously. The design is represented by a level-set model that precisely specifies the distinct material regions and their sharp interfaces as well as the geometric boundary of the structure, capable of performing topological changes and capturing geometric evolutions at the interface and the boundary. Existing techniques for eliminating de facto hinges in the design are reviewed. Further, the intrinsic deficiencies in the widely used “spring model” are discussed and a new formulation considering the “characteristic stiffness” of the mechanism is proposed. The proposed method is demonstrated with benchmark examples of compliant mechanism optimization. The result is a design with evenly distributed compliance and a more desirable characteristic, which uniquely distinguishes our method.

Commentary by Dr. Valentin Fuster
2007;():47-53. doi:10.1115/DETC2007-34531.

Research is presented on describing the deflection behavior of prismatic beams with high aspect ratio rectangular cross-sections undergoing lateral torsional buckling. The 3-D large deflection path of buckling beam tips was closely approximated by circular arcs in two planes. When deflection paths of beams with different geometric and material properties were nondimensionalized with respect to the beam length, these deflection paths were the same with very little variation. Similarly, the change in the beam tip orientation as the beams deflected also remained the same as geometry and material properties were varied.

Topics: Buckling , Deflection
Commentary by Dr. Valentin Fuster
2007;():55-66. doi:10.1115/DETC2007-34782.

The kinematic portion of a pseudo-rigid-body model (PRBM) is developed as a generalization from planar to spherical mechanisms. The topology of the spherical compliant segment and its rigid-body equivalent are derived from planar models by analogy. The nomenclature for the spherical PRBM is chosen to facilitate comparison with the planar PRBM. The motion of the compliant segment is calculated using FEA and PRBM parameters are determined. The characteristic radius and parametric angle coefficient are found to decrease as the angle subtended by the beam increases. The parameterization limit increases with increasing beam angle. The spherical PRBM is identical to the planar PRBM in the limiting case when beam angles become very small.

Commentary by Dr. Valentin Fuster
2007;():67-73. doi:10.1115/DETC2007-34836.

This paper describes the design of a novel multi-stable compliant mechanism capable of large angle deflections. The multi-stable COmpliant Rolling-contact Element (CORE), reduces friction, allows for large angular displacements, and requires no external force to remain in its multiple equilibrium positions. This paper develops and discusses seven methods to create multi-stable mechanisms from the CORE. These seven methods have different characteristics and advantages.

Commentary by Dr. Valentin Fuster
2007;():75-81. doi:10.1115/DETC2007-34969.

This paper presents an alternative to fabrication methods commonly used in compliant mechanisms research. This method integrates torsional springs made of formed wire into compliant mechanisms. In this way the desired force, stiffness, and motion can be achieved from a single piece of formed wire. Two techniques of integrating torsion springs are fabricated and modeled: helical coil torsion springs and torsion bars. Because the mechanisms are more complex than ordinary springs, simplified models, which aid in design, are presented which represent the wireform mechanisms as rigid body mechanisms using the pseudo-rigid-body model. The method is demonstrated through the design of a mechanically tristable mechanism. The validity of the simplified models is discussed by comparison to finite element models and, in the case of the torsion bar mechanism, to experimental measurements.

Commentary by Dr. Valentin Fuster
2007;():83-91. doi:10.1115/DETC2007-34971.

This paper presents a mathematical approach to synthesizing a multi-stable behavior by combining multiple bi-stable equilibrium mechanisms in series. Behavior of a bi-stable compliant mechanism, in general, is highly non-linear. Combinations of such non-linearities to capture the behavior of multi-stable (more than two stable positions) mechanisms can be very challenging. We present a simplified mathematical scheme to capture the essential parameters of bi-stability such as force-thresholds that cause the jump to next stable position etc. to derive multi-stable behavior. This mathematical simplification enables us to characterize bi-stable mechanisms using piecewise lower-order polynomials and synthesize multi-stable mechanisms through combination of bi-stable behaviors in series. We present two case studies of combinations of two and three bi-stable behaviors to generate mechanisms with four and five stable positions respectively. A design example of a quadri-stable equilibrium rotational compliant mechanism consisting two bi-stable sub-mechanisms is presented to demonstrate the effectiveness of the approach.

Commentary by Dr. Valentin Fuster
2007;():93-100. doi:10.1115/DETC2007-34977.

This paper proposes a new family of large-displacement flexural pivots. The design in this family is derived from the conventional notch-type flexures, which are capable of high rotational precision and a compact structure. However, the proposed new flexural pivots can offer a much larger range of motion (up to 60°) compared with those old flexures. In order to construct the profile of these new flexures, a method based on large-deflection axial buckling theory was introduced to determine their initial flexible curvature profiles. In addition, the characteristic comparisons and optimizations of the proposed flexures were made using Finite Element Analysis.

Topics: Displacement
Commentary by Dr. Valentin Fuster
2007;():101-109. doi:10.1115/DETC2007-35070.

This paper introduces a compliant mechanism design method that guarantees structural connectivity and planarity of the resulting design. The structural connectivity is ensured by a path-representation, while a coin-optimization process is introduced to verify the planarity of the design. A non-planar design can be “planarized” by a coin-repair process, thus all non-planar designs can be effectively excluded from the solution space. The discrete topology optimization problem is incorporated in a genetic algorithm. The resulting topology is further processed through size and shape optimization for improved stress distribution. The results from two benchmarking design examples showed that the proposed method is capable of producing planar mechanisms in a reasonable amount of computing time. The presented design method will be incorporated into an on-going research in the design of biomimetic wings for Micro-Aerial Vehicles (MAVs).

Commentary by Dr. Valentin Fuster
2007;():111-126. doi:10.1115/DETC2007-35244.

We use non-linear finite element simulations to study the convergence behavior of the honeycomb or hex cell design discretization for optimization-based synthesis of compliant mechanisms in this paper. Adjacent elements share exactly one common edge in the hex cell discretization, unlike the square cell discretization in which adjacent elements can be connected by a single node. As the single node connections in bilinear quadrilateral plane stress elements allow strain-free relative rotations, compliant mechanism designs obtained from square cell discretizations with these elements often contain elements with single node connections or point flexures. Point flexures are sites of lumped compliance, and as such, are undesirable as they lead to compliant mechanisms designs which deviate from the ideal of distributed compliance. The hex cell design discretization circumvents the problem of point flexures without any additional computational expense (e.g. filtering, extra constraints, etc.) by exploiting the geometry of the discretization. In this work we compare the elastic response of a group of four cells in which two adjacent cells have the least connectivity in both: the square and the hex discretizations. Simulations show that the hex cell discretization leads to a more accurate modeling of the displacement, stress and strain energy fields in the vicinity of the least connectivity regions than the square cell discretization. Therefore, the hex cell discretization does not suffer from stress singularities that plague the square cell discretization. These properties ensure that continuous optimization-based compliant mechanism synthesis procedures that use the hex cell discretization, exhibit a faster and more stable convergence to designs that can be readily manufactured than those that use the square cell discretization.

Commentary by Dr. Valentin Fuster
2007;():127-135. doi:10.1115/DETC2007-35345.

Although there are capacitive surface micromachined force sensors with adequate resolution for cell manipulation and microneedle injections, it comes with the sacrifice of dynamic range and linearity. In contrast, optical based force sensors can provide the desired resolution and maintain relatively large sensing ranges compared to similar capacitive sensors. Plus, optical interferometry provides a sensing method that uncouples the conflicting design parameters, such as sensitivity and linearity. The current drawback to optical interferometry is the large off-chip equipment that is currently used in the operation of optical sensors. However, innovative techniques are being applied to surface micromachined microphones that allow off-chip components to be integrated onto the sensing chip. These same techniques can easily translate to the force sensor presented in this research, due to the similarities in the sensing methods. The thrust of this work is to explore a mechanism approach for enhancing the performance of a surface micromachined optical force sensor. A new design is presented which introduces a special mechanism, known as the Robert’s mechanism, as an alternate means in which the device is structurally supported. The new design’s implementation is achievable using an equivalent compliant mechanism. Initially, an analytical set of pseudo-rigid-body-model equations were developed to model the compliant design. A more accurate model was then constructed using FEA methods. The geometric parameters of the compliant Robert’s mechanism were then optimized to obtain a sensor with improved linearity and sensitivity. Overall, the force sensor provides higher sensitivity, larger dynamic range and higher linearity compared to a similar optical force sensor that uses a simple structural supporting scheme. In summary, this paper demonstrates the effectiveness of using a mechanism approach for enhancing the performance of MEMS sensors. The expected impact is to improve biomedical experiments and help further advance research that can improve quality of life.

Commentary by Dr. Valentin Fuster
2007;():137-146. doi:10.1115/DETC2007-35449.

In this paper a new method for the synthesis of compliant mechanism topologies is presented which involves the decomposition of motion requirements into more easily solved sub-problems. The decomposition strategies are presented and demonstrated for both single input-single output (SISO) and dual input-single output (DISO) planar compliant mechanisms. The methodology makes use of the single point synthesis (SPS) which effectively generates topologies which satisfy motion requirements at one point by assembling compliant building blocks. The SPS utilizes compliance and stiffness ellipsoids to characterize building blocks and to combine them in an intelligent manner. Both the SISO and DISO problems are decomposed into sub-problems which may be addressed by the SPS. The decomposition strategies are demonstrated with illustrative example problems. This paper presents an alternative method for the synthesis of compliant mechanisms which augments designer insight.

Commentary by Dr. Valentin Fuster
2007;():147-159. doi:10.1115/DETC2007-35505.

Pop-up paper mechanisms use techniques very similar to the well-studied paper folding techniques of origami. However, popups differ in both the manner of construction and the target uses, warranting further study. This paper outlines the use of planar and spherical kinematics to model commonly used pop-up paper mechanisms. A survey of common joint types is given, including folds, interlocking slots, bends, pivots, sliders and rotating sliders. Also included is an overview of common onepiece and layered mechanisms, including single-slit, double-slit, V-fold, tent, tube strap and arch mechanisms. Each mechanism or joint is described using a kinematic or compliant mechanism representation. In addition, it is shown that more complex mechanisms may be created by combining simple mechanisms in various ways. The principles presented are applied to the creation of new pop-up joints and mechanisms. The new mechanisms employ both spherical and spatial kinematic chains. Various other applications are also mentioned which could benefit from the use of pop-up mechanism principles. Possible applications include deployable structures, packaging and instruments for minimally invasive surgery.

Commentary by Dr. Valentin Fuster
2007;():161-170. doi:10.1115/DETC2007-35535.

Nonlinear springs can simplify and improve the performance of a variety of devices, including prosthetics, MEMS, and vehicle suspensions. Each nonlinear spring application has unique load-displacement specifications that do not correspond to one general spring design. This limits the use of nonlinear springs and thus compromises the performance of these applications. This paper presents a generalized methodology, including topology, size, and shape optimization, for creating nonlinear springs with prescribed load-displacement functions. The methodology includes a new parametric model that represents nonlinear springs as a single-plane, ‘fractal’-like network of splines. The parametric model and the objective function are incorporated into a genetic algorithm optimization scheme. Nonlinear finite element analysis evaluates the large displacements of each spring design. Three nonlinear spring examples, each having uniquely prescribed load-displacement functions including a “J”-shaped, an “S”-shaped, and a constant-force function, generate designs that demonstrate the methodology’s effectiveness in designing nonlinear springs.

Commentary by Dr. Valentin Fuster
2007;():171-178. doi:10.1115/DETC2007-35536.

This paper presents a pseudo-rigid-body model (PRBM) for rolling-contact compliant beams (RCCBs). The loading conditions and boundary conditions for the RCCB can be simplified to an equivalent cantilever beam that has the same force-deflection characteristics as the RCCB. Building on the PRBM for cantilever beams, this paper defines a model for the force-deflection relationship for RCCBs. The definition of the RCCB PRBM includes the pseudo-rigid-body model parameters that determine the shape of the beam, the length of the corresponding pseudo-rigid-body links and the stiffness of the equivalent torsional spring. The behavior of the RCCB is parameterized in terms of a single parameter defined as clearance, or the distance between the contact surfaces. RCCBs exhibit a unique force-displacement curve where the force is inversely proportional to the clearance squared.

Topics: Rolling contact
Commentary by Dr. Valentin Fuster
2007;():179-190. doi:10.1115/DETC2007-35618.

This paper will present a version of failure theory suitable for designing optimal compliant mechanisms. The resulting theory will be incorporated as design objective functions within a multi-objective optimizing engine with the purpose of producing optimal and robust compliant mechanisms suitable for manufacture. Combining these failure-based objective functions with the classical ones measuring efficiency in performing a task, in the context of diversity promoting multiobjective optimization (see [1]) will demonstrate the tool’s ability to produce optimal compliant mechanisms that are failure-proof as well as provide insights into the complexity of particular design problems.

Commentary by Dr. Valentin Fuster
2007;():191-197. doi:10.1115/DETC2007-35821.

Recent interest in small Unmanned Air Vehicles (UAVs) has led to advances in wing technologies. Deployable wings reduce required storage space while providing greater range during flight. This paper presents a compliant rotating joint which is bistable and features a locking characteristic that prevents the wing from reverting back to the undeployed configuration during flight. The two stable positions occur at local strain energy minima about 90 degrees apart, but can be adjusted by the designer. A pseudo rigid body model is illustrated for the joint, based on a four-bar linkage. Such a joint mechanism can be designed for any wing, by using the pseudo rigid body model to optimize link lengths and position the instant center appropriately. In addition, the mechanism can be cut out within a single plane for ease of manufacture and assembly.

Commentary by Dr. Valentin Fuster
2007;():199-207. doi:10.1115/DETC2007-34595.

This paper presents a concept for virtual-reality-based vehicle simulation with whole-body haptics. The cable-suspended NIST RoboCrane is adapted to carry human operators in simulating a variety of vehicle motions. A realistic, immersive VR system is proposed with 3D graphics, haptic motion input devices, 3D surround-sound audio, articulating fans, and an olfactory generator. The real-world cockpit and input devices will be used to increase realism, suspended from nine active cables for motion simulation. The intent is to replace existing heavy, expensive, and dangerous Stewart-Platform-based flight simulators with a lighter, more economical, stiff, safe, high bandwidth, cable-suspended system. Many potential applications are proposed in addition to flight simulation. Our long-term goal is to create an economical, safe, realistic vehicle simulator with full-body motion for operator training, research & development, vehicle design, entertainment, rehabilitation, and therapy.

Topics: Cables , Simulation , Vehicles
Commentary by Dr. Valentin Fuster
2007;():209-215. doi:10.1115/DETC2007-34880.

Vibration isolation devices are used to attach various systems to their base structure to reduce the transmission of vibration from and/or to the base structure. Vibration isolation devices allow relative motion between the isolated system and the base platform. This relative motion is critical to the effective operation of vibration isolation devices and is used to absorb or divert vibration energy using spring and viscous damping or dry friction elements. In general, larger the allowed relative motion, more effective will be the performance of the isolation system. In certain applications, the introduced relative motion by the vibration isolation device introduces unavoidable and unwanted motion of the isolated system and can significantly degrade its performance, particularly in terms of positioning precision, or limit the range of allowable relative motion, thereby reducing the effectiveness of the isolation system. In this paper, a novel method is presented that uses appropriate linkage mechanisms to constrain relative motions that are introduced by the vibration isolation system that are not necessary for the proper operation of the vibration isolation system but their presence would degrade the performance of the entire system. As an example, a novel double-parallelogram based motion constraining mechanism is presented, which is used to constrain rotational (rocking) motion of an isolation system without hindering its relative translational motion used for vibration isolation. The design of a prototype of such a linkage mechanism used to isolate payloads from launch vehicles during the launch and the results of its successful testing are presented. Other applications of the present method are discussed.

Commentary by Dr. Valentin Fuster
2007;():217-223. doi:10.1115/DETC2007-34981.

A Leaf-type Isosceles-trapezoidal Flexural (LITF) pivot can be of great practical use for designing compliant mechanisms. The analysis of load-deflection behavior for such a pivot is essential to the study on the mechanisms which are composed of the pivots. A pseudo-rigid-body model provides a simple and accurate method. Based on the analysis of a single special loaded leaf segment, a four-bar model is presented. The four-bar model is further simplified to a pin-joint model for the simpler applications. The accuracy of both models is demonstrated by comparing results to those of non-linear finite element analysis. At last, the two models are applied to analyze the cartwheel hinge as an example.

Commentary by Dr. Valentin Fuster
2007;():225-229. doi:10.1115/DETC2007-35269.

In this paper a robotic micro-drilling technique for surgery is described. The device has been deployed in cochleostomy, a precise micro-surgical procedure where the critical stage of controlling penetration of the outer bone tissue of the cochlea is achieved without penetration of the endosteal membrane at the medial surface. The significance of the work is that the device navigates by using transients of the reactive drilling forces to discriminate cutting conditions, state of tissue and the detection of the medial surface before drill break-out occurs. This is the first autonomous surgical robot to use this technique in real-time as a navigation function in the operating room and unlike other fully autonomous surgical robotic processes it is carried out without the use pre-operative data to control the motion of the tool. To control tool points in flexible tissues requires self-referencing to the tissue position in real time. There is also the need to discriminate deflections of the tissue, tissue interface, involuntary patients/ tissue movement and indeed movement induced by the drill itself which require different strategies to be selected for control. As a result of the design of the final system, the break-out process of the drill can either controlled to the required level of pro-trusion through the flexible interface or can be avoided altogether, with the drill bit at the medial surface. This enables, for the first time, the control of fine penetration with such great precision.

Topics: Robots , Surgery
Commentary by Dr. Valentin Fuster
2007;():231-238. doi:10.1115/DETC2007-35384.

Endoscopes are used in medical practice to effect minimally invasive diagnostics and treatments through a natural or surgical orifice. The endoscope is a snakelike device with a two degree-of-freedom articulated tip that bends in any direction using internal cables actuated by knobs. In this paper we use a serial robot model of the tip to show that the tip motions are not decoupled with respect to the knob inputs nor do they have constant gains. Further in a geometrical analysis it is shown that the articulated tip always lies along a circle. A tip kinematic control strategy is developed based on small motions that is able to decouple the output motions from the input motions and provide a constant gain functions. This allows the surgeon to control the endoscope in an intuitive and efficient manner.

Topics: Endoscopes
Commentary by Dr. Valentin Fuster
2007;():239-249. doi:10.1115/DETC2007-35625.

The Momentum-exchange/electrodynamic reboost (MXER) tether system has been proposed as a highly fuel-efficient means to enable high-energy missions to the Moon, Mars and beyond by serving as an “upper stage in space”. The MXER tether system combines electrodynamic propulsion via a conducting tether with energy storage and a transfer mechanism to boost spacecraft from low Earth orbit to a high-energy orbit quickly, like a high-thrust rocket. One of the significant challenges in developing a momentum-exchange/electrodynamic reboost tether system is the design of a mechanism that will enable a high speed rendezvous and docking process in an energy efficient manner [1]. This paper will review two elements of the process of developing an appropriate mechanism to accommodate the MXER tether capture process. The paper will begin with the derivation of a qualitative and quantitative description about the nature of the capture window due to parameteric uncertainties in the MXER tether. The paper will then present a several candidate capture mechanisms and will evaluate their performance relative to the kinematic and dynamic aspects of performing the capture process.

Topics: Momentum , Mechanisms
Commentary by Dr. Valentin Fuster
2007;():251-256. doi:10.1115/DETC2007-35783.

In recent studies, a new class of planar and spatial linkage mechanisms was presented in which for a continuous full rotation or continuous rocking motion of the input link, the output link undergoes two continuous rocking motions. Such linkage mechanisms were referred to as the “motion-doubling” linkage mechanisms. This class of mechanisms was also shown to generally have dynamics advantage over regular mechanisms designed to achieve similar gross output motions. In a recent study, the application of such motion-doubling linkage mechanisms to vehicle suspension system was investigated. In the present study, the performance of a vehicle using such a suspension system is compared to a suspension system regularly used in vehicles. For a typical set of vehicle and tire parameters, the parameters of both suspension systems are optimally determined with a commonly used objective function. The performance of the two systems in the presence of various input disturbances is then determined using computer simulation. It is shown that suspension systems constructed with motion-doubling linkage mechanisms can provide a significantly superior performance as compared to a commonly used suspension system.

Commentary by Dr. Valentin Fuster
2007;():257-263. doi:10.1115/DETC2007-34178.

The dual-wheel transmission is a novel drive for wheeled mobile robots; it provides unique features: symmetric structure; load distribution; unlimited steering capacity; and self-rotation while keeping the platform stationary. This paper discusses alternative prototypes of mobile robots with dual-wheel transmissions. We find the conditions of the design parameters in each prototype to achieve isotropic designs, which guarantee optimum maneuverability.

Topics: Design , Mobile robots
Commentary by Dr. Valentin Fuster
2007;():265-271. doi:10.1115/DETC2007-34248.

This paper addresses the control of structural vibrations of a 3-PRR parallel manipulator with three flexible intermediate links, bonded with multiple lead zirconate titanate (PZT) actuators and sensors. Flexible intermediate links are modeled as Euler-Bernoulli beams with pinned-pinned boundary conditions. A PZT actuator controller is designed based on strain rate feed control (SRF). Control moments from PZT actuators are transformed to force vectors in modal space, and are incorporated in the dynamic model of the manipulator. The dynamic equations are developed based on the assumed mode method for the flexible parallel manipulator with multiple PZT actuator and sensor patches. Numerical simulation is performed and the results indicate that the proposed active vibration control strategy is effective. Frequency spectra analyses of structural vibrations further illustrate that deformations from structural vibration of flexible links are suppressed to a significant extent when the proposed vibration control strategy is employed, while the deflections caused by inertial and coupling forces are not reduced.

Commentary by Dr. Valentin Fuster
2007;():273-280. doi:10.1115/DETC2007-34362.

This study is dedicated to achieve landing posture control of a generalized twin-body system using the methods of input-output linearization and computed torque. The twin-body system is a simplified model of bipedal robot, and the success in landing posture control would prevent structural damage. To the end, the dynamic equations are built based on Newton-Euler formulation. The technique of input-output linearization is next applied to the original nonlinear equations of motion, which is followed by adopting the method of computed torque to achieve desired landing postures. While designing the controller, system singularities are circumvented by choosing controllable set of initial conditions and stable landing postures. There are two uncontrollable postures that are immovable under input torques or/and the coupling centripetal and Coriolis forces. Finally, simulation results show that the designed controller is capable of performing desired landing posture control.

Topics: Torque
Commentary by Dr. Valentin Fuster
2007;():281-290. doi:10.1115/DETC2007-34605.

Dynamics and vibrations of flexible robot arms have received considerable attention in recent years. The flexibility of the arm affects the function of the robot and complicates its dynamics as well. Generally, the base of the robot arm has some elasticity, which also affects the precision of its function. We model the robot arm as a flexible beam moving in a vertical plane and resting on two springs: one is in the vertical direction and the other one is in the rotational direction. A lumped mass, which simulates the payload, is attached to the tip of the beam. The beam translates and rotates as a rigid body and moreover it deforms in the lateral direction. The extended Hamilton principle is used to derive the governing equations of motion and their corresponding boundary conditions. We obtained three coupled differential equations: two ordinary-differential equations governing the rigid-body motion of the arm and a partial differential equation governing its deformation. An exact solution for the natural frequencies and mode shapes of the vibrations of the arm about an equilibrium position is obtained. The significance of the effect of the flexibility of the link and the base and the ratio of the mass at the tip point to the mass of the beam on the natural frequencies and mode shapes is investigated.

Topics: Robots , Vibration
Commentary by Dr. Valentin Fuster
2007;():291-296. doi:10.1115/DETC2007-34661.

The design of using a single piezoelectric (PZT) trimorph actuator ultrasonically to drive a slider for two directional motions is reported. The working principle is the use of the resonant vibration induced force provided by the PZT trimorph driven at the specific frequency. In contact with a slider, the trimorph’s force overcomes the static friction of the slider and pushes the slider moving in one direction. The backward motion of the slider is achieved similarly by the different vibration mode of the PZT trimorph operated at the different resonant frequency. The merit of this work is the design of the rectangular PZT trimorph and its modes of vibration. The 3 mm by 9 mm rectangular trimorph was made of a 50 microns thick copper layer laminated with a 175 microns thick PZT layer on each face. As for ultrasonic motor operation, only one long edge of the trimorph was clamped. When the PZT layers were driven electrically at its resonant frequency and at the right phase, the PZT’s in-plane extensional vibration will turn into bending vibration. With extensive modal analysis in the Finite Element modeling, the 3:1 ratio of the length to width of the trimorph was found for the best performances. Both resonant frequencies and associated vibration modes were all identified. The performance of the prototype was experimentally evaluated by using laser interferometer and spectrum analyzer. Under 10 Vpp and 0.5 N preload, the measurement results show that the motor achieved the velocity of 200 mm/s and generated force of 0.1 N. If we divided the generated force and the slider velocity by the motor volume, the ultrasonic motor achieved the specific force of 3,282,447 3N/m3 and the specific velocity of 4,106,280 1/m2 s, respectively. Comparing with the published data, the specific velocity in this study is 100 times larger. The results in this work are suitable for applications in auto-focusing and zooming lens in cellular phone camera.

Commentary by Dr. Valentin Fuster
2007;():297-306. doi:10.1115/DETC2007-34743.

In this paper a new method for derivation and verification of rigid and flexible body kinematic and dynamic models of complex parallel robots including crank mechanisms is presented. The rigid body kinematic model is based on standard frame transformations and involves holonomic constraints. Lagrange’s equations of the first type are used for the dynamic modeling of the rigid structure. Using Euler-Bernoulli beams and assumed modes method, a new concept for deriving flexible kinematics and dynamics is developed considering configuration-dependent end masses, called effective payloads. Furthermore a vibration analysis is accomplished and a vibration damping strategy for the parallel robot based on input shaping is described. Through the whole verification process MSC.ADAMS models and measurement data of the demonstrator SpiderMill are used.

Commentary by Dr. Valentin Fuster
2007;():307-313. doi:10.1115/DETC2007-35093.

Possible vibration of cable-driven parallel manipulators (called cable manipulators for short) is a concern for some special applications such as hardware-in-the-loop (HIL) contact-dynamics simulation of spacecraft or space robotic systems. A cable manipulator used in HIL simulation is required to be rigid enough to have a high bandwidth to respond its input. This paper provides a vibration analysis of a general 6-DOF cable manipulator. Under an excitation, a cable may deflect in both axial and lateral directions due to its inevitable flexibility. The vibrations of cable manipulators caused by cable flexibility in both axial and lateral directions are analyzed. The study demonstrated that the cable manipulator can provide sufficient rigidity for applications like HIL contact-dynamics simulation of a spacecraft or space robotic system. It is also shown that the vibration of a cable manipulator due to the lateral flexibility of cables can be ignored comparing to that due to the axial flexibility of cables.

Commentary by Dr. Valentin Fuster
2007;():315-324. doi:10.1115/DETC2007-35252.

The paper proposes a new method to neutralize the shaking force and shaking moment exerted on its supporting structure by a one-degree-of-freedom machine whose non-stationary parts move parallel to the same plane. Differently from the well-known technique that takes advantage of two counterweighing shafts for each of the harmonic components of the frame excitation that has to be counteracted, the proposed method requires three shafts per harmonic component. This seemingly additional complexity is offset by the complete freedom of selection of the shaft axis positions, a feature not enjoyed by the classical two-shaft device. An example shows application of the proposed method to a four-cylinder in-line engine.

Topics: Machinery
Commentary by Dr. Valentin Fuster
2007;():325-332. doi:10.1115/DETC2007-35288.

This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system’s dynamic model. The theory of differential flatness is used as the basic approach in these developments. Flat outputs are found that linearize the system’s dynamic model using dynamic feedback linearization, a subclass of differential flatness. It is demonstrated that this property considerably simplifies motion planning and the development of controller. Simulation results are presented in the paper, which show that the developed controller has the desirable performance with exponential stability.

Topics: Path planning
Commentary by Dr. Valentin Fuster
2007;():333-339. doi:10.1115/DETC2007-34017.

A method for the design of general analytical noncircular multi-lobe internal pitch pairs is presented. The method is based on a reshaping algorithm. A selected monotonic function can be assigned as the initial profile for the outer rotor of the designed pitch pair. This initial function will then be reshaped to satisfy that the number of lobes must be an integer. This final pitch function can then be obtained analytically. To archive smooth profile design, the C1 continuous conditions on pitch rotors are established. A dimensionless parameter geometrically interpreted as the noncircularity of pitch rotor is introduced for the systematic design of pitch pairs. Results from this research have applications to the design of noncircular gears.

Topics: Algorithms , Design , Gears , Rotors
Commentary by Dr. Valentin Fuster
2007;():341-350. doi:10.1115/DETC2007-34147.

Rigid sub-chain detection and isomorphism identification are two of the most difficult problems in the computer aided structure synthesis of kinematic chains. Based on the array representation of the loops of kinematic chains, this paper first introduces two operations of loops. Then a new theory of structure decomposition of kinematic chains is proposed on the basis of the concept of the independent loop set. After that a new method grounded on the theory is proposed for rigid sub-chain detection. Finally, the optimized algorithm for structure decomposition is presented and the corresponding program for rigid sub-chain detection is developed as well.

Topics: Chain
Commentary by Dr. Valentin Fuster
2007;():351-360. doi:10.1115/DETC2007-34148.

Isomorphism identification of graphs is one of the most important and challenging problems in the fields of mathematics, computer science and mechanisms. This paper attempts to solve the problem by finding a unique representation of graphs. First, the perimeter loop of a graph is identified from all the loops of the graph obtained through a new algorithm. From the perimeter loop a corresponding perimeter graph is derived, which renders the forms of the graph canonical. Then, by relabelling the perimeter graph, the canonical perimeter graph is obtained, reducing the adjacency matrices of a graph from hundreds of thousands to several or even just one. On the basis of canonical adjacency matrix set, the unique representation of the graph, the characteristic adjacency matrix, is obtained. In such a way, isomorphism identification, sketching, and establishment of the database of common graphs, including the graphs of kinematic chains, all become easy to realize. Computational complexity analysis shows that, in the field of kinematic chains the approach is much more efficient than McKay’s algorithm which is considered the fastest so far. Our algorithm remains efficient even when the links of kinematic chains increase into the thirties.

Topics: Chain
Commentary by Dr. Valentin Fuster
2007;():361-367. doi:10.1115/DETC2007-34173.

A plane symmetry 3-SPR parallel manipulator with 3 active limbs is proposed. The analytic formulae for solving forward/inverse displacement, velocity and acceleration are derived, the workspace and singularity poses are determined; the active forces are solved by using the virtual work theory. All of the solved results are verified by a simulation mechanism. This project is supported by NSFC (Nature Science Fund of China) 50575198.

Commentary by Dr. Valentin Fuster
2007;():369-378. doi:10.1115/DETC2007-34296.

A linkage mechanism is a device to convert an input motion into a desired motion in a machine or a robot. The traditional linkage synthesis practice is depended on the experience and intuition of the skilled designer. This practice based on trial and error approach or only size/shape changes of already-available mechanism often results in improper design. This observation has motivated us to develop a so-called “automatic” design methodology that determines the linkage type and dimensions during synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer. The main contribution of this research is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. This work shows how new idea works and verifies this new approach on the synthesis of the planar linkages consisting of links and revolute joints.

Topics: Linkages , Springs , Stiffness
Commentary by Dr. Valentin Fuster
2007;():379-388. doi:10.1115/DETC2007-34346.

This paper presents a kinematic analysis and a redesign of a variable-speed transmission mechanism. The mechanism is a seven-bar linkage where the rotation of the input crank is converted into the oscillation of the output link. The input crank rotates at a constant speed and the output link consists of an overrunning clutch mounted on the output shaft. The angle through which the clutch oscillates, for each revolution of the input crank, can be adjusted by a control arm. This arm allows a fixed pivot to be temporarily released and moved along a circular arc about a permanent ground pivot. The paper shows how to determine the angle of oscillation of the clutch for a specified position of the fixed pivot. The paper also investigates the extreme positions of the clutch corresponding to the extreme positions of a point on the coupler link. For this reason, the paper investigates the geometry of the path traced by a coupler point. The work shows how to determine the location of the ground pivot of the control arm which will cause the clutch to remain stationary during a complete rotation of the input crank. Then the paper shows how to design the control arm by using these conditions; i.e., the conditions for a redesign of the mechanism are investigated. A novel technique, in which kinematic coefficients are obtained with respect to an independent variable, is presented. This technique decouples the position equations and gives additional insight into the geometry of the mechanism.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2007;():389-397. doi:10.1115/DETC2007-34372.

In this paper we present a novel dimensional synthesis technique for approximate motion synthesis of spherical kinematic chains. The methodology uses an analytic representation of the spherical RR dyad’s workspace that is parameterized by its dimensional synthesis variables. A two loop nonlinear optimization technique is then employed to minimize the distance from the dyad’s workspace to a finite number of desired orientations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to spherical open and closed kinematic chains. Here, we specifically address the spherical RR open and 4R closed chains however the methodology is applicable to all spherical kinematic chains. Finally, we present two examples that demonstrate the utility of the synthesis technique.

Topics: Motion , Chain
Commentary by Dr. Valentin Fuster
2007;():399-407. doi:10.1115/DETC2007-34422.

This paper deals with the design of steering mechanisms in road vehicles. With this aim, the kinematic models of three types of steering linkages are considered and Ackermann steering geometry is used to define the objective function. The proposed method uses a dimensional synthesis technique based on local optimization to obtain the dimensions of the links. The problem is formulated as function generator synthesis, where the inner wheel is supported by the input link and the output link is supported by the outer wheel. The formulation presented in this paper was developed by the authors and it is capable of considering the necessary accuracy conditions in the design of this kind of linkage. Three examples are shown to illustrate the application of the method.

Commentary by Dr. Valentin Fuster
2007;():409-416. doi:10.1115/DETC2007-34427.

A modified real coded quantum-inspired evolution algorithm (MRQIEA) is herein presented for optimum synthesis of planar rigid body mechanisms (RBMs). The MRQIEA employs elements of quantum computing such as quantum bits, registers, and quantum gates, neighborhood search engine, and gradient search to form a random search algorithm for solution optimization of a wide class of problems. A brief overview of the quantum computing elements and their adaptation to the optimization algorithm is first presented. The algorithm is then adapted to the synthesis problem of RBMs. Finally, the algorithm is demonstrated and compared to other search methods by way of three examples, including two benchmark examples that have been used in the literature to assess the performance of other optimization schemes.

Commentary by Dr. Valentin Fuster
2007;():417-425. doi:10.1115/DETC2007-34515.

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, that are capable of approximating a shape change defined by a set of closed curves possessing similar arc lengths. The synthesis approach is more rigorous and more broadly applicable to dramatic changes between larger numbers of shapes than existing techniques that employ graphical methods. Link geometry is determined through an existing procedure, and those links are then joined together in a chain using numerical optimization to minimize the error in approximating the shape change. Binary links are added to this chain via a search of the design space such that actuated links can be driven monotonically to exact the shape change. The focus is single-degree-of-freedom (DOF) mechanisms that approximate closed curves, but the methodology is similarly applicable to generating mechanisms approximating sets of open curves and multi-DOF systems. The procedure is applied to synthesize an example mechanism that changes between circular, elliptical, and teardrop shapes as inspired by an aerodynamic flow field modification application.

Commentary by Dr. Valentin Fuster
2007;():427-437. doi:10.1115/DETC2007-34573.

The paper presents a general concept regarding the joint rotation space (JRS) of single loop planar and spherical N-bar linkages as well as its significance and applicability in multiple loop and spatial linkages. A JRS refers to the input domain of a linkage. The paper first discusses and classifies the JRS types of single loop five-bar linkages based on the types of the JRS boundary. The concept of sheets and pages of JRS is then introduced as an aid to understand the mobility of linkages. A sheet refers to the JRS of a linkage branch (or circuit). A JRS sheet may have one or more pages and each page refers to an uncertainty singularity free JRS. The concept is then generalized to any single loop planar and spherical N-bar linkages (N ≥ 3). The paper offers geometric insights to the input domain of a linkage and establishes a one-to-one correspondence between the input domain and the linkage configurations. The applications to the mobility identification of complex linkages are discussed and demonstrated with geared five-bar linkages, Stephenson six-bar linkages, as well as spatial RCRCR mechanisms. The paper presents a useful model explaining the fundamental principle regarding the formation of branches and sub-branches in Stephenson six-bar linkages as well as some other multiloop and spatial linkages. The Mobility similarity between multiloop linkages and spatial linkages is also highlighted.

Topics: Rotation , Linkages
Commentary by Dr. Valentin Fuster
2007;():439-448. doi:10.1115/DETC2007-34584.

Mobility identification is a common problem encountered in linkage analysis and synthesis. Mobility of linkages refers to the problems concerning branch defect, full rotatability, singularities, and order of motion. By introducing the concept of stretch rotation, the paper shows the existence of a hidden five-bar loop in a Watt six-bar linkage and how it affects the formation of branches, sub-branches, as well as the whole mobility of the entire linkage. The paper presents the first methodology for a fully automated computer-aided complete mobility analysis of Watt six-bar linkages.

Topics: Linkages
Commentary by Dr. Valentin Fuster
2007;():449-456. doi:10.1115/DETC2007-34601.

The Cam-based Infinitely Variable Transmission (IVT) is a new type of ratcheting IVT based on a three dimensional cam and follower system which provides unique characteristics such as generating specific functional speed ratio outputs including dwells, for a constant velocity input. This paper presents several mechanisms and design approaches used to improve the torque and speed capacity of this unique transmission. A compact, lightweight, and capable differential mechanism based on a cord and pulley system is developed to double the number of followers in contact with the cam at any time, thereby reducing the contact stress between the followers and the cam surface considerably. A kinematic model governing the motion of this differential is developed and a few experimental results from the prototype are presented, showing an overall increase in performance including a smooth output, a wide gear range, and the ability to shift under load. Plans for future improvements to the design, including an inverted external cam mechanism, is also presented along with the expected performance gains.

Topics: Stress , Mechanisms
Commentary by Dr. Valentin Fuster
2007;():457-465. doi:10.1115/DETC2007-34621.

In this paper the generic DOF of mechanisms is investigated. This is the DOF of almost all mechanisms, that can be built from a given set of kinematic pairs in a certain arrangement, but with arbitrary link geometry. In particular, this is the most likely DOF in the presence of link imperfections. The local DOF of a mechanism is the dimension of its configuration space. The differential DOF is the number of linearly independent velocity constraints. It is pointed out, that the local DOF can not always be inferred from the number of constraints (overconstrained mechanisms) nor can the differential DOF always be deduced from the local DOF. It is proven, that the generic DOF of a mechanism is given by the Chebychev-Kutzbach-Grübler formula δ = Σαfa−g(j−b+1), with b and j the number of bodies and joints, and the DOF of joint α. Consequently, almost all mechanism are trivial, i.e. not overconstrained.

Commentary by Dr. Valentin Fuster
2007;():467-476. doi:10.1115/DETC2007-34795.

The multiobjective optimization of Slide-o-Cam is reported in this paper. Slide-o-Cam is a cam mechanism with multiple rollers mounted on a common translating follower. This transmission provides pure-rolling motion, thereby reducing the friction of rack-and-pinions and linear drives. A Pareto frontier is obtained by means of multiobjective optimization. This optimization is based on three objective functions: (i) the pressure angle, which is a suitable performance index for the transmission because it determines the amount of force transmitted to the load vs. that transmitted to the machine frame; (ii) the Hertz pressure used to evaluate the stresses produced on the contact surface between cam and roller; and (iii) the size of the mechanism, characterized by the number of cams and their width.

Commentary by Dr. Valentin Fuster
2007;():477-482. doi:10.1115/DETC2007-34803.

Linkages are presented which generate straight-line motion of a rigid body. Typical mechanisms of this type (e.g. scissors lift or pantograph) have fixed pivots beneath the moving platform. The linkages presented here have remotely located fixed pivots and allow a range of platform motion which extends both above and beneath the line of the fixed pivots. Both exact and approximate solutions are presented, based on the Peaucellier straight-line linkage, and a synthesis example is given.

Commentary by Dr. Valentin Fuster
2007;():483-489. doi:10.1115/DETC2007-34931.

This paper presents a new method for determining whether an RR dyad will pass through a set of finitely separated positions in order. Several established solution methods have been previously documented for this problem. This method utilizes only the displacement poles in the fixed frame to assess in an intuitive fashion whether a selected fixed pivot location will result in an ordered dyad solution. A line passing through the selected fixed pivot is rotated one-half revolution about the fixed pivot, in a manner similar to a propeller with infinitely long blades, to sweep the entire plane. Order is established by tracking the sequence of the displacement poles intersected by the rotating line. With four or five positions, fixed pivot locations corresponding to dyads having any specified order are readily found. Five-position problems can be directly evaluated to determine if any ordered solutions exist, and degenerate cases of four positions for which the set of fixed pivots corresponding to ordered dyads collapses to a single point on the center point curve can be identified.

Commentary by Dr. Valentin Fuster
2007;():491-501. doi:10.1115/DETC2007-34937.

This contribution presents a review of some problems concerning with the analyses of mobility and overconstraint in kinematic chains: single-loop, parallel platforms and multi-loop kinematic chains with general topology. These analyses can be easily extended to assemblies. This review shows that some ideas accepted in the literature are either incorrect or in need of clarification.

Topics: Chain
Commentary by Dr. Valentin Fuster
2007;():503-509. doi:10.1115/DETC2007-34945.

Nonadjustable four-bar linkages can only generate the desired functions precisely at a limited number of points. With one link length adjustment, the whole desired function can be generated precisely. This paper uses the coupler or the driven link length adjustment to generate the desired functions precisely. The synthesis model of adjustable linkages is established based on the optimal link length adjustment. For different applications, the desired functions can be generated precisely by using the continuous adjustment or approximately by fixing the adjustable link at an appropriate length after the adjustable linkage is optimally synthesized. The optimal fixed length of the adjustable link is selected by minimizing the maximum absolute structural error between the generated function and the desired function. The synthesis approach proposed in this paper is verified by two demonstrated examples.

Topics: Linkages
Commentary by Dr. Valentin Fuster
2007;():511-518. doi:10.1115/DETC2007-35354.

In this paper, we present the mechanical design of a spherical four-bar mechanism for performing a motion common in manufacturing and assembly processes. The mechanism is designed to create, in a single, smooth motion, the combined rotation of a body by 90 degrees about one axis with a 90 degree rotation about an axis perpendicular to the first. A spherical four-bar mechanism is pursued as the basis for the design because the reorientation is produced mechanically rather than via a control scheme typical when higher degree of freedom systems are utilized. The design initiates with the kinematic synthesis of the spherical mechanism to guide a body through two orientations. The next step in the design is to refine the spherical fourbar based on manufacturing and operational concerns. As one of the challenges of utilizing these four-bars is tuning the starting and ending angle for the mechanism’s motion, a sensitivity analysis is performed to gauge the needed accuracy. Finally, there are details and a discussion of the proposed mechanical design.

Commentary by Dr. Valentin Fuster
2007;():519-526. doi:10.1115/DETC2007-35359.

Spherical four-bar mechanisms are classically designed to be driven via a torque applied to the input link. This paper presents a comparison of the resulting statics associated with this method of actuating a spherical four-bar versus actuating the mechanism with the force applied directly to the coupler. A force may be applied in this fashion via a spherical-prismatic-spherical, or SPS, chain mounted between the ground frame and the coupler with the prismatic joint actuated. The spherical four-bar linkage with the SPS chain connected directly to the coupler defines a spatial analogue to the Stephenson III six-bar mechanism. Moreover, this work builds on previously derived static models of spherical four-bars by considering the additional loading issues associated with links at different radii and the forces that arise from an external load on the coupler.

Topics: Torque , Stress , Mechanisms
Commentary by Dr. Valentin Fuster
2007;():527-535. doi:10.1115/DETC2007-35368.

The synthesis of a planar four-bar in which a point on the coupler reaches two specified points and orientations generates a six-fold space of solutions. The solution space increases if additional links are added to drive the mechanism, such as the Stephenson III. This paper presents an investigation of a coupler driven four-bar linkage, a Stephenson III six-bar with an RPR chain driving the four-bar sub-chain instead of the classically defined 3R chain. The software allows the designer to specify the problem and quickly scan the solution space. A comparison is constructed between a four-bar driven through a torque at the input link and a coupler-driven four-bar. Changes in branch points, the joint force index and the dynamics are observed.

Commentary by Dr. Valentin Fuster
2007;():537-545. doi:10.1115/DETC2007-35514.

A Genetic Algorithms (GA) approach to dimensional synthesis of an adaptive pliers mechanism is presented. Satisfaction functions are implemented in a custom C++ algorithm to enforce ergonomic and force-transmission goals. Using various values of selection rate and crossover rate, along with a “diversity monitor,” many solutions are found which are functionally superior to the original mechanism.

Commentary by Dr. Valentin Fuster
2007;():547-560. doi:10.1115/DETC2007-35544.

A new methodology for configuration design of metamorphic mechanisms is developed based on genetic evolutionary operation with biological building blocks. The goal is to conceive the appropriate source-metamorphic-mechanism configuration given the multiple phases of kinematic functions in motion specifications. The key enabler of configuration synthesis is the method of capturing the metamorphic configuration characteristics and the genetic evolutionary criteria and of developing genetic evolution in modeling and design. With the unique characteristics of achieving multiple working-phase functions, the metamorphic mechanisms possess two features: one, the ametabolic feature referring to the specified sub-working phases that can be accomplished by traditional mechanisms; two, the metamorphic feature occurring transition between different working phases resulting change of topology of the mechanism. Based on this transition between phases, the concept of mechanism evolution is for the first time introduced in this paper based on biological building blocks in the form of metamorphic cells and associated inner elements as the metamorphic gene. This leads to development of cell evolution and genetic aggregation forms with mechanism decomposition and evolution formulation based on mapping from the source-metamorphic-mechanism to multi-phases working configurations. Examples are given to demonstrate the concept and principles.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2007;():561-570. doi:10.1115/DETC2007-35574.

A new formula for predicting the mobility of spatial mechanisms is introduced. Instead of counting rigid links and the constraints between them, as is done in the usual Grübler-Kutzbach formulae, we count vertices and edges in a polyhedral model of the mechanism. It is well known that the conventional formula underpredicts the mobility of certain exceptional classes of mechanisms, and in particular, does not easily accommodate compound spatial mechanisms that contain planar or spherical sub-mechanisms. The new approach provides a correct mobility whenever the conventional formula does and accounts for planar and spherical sub-mechanisms in a simple manner. Additionally, we present simple modifications to correctly model certain mechanisms that have remote spherical centers. We illustrate the method on compound mechanisms constructed from scissors linkages.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2007;():571-579. doi:10.1115/DETC2007-35588.

The synthesis of six-bar linkages can yield a number of design candidates for a variety of linkage structures. Assessment criteria that sort prospective candidates are needed to assist the designer in finding effective linkage designs for further study. In this paper, we present the criteria based on easily computed measures that describe the shape and size of the linkage. These criteria are used to sort designs in four case studies, where we had previously found successful linkages by exhaustive examination.

Commentary by Dr. Valentin Fuster
2007;():581-588. doi:10.1115/DETC2007-35595.

In this paper, we consider the synthesis of a planar RR chain that guides a rigid body, or workpiece, such that it does not violate normal direction and curvature constraints imposed by contact with objects in the environment. These constraints are transformed into conditions on the velocity and acceleration of points in the moving body. We use this to formulate the synthesis equations for an RR chain, which are solved by algebraic elimination. An example of the design of a planar RR linkage and a four-bar chain in which the coupler maintains in contact with two objects in two locations is used to illustrate the results.

Topics: Linkages , Chain , Design , Equations
Commentary by Dr. Valentin Fuster
2007;():589-595. doi:10.1115/DETC2007-35720.

A spatial analogue of the Stephenson III six-bar mechanism can be formed by the connection of an SPS chain to the coupler of a spherical four-bar linkage. With the prismatic joint actuated, the spherical four-bar is driven via a force applied directly to the coupler. This linkage is termed the coupler-driven spherical four-bar mechanism, and defines an alternative to the typical scheme of actuating the four-bar via a torque applied at the input link. This paper presents software developed to assist in the kinematic synthesis of these mechanisms. In the first stage of the design, a circuit-defect free spherical four-bar is dimensioned with the capacity to guide a rigid body through two orientations. The second stage of the design is to locate the SPS leg such that the four-bar is smoothly drivable between the orientations.

Commentary by Dr. Valentin Fuster
2007;():597-605. doi:10.1115/DETC2007-34081.

There is currently research to support the construction of a walking assist machine, which machine uses a spatial parallel link mechanism for the elderly or rehabilitants. The flat steps of the assist machine move in parallel with the ground and can support the legs of a person including the soles. We developed a prototype and designed to assist people walking at up to fifty percent power. To grasp the walking phase of each leg of the equipped person, pressure sensors were laid under the thenar eminence and the heel of the sole, and the pressure variation at each sensing point was measured. For safety support, we developed a control method of the walking assist machine to fit the motion in phase by phase. Furthermore, in order to support walking indoors, we investigated the assist methods of turning around during walking and walking on a slope or stairs. A flexible link was installed in the mechanism for taking into account the twisting motions of the waist and ankle. To grasp the behavior of turning around during walking of the equipped person, pressure sensors were attached outside of the flexible link in both crural parts of the machine. As a result of the experiment wearing the machine, the equipped person could turn around during walking at will. To confirm the validity of the supporting method, muscle activity of the leg while wearing the walking assist machine evaluated by using the surface electromyography (called as “EMG”), and calculated the ratio of the integrated EMG (called as “IEMG”) with and without the walking assist machine. The initial results show that the activities of the rectus femoris muscle and the tibialis anterior muscle can be held to approximately 60 percent by wearing the walking assist machine. Furthermore, in order to support walking indoors, we investigated the assist methods of walking on a slope or stairs. The machine was equipped with a gyro sensor and an ultrasonic sensor; the angle of the slope and the size of stairs could recognize and the machine could be controled according to the signals from the sensors. As a result of the experiment wearing the machine, the equipped person could walk on a slope or stairs at will. The subject assisted with the machine was able to walk on a slope up to the angle of plus or minus fifteen degrees.

Topics: Machinery
Commentary by Dr. Valentin Fuster
2007;():607-613. doi:10.1115/DETC2007-34768.

This paper presents a possible prosthetic solution to excessive metabolic energy expended by transtibial (below the knee) amputees. This solution uses a four bar mechanism in conjunction with a spring, a motor, and a prosthetic foot as a lower limb prosthetic device. An optimization was previously performed on the mechanism parameters to mimic human ankle moments during normal walking. The cost function has been refined with the intent to reduce the required peak power input as well as to keep the link lengths of the four bar mechanism within an order of magnitude of each other. Design complications of the prototype that have arisen and likely resolutions are also included in this paper. Parts have been sized and justified based on likely size of the wearer, potential full-production costs of parts, and cost constraints.

Commentary by Dr. Valentin Fuster
2007;():615-624. doi:10.1115/DETC2007-34830.

Retinopathy of Prematurity, caused by abnormal blood vessel development in the retina of premature infants, is a leading cause of childhood blindness. It is treated using laser photocoagulation. Current methods require the surgeon to assume awkward standing positions, which can result in injury to the surgeon if repeated often. To assist surgeons in providing quality care and prevent occupational injury, a new infant surgical table was designed. The engineered solution is an attachment to a standard surgical table, saving cost and space. This takes advantage of the adjustable height and tilt provided by the standard table, while 360° rotation designed into the attachment allows the surgeon to sit during surgery. The critical cords and tubes are routed through the attachment to avoid pulling and kinking. A four-bar locking mechanism allows easy attachment to standard medical railing. Finally, a straight line mechanism provides positive locking of the rotation, allowing precise positioning of the infant.

Topics: Design , Surgery
Commentary by Dr. Valentin Fuster
2007;():625-635. doi:10.1115/DETC2007-34832.

This paper outlines the development and initial optimization of a compliant endoscopic suturing instrument. The developing field of Natural Orifice Transluminal Endoscopic Surgery requires innovative instruments to meet the size limitations inherent in this type of minimally invasive surgery; using compliant mechanisms is proposed as one method of meeting this requirement. Three initial compliant designs were created, modeled, and compared for a distal opening of 10 mm. Restricting these designs so that they must fit within a 3.3 mm working channel is currently unique in endoscopic suturing instruments. A design that utilizes contact for stress relief and intertwining parts for added deflection was selected from the three. ANSYS® was used to aid in graphical optimization to maximize the jaw opening and maximize the puncture force of the selected design. The best geometry has a distal opening of 13.8 mm at the tips and can supply a puncturing force of 6.33 N. A prototype has been machined using the optimized dimensions and is ready to be tested. This initial study in compliant suturing instrument designs has revealed response patterns for the chosen geometries that will lead to further refinements and improvements in future models.

Commentary by Dr. Valentin Fuster
2007;():637-644. doi:10.1115/DETC2007-34841.

This paper presents a new equivalent spatial mechanism for the passive motion simulation at the human ankle complex joint. The mechanism is based on the geometry of the main anatomical structures of the ankle complex, such as the shape of the talus and tibio/fibula bones at their interface, and the TiCal and CaFil ligament lengths. In particular, three sphere-to-sphere contact points at the interface have been identified and isometric fibers of both TiCal and CaFil ligaments have been considered to devise the equivalent mechanism. The proposed mechanism is a fully-parallel mechanism of type 5-5 with one degree of freedom. A procedure for the optimal synthesis of the mechanism is given. Simulation results compared with experimental data show the efficiency of the proposed mechanism to replicate the ankle passive motion, and also to reflect at the same time the main anatomical structures of the ankle joint. The new mechanism is believed to be a useful tool for both pre-operation planning and prosthesis design.

Commentary by Dr. Valentin Fuster
2007;():645-652. doi:10.1115/DETC2007-34963.

This paper aims to develop a performance measure for underactuated grasping devices, which is useful in making design decisions to obtain an optimally performing device. Underactuated fingers, defined as having more degrees of freedom than degrees of actuation, intrinsically adapt their shape to the object. However, the equilibrium configuration and grasp forces of these fingers are not fully controllable, which may limit their performance. The grasp performance measure defined in this paper consists of three aspects: (1) the ability to grasp objects, which is limited by the equilibrium conditions and constraints of both the underactuated fingers and the freely movable object; (2) the grasp stability, which takes the passive compliance of the fingers into account; (3) the ability to oppose disturbance forces on the grasped object by passively adapting the frictional grasp forces. This measure was applied to optimize a planar grasping device with two underactuated fingers, each consisting of two phalanges, able to grasp freely moving circular objects.

Commentary by Dr. Valentin Fuster
2007;():653-661. doi:10.1115/DETC2007-35067.

This paper proposes a new solution to the problem of torque minimization of the medical device SurgiScope® by connecting to the initial structure a secondary mechanical system, which generates a vertical constant force on the platform of the robotized device. The conditions for optimization are formulated by the minimization of the root-mean-square values of the input torques of the studied device. The positioning errors of the unbalanced and balanced robots are provided. A significant reduction of these errors is achieved by using the suggested balancing mechanism. The efficiency of the developed approach is illustrated by numerical simulations. Experimental validation of the obtained optimization is illustrated by a prototype developed in the National Institute of Applied Sciences of Rennes in collaboration with the “Intelligent Surgical Instruments & Systems” (ISIS) Company.

Commentary by Dr. Valentin Fuster
2007;():663-670. doi:10.1115/DETC2007-35295.

This paper describes a novel Home Lift, Position, and Rehabilitation (HLPR) Chair, designed at National Institute of Standards and Technology (NIST), to provide independent patient mobility for indoor tasks, such as moving to and placing a person on a toilet or bed, and lift assistance for tasks, such as accessing kitchen or other tall shelves. These functionalities are currently out of reach of most wheelchair users. One of the design motivations of the HLPR Chair is to reduce back injury, typically, an important issue in the care of this group. The HLPR Chair is currently being extended to be an autonomous mobility device to assist cognition by route and trajectory planning. This paper describes the design of HLPR Chair, its control architecture, and algorithms for autonomous planning and control using its unique kinematics.

Commentary by Dr. Valentin Fuster
2007;():671-679. doi:10.1115/DETC2007-35367.

A size and shape optimization routine is developed and implemented on a 1 mm multifunctional instrument for minimally invasive surgery. The instrument is a compliant mechanism, without hinges, capable of both grasping and cutting. Multifunctional instruments have proven to be beneficial in the operating room because of their ability to perform multiple tasks, thereby decreasing the total number of instrument exchanges in a single procedure. In addition, with fewer exchanges the risk of inadvertent tissue trauma as well as overall surgical time and costs are reduced. The focus of the paper is to investigate the performance effects of allowing the cross-sectional area along the length of the device to vary. This is accomplished by defining various cross-sectional segments along the device in terms of parametric variables (Wi) and optimizing the dimensions to provide a sufficient forceps jaw opening while maintaining adequate cutting and grasping forces. Two optimization problems are considered. First, all parametric segments are set equal to one another permitting all cross-sections to vary uniformly and achieving size optimization. Second, each segment is defined as a separate design variable to allow segments to vary independently and thereby achieving shape optimization. Due to the device’s symmetry, one-half of the mechanism is modeled as a cantilever beam undergoing large deformation. ANSYS’ optimization module is employed using the first order method because it is capable of performing optimization considering non-linear deformation and multiple loading conditions. Finally, prototypes are fabricated using wire EDM and prototype evaluations are conducted to compare size versus shape optimization, and to validate ANSYS as the solution method.

Commentary by Dr. Valentin Fuster
2007;():681-687. doi:10.1115/DETC2007-35616.

An objective of this study is to simulate the backward walking motion of a full-body digital human model. The model consists of 55 degree of freedom – 6 degrees of freedom for global translation and rotation and 49 degrees of freedom representing the kinematics of the entire body. The resultant action of all the muscles at a joint is represented by the torque for each degree of freedom. The torques and angles at a joint are treated as unknowns in the optimization problem. The B-spline interpolation is used to represent the time histories of the joint angles and the well-established robotics formulation of the Denavit-Hartenberg method is used for kinematics analysis of the mechanical system. The recursive Lagrangian formulation is used to develop the equations of motion, and was chosen because of its known computational efficiency. The backwards walking problem is formulated as a nonlinear optimization problem. The control points of the B-splines for the joint angle profiles are treated as the design variables. For the performance measure, total dynamic effort that is represented as the integral of the sum of the squares of all the joint torques is minimized using a sequential quadratic programming algorithm. The solution is simulated in the Santos™ environment. Results of the optimization problem are the torque and joint angle profiles. The torques at the key joints and the ground reaction forces are compared to those for the forward walk in order to study the differences between the two walking patterns. Simulation results are approximately validated with the experimental data which is motion captured in the VSR Lab at the University of Iowa.

Commentary by Dr. Valentin Fuster
2007;():689-695. doi:10.1115/DETC2007-34202.

This paper presents a family of novel lower-mobility decoupled parallel mechanisms (DPMs), which consists of one 5-DOF (degree of freedom) DPM, two 4-DOF DPMs, three 3-DOF DPMs, and three 2-DOF DPMs. The basic feature of this family is that the moving platform and the fixed base of the DPMs are connected by two limbs and the motion of the moving platform is fully decoupled. Then the constraint screw method is used to analyze the motion feature of all DPMs presented in this paper. The mobility of these DPMs has also been calculated by the Modified Grubler-Kutzbach criterion. All the DPMs in this paper are simple and no computation is required for real-time control.

Commentary by Dr. Valentin Fuster
2007;():697-703. doi:10.1115/DETC2007-34378.

Rensselaer’s Geotechnical Centrifuge Center is a resource for conducting research into the behavior of soils, earthen structures and other materials under high g-force conditions. The 3m radius centrifuge can accelerate a roughly 1m × 1m × 1m payload up to as much as 200 g’s. Under such loading, properly prepared soil samples accurately simulate deep soil conditions at 1 g. The system also includes an In-flight Robot that provides the capability to perform experiments while the centrifuge is in operations, as well as a 2–D shaker and associated 2–D Laminar Box that permit earthquake simulations while in flight. However prior to the implementation of the Auxiliary Axis, pilings were limited to a maximum usable length of approximately 15cm. The objective of Auxiliary Axis is to provide the capability to handle long pilings (up to 35cm) in situations where both the 2–D Shaker and 2–D Laminar Box are used. The Aux Axis is attached to the exterior of the in-flight robot when needed, and removed when not. The Aux Axis is designed to perform in a 50 g’s environment which holds some unique engineering concerns. It is designed so that installation and removal is as simple as possible, and can typically be completed in about 30 minutes. The Aux Axis is powered by the existing robot Z axis motor and belt drive system. Consequently, both the Z axis and the Aux Axis move simultaneously when the Aux Axis is installed. The Aux Axis is geared approximately 8.42 times higher than the Z axis so that it moves much further than the Z axis during operation. This permits the pilings; which are attached to the Aux Axis, to be fully inserted into the soil sample before the Z axis has moved far enough to interfere with the top of the 2–D Laminar Box.

Topics: Robots , Design , Flight
Commentary by Dr. Valentin Fuster
2007;():705-714. doi:10.1115/DETC2007-34440.

This paper describes the process of developing a novel biomimetic autonomous underwater vehicle (AUV) inspired by jellyfish locomotion. Our interest in an AUV that mimics jellyfish locomotion stems from the jellyfish’s simplistic and robust physiology and neurological makeup. Jellyfish swimming gates are controlled by a neural architecture consisting of an outer nerve ring and an inner nerve ring. The inner nerve ring is responsible for incorporating the sensory input from the outer ring and innervating the subumbrellar swimming muscles. Additionally, cells in the inner ring generate endogenous rhythms and act as pacemakers. The system of pacemakers generates the highly maneuverable swimming gates that can be observed in jellyfish; swimming vertically, turning and hovering. The swimming gates have been shown to correspond to the dynamics of the response of a system of coupled identical van der Pol oscillators. These oscillators are capable of creating in-phase, out-of-phase and “asymmetric” phase-locked dynamics that are plausibly related to the basic modes of jellyfish locomotion of coordinated bout swimming, hovering, and turning, respectively. In addition, the system of oscillators is fault tolerant; if the modeled system of oscillators is disrupted, analogous to sections of the jellyfish being damaged, the oscillators adjust and maintain effective swimming gates allowing the jellyfish to remain mobile. The simplicity and fault tolerance of the oscillatory system makes it an ideal model for a locomotion control system for an AUV. The objective of the Jellyfish AUV project is to emulate the locomotion and control mechanisms of the biological jellyfish to create a simple and robust AUV, which is both highly maneuverable and low in cost. The iterative design process that resulted in a working Jellyfish AUV is detailed in this paper. Numerous designs were created, exploring different combinations of actuator mechanisms, body types and control systems. Different actuators were evaluated for their ability to meet our design requirements. These actuators ranged from off the shelf servos to the more exotic shape memory alloys (SMAs) and ionic polymer metal composites (IPMCs.) By the completion of the prototyping phase of the Jellyfish AUV project we had created a low cost AUV using off the shelf components including, servos, linkages and a microprocessor based control system. The input to the servos was derived from a system of coupled oscillators which were tuned to mimic the observation jellyfish gates. In addition, using the Jellyfish AUV prototype, we showed that the identified servo input patterns roughly translate to swimming, hovering, and turning.

Commentary by Dr. Valentin Fuster
2007;():715-724. doi:10.1115/DETC2007-34472.

This paper presents the concept and design of a unique three-legged walking robot, and results from the simulation and experiments of a single step tripedal gait. The STriDER (Self-excited Tripedal Dynamic Experimental Robot) incorporates aspects of passive dynamic walking into a stable tripedal platform and is capable of changing directions. To initiate a step, the legs are oriented to push the center of gravity outside of the stance polygon, and as the body of the robot falls forward, the swing leg naturally swings in between the two stance legs and catches the fall. Once all three legs are in contact with the ground, the robot regains its stability and the posture of the robot is then reset in preparation for the next step. The changing of the direction is done by a unique way of changing the sequence of which of the three legs is the swing leg. To guide the design of the robot, a dynamic model was developed and a simulation of a single step tripedal gait was performed to allow for tuning of several design parameters, including the mass properties and link dimensions. By considering the two stance legs as a single effective link connected to the ground, the robot can be modeled as a planar four-link pendulum in the sagittal plane. Further development of the simulation also allowed for optimization of the design parameters to create an ideal gait for the robot. A self-excited method of actuation, which seeks to drive a stable system toward instability, was used to control the robot. This method of actuation was found to be robust across a wide range of design parameters and relatively insensitive to controller gains. The design of the first prototype and result from the experiments are presented with a discussion of future work.

Commentary by Dr. Valentin Fuster
2007;():725-732. doi:10.1115/DETC2007-34580.

This work is part of a project which aims at the development of underwater generators using oscillating wings. One of the important challenges in the design of a system collecting the kinetic energy of a fluid is the transformation of this energy into electric power [1]. Since it is not possible to pass directly from the movement of a fluid to electric power, it is necessary to conceive an intermediate mechanical system. Its function is to convert the kinetic energy of the fluid into kinetic energy of a mechanism capable of converting kinetic energy into electric power. In this work, the mechanical system also has an additional function, i.e., to guide the orientation of the blades (wings) throughout the cycle of movement in order to maximize the efficiency.

Topics: Design , Wings , Mechanisms
Commentary by Dr. Valentin Fuster
2007;():733-740. doi:10.1115/DETC2007-34797.

The design of robotic end effectors can be loosely classified into two different types: complex anthropomorphic hands which allow for manipulation and simple open/close grippers which do not. This article investigates a design of a simple, industrial feasible end effector that allows for in-hand manipulation of parts. This end effector can be utilized in conjunction with a vision system to eliminate parts feeders and be able to pick parts straight from bins. The design utilizes passive joints that, when in a particular configuration, align (a self-motion singularity) to allow in-hand manipulation without regrasping or finger gaiting. A prototype end effector was fabricated and tested to prove the concept.

Topics: Design , Robotics , Grippers
Commentary by Dr. Valentin Fuster
2007;():741-750. doi:10.1115/DETC2007-34930.

From the viewpoint of kinematics, a type of 3 degrees of freedom (dofs) UPS/3RPaPaR overconstrained parallel mechanism (Pa means the hinged 4R parallelogram) with pure translational motion is presented for the development of automatic assembly devices or as a regional structure in the hybrid parallel platform. In the beginning, the formation & mobility are elucidated and the 4×4 transformation matrix & the D-H notation with specific geometric constraints verify the pure translational motion. The forward and inverse kinematic analyses are then established in the analytical closed-form through the matrix method. Besides, we take a numerical illustration for the confirmation of correctness of the derived equations. The determination of workspace is also attained by the intersection of volumes swept by each limb. In addition, the Jacobian matrix and its condition number indicated by Euclidean norm as a function of design parameters are further achieved. Finally, the singularity analysis of the configuration based on the direct and inverse kinematic J -matrix during the movement is identified in detail.

Commentary by Dr. Valentin Fuster
2007;():751-762. doi:10.1115/DETC2007-34954.

Static balancing is a well-known technique in mechanism synthesis to achieve equilibrium throughout the range of motion, for instance to eliminate gravity from the equations of motion. Another application of static balancing is in spring-to-spring balancing where the influence of n springs on the mechanism behavior (e.g. input torque) are balanced by m other springs (n and m both non-zero positive integers). In this category of balanced mechanism, design methodology and examples exist based on zero-free-length springs, i.e. linear extension springs in which the force is proportional to the length of the spring, rather than to its elongation. The present paper will present for the first time the design of perfect spring-to-spring balancers with higher-order zero-free-length springs, i.e. springs in which the force is proportional to a (positive integer) power of its length. A general approach will be given together with four new mechanisms incorporating springs ranging from two third-order springs in the simplest example, to four equal thirteenth order springs plus one first order spring in the most complex example.

Topics: Springs
Commentary by Dr. Valentin Fuster
2007;():763-772. doi:10.1115/DETC2007-35068.

This paper deals with the new results concerning the topologically decoupled parallel manipulators called PAMINSA. The conceptual design of these manipulators, in which the copying properties of pantograph linkage are used, allows obtaining a large payload capability. A newly synthesized fully decoupled 3 degrees of freedom manipulator is discussed and a systematic approach for motion generation of input point of each limb is presented. It is shown that the conditions of complete static balancing of limbs are not effective in the case of dynamic mode of operation. This is approved by numerical simulations and experiments. A significant contribution of this paper is also the experimental validation of the suggested design concept. It is shown experimentally for the first time that the static loads on the rotating actuators, which displace the platform in the horizontal plane, are cancelled.

Topics: Stress , Design , Manipulators
Commentary by Dr. Valentin Fuster
2007;():773-780. doi:10.1115/DETC2007-35257.

This paper illustrates a kinematic study of human torso motion in order to design and transfer human-like motion on humanoid robots. The realization is done using motion capture data and an optimization based inverse kinematic approach for mapping motion data to skeleton models with the main focus on reproducing realistic torso motion. The kinematic model is based on a multiybody approach using relative coordinates. According to the difficulty of marker based motion reconstruction of human torso movements a detailed multibody model of the spine with a coupling structure between vertebrae based on medical data is introduced. Then, a new formulation describing the kinematic constraints between pelvis and shoulder girdle is presented in order to simplify modeling effort while maintaining natural motion of the torso. Results are compared for key movements with common models. The developed models will be used for design application in the Collaborative Research Center 588 “Humanoid Robots - Learning and Cooperating Multimodal Robots”.

Topics: Motion
Commentary by Dr. Valentin Fuster
2007;():781-789. doi:10.1115/DETC2007-35404.

The All-Terrain Hex-Limbed Extra-Terrestrial Explorer (ATHLETE) is a six limbed vehicle designed for both mobility and manipulation. Each limb has six active degrees-of-freedom, plus a powered wheel. Along the axis if each wheel is a mechanical interface that allows the integration of tools that can make use of the wheel actuator. Thus each limb can act as a leg for walking, an active suspension for a driven wheel, or a manipulator with an actuated tool. Fundamental to the operation of the system is the ability to control limb pose, overall body pose, as well as regulate limb forces. Joint torques are estimated from the difference between the incremental and absolute encoder readings on each joint. Forces are then computed from joint torques and force regulation is performed by modifying the limb positions. Force regulation allows the vehicle to lift larger payloads and traverse terrain while actively complying to terrain features.

Topics: Force , Modeling , Stiffness
Commentary by Dr. Valentin Fuster
2007;():791-799. doi:10.1115/DETC2007-35582.

Over the last decade, cable-driven parallel mechanisms have been used for several purposes. In this paper, a novel application is proposed, namely, using two 6-DOF cable-driven parallel mechanisms sharing a common workspace to obtain the mechanical base for the design of a locomotion interface. The methodology used to develop the architecture of the mechanisms is presented and the two main criteria used to optimize the geometry are described. These criteria are based on the Wrench-Closure Workspace (WCW) and a detection of the mechanical interferences between all the entities of the locomotion interface (cables and moving bodies). Then, the final design is described and its performances are given. Finally, in order to validate the relevance of the mechanism for the locomotion interface’s design, tensile forces in the cables are computed to observe maximal values reached during a typical human gait trajectory.

Commentary by Dr. Valentin Fuster
2007;():801-809. doi:10.1115/DETC2007-35612.

Soft robotic manipulators, unlike their rigid-linked counterparts, deform continuously along their lengths similar to elephant trunks and octopus arms. Their excellent dexterity enables them to navigate through unstructured and cluttered environments and handle fragile objects using whole arm manipulation. Soft robotic manipulator design involves the specification of air muscle actuators and the number, length and configuration of sections that maximize dexterity and load capacity for a given maximum actuation pressure. This paper uses nonlinear models of the actuators and arm structure to optimally design soft robotic manipulators. The manipulator model is based on Cosserat rod theory, accounts for large curvatures, extensions, and shear strains, and is coupled to nonlinear Mooney-Rivlin actuator model. Given a dexterity constraint for each section, a genetic algorithm-based optimizer maximizes the arm load capacity by varying the actuator and section dimensions. The method generates design rules that simplify the optimization process. These rules are then applied to the design of pneumatically and hydraulically actuated soft robotic manipulators, using 100 psi and 1000 psi maximum pressure, respectively.

Topics: Design , Manipulators
Commentary by Dr. Valentin Fuster
2007;():811-819. doi:10.1115/DETC2007-35728.

This paper describes a research project being conducted to develop a flexible actuator to be used in orthotic and robotic devices. A unique Continuum Hydraulic/Pneumatic Actuator (CHPA) has been designed at the University of Wisconsin-Madison Fluid Power Research Laboratory (UW-FPRL). As the name suggests, the CHPA can be hydraulically or pneumatically energized to produce a pushing force. The actuator is being developed to flex fingers to assist the gripping capability of persons who have a combination of diminished strength and motor control. The CHPA is implemented within a powered hand orthosis (PHO) and can feasibly be used with end effectors. A glove-like, non-bulky, and non-patient specific PHO prototype was fabricated to be used in conjunction with the actuator. Test results indicate that with component development and improved fabrication methods, the performance of the CHPA can be optimized for common gripping tasks. At an operating pressure of 120 psi (830 kPa) an actuator 0.35 inches (9 mm) in diameter and 4.5 inches (114 mm) in length provides (distal) pushing forces between 5–6 pounds (22–27 N) and produces corresponding (palmar) finger-tip forces in the range of 2–5 pounds (9–22 N). Future efforts will focus on optimizing the CHPA mechanism, it’s configuration within the orthosis and integrating a suitable control interface.

Commentary by Dr. Valentin Fuster
2007;():821-827. doi:10.1115/DETC2007-34168.

A hybrid five bar mechanism is a typical planar parallel robot. It is a configuration that combines the motions of two characteristically different motors by means of a five bar mechanism to produce programmable output. Hybrid five bar mechanism is the most representative one of hybrid mechanism. In this paper, considering the bond graph can provide a compact and versatile representation for kinematics and dynamics of hybrid mechanism, the dynamics analysis for a hybrid five-bar mechanism based on power bond graph theory is introduced. Then an optimization design of hybrid mechanism is performed with reference to dynamic objective function. By the use of the properties of global search of genetic algorithm (GA), an improved GA algorithm is proposed based on real-code. Optimum dimensions are obtained assuming there are no dimensional tolerances or clearances. Finally, a numerical example is carried out, and the simulation result shows that the optimization method is feasible and satisfactory in the design of hybrid mechanism.

Commentary by Dr. Valentin Fuster
2007;():829-837. doi:10.1115/DETC2007-34291.

The paper examines hybrid force/velocity control of a pneumatic gantry robot for contour tracking. Both experimental and simulation results are presented. The control system is structured to control the contact force and the tangential velocity simultaneously. Controller tuning and model validation results are given for a fixed gain PI-based hybrid force/velocity controller. A simple yet effective model is presented in sufficient detail such that other researchers can perform their own simulations to investigate the utility of their own controller designs. The model is used to demonstrate the negative effects of Coulomb friction. Future work will focus on friction compensation techniques to improve performance.

Commentary by Dr. Valentin Fuster
2007;():839-845. doi:10.1115/DETC2007-34308.

A novel CAD geometric variation approach for solving active-passive forces of some parallel manipulators with SPR-type active legs is proposed. First, some methodical formulae for solving the active/constrained force matrix and active/constrained forces are derived. Second, some basic techniques for constructing the force simulation mechanism are described for solving the force matrix and active/constrained forces. Third, a 3SPR, a 2SPS+2SPR, and a 4SPS+SPR parallel manipulators are presented, respectively, to illustrate how to solve their pose parameters, active/constrained force matrices, and active/constrained forces by the approach. The solving results have been verified by the analytic approach.

Commentary by Dr. Valentin Fuster
2007;():847-854. doi:10.1115/DETC2007-34786.

This paper presents the modification of an existing planar parallel mechanism from actuation redundancy to kinematic redundancy. An additional joint is introduced in the initial mechanism in order to make the modification and to auto-calibrate the mechanism by measuring the displacement of this additional joint. The first simulation results are presented and a discussion about it is proposed as a conclusion.

Topics: Robots , Automobiles
Commentary by Dr. Valentin Fuster
2007;():855-866. doi:10.1115/DETC2007-34975.

In this paper the kinematic and the dynamic analysis, and a nonlinear control strategy for a planar three-degree-of-freedom tensegrity robot manipulator are addressed. A geometric method is used to obtain the set of equations that describe the position analysis. Initially, solutions to the problems concerning forward and reverse kinematic analysis are presented; then, the forward velocity coefficients matrix is obtained analytically. The Lagrangian approach is used to deduce the dynamic equation of motion and its main properties are described using the nonlinear control system theory. Finally, a feedback-linearization-based nonlinear control scheme is applied to the mechanism to follow a prescribed path in the Cartesian coordinate system. The obtained results show that lightweight mechanisms which incorporate tensegrity systems could be used in a positioning problem.

Commentary by Dr. Valentin Fuster
2007;():867-876. doi:10.1115/DETC2007-34988.

In this paper we follow two approaches in optimal nonlinear control of a snake-like robot. After deriving the dynamic equations of motion using Gibbs-Appell method, reducing these equations, and some assumptions, feedbacklinearization method was used to linearize the nonlinear system. The obtained controller is used in simulations to control robot to track a desired line, with minimum required torques. Two goals are desired. First the robot’s head is expected to track a distinct line with a given speed. And next, tracking the serpenoid curve is desired. The simulation results prove the controller efficiency. The robustness of the designed controller is shown by comparing the torques with the required torques using a PD controller. Additionally, although we had model mismatches and unmodeled dynamics in controller part, we achieved the desired goals.

Commentary by Dr. Valentin Fuster
2007;():877-885. doi:10.1115/DETC2007-35048.

Considering slippage in the end-effectors of a set of two cooperating manipulators grasping an object, this paper presents a new dynamic modeling and control synthesis of grasping phenomenon. This dynamic modeling is based on a new formulation for frictional contact where equality and inequality equations in the standard Coulomb Friction model are converted all to a single second order differential equation with switching coefficients. Accuracy of the friction model is verified by comparing its results with those of SimMech. Then equations of motion are reduced to conventional form for nonconstrained system. Assuming the new reduced order system to be BIBO, internal stability of the whole system is analyzed. In the control synthesis of the system a multi phase controller is utilized to control the trajectory tracking of the object as well as slippage control of the end-effectors on the object surfaces. For the proposed controller, a proof is given for system stability and its performance and robustness are shown numerically. The results show superiority of the method and its desirable and excellent performance.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2007;():887-896. doi:10.1115/DETC2007-35221.

The Interactive Robotics Unit of CEA LIST has developed a very challenging robotic carrier (called P.A.C.) which is able to perform high range intervention tasks inside blind hot cells. This long reach multi-link carrier has 11 degrees of freedom (DOF), an operational range over 6 meters of full extension and weighs less than 30 kg. The gravity effect in the manipulator is largely compensated by a special mechanical structure (the parallelogram) that helps to reduce the size of the actuators used to operate the robot. Due to its size and weight, this large robot manipulator holds lots of elastic and geometric deformations. Hence, it presents very low position accuracy. A flexible model is developed to take into account most of the structure deformations. A calibration method of the robot flexible parameters is used to reduce the positioning error of the end effector and the intermediate joints. Then, a second calibration method of the robot using generalized error matrices is applied to further reduce the residual positioning error of the system. These matrices are a polynomial function of the system geometry and joint variables. This method is first tested by simulation to ensure its viability on large manipulators. After encouraging simulation results, an experimental field is made for the calibration of the PAC manipulator. Results show that the adopted flexible model, with the new calibrated parameters, followed by the polynomial model is a good combination to correct and reduce the system errors.

Commentary by Dr. Valentin Fuster
2007;():897-903. doi:10.1115/DETC2007-35415.

This work deals with the robustness and controllability analysis for autonomous navigation of two-wheeled mobile robots. The analysis of controllability of the systems at hand is conducted using both the Kalman rank condition for controllability and the Lie Algebra rank condition. We show that the robots targeted in this work can be controlled using a model for autonomous navigation by means of their dynamics model: kinematics will not be sufficient to completely control these underactuated systems. After having proven that these autonomous robots are small-time locally controllable from every equilibrium point and locally accessible from the remaining points, the uncertainty is modeled resorting to a multiplicative approach. The dynamics response of these robots is analyzed in the frequency domain. Upper bounds for the complex uncertainty are established.

Commentary by Dr. Valentin Fuster
2007;():905-914. doi:10.1115/DETC2007-35664.

The analytical models of a wheeled mobile robot (WMR) are often derived based on the assumption that the surface on which it manoeuvres is free from any irregularities. However, the wheels of a WMR are likely to encounter small but unavoidable obstacles. The interaction between stationary obstacles and the wheels of the mobile robot can adversely affect the stability of the payload as well as the robot’s handling control. The limited understanding of the mechanism of wheel-obstacle interaction and its implication on the overall dynamics of a WMR has hindered the development of control tools that may be used to limit the adverse effects of traversing surface irregularities. In this paper, vectorial mechanics approach is used to model the dynamics of wheeled mobile robots (WMRs) travelling over localised surface irregularities. This model is employed in conjunction with temporal trajectory functions to compute the traction force requirements of WMRs traversing obstacles of specified profiles. The obstacles are in the form of sinusoidal humps which are decomposed into positive and negative sinusoidal ramps. It is shown that a compromise can be obtained between the minimum times requirement for obstacle traversing, the traction force requirements, and the geometrical properties of the obstacles. The traction force can become negative which implies the need to switch to a braking action. This switch between the traction mode and braking mode of the actuators can be prevented if an optimal time for the obstacle traversing is selected a-priori. It is also shown that the relationship between the traction or breaking force magnitude and the manoeuvre time is non-linear and that the traction force requirements are much greater at small manoeuvre times than at big manoeuvre times. In addition, it is shown that the grade of an obstacle, which depend on its length and height, affect the traction requirements.

Commentary by Dr. Valentin Fuster
2007;():915-925. doi:10.1115/DETC2007-35750.

Modern manufacturing systems are increasingly becoming highly dynamic due to rapid changes in market and government regulations, as well as the integration of emerging technologies. To address the challenges of uncertainty, a flexible platform is critically needed for developing a new generation of manufacturing systems. This paper presents a mobile agent-based framework that supports dynamic deployment of control algorithms and operations in multi-robotic systems. The framework is based on a mobile agent system called Mobile-C. It uses Ch, an interpretive C/C++ environment, for robot programming. Since Ch has been ported to most existing computer platforms, the framework can control robots that work in different operating systems. Using a robot package in Ch as a middleware, control programs are portable to heterogeneous robots and associated mechatronic devices. The presented framework has been implemented and validated in an experimental robotic cell that consists of a Puma 560, an IBM 7575, and a conveyor system. The results show that the mobile agent approach can effectively deploy and execute new control algorithms and operations as mobile agents on any sub-system in a network.

Topics: Robotics
Commentary by Dr. Valentin Fuster
2007;():927-932. doi:10.1115/DETC2007-35876.

A single wheel, gyroscopically stabilized robot is a sharp-edged wheel actuated by a spinning flywheel for steering and a drive motor for propulsion. The spinning flywheel acts as a gyroscope to stabilize the robot and it can be tilted to achieve steering. In this paper first the kinematics of a single wheel robot, like Gyrover, in water is considered and then a simple mechanism for its movement in water is proposed. After hydrodynamic analysis of the robot a complete dynamics model is designed with Lagrange energy method. The only simplification used here is neglecting the added mass effect in hydrodynamic analysis. This complete model can be used for examining the behavior of the robot in designing a controller. This work is a significant step towards a fully automatic control of such a dynamically stable but statically unstable robots.

Commentary by Dr. Valentin Fuster
2007;():933-941. doi:10.1115/DETC2007-35894.

This paper describes the kinematics and dynamics of a spherical parallel wrist called 3-C RU after the topology of its legs. After a mobility analysis showing the geometrical conditions that yield motions of pure rotation, its kinematics is worked out in closed-form for both position and velocity problems. Then inverse and direct dynamics models are developed and the latter is investigated by the use of the multibody NOC method. Seven bodies are considered by the models: two links for each one of the three legs and the moving platform, while inertial joints parameters have been neglected. Finally, numerical simulations are presented to validate the model. This architecture adopts kinematic pairs that make it suitable for being realized at a mini- or microscale. The Authors are presently developing the design of a robot based on such a concept.

Commentary by Dr. Valentin Fuster
2007;():943-950. doi:10.1115/DETC2007-34237.

The paper presents fully-isotropic redundantly-actuated parallel wrists (RaPWs) with three degrees of freedom. The mobile platform has three independent rotations. A method is proposed for structural synthesis of fully-isotropic RaPWs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian mapping the two vector spaces of fully-isotropic RaPWs presented in this paper is 3×3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Redundant actuation is used to obtain fully-isotropic parallel wrists with three degrees of freedom. As far as we are aware, this paper presents for the first time in the literature the use of redundancy to design fully-isotropic parallel wrists as well as solutions of fullyisotropic RaPWs with three degrees of freedom.

Commentary by Dr. Valentin Fuster
2007;():951-961. doi:10.1115/DETC2007-34250.

Singular configurations (singularities) are mechanism configurations where the instantaneous kinematics is locally undetermined. Since the indetermination of the instantaneous kinematics causes serious problems both to the static behavior and to the motion control of the mechanism, the research of all the singularities (singularity analysis) is a mandatory step during the design of mechanisms. This paper presents a new approach to implement the singularity analysis of planar mechanisms. The proposed technique extends the use of the instant center properties to the singularity analysis of planar mechanisms with more than one degree of freedom (dof). It exploits the results of previous works by the author in which a geometric and analytic technique has been presented to address the singularity analysis of single-dof planar mechanisms.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2007;():963-970. doi:10.1115/DETC2007-34286.

The 6-DOF cable-driven mechanism under study in this paper is a feed positioning device for the Large Adaptive Reflector (LAR). The LAR is a concept of a very large orientable radio antenna. The study aims at optimizing the geometry of the cable mechanism to maximize the portion of the desired workspace in which the mechanism can remain in static equilibrium under the predicted external forces and torques. A general test to rapidly compute if the set of external forces and torques can be balanced is developed. This test is applicable to mechanisms with an arbitrary number (minimum six) of cables. Architectures with six to nine cables are optimized and compared. The conclusion of this study is that the prescribed task is unlikely to be achievable by this type of mechanism. Some design guidelines to improve the performance of a large cable-driven mechanism kept under tension by an aerostat are also provided.

Commentary by Dr. Valentin Fuster
2007;():971-978. doi:10.1115/DETC2007-34345.

Two severe problems may arise, while planning a path for a parallel manipulator. First, it might be impossible to reach a desired configuration at all, and second, any possible path leading to a desired configuration might cross a parallel singularity, which could provoke the loss of platform control and jeopardize the structural integrity of links and actuators. These two problems are strictly related to the topological properties, connectedness in particular, of the configuration space and of the singularity locus. This paper presents a new numerical method based on differential topology, which is able to identify and count the disjoint regions composing the configuration space, and the disjoint regions into which the configuration space is split by the singularity locus. After this classification, it is always possible to find a path connecting any two configurations, if any exists. This path is singularity-free, if any singularity-free path exists. The method is applied to 3RR R planar manipulators, with actuators on the middle joint of each leg.

Commentary by Dr. Valentin Fuster
2007;():979-989. doi:10.1115/DETC2007-34433.

This paper introduces a reconfigurable one degree-of-freedom spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of noncircular gears into a six degree-of-freedom closed-loop spatial chain. The gear pairs are designed based on the given mechanism parameters and the user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, [[ellipsis]], and the eleventh is parallel to the twelfth. This paper presents the detailed reverse kinematic analysis of this specific geometry. A numerical example is presented.

Commentary by Dr. Valentin Fuster
2007;():991-999. doi:10.1115/DETC2007-34459.

In this work, the application of the Dykstra’s alternating projection method to find the minimum-2-norm solution for actuator forces is discussed in the case when lower and upper bounds are imposed on the actuator forces. The lower bound is due to specified pretension desired in the cables and the upper bound is due to the maximum allowable forces in the cables. This algorithm presents a systematic numerical method to determine whether or not a solution exists to the cable forces within these bounds and, if it does exist, calculate the minimum-2-norm solution for the cable forces for a given task force. This method is applied to an example 2-DOF translational cable-driven manipulator and a geometrical demonstration is presented.

Topics: Cables , Manipulators
Commentary by Dr. Valentin Fuster
2007;():1001-1011. doi:10.1115/DETC2007-34471.

The unique three-legged walking robot STriDER (Self-excited Tripedal Dynamic Experimental Robot) utilizes a novel tripedal gait which incorporates aspects of passive dynamic walking into a stable tripedal platform to walk efficiently, and is also capable of changing directions. This unique tripedal gait, however, requires three abductor joints to align two of the three body swing rotator joints in the body, depending on the direction of the step the robot takes. In an earlier prototype of STriDER, the three abductor joints were independently actuated using three DC motors to align the rotator joints which made the robot heavy and inefficient. In this paper, we present the synthesis, analysis, and mechanical design of a novel mechanism for actuating the three abductor joints of this unique three-legged walking robot to generate the required motion using only a single actuator. The mechanism utilizes an internal gear set to generate a Hypotrochoid path curve and uses pin-in-slot joints to coordinate the motion of the three abductor joints to guide them through the four sets of positions required to enable the robot to walk efficiently. A brief description and background of the tripedal locomotion robot STriDER is presented first, followed by the design constraints and requirements of the abductor joint mechanism. Synthesis and kinematic analysis of the mechanism is presented with a study of the force transmission characteristics for a quasi-static case. A description of the detailed mechanical design, results from the experiments, and a conclusion with a discussion for future work is presented next.

Topics: Robots , Mechanisms
Commentary by Dr. Valentin Fuster
2007;():1013-1020. doi:10.1115/DETC2007-34496.

The force-moment capabilities of branch-redundant planar-parallel manipulators (PPMs) are investigated. A previously developed explicit methodology for generating the force-moment capabilities of redundant PPMs is used on three different PPM architectures. The results for the 4-R RR, 4-R PR, 4-P RR layouts (where the underline denotes the actuated joint in each branch) are presented and discussed. For the revolute-actuated layouts, it was shown that the force-moment capabilities for the 4-R RR were in general better than those of the 4-R PR for the chosen manipulator parameters. The presented analysis is an effective tool for designing PPMs to determine the largest forces and moments that can be applied at any point within the workspace.

Commentary by Dr. Valentin Fuster
2007;():1021-1030. doi:10.1115/DETC2007-34513.

This paper presents an approach to obtain the first-order speed ratios for three-degree-of-freedom spatial mechanisms that allow three degrees of translational freedom. The approach eliminates the need to locate the canonical frame and find the instantaneous invariants of motion and provides a direct method of obtaining the first-order speed ratios. The expressions for the speed ratios of the articulated arm subassembly are analyzed, and the regions of the workspace wherein the joints have dwells in their trajectories are identified. The first-order Taylor series is used for joint coordination, allowing the system to track a predefined spatial path. An example illustrating the application of curvature theory to spatial path tracking with a specific articulated arm subassembly is presented.

Commentary by Dr. Valentin Fuster
2007;():1031-1039. doi:10.1115/DETC2007-34540.

Parallel robots are showing a high potential for the application in machine tools requesting high stiffness and dynamics. Nevertheless, a broad use of parallel mechanisms in machine tools is nowadays avoided by the minor accuracy of parallel kinematic machines compared to conventional machine tool structures, which entails the need for complex calibration algorithms. In this paper, a strategy to avoid the calibration of parallel kinematic machines by rearranging the measurement system to the end effector is presented. Because this rearrangement entails a massive modification of the machine tools control circuit that causes stability problems, first tests of the concept have been carried out via simulation. The focus of these tests was to determine the necessary dynamic parameters of a suitable machine tool’s structure. The results of these tests are used to derive guidelines for the design of a machine tool with direct pose measurement. Finally, a design approach for a suitable machine tool is presented.

Topics: Robots
Commentary by Dr. Valentin Fuster
2007;():1041-1052. doi:10.1115/DETC2007-34606.

This paper presents the forward and inverse displacement analysis of a novel three-legged walking robot STriDER (Self-excited Tripedal Dynamic Experimental Robot). STriDER utilizes the concept of passive dynamic locomotion to walk, but when all three feet of the robot are on the ground, the kinematic structure of the robot behaves like an in-parallel manipulator. To plan and control its change of posture, the kinematics of its forward and inverse displacement must be analyzed. First, the concept of this novel walking robot and its unique tripedal gait is discussed including strategies for changing directions, followed by the overall kinematic configuration and definitions of its coordinate frames. When all three feet of the robot are on the ground, by assuming there are no slipping at the feet, each foot contact point are treated as a spherical joint. Kinematic analysis methods for in-parallel manipulators are briefly reviewed and adopted for the forward and inverse displacement analysis for this mobile robot. Both loop-closure equations based on geometric constraints and the intersection of the loci of the feet are utilized to solve the forward displacement problem. Closed-form solutions are identified and discussed in the cases of redundant sensing with displacement information from nine, eight and seven joint angle sensors. For the non redundant sensing case using information from six joint angle sensors, it is shown that closed-form solutions can only be obtained when the displacement information is available from non-equally distributed joint angle sensors among the three legs. As for the case when joint angle sensors are equally distributed among the three legs, it will result in a 16th-order polynomial of a single variable. Finally, results from the simulations are presented for both inverse displacement analysis and the non redundant sensing case with equally distributed joint angle sensors. It was found that at most sixteen forward displacement solutions exist if displacement information from two joint angle sensors per leg are used and one is not used.

Commentary by Dr. Valentin Fuster
2007;():1053-1062. doi:10.1115/DETC2007-34692.

Parallel manipulators have many attractive features, such as a high strength to weight ratio, with great potential for applications in manufacturing and construction industry. Cable actuated parallel manipulators are a special case of parallel robots, where the limbs are replaced by cables, offering increased scalability of the structure. However, cable actuated manipulators have larger errors in positioning because of cable extensions and changes in the effective spool diameter. Also, the direct kinematics solution is no longer meaningful once the robot crosses the workspace boundary. Finally, it is necessary to start from a pre-calibrated home position where the cable lengths are known. In this work we address the pose estimation and control for a cable robot using visual and inertial measurements as well as information from the direct kinematics. We demonstrate the algorithm on a prototype with a working volume of 2m × 4.6m × 6m.

Commentary by Dr. Valentin Fuster
2007;():1063-1070. doi:10.1115/DETC2007-34770.

In this study, the concept of force and moment-workspaces is introduced. The force-moment capability analysis of parallel-manipulators is used to generate the force and moment workspaces. Force and moment workspaces of the manipulator are used to visualize the boundary of the workspace along with the sustainable/applicable value of force or moment depending on the maximum limits of the manipulator’s actuators. A method which analytically sets the greatest number of actuators to their maximum values is used for the determination of the force and moment workspaces. Four cases, two for finding the maximum magnitude of force with the value of moment either prescribed or associated and two for finding the maximum magnitude of moment with a prescribed or associated force, are explained and discussed. The redundantly-actuated 3-RRR S (all revolute joints actuated), six degree-of-freedom parallel manipulator is used as an example case for the analysis. The results show that a more even force/moment distribution is achieved for points lying inside the boundary of the maximum reachable workspace. It is shown that the proposed force and moment workspaces are an effective design tool for parallel manipulators. In addition, these force and moment workspaces can be seen as an efficient tool for task planning.

Topics: Force , Manipulators
Commentary by Dr. Valentin Fuster
2007;():1071-1080. doi:10.1115/DETC2007-34780.

Common robotic tracking tasks consist of motions along predefined paths. The design of time-optimal path-constrained trajectories for robotic applications is discussed in this paper. To increase industrial applicability, the proposed method accounts for robot kinematics together with actuator velocity, acceleration and jerk limits instead of accounting for the generally more complex dynamic equations of a manipulator with actuator torque and torque-rate limits. Besides actuator constraints also constraints acting on process level are accounted for. The resulting non-convex optimization problem is solved using a cascade of genetic algorithms and Nelder-Mead’s method. Simulations performed on a Puma 560 manipulator model show that for a proper choice of the kinematic constraints results can be obtained that match the quality of those obtained using the more complex dynamic constraint approach.

Commentary by Dr. Valentin Fuster
2007;():1081-1090. doi:10.1115/DETC2007-34938.

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

Commentary by Dr. Valentin Fuster
2007;():1091-1100. doi:10.1115/DETC2007-34992.

This paper discusses the classification and enumeration of topological structures of robotic mechanisms, aiming to develop practical robotic mechanisms with unconventional topological structures. First, we consider the features of topological structures of conventional robotic mechanisms and we point out that almost all of these can be constructed by using only one simple basic unit and two simple connection rules. Then, we present an efficient way to enumerate the topological structures which cannot be constructed from the basic unit and the connection rules, or unconventional topological structures. Then, we discuss the sequence required to construct robotic mechanisms from the enumerated unconventional topological structures. In the discussion, some effective tools, “graph division”, “graph management tool” and “DOF setting based on Kuzbach criterion”, which help designers construct a variety of mechanisms from the same topological structure are introduced. Finally, some examples of the sequences allowing the generation of robotic mechanisms with unconventional topological structures are shown.

Topics: Robotics , Mechanisms
Commentary by Dr. Valentin Fuster
2007;():1101-1107. doi:10.1115/DETC2007-35026.

The Dual-Arm Cam-Lock (DACL) robot manipulators are reconfigurable arms formed by two parallel cooperative manipulators. Some of their joints may lock into each other. Therefore, the arms normally operate redundantly. However, when higher structural stiffness is needed these two arms can lock into each other in specific joints and loose some degrees of freedom. In this paper, the dynamics of the DACL robot is discussed and parametrically formulated. On the other hand, the criteria and implementation of genetic algorithm (GA) to optimize the configuration of DACL robot manipulators at a specific point with the objective to maximize the cooperatively applicable task-space force in a desired direction are addressed. To obtain a more efficient process, an initial population is generated satisfying the geometrical constraints of the planar arms.

Commentary by Dr. Valentin Fuster
2007;():1109-1117. doi:10.1115/DETC2007-35118.

This paper deals with the problem of synthesizing planar rational motions under the kinematic constraints of planar 6R closed chain. It follows our previous work on the synthesis of rational motions under the kinematic constraints of planar open chains. Planar quaternions are used to represent planar displacements. In this way, the problem of rational motion interpolation is transformed into that of rational curve interpolation, and the kinematic constraints of a planar 6R closed chain are transformed into geometric constraints for the rational interpolation. An algorithm for the constrained motion interpolation is developed that detects an extreme position on the rational motion that violates the kinematic constraints. This position is then modified so that it is in compliance with the kinematic constraints and is added to the list of positions to be interpolated. By restricting the kinematic constraints to 5R and 4R closed chains, the algorithm is also applicable to the problem of synthesizing planar rational motions for 5R and 4R closed chains.

Topics: Motion , Chain , Interpolation
Commentary by Dr. Valentin Fuster
2007;():1119-1123. doi:10.1115/DETC2007-35260.

Type-II singularities exist in parallel manipulators commonly. At this kind of singularities, the end-effector is locally movable and uncertain even when all the actuate joints are located. In order to explore a possible approach to obtain the concrete output of the mobile platform at the very small vicinity (germ space) of the singular point, in this paper, the configuration bifurcation characteristics at the germ space have been investigated. At first, the type-II singularity has been identified with Golubitsky-Schaeffer normal form. The result shows that the type-II singular points belong to the turning points. Then, the configuration bifurcation equation is reduced into one dimensional form. Based on this one dimensional equation, the unperturbed and perturbed configuration bifurcation behaviors at the germ space of the turning point have been analyzed. It is found that all configuration branches converged in the same singular point in the unperturbed system can be separated in the perturbed system. This discovery has presented a possible approach to control the parallel manipulator passing through the singular point with a desired configuration.

Commentary by Dr. Valentin Fuster
2007;():1125-1132. doi:10.1115/DETC2007-35281.

This paper presents a novel type of five-degree-of-freedom parallel mechanism generating the 3T2R motion with linear inputs. The kinematic geometry of the mechanism is presented and several important kinematic issues including the inverse kinematic problem, the vector-loop velocity equations, the constant orientation workspace and the singularity configurations are investigated. The principal contribution of this study is the determination of the workspace based on algebraic geometry (Bohemian domes) and the study of the the singularity configurations. Based on the results, some optimization hints are proposed to refine the kinematic properties.

Commentary by Dr. Valentin Fuster
2007;():1133-1139. doi:10.1115/DETC2007-35306.

The paper is concerned with path planning for mobile robots. Specifically, the discussion is related to the following problem: Given an ordered sequence of points on the plane, construct a path that fits these points and satisfies certain smoothness requirements. These requirements may be different in different problems and imply basically that the constructed path is to be realizable. Such a problem arises, e.g., when it is required to follow in an automated mode a path stored as a discrete set of points, which, e.g., were collected by a GPS receiver installed on a car when it followed this path for the first time. Due to errors inherent in the data points, the shape of the curve approximating the desired path turns out often inappropriate. The shape of the curve can be improved by applying the so-called fairing, which consists in moving the original data points with the aim to minimize some fairness criterion. Adequate small variations of the data points preserve the proximity of the resulting path to the original data points and make it fairer. In the paper, a new global fairing method is proposed. It reduces the problem of constructing a fair cubic B-spline curve to solving a quadratic programming problem with simple constraints. The fairing criterion is based on minimizing jumps of the spline third derivative. The discussion is illustrated by numerical examples of fairing two actual paths constructed by data points collected by a GPS/GLONASS receiver mounted on a moving vehicle.

Commentary by Dr. Valentin Fuster
2007;():1141-1149. doi:10.1115/DETC2007-35371.

So far, in the derivation of the singularity equations of Gough-Stewart platforms, all research works defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough-Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point of the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.

Topics: Equations
Commentary by Dr. Valentin Fuster
2007;():1151-1164. doi:10.1115/DETC2007-35393.

The robotic motion planning criteria has evolved from kinematics to dynamics in recent years. Many research achievements have been made in dynamic motion planning, but the externally applied loads are usually limited to the gravity force. Due to the increasing demand for generic tasks, the motion should be generated for various functions such as pulling, pushing, twisting, and bending. In this presentation, a comprehensive form of equations of motion, which includes the general external loads applied at any points of the system, is derived and implemented. An optimization-based algorithm is then developed to generate load-effective motions of redundant manipulators (single-loop and tree-structured chains) that guarantee the execution of the generic tasks under limited actuator capacities. It is shown that if the external loads are not incorporated in the motion planning formulation, then the generated motions do not always guarantee the execution of the task, especially when a large load is desired. By using our algorithm, the load-effective motions can be found that are executable for given external loads. The proposed method is also applicable in predicting realistic dynamic human motions. Some dual-arm human tasks are simulated to show different motions to sustain different amounts of external loads. Our formulation for general external loads will further advance the current motion planning methods for redundant manipulators.

Commentary by Dr. Valentin Fuster
2007;():1165-1172. doi:10.1115/DETC2007-35437.

The reduction ratio of the driving system plays a very important role in the accelerating and decelerating capacity for a parallel manipulator. In this paper, the virtual work principle was employed to develop the inverse dynamics model of a novel high-speed parallel manipulator. A new S-curve speed profile was introduced and adopted to plan the trajectory of the end-effecter of the manipulator in the operation space. Aiming at the minimal operation time, a reduction ratio optimal selection method of the driving system was presented, which can make full use of the advantages of the AC servomotor and consequently reduce the cost of the manipulator.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2007;():1173-1182. doi:10.1115/DETC2007-35500.

The maximal singularity-free workspace of parallel mechanisms is a desirable criterion in robot design. However, for a 6-dof parallel mechanism, it is very difficult to find an analytic method to determine the maximal singularity-free workspace around a prescribed point for a given orientation. Hence, a numerical algorithm is presented in this paper to compute the maximal singularity-free workspace as well as the corresponding leg length ranges of the MSSM Gough-Stewart platform. This algorithm is based on the relationship between the maximal singularity-free workspace and the singularity surface. Case studies with different orientations are performed to demonstrate the presented algorithm. The results obtained can be applied to the geometric design or parameter (leg length) setup of the MSSM parallel robots.

Commentary by Dr. Valentin Fuster
2007;():1183-1193. doi:10.1115/DETC2007-35516.

This paper applies the ‘technomimetics’ concept to generate a new class of parallel mechanisms inspired by origami folds. This new class of 3-DOF (Degree of Freedom) parallel mechanisms is constructed with 3-RPRP architecture. When the geometric constraints mentioned in this paper are applied, the mechanisms will be allowed to rotate around the x and y axes and translate vertically along the z axis, while the centre of the platform remains concentric to the centre of its base. This paper investigates both position and geometry of these mechanisms and identifies the closed form solutions for the inverse kinematics problem. The differential kinematical analysis is developed by deriving the Jacobian matrix through screw theory and the singularities are identified with workspace analysis. The paper ends with isotropic configuration analysis and illustrates the characteristics of the new mechanisms.

Commentary by Dr. Valentin Fuster
2007;():1195-1203. doi:10.1115/DETC2007-35531.

A six-DOF wrist-partitioned fully parallel manipulator is a parallel manipulator in which three of the six actuated joints are used to control the position of a point on the moving platform while the other three are further used to control the orientation of the moving platform. Such parallel manipulators are in fact the parallel counterparts of the wrist-partitioned serial manipulators, which are widely used in industry. Unlike parallel manipulators of a general structure, a six-DOF wrist-partitioned fully parallel manipulator usually has simple kinematic characteristics such as its forward displacement analysis and singularity analysis are easy to solve. This paper deals with the type synthesis of six-DOF wrist-partitioned fully parallel manipulators. An approach is first proposed for the type synthesis of this class of parallel manipulators. Using the proposed approach, six-DOF wrist-partitioned fully parallel manipulators can be constructed from the types of three-DOF non-overconstrained spherical parallel manipulators. A large number of six-DOF wrist-partitioned fully parallel manipulators are then obtained, and several types of practical relevance are also identified.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2007;():1205-1211. doi:10.1115/DETC2007-35542.

This paper investigates the algorithm of origami carton folding with a multi-fingered robotic carton-packaging system. The equivalent mechanism structure of origami cartons is developed by modeling carton boards as links and creases as revolution joints. The trajectories of carton folding are analyzed by the mechanism model. Particularly the vertex of the carton is identified as a spherical linkage. A path planning algorithm is then generated based on the trajectory that is passed on to the tip of a five-bar robotic finger and the finger configuration space is identified. A test rig with two robotic fingers was developed to demonstrate the principle.

Commentary by Dr. Valentin Fuster
2007;():1213-1221. doi:10.1115/DETC2007-35700.

Localization is one of the critical issues in the field of multi-robot navigation. With an accurate estimate of the robot pose, robots will be able to navigate in their environment autonomously with the aid of flexible path planning. In this paper, the infrastructure of a Distributed Vision System (DVS) for multi-robot localization is presented. The main difference between traditional DVSs and the proposed one is that multiple overhead cameras can simultaneously localize a network of robots. The proposed infrastructure is comprised of a Base Process and Coordinate Transform Process. The Base Process receives images from various cameras mounted in the environment and then utilizes this information to localize multiple robots. Coordinate Transform Process is designed to transform from Image Reference Plane to world coordinate system. ID tags are used to locate each robot within the overhead image and camera intrinsic and extrinsic parameters are used to estimate a global pose for each robot. The presented infrastructure was recently implemented by a network of small robot platforms with several overhead cameras mounted in the environment. The results show that the proposed infrastructure could simultaneously localize multiple robots in a global world coordinate system with localization errors within 0.1 meters.

Topics: Robots
Commentary by Dr. Valentin Fuster
2007;():1223-1234. doi:10.1115/DETC2007-35727.

The work reported in this paper brings together the kinematics of spherical closed chains and the recently developed freeform rational motions to study the problem of synthesizing rational interpolating motions under the kinematic constraints of spherical 6R closed chains. The results presented in this paper are extension of our previous work on the synthesis of piecewise rational spherical motions for spherical open chains. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of spherical closed chains in the Cartesian space. Quaternions are used to represent spherical displacements. The problem of synthesizing smooth piecewise rational motions is converted into that of designing smooth piecewise rational curves in the space of quaternions. The kinematic constraints are transformed into geometric constraints for the design of quaternion curves. An iterative algorithm for constrained motion interpolation is presented that detects the violation of the kinematic constraints by searching for those extreme points of the quaternion curve that do not satisfy the constraints. Such extreme points are modified so that the constraints are satisfied and the resulting new points are added to the ordered set of the initial positions to be interpolated. An example is presented to show how this algorithm produces smooth spherical rational spline motions that satisfy the kinematic constraints of a spherical 6R closed chain. The algorithm can also be used for the synthesis of rational interpolating motions that approximate the kinematic constraints of spherical 5R and 4R closed chains within a user-defined tolerance.

Topics: Motion , Chain , Interpolation
Commentary by Dr. Valentin Fuster
2007;():1235-1244. doi:10.1115/DETC2007-34466.

In this paper a complete system of Euclidean invariants is presented to study circular surfaces with fixed radius. The study of circular surfaces is simplified to the study of two curves: the spherical indicatrix of the unit normals of circle planes and the spine curve. After the geometric meanings of these Euclidean invariants are explained, the distribution parameter of a circular surface is defined. If the value of the distribution parameter of a circular surface is 0, the circular surface is a sphere. Then the relationship between the moving frame {E 1 , E 2 , E 3 } and the Frenet frame {t , n , b } of the spine curve is investigated, and the expressions of the curvature and torsion of the spine curve are obtained based on these Euclidean invariants. The fundamental theorem of circular surfaces is first proved. Next the first and second fundamental forms of circular surfaces are computed. The last part of this paper is devoted to constraint circular surfaces. The sufficient and necessary condition for a general circular surface to be one that can be generated by a series-connected C’R, HR, RR, or PR mechanism is proved.

Commentary by Dr. Valentin Fuster
2007;():1245-1253. doi:10.1115/DETC2007-34620.

Transverse-regularity is a point-wise manipulator property, ensuring that the singular set Σ is locally a smooth manifold. A generic manipulator is one which is transverse-regular in any configuration. The contribution of this paper is a necessary and sufficient condition for transverse-regularity. The condition is based on the manipulator’s joint screws and their screw products. An expression for the tangent space to Σ at transverse-regular singularities is derived. It is shown that a manipulator is non-generic if it can attain a pose where the rank of the manipulator’s screw system together with the screw products is not the maximal rank of the Jacobian. A necessary and sufficient criterion for degree-one singularities is given in terms of the mechanism’ joint screws. In particular, any non-redundant manipulator is transverse-regular in a degree-one singularity.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2007;():1255-1263. doi:10.1115/DETC2007-34927.

Jacobian-based control algorithms for the attitude control of a rigid body undergoing a series of forward and reverse rotations are proposed in this paper. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is singular as well as a null matrix at the identity that makes the conventional Jacobian formulation break down. In order to handle the singularities involved in FR rotations, the Jacobian algorithm is reformulated and implemented so as to synthesize the FR rotation for a desired orientation change. We introduce the single-step and multiple-step Jacobian methods in this paper. The single-step Jacobian method synthesizes a specific FR rotation that enables the rigid body to reach a given desired orientation through a single step. The multiple-step Jacobian method synthesizes physically feasible FR rotations on an incremental optimal path to a desired orientation. A comparison with existing control algorithms for FR motions verifies the fast convergence property of the Jacobian-based algorithm and the accuracy of the solutions.

Topics: Algorithms
Commentary by Dr. Valentin Fuster
2007;():1265-1273. doi:10.1115/DETC2007-34936.

Setting aside paradoxical linkages such as Bennett’s, Bricard’s or Goldberg’s, the mobility of single loop linkages seemed, with the developments on mobility analysis carried out in the last five years, a closed chapter in kinematic research. However, recent developments on the mobility of parallel platforms have shed additional insight into the problem. This contribution attempts to unify the results obtained in the last five years in the area of mobility of single-loop kinematic chains to state what appears to be a final word on the subject.

Topics: Linkages
Commentary by Dr. Valentin Fuster
2007;():1275-1281. doi:10.1115/DETC2007-35053.

For a planar motion of a body, there exists an instantaneous center of zero velocity or what is known as the centrode . In three-dimensions, the same is represented by the instantaneous screw axis. In two dimensions, however, there is a geometric method of construction the instant center by using the velocity vectors of two points of the body. The instant center is the point of intersection of the lines perpendicular to the two velocity vectors. This type of construction, however, did not exist for the instantaneous screw axis. In this paper, we present such a geometric construction for the instantaneous screw axis using line geometry.

Topics: Geometry
Commentary by Dr. Valentin Fuster
2007;():1283-1288. doi:10.1115/DETC2007-35265.

This paper deals with analysis of the gain of the degree-of-freedoms at a singular point for the Gough-Stewart platform. Through investigating the configuration bifurcation behaviors of the manipulator, it is found that two assembly configuration branches corresponding with the same input parameters intersect at the singular point, and it is easy for the component to jump from its original configuration branch to the other configuration branch if two configuration branches are close enough in the vicinity of the singular point. With the aid of the maximum loss-control domain, which reflects the configuration bifurcation characteristic at the singular points and the control precision of systems, the gain of degree-of-freedoms for the Stewart platform are analyzed. The research shows that the gain of degrees of freedom mainly depends on the configuration bifurcation characteristic in the vicinity of the singular points. The parallel manipulator with a higher control precision will obtain fewer degree-of-freedoms and its configuration is easy to be controlled in the vicinity of the singular point. This investigation has potential applications in selecting joints’ clearance and determining the control precision of the Stewart platform.

Commentary by Dr. Valentin Fuster
2007;():1289-1298. doi:10.1115/DETC2007-35328.

In this paper, a computational approach suitable to compute the instantaneous mobility of manipulators in any kind of configuration (either singular or nonsingular) using a general purpose software is presented. Although the procedure is applicable to any formulation of the velocity equation, in this paper authors have used a point-based jacobian formulation of the manipulator. The end-effector’s instantaneous mobility is analyzed, first discriminating among its rotational, translational and passive freedoms, and then computing its principal screws. Then, either its instantaneous screw systems or certain instantaneous pitch surfaces can be depicted. The approach is illustrated with its application to the 3-URU DYMO parallel manipulator.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2007;():1299-1304. doi:10.1115/DETC2007-35765.

In the two position theory of finite kinematics, we are concerned with not only the displacement of a rigid body, but also with the displacement of a certain element of the body. This paper deals with the displacement of a line and reveals the regulus that characterizes such a displacement. Residing on a special hyperbolic paraboloid, the regulus is obtained by the intersection of three linear line complexes corresponding to a specific set of basis screws of a 3-system. The degeneration of the regulus when two positions of a line intersect is also discussed. In this paper, the regulus of intersection is obtained geometrically as well as analytically. The discovery of the regulus lays a geometric foundation for dealing with line-based problems in computational kinematics and computational line geometry.

Topics: Displacement
Commentary by Dr. Valentin Fuster
2007;():1305-1311. doi:10.1115/DETC2007-35768.

This paper studies the problem of analyzing the motion of the coupler link of a planar 4R closed kinematic chain from the viewpoint of constrained motion interpolation. The kinematics of the planar 4R chain is formulated using planar quaternions. The four-point interpolatory subdivision scheme for curves in the field of Computer Aided Geometric Design (CAGD) is extended to planar quaternions for the generation of an inbetween candidate position of the coupler link from a given set of four key positions. The candidate position is then checked and modified according to the kinematic constraints of the planar 4R chain. The resulting new inbetween position that satisfies the kinematic constraints is then inserted into the given set of key positions. In the early stage of this refinement process, each new inbetween position must be made to satisfy the 4R kinematic constraints exactly to ensure the correct motion. When there is sufficient number of coupler positions, one can use the unconstrained four-point interpolatory scheme to generate the inbetween positions to allow for fast animation of the coupler motion.

Commentary by Dr. Valentin Fuster
2007;():1313-1318. doi:10.1115/DETC2007-35916.

A fully-symmetrical 5-DoF 3R2T parallel manipulator has three rotational and two translational freedoms. It may be adopted in motion simulation for a spinal column. However, kinematics of these manipulators has not been studied very well because of their short history. To study the characteristics of these manipulators, a 5-RRR (RR) prototype is manufactured. Both forward/reverse position solution and singularity are analyzed in this paper. The work presented in this paper will be helpful for understanding the property of other fully-symmetrical 5-DoF 3R2T parallel manipulator because of their similar constraint relationship.

Commentary by Dr. Valentin Fuster

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