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30th Annual Mechanisms and Robotics Conference

2006;():3-11. doi:10.1115/DETC2006-99047.

This paper presents the synthesis of optimally unstable two-phalanx underactuated fingers. The method to obtain a design unable to grasp almost any object under normal conditions is presented. The technique relies on the careful analysis of the grasp-state plane and equilibrium curve associated to two-phalanx underactuated fingers. First, results of the analysis of the grasp-state plane are recalled. Second, unstable configurations and paradoxical equilibrium are presented. Then, the synthesis of optimally unstable fingers is detailed. Finally, applications of these unstable fingers are proposed.

Commentary by Dr. Valentin Fuster
2006;():13-22. doi:10.1115/DETC2006-99461.

The increasing interest in active solutions for the compensation of static and quasi-static displacements at tooling machines, like mechatronics and adaptronics for example, must be looked at with regard to high dynamics and accuracy. Mechatronical systems for the compensation of displacements allow for high manufacturing accuracy and at the same time high machine dynamics. The high system costs make an application in industrial environments impossible. Besides mechatronics the area of adaptronics shows a high potential for cost reduction and system integration with a comparable functionality. This article describes the compensation for piezoelectric transducer stacks in the static and quasi-static range in particular. The piezoelectric transducers stand out for their excellent properties as actuators such as positioning accuracy and dynamics. The multifunctional properties of piezoelectric transducers allow for the spatial and functional integration of sensor and actuator for the realization of active components. Due to a limited time constant for the use of piezoelectric transducers as sensor, static loads must be transformed into a dynamic input signal for the transducer. The interdisciplinary design of the overall system is of vital importance. It is described and discussed by the example of the realization of an adaptronic strut with controllable elongation for parallel kinematics and an adaptronic hydrostatic pressure pocket unit for an intelligent hydrostatic leveling system.

Topics: Stress , Design
Commentary by Dr. Valentin Fuster
2006;():23-30. doi:10.1115/DETC2006-99740.

The dynamic stiffness of a grinding machine influences the process stability enormously. Among other things the stability of the grinding process is affected by influences like the specification of the grinding wheel, the condition of the workpiece and machine parameters. Unfavorable combinations of these lead to chatter vibrations of the machine and chatter marks on the workpiece. This paper presents the results of experimental and theoretical investigations of the vibration behavior of a grinding machine and the design of active modules. These modules will be implemented in the structure of the machine to minimize the vibrations and additionally increase its static stiffness of the machine.

Commentary by Dr. Valentin Fuster
2006;():31-37. doi:10.1115/DETC2006-99041.

The mechanism studied in this paper is a three degree of freedom 6×6 tensegrity structure. A tensegrity structure is one that balances internal (pre-stressed) forces of tension and compression. These structures have the unique property of stabilizing themselves if subjected to certain types of disturbances. The structure analyzed in this paper consists of two rigid bodies (platforms) connected by a total of six members. Three of the members are noncompliant constant-length struts and the other three members consist of springs. For typical parallel mechanisms, if the bottom platform is connected to the ground and the top platform is connected to the base by six compliant leg connectors, the top platform will have six degrees of freedom relative to the bottom platform. However, because three of the six members connecting the two platforms are noncompliant constant-length struts, the top platform has only three degrees of freedom. The primary contribution of this paper is the analysis of the three degree of freedom tensegrity platform. Specifically, given the location of the connector points on the base and top platforms, the lengths of the three noncompliant constant-length struts, and the desired location of a point embedded in the top platform measured with respect to a coordinate system attached to the base, all possible orientations of the top platform are determined.

Commentary by Dr. Valentin Fuster
2006;():39-53. doi:10.1115/DETC2006-99042.

Advantages and problems related to the use of compliant hinges in articulated robotic structures are briefly discussed. A novel kind of elastic joint made with close-wound helical springs is then described. It is capable of large angular displacement so that it can be conveniently applied in manipulation devices like the humanoid robot hand developed at the University of Bologna. The results of this application encourage a systematic investigation on the properties of this kind of joints, not previously described in the literature, aiming at mechanical characterization and definition of design criteria. To this purpose, the paper outlines a general investigation programme, where theoretical models, Finite Elements analysis and experiments jointly contribute to the evaluation of the hinge stiffness and to the identification of influential design parameters. Preliminary results related to evaluation of the stiffness about the principal bending axis are then examined and discussed, comparing the results obtained from experiments with those achieved by means of a simplified mathematical model and the correspondent FE analysis. An auxiliary parameter is finally introduced in order to define a general criterion for the design of spring-based hinges subjected to large deflection.

Topics: Hinges , Springs , Stiffness
Commentary by Dr. Valentin Fuster
2006;():55-63. doi:10.1115/DETC2006-99048.

This paper presents an analysis of a two-phalanx linkage-driven underactuated finger with substantial compliance in all the joints of the system. The primary goal of the paper is to illustrate with an example, the theoretical issues faced in designing compliant underactuated fingers. To this aim, a two-phalanx linkage-driven underactuated finger is analyzed throughout the paper to clarify the concepts presented. First, a method to compute the contact forces generated by compliant underactuated fingers is presented and discussed. Finally, the self-mobility of the finger is discussed and a method to predict if this mobility will converge to a stable grasp or not is presented. The paper presents an exemplified theoretical analysis whose layout provides very useful insights for the design of compliant underactuated fingers and emphasizes the challenges to be met in order to design successful prototypes.

Topics: Linkages
Commentary by Dr. Valentin Fuster
2006;():65-76. doi:10.1115/DETC2006-99190.

Since long time flexure hinges have been used in high precision devices instead of conventional bearings, e.g. ball or sliding bearings. Due to the natural lack of backlash, friction and slip-stick effects in flexure hinges, the accuracy of positioning or measurement devices can be highly increased. Recent applications for flexure hinges are seen in parallel robots. The integration of flexure hinges in parallel structures is quite simple because all joints, except for the drives, are passive. Since flexure hinges gain their mobility from an elastic and plastic deformation of matter, their kinematic behavior differs from the kinematics of ideal rotational joints. This leads to deviations of the compliant mechanism and its rigid body model. In this paper a kinematic model is proposed which allows for a compensation of the introduced hinge errors. Furthermore the dynamic model of a compliant parallel robot is derived and verified by means of simulation studies. This dynamic model can be used e.g. for model-based robot control algorithms or for the dimensioning of drives for compliant mechanisms.

Topics: Robots , Modeling
Commentary by Dr. Valentin Fuster
2006;():77-89. doi:10.1115/DETC2006-99266.

This paper presents a framework for the design of a compliant system; that is, the concurrent design of a compliant mechanism with embedded actuators and embedded sensors. We focus on methods that simultaneously synthesize optimal structural topology and placement of actuators and sensors for maximum energy efficiency and adaptive performance, while satisfying various weight and performance constraints. The goal of this research is to lay a scientific foundation and a mathematical framework for distributed actuation and sensing within a compliant active structure. Key features of the methodology include (1) the simultaneous optimization of the location, orientation, and size of actuators concurrent with the compliant transmission topology and (2) the concepts of controllability and observability that arise from the consideration of control, and their implementation in compliant systems design. The methods used include genetic algorithms, graph searches for connectivity, and multiple load cases implemented with linear finite element analysis. Actuators, modeled as both force generators and structural compliant elements, are included as topology variables in the optimization. Results are provided for several studies, including: (1) concurrent actuator placement and topology design for a compliant amplifier and (2) a shape-morphing aircraft wing demonstration with three controlled output nodes. Central to this method is the concept of structural orthogonality, which refers to the unique system response for each actuator it contains. Finally, the results from the controllability problem are used to motivate and describe the analogous extension to observability for sensing.

Topics: Sensors , Actuators
Commentary by Dr. Valentin Fuster
2006;():91-100. doi:10.1115/DETC2006-99298.

This paper discusses topology, shape and size optimization of fully compliant mechanisms for path generation applications using curved frame elements and genetic algorithm. The topology optimization problem is treated as a discrete ‘0-1’ problem wherein the elastic modulus is chosen as 0 or some pre-specified value, and no intermediate value in between. As the Young’s moduli are discrete topology design variables, function based genetic algorithm is employed for optimization. The size optimization variables are the lengths, in-plane widths and out-of-plane thicknesses of frame elements. Shape optimization is performed using the end slopes. Kirchhoff’s shallow arch beam theory is employed along with co-rotational geometrically nonlinear formulation. Synthesis examples are presented to demonstrate the applicability of min-max criterion proposed to achieve a curved path specified using precision points.

Commentary by Dr. Valentin Fuster
2006;():101-107. doi:10.1115/DETC2006-99344.

The elastic dynamic performances are studied for a piezodriven 3-DOF compliant precision micro-positioning stage with flexure hinges. Firstly, the dynamic equations of motion of the system are developed. The flexure hinges are modeled by using the varying section frame element, and the element stiffness and mass matrices are presented. Secondly, the lower order modal frequencies and damping factors are experimentally identified and the analysis model is proved to be feasible. Finally, an input-tuning concept aimed to improve dynamic actuation performances is proposed. The quintic tuning function is employed in the dynamic analysis for the system. Simulation results show that the residual vibration and the input couplings induced by the inputs are improved significantly after the tuning function is applied during actuation.

Commentary by Dr. Valentin Fuster
2006;():109-118. doi:10.1115/DETC2006-99345.

Displacement-amplifying compliant mechanisms (DaCMs) reported in literature are mostly used for actuator applications. This paper considers them for sensor applications that rely on displacement measurement, and evaluates them objectively. The main goal is to increase the sensitivity under constraints imposed by several secondary requirements and practical constraints. A spring-mass-lever model that effectively captures the addition of a DaCM to a sensor is used in comparing eight DaCMs. We observe that they significantly differ in performance criteria such as geometric advantage, stiffness, natural frequency, mode amplification, factor of safety against failure, cross-axis stiffness, etc., but none excel in all. Thus, a combined figure of merit is proposed using which the most suitable DaCM could be selected for a sensor application. A case-study of a micro machined capacitive accelerometer and another case-study of a vision-based force sensor are included to illustrate the general evaluation and selection procedure of DaCMs with specific applications. Some other insights gained with the analysis presented here were the optimum size-scale for a DaCM, the effect on its natural frequency, limits on its stiffness, and working range of the sensor.

Commentary by Dr. Valentin Fuster
2006;():119-127. doi:10.1115/DETC2006-99415.

This paper proposes a methodology for the design of a sub-centimetre underactuated compliant gripper. The gripper is optimized in order to maintain a proper force distribution on the phalanges and to avoid the deformation of soft objects. In order to keep the design simple and to limit the complexity of the control, each finger is based on a planar five-bar linkage. The five-bar mechanism is a well known and efficient underactuated mechanism. In this work, the revolute joints are replaced by flexible hinges in order to allow the miniaturization of the mechanism and make it easy to clean and sterilize. The behaviour of the prototypes built shows the effectiveness of the proposed method.

Topics: Design , Grippers
Commentary by Dr. Valentin Fuster
2006;():129-141. doi:10.1115/DETC2006-99430.

In this paper, we investigate power flow in compliant mechanisms that are employed in dynamic applications. More specifically, we identify various elements of the energy storage and transfer between the input, external load, and the strain energy stored within the compliant transmission. The goal is to design complaint mechanisms for dynamic applications by exploiting the inherent energy storage capability of compliant mechanisms in the most effective manner. We present a detailed case study on a flapping mechanism in which we compare the peak input power requirement in a rigid-body mechanism with attached springs versus a distributed compliant mechanism. Through this case study, we present two different approaches, (1) generative-load exploitation and (2) reactance cancellation, to describe the role of stored elastic energy in reducing the required input power. In contrast to a conventional mechanism with a spring, stress and strain in a compliant mechanism are more uniformly distributed. The entire mechanism stores energy rather than just a spring, providing more energy storage per unit mass. We propose a compliant flapping mechanism and its evaluation using nonlinear transient analysis. The input power requirement of the proposed compliant flapping mechanism is found to be 48% and 10% less than those of the four-bar flapping mechanism without and with a spring, respectively. The results show that a compliant mechanism can be a better alternative to a rigid-body mechanism with attached springs.

Commentary by Dr. Valentin Fuster
2006;():143-149. doi:10.1115/DETC2006-99439.

The design obtained from a topology optimization problem can largely depend on the type of the ground structure used. A new type of ground structure containing hinged beam elements is described in this paper that reduces the dependence of the optimal design on the ground structure. Apart from the beam and truss elements that have traditionally been used, two new types of elements are introduced: 1) a beam with a hinge on one end and a solid connection on the other end, 2) beam element with hinges on both ends. These elements are particularly useful when applied to a compliant mechanism design using a truss/beam type ground structure. A couple of compliant mechanism problems are solved to demonstrate the effectiveness of these elements.

Commentary by Dr. Valentin Fuster
2006;():151-157. doi:10.1115/DETC2006-99453.

Significant reduction in cost and time of bistable mechanism design can be achieved by understanding their bistable behavior. This paper presents bistable compliant mechanisms whose pseudo-rigid-body models (PRBM) are four-bar mechanisms with a torsional spring. Stable and unstable equilibrium positions are calculated for such four-bar mechanisms, defining their bistable behavior for all possible permutations of torsional spring locations. Finite Element Analysis (FEA) and simulation is used to illustrate the bistable behavior of a compliant mechanism with a straight compliant member, using stored energy plots. These results, along with the four-bar and the compliant mechanism information, can then be used to design a bistable compliant mechanism to meet specified requirements.

Topics: Springs , Mechanisms
Commentary by Dr. Valentin Fuster
2006;():159-171. doi:10.1115/DETC2006-99459.

This paper explores the feasibility of using compliant-ortho-planar springs (COPS) for rotational applications. The primary motivation is the application of COPS to a rubber v-belt continuously variable transmission (CVT). Although stresses and stress concentrations are important for the design of a COPS, this paper will focus on the behavior of a COPS resulting specifically from its rotation. This paper focuses on issues related to stress stiffening and lateral instability. Both phenomena are a direct result of the inertial loads a COPS would experience in a rotating environment. The results show how stress stiffening and lateral buckling are influenced by design parameters. Conclusions and recommendations for further research are presented.

Topics: Springs
Commentary by Dr. Valentin Fuster
2006;():173-181. doi:10.1115/DETC2006-99460.

Pseudo-rigid-body models help expedite the compliant mechanism design process by aiding the analysis and synthesis of candidate design solutions, using loop-closure techniques for rigid-body mechanisms. Presently, these models are available only for relatively simple compliant beam geometries and loading situations. The chain algorithm is an alternate method for the design and analysis of compliant mechanisms. Though more versatile, insofar as the geometry and loading are concerned, it is not possible to implement this technique in analysis or synthesis problems involving loop-closure equations. This paper proposes the construction of a generalized “pseudo-rigid-body model chain;” it allows the use of pseudo-rigid-body models in conjunction with the chain algorithm to obtain the deformation kinematics of complex compliant members. Such a “pseudo-rigid-body model chain” would possess dual advantages of expediency of modeling through the use of pseudo-rigid-body representations of compliant segments, and the inherent flexibility of the chain algorithm to geometry and load boundary conditions. The proposed technique involves discretization of the planar continuum into initially straight, equal length compliant segments, whose deflections due to the applied load boundary conditions are then determined using appropriate pseudo-rigid-body models. Such a model could potentially be used in the solution of compliant mechanism design and analysis problems when coupled with the use of loop-closure equations.

Topics: Algorithms , Chain
Commentary by Dr. Valentin Fuster
2006;():183-190. doi:10.1115/DETC2006-99463.

Pseudo-rigid-body models help expedite the compliant mechanism design process by aiding the analysis and synthesis of candidate design solutions, using loop-closure techniques for rigid-body mechanisms. Presently, these models are available only for relatively simple compliant beam geometries and loading situations. The pseudo-rigid-body model chain algorithm provides reasonable approximations of the deformed shape of complex compliant members; however, it has one major limitation. The elastic deformation of each compliant segment under combined load boundary conditions is obtained by superposing the pseudo-rigid-body model displacements due to i) the force and ii) the moment loads, respectively. Hence, each segment needs to be characterized by two separate pseudo-rigid-body models in order to accurately determine its deformation kinematics. Such an idealization of compliant segments would present significant challenges when attempting to represent the pseudo-rigid-body model chain in vectorial form, as in planar vector loop-closure methods. Vectorial modeling would be possible if each flexible segment in the chain could be represented by an “equivalent pseudo-rigid-body model.” This paper proposes the concept of a rudimentary equivalent pseudo-rigid-body model to represent compliant segments with combined load boundary conditions in the pseudo-rigid-body model chain algorithm. Such a model may help overcome the difficulties confronted in the potential implementation of the pseudo-rigid-body model chain in planar vector loop-closure solution techniques.

Commentary by Dr. Valentin Fuster
2006;():191-198. doi:10.1115/DETC2006-99465.

The design of compliant mechanisms has been aided by the development of pseudo-rigid-body models to predict the motion of flexible members undergoing large displacements. Many of these models are based on the fact that the end of a cantilever beam follows a near-circular path when planar loads are applied. This paper shows that the application of 3-dimensional end-loading causes a beam to follow a near-spherical path, even for beams with non-circular cross-sections. A 3D pseudo-rigid-body model is presented that allows the motion of an end-loaded rectangular beam to be predicted using a rigid link and a spherical joint. Two sets of deflection limits for 0.5% error are presented and shown to be dependent upon the aspect ratio of the cross-section of the beam. The model has the potential for aiding in the design of spatial compliant mechanisms and analysis of planar compliant mechanisms undergoing large out-of-plane motions.

Commentary by Dr. Valentin Fuster
2006;():199-207. doi:10.1115/DETC2006-99601.

Researchers in the field of optimal synthesis of compliant mechanisms have been working to develop tools that yield distributed compliant devices to perform specific tasks. However, it has been demonstrated in the literature that much of this work has resulted in mechanisms that localize compliance rather than distribute it as desired. In fact, Yin and Ananthasuresh (2003) [1] demonstrate that based on the current formulation of optimality criteria and analysis via the finite element (FE) technique, a lumped compliant device will always exist as the minimizing solution to the objective function. The addition of constraints on allowable strain simply moves the solution back from this objective. Therefore, modification to the standard optimality criteria needs to take place. Yin and Ananthasuresh [1] proposed and compared several approaches that include distributivity-based measures within the optimality criteria, and demonstrated the effectiveness of this approach. In this paper, the authors propose to build on this problem. In a similar manner, a general approach to the topology synthesis problem will be suggested to yield mechanisms in which the compliance is distributed throughout the device. This work will be based on the idea of including compliance distribution directly within the objective functions, while addressing some of the potential limiting factors in past approaches. The technique will be generalized to allow simple addition of criteria in the future, and to deliver optimal designs through to manufacture. This work will first revisit and propose several quantitative definitions for distributed compliant devices. Then, a multi-objective formulation based on a non-dominating sort and Pareto set method will be incorporated that will provide information on the nature of the problem and compatibility of employed objective functions.

Commentary by Dr. Valentin Fuster
2006;():209-219. doi:10.1115/DETC2006-99639.

In this paper, we investigate a methodology for the conceptual synthesis of compliance at a single point based on a building block approach. The methodology lays the foundation for more general compliant mechanism synthesis problems involving multiple points of interest (i.e. inputs and outputs). In the building block synthesis, the problem specifications are decomposed into related sub-problems if a single building block cannot perform the desired task. The sub-problems are tested against the library of building blocks until a suitable building block is determined. The synthesized design is composed of an assembly of the building blocks to provide the desired functionality. The building block approach is intuitive and provides key insight into how individual building blocks contribute to the overall function. We investigate the basic kinematic behavior of individual building blocks and relate this to the behavior of a design composed of building blocks. This serves to not only generate viable solutions but also to augment the understanding of the designer. Once a feasible concept is thus generated, known methods for size and geometry optimization may be employed to fine tune performance. The key enabler of the building block synthesis is the method of capturing kinematic behavior using Compliance Ellipsoids. The mathematical model of the compliance ellipsoids facilitates the characterization of the building blocks, transformation of problem specifications, decomposition into sub-problems, and the ability to search for alternate solutions. The compliance ellipsoids also give insight into how individual building blocks contribute to the overall kinematic function. The effectiveness and generality of the methodology are demonstrated through a synthesis example. Using only a limited set of building blocks, the methodology is capable of addressing generic kinematic problem specifications.

Commentary by Dr. Valentin Fuster
2006;():221-230. doi:10.1115/DETC2006-99657.

A spring’s nonlinear load-displacement function is described by three factors, the (i) shape function, (ii) load-range, and (iii) displacement-range. The shape function encompasses the nonlinear relationship between the load and displacement, and therefore, is the most difficult factor to match. In this paper, we present a general scheme for topology, size, and shape optimization of nonlinear springs for prescribed load–displacement shape functions, while simultaneously meeting manufacturing, space, and stress constraints. This paper presents the objective function and a novel, floating point parametric model used within a genetic algorithm optimization scheme. The nonlinear springs all undergo large deformations and are evaluated by nonlinear finite element analysis. Two examples are included to demonstrate the effectiveness of the methodology in synthesizing nonlinear springs that match a prescribed load-displacement shape function.

Commentary by Dr. Valentin Fuster
2006;():231-239. doi:10.1115/DETC2006-99661.

An automated design synthesis method is developed to design an airfoil with a reconfigurable shape, which can change from one type of geometry to another. A design synthesis method using unit truss approach and particle swarm optimization is presented. In the unit truss approach, unit truss is used as a new unit cell for mechanics analysis of cellular structures, including lightweight structures and compliant mechanisms. Using unit truss approach, axial forces, bending, torsion, nonlinearity, and buckling in structures can be considered. It provides good analysis accuracy and computational efficiency. A synthesis method using unit truss approach integrated with particle swarm optimization is developed to systematically design adaptive cellular structures, in particular, compliant mechanisms discussed in this paper. As an example study, the authors realize the design synthesis of a compliant mechanism that enables an entire closed-loop airfoil profile to change shape from NACA 23015 to FX60-126 for the desired morphing wing. The nonlinear behavior of compliant mechanisms under large deformation is considered. The resulting design is validated by testing its robustness and considering nonlinearity.

Commentary by Dr. Valentin Fuster
2006;():241-250. doi:10.1115/DETC2006-99715.

A new approach for the synthesis of a compliant link experiencing nonlinear deformations is herein introduced. The model is being proposed as an alternative to the pseudo-rigid-body model widely used in compliant mechanisms synthesis. The proposed approach is based on the exact elliptic integral equations that govern beam deformations. The model entails the determination of a few parameters in an optimum sense that would move the endpoint of the beam through several desired positions with minimal error. A tabu-gradient optimization algorithm is employed to search the design space for an optimum solution that minimizes the square of the error between the desired and the generated endpoint positions while satisfying a set of relevant constraints. Attributes of the model are highlighted by way of several examples. A brief outline on how the proposed model is used as the basis for compliant mechanism synthesis is presented and demonstrated by way of two examples.

Commentary by Dr. Valentin Fuster
2006;():251-257. doi:10.1115/DETC2006-99752.

Over-constraint is an important concern in mechanism design because it can lead to a loss in desired mobility. In distributed-compliance flexure mechanisms, this problem is alleviated due to the phenomenon of elastic averaging, thus enabling performance-enhancing geometric arrangements that are otherwise unrealizable. The principle of elastic averaging is illustrated in this paper by means of a multi-beam parallelogram flexure mechanism. In a lumped-compliance configuration, this mechanism is prone to over-constraint in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear load-stiffening and elasto-kinematic effects in the constituent beams have an important role to play in the over-constraint and elastic averaging characteristics of this mechanism. Therefore, a parametric model that incorporates these nonlinearities is utilized in predicting the influence of a representative geometric imperfection on the primary motion stiffness of the mechanism. The proposed model utilizes a beam generalization so that varying degrees of distributed compliance are captured using a single geometric parameter.

Commentary by Dr. Valentin Fuster
2006;():259-265. doi:10.1115/DETC2006-99307.

This article presents a way to draw Euler angles such that the proper operation and application becomes immediately clear. Furthermore, Euler parameters, which allow a singularity-free description of rotational motion, are discussed within the frame-work of quaternion algebra and are applied to the kinematics and dynamics of a rigid body.

Commentary by Dr. Valentin Fuster
2006;():267-273. doi:10.1115/DETC2006-99059.

The Institute of Mechanism Theory and Machine Dynamics of RWTH Aachen University houses a large collection of more than 200 mechanisms and models. Partly they are used to illustrate and visualize kinematic basics and methods taught to students. Furthermore these models are also used as a basis for mechanical designers looking for a solution to their motion tasks in different machinery such as packaging or processing machines. These models span a wide arch from historic models showing e.g. sewing machines from the late 19th century, typewriters from the early 20th century and acrylic glass models still used today in university lectures where they are placed on the overhead projector. With the swift development of the internet as the major base for information retrieval, new ideas about knowledge presentation have come up. Today it is obvious that fast and easy access to information is a major success factor in most areas both economics and science and is therefore of eminent importance. New developments in information technology and related software have created new possibilities for the presentation of scientific knowledge also in mechanism theory [1]. In this paper the IGM-Mechanism Encyclopaedia and the Digital Mechanism Library will be presented. Both use the possibilities of the internet to make basic and specific knowledge for the analysis and synthesis of mechanisms available to a broad public.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2006;():275-279. doi:10.1115/DETC2006-99107.

This paper studies sensing element designs in ancient seismometers and describes the developments of ancient earthquake instruments. A basic seismograph comprises a seismometer, a recording system, and a timing system. The major difficulty in the development of a seismograph was the design of the seismometer. And, the break through was the use of a pendulum system as a sensing element that responded to ground motion and did not move with the ground. Early seismoscopes were primarily intended to determine that an earthquake had happened. The first seismoscope invented by Zhang Heng was Hou Feng Di Dong Yi made in ancient China around the year 132 AD. The truly successful seismographs were first designed and built in the 1880s by a group of British scientists in Japan. In 1906, Boris Galitzin developed a working electromagnetic seismograph with a great sensitivity. Finally, a comparison with the recording systems of ancient seismographs is concluded.

Commentary by Dr. Valentin Fuster
2006;():281-290. doi:10.1115/DETC2006-99116.

Dr.-Ing. E.h. Kurt Hain was born 1908 in Leipzig and died 1995 in Braunschweig. He was a pioneer of applied kinematics in Germany. He also visited American universities four times starting in 1957. He wrote 13 books and about 380 articles on nearly all partial fields of kinematics. This paper tries to give a complete survey of his lifework and describes a national research approach to preserve his heritage for future generations of mechanical engineers.

Topics: Kinematics
Commentary by Dr. Valentin Fuster
2006;():291-300. doi:10.1115/DETC2006-99165.

The second half of 19-th century can be considered the Golden Age of TMM for the achieved theoretical and practical results that stimulated and obtained enhancements of machinery for Industrial Revolution. Burmester and Allievi can be considered as significant examples of that time for their personality and professional experiences as well as for their works on Kinematics of Mechanisms. In this paper a survey is presented on their curriculum and scientific main works on Mechanism Design with the aim also to stress similarities and differences in the life of kinematicians and in developments of Mechanism Design at the end of 19-th century.

Topics: Design , Mechanisms
Commentary by Dr. Valentin Fuster
2006;():301-310. doi:10.1115/DETC2006-99198.

In this paper, we have presented the personality and activity of Agustin Betancourt who can be considered among the first modern mechanical (industrial) engineers with a strong formation and expertise in TMM. Indeed his activity can be considered as a significant example of personality in the early modern developments of TMM but also how TMM formation has been useful for engineers and managers in the overcoming Industrial Revolution. In particular, Betancourt can be seen as an emblematic example of the international vision of TMM and its application, since he has been a successful scientist, engineer, and manager in Spain, France, and then Russia.

Topics: Engineers
Commentary by Dr. Valentin Fuster
2006;():311-323. doi:10.1115/DETC2006-99604.

The wagon odometer (or “roadometer”), designed, built, and implemented on the Mormon Trail, has generated much interest because of the documentation of the odometer’s design, the unusual circumstances under which it was developed, the impact it made on the settlement of the West, and the epic nature of the Mormon Exodus. This paper reviews first-person accounts documenting the odometer’s development, discusses the odometer’s impact, and reviews myths and misconceptions surrounding the odometer. In contrast to previous assumptions, this paper argues that enough information is provided from the accounts, combined with knowledge of gear design, to determine the actual gear sizes. Calculations and arguments are provided to support the idea that the gear diameters were 15 inches (38 cm) for the 60-tooth gear, 10 inches (25 cm) for the 40-tooth gear, and 1 inch (2.54 cm) for the 4-tooth gear.

Topics: Mechanisms , Gears , Design
Commentary by Dr. Valentin Fuster
2006;():325-328. doi:10.1115/DETC2006-99038.

Two novel spherical 3-DOF (degrees of freedom) parallel manipulators with circular prismatic pairs are proposed. One is 3-PC (RR)N parallel mechanism, where PC denotes a circular prismatic pair, (RR)N denotes two revolute pairs whose axes intersect at a common point N. The other is 3-PC RN S parallel mechanism. All the revolute axes in three limbs intersect at a common point N. The three circular prismatic pairs can be actuated. Mobility and singularity of this mechanism is analyzed via screw theory. Due to the circular prismatic pair, the rotational DOF of the moving platform about the z axis is decoupled from the other two rotational DOFs.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2006;():329-338. doi:10.1115/DETC2006-99081.

A variational approach to geometric width control in topology optimization is presented in this paper. Different from conventional topology optimization approaches which only consider optimizing performance-describing objective functions, a quadratic energy functional governing the feature characteristic of geometric width is employed. In this manner, the geometric feature of the designed structure as well as its functional performance is accounted for. In addition, the quadratic energy function can be seamlessly integrated into the level set model that represents the geometry of the structure implicitly. The approach is demonstrated with benchmark examples of structure optimization and compliant mechanism optimization. The preliminary results show that this method is capable of generating strip-like (or beam) designs with specified feature width, which is a highly desirable characteristic and uniquely distinguishes the proposed method.

Commentary by Dr. Valentin Fuster
2006;():339-347. doi:10.1115/DETC2006-99103.

In this paper we present a web-based computer-aided design modeling and manufacturing methodology for spherical mechanisms. Our purpose is to facilitate the analysis, dynamic simulation, and manufacture of one degree of freedom spherical four-bar mechanisms. First, a brief review of some of the current computer-aided design (CAD) software for spherical four-bar mechanisms, e.g. SPHINX , SPHINX PC, ISIS , and OSIRIS is presented. These software packages provide the three-dimensional visualization and computational capabilities necessary to design spherical four-bar mechanisms. However, to date no readily available and effective tools exist to aid in the modeling and manufacture of spherical mechanisms. Next, the kinematics of spherical four-bar mechanisms are reviewed as they pertain to their geometric modeling and manufacture. Finally, we present our web-based implementation of a computer-aided modeling, simulation, and manufacturing methodology for spherical four-bar mechanisms called SPHINX CAM-Pro|E. SPHINX CAM-Pro|E, when used with the CAD tools mentioned above, facilitates the design, dynamic simulation, prototyping, and manufacture of spherical four-bar mechanisms.

Commentary by Dr. Valentin Fuster
2006;():349-358. doi:10.1115/DETC2006-99129.

This paper presents a new DOF formula for mechanism Its main feature is that the calculation of mobility has a single value for a given mechanism without the set of constraint equations, each of parameters in the formula can be correctly determined by simple symbol operation. The formula shows the map relationship between DOF and topological structure of a mechanism. It is embodied in the following aspects: (1) Dimension type: so that topological structure of a mechanism can be represented by symbols. (2) Orientation and location characteristic matrix: so that rank of a mechanism can be calculated by symbolic operation. (3) Orientation and location characteristic equation of serial mechanism and its symbolic operation. (4) Orientation and location characteristic equation of parallel mechanism and its symbolic operation. (5) The DOF calculation based on orientation and location characteristic equations of serial and parallel mechanisms. The DOF formula presented in this paper has already been used for topological analysis and synthesis of parallel mechanisms and its advantages has been proven.

Commentary by Dr. Valentin Fuster
2006;():359-370. doi:10.1115/DETC2006-99156.

This paper provides geometric insight into the duality between the kinematics of epicyclic gear trains and the statics of beam systems. The two devices have inherent geometrical relationships that allow the angular velocities of the gears in a gear train to be investigated from a knowledge of the forces acting on the dual beam system, and vice-versa. The primary contribution of the paper is the application of this duality to obtain the dual beam system for a given compound epicyclic gear train. The paper develops a systematic procedure to transform between the first-order kinematics of a gear train and the statics of the dual beam system. This provides a simple and intuitive approach to study the speed ratios of an epicyclic gear train and the force ratios of the dual beam system. The speed ratios are expressed in terms of kinematic coefficients, which are a function of the position of the input gear and provide insight into the gear train geometry. Several numerical examples of simple and compound epicyclic gear trains are presented to demonstrate the simplicity of the proposed approach. The analytical equations that are developed in the paper can be incorporated, in a straightforward manner, into a spreadsheet that is oriented towards an epicyclic gear train satisfying specific design requirements.

Commentary by Dr. Valentin Fuster
2006;():371-380. doi:10.1115/DETC2006-99166.

In this paper, we have reported results of experimental activity for a characterization of mechanical transmissions with gears or cams. The study has been focused on specific transmission characteristics that are related to a mechanical blood pumping design. In particular, experimental tests have been analyzed to understand benefits and drawbacks for using non-circular gears and polynomial cams in pure mechanical transmissions with limited motion regulation but with specific prescribed motion law.

Topics: Blood , Gears
Commentary by Dr. Valentin Fuster
2006;():381-390. doi:10.1115/DETC2006-99206.

This paper explains how Geometric Constraint Programming can be applied to solve function generation problems with finitely-separated positions using a number of different mechanisms. Geometric Constraint Programming uses the sketching mode of commercial parametric computer-aided design software to create kinematic diagrams whose elements are parametrically related so that when a parameter is changed, the design is modified automatically. Geometric constraints are imposed graphically through the user interface, and the numerical solvers integrated into the software solve the relevant systems of non-linear equations without the user explicitly formulating those equations. A key advantage of using Geometric Constraint Programming for function generation is that the same approach can be applied to any mechanism, so no unique algorithms are required. Furthermore, because the implementation is relatively straightforward regardless of the chosen mechanism, the designer can quickly and easily generate solutions for a large number of precision points and/or with complex mechanisms to provide a very accurate match to the desired function. Examples of function generation with a four-bar linkage, a six-bar linkage, and a seven-bar linkage illustrate the benefits of the proposed methodology.

Commentary by Dr. Valentin Fuster
2006;():391-397. doi:10.1115/DETC2006-99207.

Use of a symmetric crank-rocker four-bar linkage is presented as an alternative to the standard bicycle crank. With the coupler being the driven link, a kinematic and force-transmission analysis is presented. Results of constrained nonlinear optimization for geometric synthesis show a substantial improvement in mechanical efficiency compared to the state of the art. Dead-center positions are also eliminated. Potential applications to other linear-to-rotary power transmission devices, such as internal-combustion engines, are also discussed.

Topics: Linkages , Design , Bicycles
Commentary by Dr. Valentin Fuster
2006;():399-411. doi:10.1115/DETC2006-99219.

The designer’s main challenge when counterweight balancing a linkage is to determine the counterweights that realize an optimal trade-off between the dynamic forces of interest. This problem is often formulated as an optimization problem that is generally nonlinear and therefore suffers from local optima. It has been shown earlier, however, that, through a proper parametrization of the counterweights, a convex program can be obtained. Convex programs are nonlinear optimization problems of which the global optimum is guaranteed to be found with great efficiency. The present paper extends this previous work in two respects: (i) the methodology is generalized from four-bar to planar N-bar (rigid) linkages and (ii) it is shown that requiring the counterweights to be realizable in practice can be cast as a convex constraint. Numerical results for a Watt six-bar linkage suggest much more balancing potential for six-bar linkages than for four-bar linkages.

Topics: Linkages
Commentary by Dr. Valentin Fuster
2006;():413-418. doi:10.1115/DETC2006-99263.

Several industrial applications require devices to operate in two or more phases with single degree of freedom motion in each phase. Variable topology mechanisms meet such requirements, one typical application of such devices being in circuit breakers. In this paper we discuss the synthesis of such devices for a variety (FSP, ISP and MSP) of motion specifications. The loci of pivots are determined.

Commentary by Dr. Valentin Fuster
2006;():419-427. doi:10.1115/DETC2006-99353.

The paper presents a new procedure to design a two-pulley synchronous belt transmission connecting, with no belt tensioner, two parallel-axis shafts with a variable velocity ratio. The procedure takes into account the limited number of choices for pitch and length of off-the-shelf synchronous belts, which translates into the need of fine-adjusting either the center distance or the law of motion. Differently from other approaches reported in the technical literature, the suggested method is based on the numerical solution of a set of functional equations. A numerical example shows application of the proposed method to a case study.

Topics: Design , Timing belts
Commentary by Dr. Valentin Fuster
2006;():429-438. doi:10.1115/DETC2006-99431.

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

Commentary by Dr. Valentin Fuster
2006;():439-446. doi:10.1115/DETC2006-99487.

In this study an analysis of rotor profiles geometry in internal epitrochoidal pumps and a systematic study of their performance as a function of the geometrical parameters are introduced. Internal pumps are used in various fields, like automotive, alimentary, or medical-scientific. This machines consist of two rotors: generally the inner rotor has epitrochoidal profile and the profile of the outer rotor is determined as conjugate to the inner one. The rotor geometry and the final performance of the whole machine has been studied by many researchers, using different methods. In this paper the construction of the profiles is performed by the theory of gearing, in order to calculate performance indexes. In particular the pump type with epitrochoidal outer rotor has been considered. Even if it is impossible to establish an optimal profile valid for every application, the analysis of the results obtained allows to choose the design parameters, in order to optimize the shape of the rotors for any particular application.

Topics: Design , Pumps
Commentary by Dr. Valentin Fuster
2006;():447-452. doi:10.1115/DETC2006-99555.

A great deal of energy is lost to friction in power-transmitting devices, especially geared mechanisms. Based on a mechanism equivalence relationship between a four-bar mechanism and a geared mechanism, a procedure is developed for generating custom gear-tooth profiles using the concept of instant centers. These tooth profiles make use of roller elements between the teeth in order to eliminate the rolling-sliding contact which occurs in typical gear meshes, thus reducing power losses. Practical applicability and design constraints are investigated and preliminary results presented.

Topics: Friction , Linkages , Gears
Commentary by Dr. Valentin Fuster
2006;():453-462. doi:10.1115/DETC2006-99576.

A spreadsheet based mechanism analysis and animation system is presented in this article. The system is developed in Excel using Ch, an embeddable C/C++ interpreter, and Ch Mechanism Toolkit. It allows users to develop and solve complicated planar mechanism problems conveniently using an easy to use Excel spreadsheets as the front end. Users can input the required data to define a mechanism in an Excel spreadsheet and execute script files associated with the work cells. The spreadsheet based system can be used for kinematic and dynamic analysis, graphical plotting, and animation for four-bar, crank-slider, fivebar, and sixbar linkages. Examples are provided to illustrate its ease of use. The source code and demos are available for downloading from the internet.

Topics: Design , Mechanisms
Commentary by Dr. Valentin Fuster
2006;():463-468. doi:10.1115/DETC2006-99598.

The cam fatigue life of the translating roller-follower system is studied for polynomial and cycloidal displacement functions. The stress distribution in the contact zone between the cam and the roller-follower is determined by using a computer program. The “volume under risk” where the stress field is higher than the endurance limit is determined. Ioannides-Harris (IH) theory is used on the ‘volume under risk’ and the expected fatigue life is calculated. The effects of cam base circle radius, follower offset, follower total lift and cam angular velocity on the fatigue life are studied. The primary design parameter governing the cam fatigue life is found to be the base circle radius. The fatigue life curve shows an improvement in the life up to a critical base circle radius value. Any further increase in the base circle radius appears as a decrease in the fatigue life.

Commentary by Dr. Valentin Fuster
2006;():469-474. doi:10.1115/DETC2006-99634.

In this paper, the operation and analysis of a novel, highly configurable, infinitely variable transmission of the ratcheting drive type is presented. This particular drive uses a cam and a number of cam followers rotatably mounted to a carrier plate to generate an oscillatory motion in an equal number of planet gears. A number of indexing clutches are then used to rectify this motion into a rotational output. A full description of the mechanism, including its components, operation, and kinematic equations are presented. There are a number of inversions of this device, and their characteristics and limitations are discussed. In addition, a method is presented to select the most suitable inversion, gearing, and follower velocity for a given application.

Commentary by Dr. Valentin Fuster
2006;():475-482. doi:10.1115/DETC2006-99683.

Without solving any nonlinear contact equations usually encountered in traditional approaches, a relative simple, yet useful procedure to the profile determination of a globoidal cam with a conical roller-follower turret is presented. From the machining point of view for such a spatial cam cut by a conical milling/grinding tool by following its angular roller-follower turret motion, the surface geometry of the cam can be represented as the swept surfaces of the tool paths of the used cutter with a size equal to the conical roller-follower of the cam. To determine the swept surfaces of the conical tool paths, the pitch surface generated by the locus of the tool center is first identified. Subsequently, to locate the swept surfaces for the cam surfaces, the meshing vectors and meshing angles are then defined based on the pitch surface. To verify the feasibility and accuracy of the proposed procedure, both analytical formulations and numerical results are shown and compared to those obtained by an earlier technique based on the theory of screws.

Topics: Rollers
Commentary by Dr. Valentin Fuster
2006;():483-493. doi:10.1115/DETC2006-99713.

This paper presents an interval analysis based approach for analysis and optimization of planar mechanisms including the effect of link lengths tolerances and joint clearances. Mathematical models describing the effect of the mechanical errors on the desired output parameters of the mechanism are derived, followed by the commissioning of an ant-gradient based optimization scheme to find the maximum possible deviations in them. A new optimization approach is also devised to design a four bar mechanism with “minimal” sensitivity to clearances and tolerances. An analysis case study is presented and the results are displayed in the form of fuzzy membership functions and compared with results obtained using a similar approach. An example on optimum synthesis of a four-bar mechanism with joint clearances and link tolerances for hybrid exact/approximate points trajectory is also presented. Insights based on the assessment of the results are introduced.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2006;():495-499. doi:10.1115/DETC2006-99717.

Presented in this paper is a 4-dof robomech consisting of a stack of two five-bar (5R) chains with multiple end effectors to perform two distinct yet coordinated tasks simultaneously. The over-constrained kinematics chain cannot traverse continuous trajectories but may be synthesized to move the end effectors through a set of desired locations. The article elaborates on the architecture of the proposed robomech, establishes its kinematics relations and constraints, and provides dimensional synthesis scheme based on genetic algorithm and gradient search methods. A case study featuring the robomech performing spot welding operation along two distinct trajectories is included to demonstrate the applicability of the proposed robomech.

Topics: Chain , End effectors
Commentary by Dr. Valentin Fuster
2006;():501-511. doi:10.1115/DETC2006-99727.

The combination of static balancing and tensegrity structures has resulted in a new class of mechanisms: Statically Balanced Tensegrity Mechanisms. These are prestressed structures that are in equilibrium in a wide range of positions, and thus exhibit mechanism-like properties. This paper describes the design of a prototype model of a statically balanced tensegrity mechanism based on a classic tensegrity structure.

Topics: Design , Mechanisms
Commentary by Dr. Valentin Fuster
2006;():513-518. doi:10.1115/DETC2006-99750.

In this paper, the effects of cross-sectional geometry and friction on the mechanical advantage and efficiency of the whole skin locomotion (WSL) mechanism concentric solid tube (CST) model are presented. WSL is a novel locomotion mechanism for mobile robots, which is inspired by the motility mechanisms of single celled organisms that use cytoplasmic streaming to generate pseudopods for locomotion. It works by way of an elongated toroid which turns itself inside out in a single continuous motion, effectively generating the overall motion of the cytoplasmic streaming ectoplasmic tube in amoebae. WSL can be considered as a new class of mechanism that converts the expanding and contracting motion of rings to an everting motion of the body. A brief description of the WSL mechanism is presented first, followed by the mechanics of a single and multiple actuator rings over a CST showing the relationship between the input ring tension force and the output propulsion force for a quasi-static case. Then a study of the force transmission characteristics is presented by studying the effects of cross-section geometry and friction on the efficiency and mechanical advantage of a single actuator ring over a semicircular and composite cross section CST.

Commentary by Dr. Valentin Fuster
2006;():519-527. doi:10.1115/DETC2006-99350.

In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2006;():529-538. doi:10.1115/DETC2006-99594.

Momentum eXchange Electrodynamic Reboost, or MXER, tether systems have been proposed to serve as an “upper stage in space” [1]. A MXER tether station would boost spacecraft from low Earth orbit to a high-energy orbit quickly, like a high-thrust rocket. Then, using the same principles that make an electric motor work, it would slowly rebuild its orbital momentum by pushing against the Earth’s magnetic field without using any propellant. One of the significant challenges in developing a momentum-exchange / electrodynamic reboost tether system is in the analysis and design of the capture mechanism and its effects on the overall dynamics of the system [2]. A capture mechanism that provides nearly passive operation is presented and described in [3] and led to the fabrication of a prototype article of this mechanism. This paper will describe the process of testing this prototype in a dynamically similar environment and validating an associated dynamic model. The primary contributions of this paper will be a description of the proposed capture mechanism concept and associated testing process and the validation of a dynamic model of this mechanism.

Commentary by Dr. Valentin Fuster
2006;():539-545. doi:10.1115/DETC2006-99067.

Photoelastic materials develop colored fringes under white light when subjected to mechanical stresses which can be viewed through a polariscope. This technique has traditionally been used for stress analysis of loaded components, however, this can also be potentially used in sensing applications where the requirement may be measurement of the stimulating forces causing the generation of the fringes. This leads to inverse photoelastic problem where the developed image can be analyzed for the input forces. However, there could be infinite number of possible solutions which cannot be obtained by conventional techniques. This paper presents neural networks based approach to solve this problem. Experiments conducted to prove the principle have been verified with theoretical results and finite element analysis of the loaded specimens. The technique, if fully developed, can be implemented for any generalized case involving complex fringe patterns under different loading conditions for whole-field analysis of the stress pattern, which may find application in a variety of specialized areas including biomedical engineering and robotics.

Commentary by Dr. Valentin Fuster
2006;():547-556. doi:10.1115/DETC2006-99111.

This research aims to develop a portable haptic master hand with 20 degrees of freedom (DOF). Master hands are used as haptic interfaces in master-slave systems. A master-slave system consists of a haptic interface that communicates with a virtual world or an end-effector for tele-operation, such as a robot hand. The thumb and fingers are usually modeled as a serial linkage mechanism with 4 DOF. So far, no 20 DOF master hands have been developed that can exert perpendicular forces on the finger phalanges during the complete flexion and extension motion. In this paper, the design and development of two concepts of a portable 4 DOF haptic interface for the index finger is presented. Concept A is a statically balanced haptic interface with a rolling-link mechanism (RLM) and an integrated constant torque spring per DOF for perpendicular and active force feedback. Concept B utilizes a mechanical tape brake at the RLM for passive force feedback. The systematic Pahl and Beitz design approach is used as an iterative design method.

Commentary by Dr. Valentin Fuster
2006;():557-563. doi:10.1115/DETC2006-99446.

A multifunctional forceps-scissors instrument is designed for minimally invasive surgery. The device is a compliant mechanism capable of both grasping and cutting. The focus of the paper is on the design optimization and a detailed finite element analysis of the compliant mechanism. One-half of the symmetric compliant mechanism is modeled as a cantilever beam of rectangular cross-section undergoing large deformation. The optimization problem is solved graphically where all feasible designs (i.e., those that satisfy the stress and geometric constraints) are displayed on performance space plots. Using this method it is easy to visualize the performance space and to select a suitable design; however, it is found that it is not possible to simultaneously maximize free deflection and blocked force in the forceps or scissors modes. A detailed finite element analysis was conducted using ANSYS to model the multiple loading conditions. A prototype instrument, fabricated from stainless steel using wire EDM with the precision of +/- 2 μm, has been tested for comparison of actual and predicted results.

Commentary by Dr. Valentin Fuster
2006;():565-573. doi:10.1115/DETC2006-99622.

When humans hop or run on compliant surfaces they alter the stiffness of their legs so that the overall stiffness of the leg-surface system remains the same. Adding a spring in parallel to the ankle joint incites a similar neuromuscular response; humans decrease their biological ankle stiffness such that the overall ankle stiffness remains unchanged. These results suggest that an elastic exoskeleton could be effective at reducing the metabolic cost of locomotion. To further increase our understanding of human response we have developed an elastic knee brace that adds a stiff spring in parallel to the knee. It will be used as a test platform in ascertaining the neuromuscular effects of adding a parallel knee spring while hopping on one leg. This paper focuses primarily on the mechanical design and implementation of our elastic knee orthosis. Results of the forthcoming studies of human subjects wearing this knee orthosis will be presented in a separate article that will focus on the biomechanics and the neuromuscular adaptations of the human body. Prior research found that the neuromuscular response to hopping on compliant surfaces was the same when running on compliant surfaces. We expect that our results from hopping with springs in parallel with the knee will also be applicable to running. This elastic knee brace represents the first phase of an ongoing research project to develop a passive compliant lower-body exoskeleton to assist in human running. It is expected that this research will benefit healthy individuals as well as those with disabilities causing decreased muscle function.

Commentary by Dr. Valentin Fuster
2006;():575-581. doi:10.1115/DETC2006-99733.

With over 600, 000 people each year surviving a stroke, it has become the leading cause of serious long-term disability in the United States [1,2,3]. Studies have proven that through repetitive task training, neural networks can be re-mapped thus increasing the mobility of the patient [4–8]. This paper is a continuation of Kartik Bharadwaj’s and Arizona State University’s research on the Robotic Gait Trainer [9]. This work is funded in part by the National Institutes of Health (NIH), grant number - 1 R43 HD04067 01. Previously the gait cycle was fixed at two seconds. For a smooth gait the patient had to be trained to follow the frequency of the robot. Audible cues were sounded to help the patient keep rhythm with the robot. This device now has an updated control methodology based on a Matlab and Simulink platform that allows the robot to dynamically adjust to the patient’s pace of gait. Data collected from an able-bodied person walking with the new device showed that the device dynamically adjusted to any normal range of walking gait. This more flexible design will allow the patient to focus more on the therapy and walk at his/her natural pace.

Commentary by Dr. Valentin Fuster
2006;():583-589. doi:10.1115/DETC2006-99734.

This paper presents a methodology for design of dissipative assist robots with proven stability during set-point control. A dissipative assist robot is defined as one where the actuators continuously dissipate energy from the robot until the robot reaches the desired set-point. It is shown in this paper that a general assist robot under well known control laws is not dissipative. However, by appropriately designing the robot through inertia redistribution, the dynamic equations can be modified so that the control laws can now be proven to be both dissipative and stable under set-point control. The proposed method is demonstrated through simulation of a 3-link planar manipulator used as an assist robot to modify human functional movements in a vertical plane.

Topics: Robots , Design
Commentary by Dr. Valentin Fuster
2006;():591-599. doi:10.1115/DETC2006-99745.

Static balancing is a useful concept to reduce operating effort of mechanisms. Very often, spring mechanisms are used to achieve a constant total potential energy, thus eliminating any preferred position. The springs and the mechanism dimensions are designed to exactly or approximately balance other forces present in the mechanism, such as gravity. Quasistatically, the mechanism, once statically balanced, can be moved virtually without operating energy. In some cases it is desirable to adjust the balancer characteristic, for instance due to a change of payload in a gravity balanced mechanism. The adjustment of present static balancers requires significant operating energy. This paper will present a novel principle to adjust spring and linkage-based static balancers with no need for external energy. This principle will be explained and several variants will be shown. A mobile arm support for people with neuromuscular diseases is used as a design example. These people have very limited force and rely on their arm support to move their arms. When picking up objects their support mechanism should ideally be adjusted. Due to the limited available muscle force, this application greatly benefits from an energy-free adjustment.

Topics: Gravity (Force)
Commentary by Dr. Valentin Fuster
2006;():601-613. doi:10.1115/DETC2006-99315.

Pauling, Corey and Branson in their seminal paper in 1951 reported numerical values for the bond lengths and bond angles for a peptide unit in proteins. These values became the standard model for several decades after that. This classic peptide model was either confirmed or improved upon by other researchers over the years, by using more advanced X-Ray diffraction equipments. In this paper, we have made an attempt to calibrate the values of these bond lengths and bond angles based on a systematic and deterministic approach applied to a collection of proteins defined structurally in the Protein Data Bank (PDB). Our method is based on the assumption that a peptide chain is a serial chain of identical rigid bodies connected by revolute joints (i.e. dihedral angles). The proposed procedure first computes the best estimate for the dihedral angles in the presence of inaccuracies in the atoms’ coordinates data. Then these values are used to find the conformation of the peptide chain using the calibrated model of the peptide unit. Through an optimization process, the structural error (RMSD of all atoms) between the resultant conformation and the PDB data is minimized to yield the best values for the bond length and bond angles in the calibrated peptide unit. Our numerical experiments indicate that by making small changes in the Pauling-Corey peptide model parameters (0.15% to 8.7%) the structural error is reduced significantly (3.0% to 57.4%). The optimum values for the bond angles and bond lengths are as follow: Bond Lengths: N-C(A): 1.4721Å, C(A)-C: 1.6167Å, C-N: 1.2047Å, C=O: 1.1913Å and N-H: 0.9621Å. Bond Bending Angles: N-C(A)-C: 109.6823°, C(A)-C=0: 119.518°, C(A)-C-N: 114.5553°, O=C-N: 125.9233°, C-N-H: 123.5155°, C-N-C(A): 121.5756°, C(A)-N-H: 114.901°. Peptide bond torsion angle: ω: 179.4432°.

Topics: Proteins
Commentary by Dr. Valentin Fuster
2006;():615-622. doi:10.1115/DETC2006-99363.

An XY planar platform for nanoscale positioning objective is developed in this study. The platform is constructed with flexure hinge mechanism, and each axis of the platform is driven by piezoelectric stack actuator. Note that the entire structure of the platform for the two axes is on the same plane not like the usual XY platform piled up with independent axial structure. It is found mutual disturbance exists in such a planar platform by both ANSYS analysis and practical experiment. As the mutual disturbance is defined by an approximate linear function, and the nonlinear hysteresis effect is solved by means of the Preisach model, appropriate command signal is computed. The feedforward controller on the basis of the established hysteresis model, the PID-based feedback controller with the optimal gains searched by the Ziegler-Nichols method and the genetic algorithm, and the composite (feedforward+feedback) controller are designed and examined by experiment respectively. From the experimental results, it indicates each type of controller can achieve a certain level of accuracy. The composite controller, of course, performs best, and is able to reach the target of about 10nm for large stroke and 1nm for fine stroke. It concluded that the designed planar platform has the advantage of small space and low cost can still be controlled well to satisfy the nanoscale precision requirement.

Topics: Design
Commentary by Dr. Valentin Fuster
2006;():623-628. doi:10.1115/DETC2006-99684.

In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.

Commentary by Dr. Valentin Fuster
2006;():629-634. doi:10.1115/DETC2006-99701.

The design hypothesis, architectures, and preliminary computational results of a peptide based nanoTweezer are presented in this paper. We engineered the α-helical coiled coil portion of the yeast transcriptional activator peptide called GCN4 to obtain an environmentally-responsive nanoTweezer. The dimeric coiled coil peptide consists of two identical ~4.5 nm long and ~3 nm wide polypeptide chains. The actuation mechanism depends on the modifying electrostatic charges along the peptide by varying the pH of the solution resulting in the reversible movement of helices and therefore, creating the motion of the tweezer. Preliminary molecular dynamics results indicated that pH changes led to a reversible deflection of 1–2 nm with the nanoTweezer. The force profile of the nanoTweezer motion and some potential applications are also discussed.

Topics: Design , Modeling
Commentary by Dr. Valentin Fuster
2006;():635-644. doi:10.1115/DETC2006-99001.

This paper describes the dynamical modelling for the simulation of the quadrirotor Helicopter in order to see the influence of the flexibility on the dynamical model. We consider a quadrirotor Helicopter like a multibody systems constituted of the flexible and rigid substructures interconnected by of articulation joint. We use the variationnal Lagrangian approach to define the equations governing the motion. Deformations modes are used to represent elastic deformations of the substructure relative to a body reference frame. The displacement functions shape of the flexible components is obtained by a finite element discretization technique. The numerical application is related to the quadrirotor XSF developed in the LSC (Laboratory of Complex Systems).

Topics: Modeling
Commentary by Dr. Valentin Fuster
2006;():645-654. doi:10.1115/DETC2006-99024.

With the magnification of the belt conveyor, dynamic analysis and dynamic design have become indispensability means in the design of belt conveyor. In this article, we build the finite-element model of the starting and stopping process, which bases on the multi-driving belt conveyor system, and the dynamic calculation method of multi-driving system basing on power tracing. According to the reasonable starting curve, we start the first driving/drive, and then the rest drives trace the first driving in order. We bring forward the starting curve of trapezium acceleration from the existing S-curve. We develop the dynamic analysis software of belt conveyor and test the correctness of its calculation and software by the computer simulation of the actual system. The method had been applied in the system design of 7.6 km belt conveyor in Jincheng city, Shanxi province.

Commentary by Dr. Valentin Fuster
2006;():655-665. doi:10.1115/DETC2006-99060.

This research is concerned with the design, modeling, and testing of a dual piezoelectric controlled electro-hydraulic actuator for use in camless engine applications. The design utilizes two piezoelectric actuated spool valves located on either side of a piston to effectively control the volume and timing of pressurized oil entering and exiting the piston chamber. A system model relating spool displacement to piston displacement was created and tested within Matlab/Simulink. To demonstrate the design, a bench top prototype was created and programmed using Matlab/Simulink, dSpace, and ControlDesk. Testing was conducted using both time domain and frequency analysis. All test results indicate a close correlation between the prototype and the final system model.

Topics: Actuators , Design
Commentary by Dr. Valentin Fuster
2006;():667-676. doi:10.1115/DETC2006-99122.

Characteristics of magnetic–levitation system are studied using dynamic models that include motion–dependent lift, drag, slip, and roll motions. In addition, the contact constraint between the vehicle and the track is modeled using the penalty method. Unknown numerical parameters are identified using the optimization technique. The numerical tests are focused on the damping characteristic, stability in lifting and slip motions, the lifting efficiency compared with the concentric force, and contact with track.

Commentary by Dr. Valentin Fuster
2006;():677-687. doi:10.1115/DETC2006-99139.

Rigid-body impact modeling remains an intensive area of research spurred on by new applications in robotics, biomechanics, and more generally multibody systems. By contrast, the modeling of non-colliding contact dynamics has attracted significantly less attention. The existing approaches to solve non-colliding contact problems include compliant approaches in which the contact force between objects is defined explicitly as a function of local deformation, and complementarity formulations in which unilateral constraints are employed to compute contact interactions (impulses or forces) to enforce the impenetrability of the contacting objects. In this article, the authors develop a novel approach to solve the non-colliding contact problem for objects of arbitrary geometry in contact at multiple points. Similarly to the complementarity formulation, the solution is based on rigid-body dynamics and enforces contact kinematics constraints at the acceleration level. Differently, it leads to an explicit closed-form solution for the normal forces at the contact points. Integral to the proposed formulation is the treatment of tangential contact forces, in particular the static friction. These friction forces must be calculated as a function of microslip velocity or displacement at the contact point. Numerical results are presented for three test cases: 1) a thin rod sliding down a stationary wedge; 2) a cube rotating off the stationary wedge under application of an external moment and 3) the cube and the wedge both moving under application of a moment. To ascertain validity and correctness, the solutions to frictionless and frictional scenarios obtained with the proposed formulation are compared to those generated by using a commercial simulation tool MSC ADAMS.

Commentary by Dr. Valentin Fuster
2006;():689-697. doi:10.1115/DETC2006-99167.

This paper focusses on reducing, through counterweight addition, the vibration of an elastically mounted, rigid machine frame that supports a linkage. In order to determine the counterweights that yield a maximal reduction in frame vibration, a non-linear optimization problem is formulated with the frame kinetic energy as objective function and such that a convex optimization problem is obtained. Convex optimization problems are nonlinear optimization problems that have a unique (global) optimum, which can be found with great efficiency. The proposed methodology is successfully applied to improve the results of the benchmark four-bar problem, first considered by Kochev and Gurdev. For this example, the balancing is shown to be very robust for drive speed variations and to benefit only marginally from using a coupler counterweight.

Commentary by Dr. Valentin Fuster
2006;():699-707. doi:10.1115/DETC2006-99170.

Understanding how manufacturing variation affects manipulator fit and function is of the utmost importance. There are currently many techniques to determine these effects. Many of them for robotic manipulators only apply to the static analysis, but there is a need to determine the dynamic effects. This paper outlines how polynomial chaos theory (PCT) can be utilized to solve both the static (aka tolerance stack-up) and dynamic analyses. To show the power of the procedure, it is applied to a simple planar two link manipulator with geometric variation of the link lengths.

Commentary by Dr. Valentin Fuster
2006;():709-718. doi:10.1115/DETC2006-99218.

In this paper, a numerical-experimental procedure is proposed for an identification of parameters in cam transmissions. Models with lumped parameters are defined specifically for cam transmissions. Experimental tests are carried out on main components of a cam transmission in order to estimate the values of mass, damping and stiffness lumped parameters through a low-cost easy-operation procedure. Experimental tests are also carried out in order to characterize the dynamic behaviour of a whole cam transmission. A comparison of numerical and experimental results is used in order to calibrate the values of lumped parameters. Experimental tests have been carried out by means of suitable test-beds for cams that have been built specifically at University of Brescia and at LARM in Cassino as alternative testing solutions.

Topics: Cams , Damping , Testing , Stiffness
Commentary by Dr. Valentin Fuster
2006;():719-727. doi:10.1115/DETC2006-99243.

A time-accurate finite element model for simulating the fully-coupled dynamic response of flexible multibody systems and liquid sloshing in tanks is presented. The semi-discrete combined solid and fluid equations of motions are integrated using a time-accurate parallel explicit solver. The FE model consists of: hexahedral, beam, and truss solid elements; rigid bodies; joints; actuators; hexahedral incompressible fluid elements; and quadrilateral fluid-solid interface elements. The fluid mesh is modeled using a very light and compliant solid mesh which allows the fluid mesh to move/deform along with the tank using the Arbitrary Lagrangian-Eulerian formulation. The fluid’s free-surface is modeled using an acceptor-donor volume-of-fluid based algorithm. The motion of the solid and fluid is referred to a global inertial Cartesian reference frame. A total Lagrangian deformation description is used for the solid elements. The penalty technique is used to model the joints. Numerical simulations are presented for a half-filled tank supported by linear springs mounted on a test fixture.

Commentary by Dr. Valentin Fuster
2006;():729-733. doi:10.1115/DETC2006-99258.

A dynamical model of a four-span rotor system with multi-discs is built up, considering nonlinear oil-film forces, based on a 300 thousand kilowatt turbine-generator test rig. The bifurcation features of the system are studied with numerical integration technique. It is revealed that the proposed multi-span rotor model can express the fundamental dynamic characteristics of such a nonlinear system. Some bifurcations and chaotic motions may occur according to the calculated results. In coupling analyses, each rotor span also affects dynamically on the other, and the second span affects on the whole system in a serious way.

Commentary by Dr. Valentin Fuster
2006;():735-740. doi:10.1115/DETC2006-99504.

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 the present study, the use of the motion-doubling linkage mechanisms in the construction of vehicle suspension systems is investigated. The performance of the resulting vehicle suspension system is compared to that of 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, which is defined as the standard deviation of the vertical acceleration of the vehicle. Using numerical simulation, it is shown that the suspension system constructed with a motion-doubling linkage mechanism has a significantly better performance as compared to a standard suspension system.

Commentary by Dr. Valentin Fuster
2006;():741-748. doi:10.1115/DETC2006-99602.

In this paper we present new experimental results for a novel underactuated system called the ROBOTRIKKE. The ROBOTRIKKE is a three-wheeled system that can be driven by periodic motion of its front steering wheel combined with rocking side-to-side motion of a robotic rider. We present two new generations of the ROBOTRIKKE including a ABS model made using Shape Deposition Manufacturing (SDM). We present modeling, simulation and experimental results for gait generation for the ROBOTRIKKE using a combination of periodic inputs for the steering axis and a rider. We show how a rocking motion (as used by human riders) can be used to improve the performance of the ROBOTRIKKE.

Topics: Design , Modeling , Robotics
Commentary by Dr. Valentin Fuster
2006;():749-758. doi:10.1115/DETC2006-99671.

One of the primary concerns associated with the machining process involves excess vibrations that can adversely affect the ability of the machine tool to accurately produce parts. This paper presents the development of a method by which the vibrational characteristics of machine tools exhibiting a parallel kinematic machine architecture may be modeled. Theoretical and experimental results are compared to demonstrate the validity of the modeling approach. The resulting model provides an effective means to guide the machine design process for the purposes of enhancing performance and improving control.

Commentary by Dr. Valentin Fuster
2006;():759-764. doi:10.1115/DETC2006-99704.

In recent studies, the authors presented a special class of planar and spatial linkage mechanisms 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. It was also shown that in a special case of such mechanisms, the fundamental frequency of the input motion is doubled. This class of mechanisms generally has dynamics advantage over regular mechanisms designed to achieve similar gross output motions. In the present study, it is shown that in general and for the same gross output motion, motion-doubling mechanisms require lower input torques, and that the high harmonics of the input torque have smaller amplitudes. The high harmonic components present in the input torque are the main source of vibration and control problems in the system or device that the mechanism operates and its own structure. It is therefore concluded that when vibration and motion precision is of concern, such as in high-speed and precision machinery, motion-doubling mechanisms are generally more suitable from the potential vibration excitation and control points of view and actuating torque requirements.

Commentary by Dr. Valentin Fuster
2006;():765-776. doi:10.1115/DETC2006-99746.

MXER-type tether systems are envisioned to transfer payloads from low-energy orbits to higher-energy orbits using propellant-free thrust. This paper deals with the process of dynamic model verification of these MXER-type tether system. The dynamics is solved using two different formulations. Four different test cases are considered for comparision. These different cases attempt to isolate and observe some component of tether dynamic response.

Topics: Dynamic models
Commentary by Dr. Valentin Fuster
2006;():777-785. doi:10.1115/DETC2006-99016.

This paper introduces a new concept for a contour crafting construction system. Contour crafting is a relatively new layered fabrication technology that enables automated construction of whole structures. The system proposed here consists of a mobile contour crafting platform driven by a translational cable-suspended robot. The platform includes an extrusion system for laying beads of concrete as well as computer-controlled trowels for forming the beads as they are laid. This system is fully automated and can be used to construct concrete structures rapidly and economically. The novel attributes of this system enable significant improvements over other proposed contour crafting systems, including easier portability, lower cost, and the potential to build much larger structures. This paper presents the kinematics and statics of the proposed system, and uses the reachable workspace of the robot as well as the corresponding cable tensions to approximate the maximum size structure that can be built using this manipulator.

Topics: Cables , Robotics
Commentary by Dr. Valentin Fuster
2006;():787-793. doi:10.1115/DETC2006-99054.

Autonomous mobile robot increasingly expands its functionality into various applications where the long-term autonomous capability is necessary. These applications, warehouse service, building inspection, exploration of unknown terrains and military reconnaissance, require the mobile robot to correspond with the command of remote operators or environments. To meet this requirement, automatic recharging station can be used for a robot not to be taken offline. However, the range of docking error is wide by various homing algorithms and kinds of sensors. This paper describes a new docking mechanism developed to compensate entry error of robot in homing and to maintain robust state in the process of recharging battery without actuators and sensors. The proposed mechanism is self-adjustable to position and orientation of robot and reconfigures its states by driving force of mobile robot without any active energy elements. The geometric parameters are determined to avoid mechanical interference in docking procedure and specifications of springs are obtained from optimization which maximizes the grip force with constraint induced at each docking process. The docking mechanism can compensate for ±5cm lateral offset error and ±30° orientation error of mobile robot and holds it over 20N load after docking is finished.

Commentary by Dr. Valentin Fuster
2006;():795-802. doi:10.1115/DETC2006-99065.

This paper is devoted to the kinematic design of a new six degree-of-freedom haptic device using two parallel mechanisms. The first one, called orthoglide, provides the translation motions and the second one, called agile eye, produces the rotational motions. These two motions are decoupled to simplify the direct and inverse kinematics, as it is needed for real-time control. To reduce the inertial load, the motors are fixed on the base and a transmission with two universal joints is used to transmit the rotational motions from the base to the end-effector. Two alternative wrists are proposed (i), the agile eye with three degrees of freedom or (ii) a hybrid wrist made by the assembly of a two-dof agile eye with a rotary motor. The last one is optimized to increase its stiffness and to decrease the number of moving parts.

Commentary by Dr. Valentin Fuster
2006;():803-810. doi:10.1115/DETC2006-99121.

The motivation of this work is to synthesize a kicking pattern for a humanoid robot with consideration of various objectives such as retaining its balance even after the kick is done and reducing the undesired angular momentum using both hands and torso. This kick pattern is designed so that a desirable ball velocity is achieved. In this paper, the law of conservation of angular momentum is used to generate a less energy consuming trajectory. Effectiveness of the proposed method is verified using computer simulation and is tested on Sharif CEDRA humanoid robot.

Topics: Humanoid robots
Commentary by Dr. Valentin Fuster
2006;():811-816. doi:10.1115/DETC2006-99140.

A mechanical locomotive device that uses square wheels has been developed (patent pending), and a working prototype of one configuration has been built. This invention has applications to current locomotive devices, like robots or vehicles, as well as the potential to be used in micro devices (MEMS). The prototype uses a motor to create a moving force (a weight in this case), which moves in a repeating pattern, that in turn causes the device to move in a straight line, and there is no direct connection between the ground and the motor. Consequently, the device could work using any means to produce a moving force (weight, electrostatic, electromagnetic, aerodynamic, and so on). This paper describes the gait of the square wheels and looks at a sample of the results of standard dynamic modeling and analysis to understand the strengths and limitations of this new device.

Topics: Motion , Wheels
Commentary by Dr. Valentin Fuster
2006;():817-824. doi:10.1115/DETC2006-99177.

We present our three-cable haptic interface (TCHI) concept, plus modeling and simulation, hardware implementation, and initial experimental results. This device is based on a previous system developed by Italian researchers. Cable devices are limited since they cannot push on the user, but only apply positive tension. In addition, this TCHI is further limited since it has no actuation redundancy and forces can only be applied within the tetrahedron formed by the fingertip point and base cable attachment points. Despite these limitations, which are explored herein, we believe the simplicity of this haptic interface can make it a serious competitor of existing commercial devices in terms of workspace, force application, cost, safety, and stiffness.

Topics: Cables
Commentary by Dr. Valentin Fuster
2006;():825-832. doi:10.1115/DETC2006-99180.

This paper discusses the design and control of a new ball-wheel drive mechanism for a robust omnidirectional wheeled mobile platform. This platform, integrated with a manipulator, is designed for use in highway maintenance and construction, which is a generally unstructured and congested environment. The proposed ball wheel mechanism can move in all directions on the plane, instantaneously and isotropically. For accurate motion with parametric uncertainty in the dynamic model, an adaptive controller is applied to the trajectory tracking control of the single ball wheel platform. The redundant drive system of the ball wheel mechanism changes its configuration according to the heading direction by changing the contact pressure between the drive wheel and the sphere. A weighted torque optimization method is used for the resolution of redundancy and for smooth reconfiguration. The experimental results demonstrate the effectiveness of the proposed method.

Commentary by Dr. Valentin Fuster
2006;():833-842. doi:10.1115/DETC2006-99197.

A parallelogram-based four degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Schönflies motion, that allows the end-effector to translate in all directions and rotate around an axis parallel to a fixed direction. The Theory of Group of Displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and a improved stiffness to the manipulator. The paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator and some technical applications in which the manipulator can be used are presented.

Topics: Motion , Manipulators
Commentary by Dr. Valentin Fuster
2006;():843-850. doi:10.1115/DETC2006-99204.

It is expected that unmanned on-orbit satellite servicing will soon become state-of-the-art operations. Such tasks will require new robotic tools. In this context, this paper presents the development of a grasping tool for the handling of satellitic thermal blankets. The mechanical design of the tool is first addressed. Mainly, actuated jaws adapted to grasp and lift a thermal blanket attached with velcros are developed. Also, passive compliance is included in order to cope with a position controlled robotic arm and a rigid surface. Then, sensing issues are discussed and included in the design. These features are integrated in a prototype mainly built of plastic by rapid prototyping. Finally, experimental results show that the tool developed in this work is capable of effectively removing thermal blankets.

Topics: Satellites
Commentary by Dr. Valentin Fuster
2006;():851-858. doi:10.1115/DETC2006-99222.

The LAR is a concept of a large orientable radiotelescope composed namely of a cable-driven parallel mechanism used to position and orient a feed plate. This document presents a first analysis of this mechanism’s orientation capability. The rotational kinematic sensitivity is defined here as the possible change in orientation occuring under a change in the actuation. After the application is described, common tools related to such problems are reviewed to explain why they are not totally suitable in this context. The velocity equation of the mechanism is then partitioned to obtain a quantification of the orientation kinematic sensitivity that is physically relevant. The study of a potential architecture’s rotational kinematic sensitivity is presented. Finally, the numerical and experimental validation of the approach are discussed.

Commentary by Dr. Valentin Fuster
2006;():859-865. doi:10.1115/DETC2006-99248.

In this paper, we examine the development of a framework for musculoskeletal system analysis, leveraging screw-theoretic techniques traditionally employed for the analysis of articulated multi-body systems (MBS). The case study of analysis of bite-and muscle-forces in the jaws of members of the felid (cat) family is intended to highlight the critical aspects. The underlying articulated structure and superimposed musculature of the felid jaws permit modeling as a parallel articulated MBS. Specifically, such systems share many common features with the subclass of cable actuated parallel MBS, including redundancy in actuation and unidirectional nature of actuation forces. The screw-theoretic model formulation is intended to enable development of a computationally efficient scheme for resolving such redundancy while retaining explicit geometric meaning in terms of lines of action, motions, and forces. The resulting low-order computational model is well suited for iterative “what-if” force optimization and muscle location studies. A MATLAB based GUI was developed and validated to help the user implement such iterative simulation-based muscle location studies in simulation or on a Hardware-in-the-Loop test-bed.

Commentary by Dr. Valentin Fuster
2006;():867-876. doi:10.1115/DETC2006-99420.

This paper presents a concept for a new type of haptic exoskeleton: REACH, the Robotic Exoskeleton with Advanced Cobot Haptics. This exoskeleton is the first ever concept for integrating cobot technology into a wearable exoskeleton device. This exoskeleton represents a significant improvement in haptic exoskeleton technology by providing high-performance haptic feedback to a user’s whole arm while at the same time guaranteeing the user’s safety. The overall design concept is presented, including the use of a spherical 3RRR parallel mechanism to implement the shoulder joint. The detailed design of the shoulder joint mechanism is then presented. The kinematic parameters of the shoulder joint are selected such that its range of motion matches the motion of a user’s shoulder while also avoiding collisions. In addition, to avoid singularities and maximize dexterity the mechanism design is optimized using the inverse condition number of the Jacobian matrix.

Topics: Design , Haptics , Mechanisms
Commentary by Dr. Valentin Fuster
2006;():877-883. doi:10.1115/DETC2006-99510.

This research examines the dynamics and control of an aerial robotic system to determine its feasibility and general design features. The robotic system consists of a cable driven trolley and a camera platform suspended and controlled by six cables designed in a configuration similar to the Stewart platform. The camera and trolley cables are driven through winches controlled by electric motors. An algorithm is developed based on the sliding mode approach to simultaneous control the trolley trajectory and the full three-dimensional camera linear and rotational motion. Trolley cable flexibility and fundamental vibration mode is included in the analysis though not directly controlled at this stage. Wind forces are also included in the model as unknown but bound disturbances. A working prototype of the system has also been developed and its general features are introduced in this paper.

Commentary by Dr. Valentin Fuster
2006;():885-891. doi:10.1115/DETC2006-99614.

This paper describes a test rig that is used to design and test sensor suites for unmanned air vehicles (UAV) operating in near-earth like environments such as forests, caves and urban canyons. The test rig employs a six degree-of-freedom gantry. Inside its workspace is a full-scale diorama of the environment. Surrounding the gantry are lamps, fans, and generators to reproduce lighting, rain and obscurants typical of such environments. A sensor pod is mounted at the gantry end-effector. The acquired data is fed into a high-fidelity math model of the real UAV. The output is then used to drive the gantry to move the sensor pod in the real world environment. The net effect is a hardware-in-the-loop system that emulates the real UAV’s motions and responses in near-Earth environments. The test rig is important because there is little to no data on sensor performance metrics of UAV in near-Earth environments.

Commentary by Dr. Valentin Fuster
2006;():893-902. doi:10.1115/DETC2006-99616.

The determination of the interference geometry between two arbitrary objects is an essential problem encountered in the simulation of continuous contact dynamics and haptic interactions. In these applications, with known material properties, the interbody contact force is only a function of the interference geometry between two objects. Here a theoretical basis and algorithms for the calculation of the interference geometry, such as overlap region, contact area and normal, and interference volume, are presented. Two methods to obtain the contact area and normal are analyzed: an area-weighted method and a best-fitting method. The geometric properties of the area-weighted method are presented and the degenerate cases related to both methods are discussed. Methods to calculate the application point of an interbody contact force are discussed. Some numerical simulation results are presented based on the implementation of the geometric algorithms, which are verified by comparison with hand calculation. The continuity of contact normal and its application point are demonstrated for a case in which the contacting objects smoothly move with respect to each other in the simulation.

Topics: Geometry
Commentary by Dr. Valentin Fuster
2006;():903-911. doi:10.1115/DETC2006-99645.

This paper examines the nature of joint coupling in underactuated grippers for environments where object properties and location may not be well known. A grasper consisting of a pair of two-link planar fingers with compliant revolute joints was simulated as it was actuated after contact with a target object. The joint coupling configuration of the gripper was varied in order to maximize successful grasp range and minimize contact forces for a wide range of target object size and position. A normal distribution of object position was assumed in order to model sensing uncertainty and weight the results accordingly. The results show that proximal-distal joint torque ratios of around 0.6 produced the best results for cases in which sensory information available for the task was poor, and ratios of around 1.0 produced the best results for cases in which sensory information available for the task was good.

Topics: Design , Grippers
Commentary by Dr. Valentin Fuster
2006;():913-918. doi:10.1115/DETC2006-99658.

This paper describes a new sensor system for improving the accuracy of the range information using multiple IR range sensors. Environment and obstacle sensing is the key issue for mobile robot localization and navigation. Laser scanners cover 180° and are accurate but too expensive. Radial range sensors such as laser scanners, IR scanners and Ultrasonic range sensor rings have blind spots so that a small obstacle not close enough to the sensor may be easily missed. It is necessary to develop a low cost sensor system which covers 360° with small blind spots. A sensor system with 12 IR range sensors is designed and implemented. The problem of the 2D sensor systems is, they measure the nearby obstacles on a plane where the sensors are located. In order to scan the environment vertically, a 2.5D sensor system is designed and the experimental result shows the effectiveness of the proposed sensor system.

Topics: Sensors
Commentary by Dr. Valentin Fuster
2006;():919-923. doi:10.1115/DETC2006-99664.

This paper presents mobile robot localization using IRID (InfraRed IDentification) as artificial landmarks. IRID is implemented with IR LEDs and photo transistors. Different from RFID, IRID has highly deterministic characteristics. By putting several IRID LEDs on the ceiling, the floor is divided into several sectors and each sector is set to have a unique identification. IRID tells which sector the robot is in, but the size of the uncertainty is still too large because the sector size is too large. This paper presents an algorithm which combines both the encoder and the IRID information so that the size of the uncertainty becomes smaller. It also introduces a framework which can be used with other types of the artificial landmarks. The characteristics of the developed IRID and the proposed algorithm are verified from the experiments.

Topics: Mobile robots
Commentary by Dr. Valentin Fuster
2006;():925-932. doi:10.1115/DETC2006-99699.

Deep space drilling is necessary for appropriate chemical and biological sampling for subsurface exploration. The Robotic Planetary Drilling System (RPDS), which is currently being developed by our team, is designed to be a compact self-propelled, steerable electromechanical drilling system that can penetrate into large depths in planetary bodies. In this paper we present the detailed innovative mechanical design of the RPDS. Its main components are: a) the drill bit/cuttings bucket, b) the rotary propulsion unit including novel three 3-degree of freedom (DOF) propulsion actuators, c) the power/control module, d) the non-rotating steering unit including three 1-DOF steering actuators and e) the communication module. Three 3-DOF propulsion actuators uniformly distributed around the rotary propulsion unit impart rotating, linear motion to the drilling bit, while another three 1-DOF steering actuators provide the steering force for automatic directional control. The RPDS is propelled in the manner of a turning screw, which offers simpler kinematics structure, higher efficiency and thus, potential for miniaturization and deep drilling. The mathematical modeling and analysis of the RPDS that were conducted to evaluate its performance are also being presented in this paper.

Commentary by Dr. Valentin Fuster
2006;():933-939. doi:10.1115/DETC2006-99751.

A current problem for mobile robots in unstructured environments is their lack of general mobility. Wheeled, treaded, and legged robots each have their advantages and disadvantages, but they all lack the flexibility to be able to cope with a wide range of terrain. The actuated spoke wheel system was presented in an earlier work as an alternative locomotive method that allows unique mobility capabilities to cope with various situations. This paper presents the three-dimensional kinematic analysis of the actuated spoke wheel system with no slip and no bounce constraints at the ground contacts for a robot using a two actuated spoke wheel configuration. The first analysis will cover the case when the axle is coplanar with the line connecting the contact points, called the pivot line, and show results from two examples, corresponding to steady state turning and, in the special case, straight-line walking. The second case will describe the configuration when the pivot line is skew with the axle, comparing the robot in this configuration to an SPPS spatial mechanism. This comparison will lead to the recommendation of a more general model, based on the SPPS mechanism, that will be used to analyze the motion in both configurations.

Topics: Robots , Wheels
Commentary by Dr. Valentin Fuster
2006;():941-947. doi:10.1115/DETC2006-99019.

The velocity Jacobian matrix and the force Jacobian matrix are important index for kinematics, singularity and dynamics analyses of parallel manipulators. A novel computer variation geometric approach is proposed for solving the velocity Jacobian matrix and the force Jacobian matrix of parallel manipulators with linear driving limbs, as well as the determinant of Jacobian matrix. First, basic computer variation geometry techniques and definitions are presented for designing the simulation mechanisms, and several simulation mechanisms of parallel manipulators with linear driving limbs are created. Second, some velocity simulation mechanisms are created and the partial derivatives in Jacobian matrix are solved automatically and visualized dynamically. Based on the results of the computer simulation, the velocity Jacobian matrix and force Jacobian matrix are formed and the determinant of Jacobian matrix is solved. Moreover, the simulation results prove that the computer variation geometry approach is fairly quick and straightforward, and is accurate and repeatable. This project is supported by NSFC No. 50575198.

Commentary by Dr. Valentin Fuster
2006;():949-955. doi:10.1115/DETC2006-99028.

This paper firstly introduces a kinematic principle of singularity. It is a sufficient and necessary condition to identify singularity. Using the condition this paper systematically studies the singularity of 3-RPS parallel manipulator. A simple singularity equation is derived and the complete singularity loci in the three-dimensional space are illustrated. In order to analyze the singularity property and verify the correctness of the derived equation the line-geometry and the constraint screw theory are used. Some important singularity properties and the distribution characteristics are presented.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2006;():957-963. doi:10.1115/DETC2006-99031.

This paper presents the mobility analysis, the inverse and forward displacement analysis, and workspace of a novel 3-DOF 3-RPUR parallel manipulator. Closed-form inverse displacement solutions are obtained by the Denavit-Hartenberg method. The forward displacement problem is analyzed by using the continuation method and proved applying the result of the inverse displacement analysis. The workspace of the mechanism is also obtained. A numerical example is given in the paper.

Commentary by Dr. Valentin Fuster
2006;():965-975. doi:10.1115/DETC2006-99076.

A new micromechanism, the Spherical Bistable Micromechanism (SBM), is described. The SBM has several advantageous features, which include: two stable positions that require power only in transitioning from one to the other; robustness against small disturbances; and an output link with a stable out-of-plane orientation. The SBM may be useful in applications such as 2-D optical mirror arrays or in erecting out-of-plane structures.

Commentary by Dr. Valentin Fuster
2006;():977-983. doi:10.1115/DETC2006-99109.

The paper once again deals with the mobility analysis methodology of mechanisms based on constraint screw. It is a very important subject in mechanism theory lasting about 150 year. Firstly, the paper introduces some background and then the methodology. The paper focuses on analysis of some “paradoxical mechanisms”, including classical mechanism and modern parallel mechanisms, such as Bennett mechanism, Delta robot, Tsai’s CPM mechanism and so on. All the results prove that for the difficult mobility problem the analysis procedures are quite simple and convenient, and will easily be held by numerous mechanical engineers. The complicated problem is solved only by using a pencil, a sheet of paper and just for a few minutes.

Topics: Robots , Mechanisms
Commentary by Dr. Valentin Fuster
2006;():985-995. doi:10.1115/DETC2006-99239.

Discretely-actuated manipulators are defined in this paper as serial planar chains of many links where the actuation of one link with respect to the previous link occurs in one of three discrete positions. Because of the limited end-effector workspace, a link may be manually connected to the previous link in one of four 90° orientations to assist in generating a workspace corresponding to specific applications. Given an application workspace, the assembly configuration synthesis strategy presented here is a novel approach to determine the nominal configuration (all actuators in their 0° position) of the serial chain. The solved configuration will cover an application grid area using its discrete actuation with no change in nominal configuration. The unique application workspace, defined as a planar grid area, requires the end effector to be positioned somewhere within each specific element of the grid. The synthesis strategy is made up of three stages with each stage having tests that increase in computation and difficulty that a potential configuration must pass or be eliminated. Critical to the tests is the ability to quickly model and approximate the end-effector workspace of a configuration and a new method for this approximation is described.

Commentary by Dr. Valentin Fuster
2006;():997-1004. doi:10.1115/DETC2006-99283.

In this paper we show that kinematic errors in serial manipulators propagate by convolution on the Euclidean motion group. When errors are small, covariances describing error probability densities can be propagated in place of explicitly performing the convolution. We investigate the robustness of covariance propagation formulas in the context of individual joint errors that are small, but result in overall end-effector errors that are not necessary small.

Commentary by Dr. Valentin Fuster
2006;():1005-1016. doi:10.1115/DETC2006-99532.

This paper presents a novel robotic hand with a metamorphic palm which changes the traditional structure of a robotic hand. Based on this new hand structure, the paper investigates motion of robotic fingers with respect to the palm by introducing finger operation-planes and by revealing the relationship between finger motion and palm motion. The study presents normals of the finger operation-planes as function of the input angle of the palm and relates finger motion to palm motion. This leads to the co-axial condition of the finger-palm relationship that is then converted to the coplanar condition of normals of all finger operation-planes. The paper then maps the known normals of the first two finger operation-planes to a spherical image space and produces the Gaussian image of normals and a cone of a normal, leading to differential geometry based analysis of the normals of the operation planes and synthesis of the metamorphic palm.

Commentary by Dr. Valentin Fuster
2006;():1017-1027. doi:10.1115/DETC2006-99559.

Discretely-actuated manipulators are defined in this paper as serial planar chains of many links and are an alternative to traditional robotic manipulators, where continuously variable actuators are replaced with discrete, or digital actuators. Benefits include reduced weight and complexity, and predictable manipulation at lower cost. Challenges to using digital manipulators are the discrete end-effector positions which make the inverse kinematics problem difficult to solve. Furthermore, for a specific application position in the manipulator workspace, there may not be an actual end-effector position. This research has relaxed the inverse kinematics problem around this challenge making each application position an element of a grid in which the end effector must reach. There may be many possible end-effector positions that would reach the element goal, the solution uses the first one that is found. The inverse kinematics solution assumes the assembly configuration of the digital manipulator is already solved specifically for the application grid. The Jacobian function, normally used to solve joint velocities, can be used to identify the exact shift vectors that are used for the inverse kinematics. Three methods to solve this problem are discussed and the third method was implemented as a four-part solution that is a directed and manipulated search for the inverse kinematics solution where all four solutions may be needed. A discussion of forward kinematics and the Jacobian function in relation to digital manipulators is also presented.

Commentary by Dr. Valentin Fuster
2006;():1029-1036. doi:10.1115/DETC2006-99570.

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schönflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are: (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2006;():1037-1046. doi:10.1115/DETC2006-99628.

There are usually several motion patterns having the same DOF (degree of freedom). For example, planar motion, spherical motion, and spatial translation are motion patterns with 3-DOF. An f-DOF parallel mechanism with multiple operation modes is a parallel mechanism that can generate different motion patterns with f DOF. Up to now, no method has been proposed for the type synthesis of parallel mechanisms with multiple operation modes. This paper presents a general method for the type synthesis of parallel mechanisms with multiple operation modes. Using the proposed approach, 3-DOF parallel mechanisms with both spherical and translational modes, i.e., parallel mechanisms generating both the spherical motion pattern and the spatial translational motion pattern, are generated systematically. A large number of parallel mechanisms with both spherical and translational modes are obtained.

Commentary by Dr. Valentin Fuster
2006;():1047-1056. doi:10.1115/DETC2006-99687.

While robotic assembly at the centimeter and meter length scale is well understood and is routine in the manufacturing industry, robotic grasping and manipulation for meso-scale assembly at the millimeter and sub-millimeter length scales are much more difficult. This paper explores an possible way to manipulate and assemble planar parts using a micro-manipulator with a single probe capable of pushing parts on a planar surface with visual feedback. Specifically, we describe a study of the uncertainty associated with planar surface friction with a goal of developing a model of manipulation primitives that can be used for assembly. We describe a series of experiments and data analysis algorithms that allow us to identify the main system parameters for quasi-static operation, including the friction coefficient and the force distribution, while characterizing the uncertainty associated with these parameters. This allows us to bound the range of motions resulting from the uncertainty, which is necessary to design robust open-loop meso-scale manipulation and assembly motion plans.

Commentary by Dr. Valentin Fuster
2006;():1057-1066. doi:10.1115/DETC2006-99736.

Under-actuated systems are unavoidable in certain applications. For example, a biped can not have an actuator between the foot and the ground. For industrial robots, underactuation is preferable due to cost considerations. A fully actuated system can execute any joint trajectory. However, if the system is under-actuated, not all joint trajectories are attainable. For such systems, it is difficult to characterize attainable joint trajectories analytically and numerical methods are generally used to characterize them. This paper investigates the property of differential flatness for under-actuated planar open chain robots and study its dependence on inertia distribution within the system. Once this property is established, trajectory between any two points in its differentially flat output space is feasible and can be shown to be consistent with the dynamics of the under-actuated system. It is shown that certain choices of inertia distributions make an under-actuated open-chain planar robot with revolute joints feedback linearizable, i.e., also differentially flat. Hence, both cyclic and point to point trajectories can be guaranteed with these under-actuated systems. The methodology proposed is demonstrated with an under-actuated three degree-of-freedom planar robot.

Topics: Motion , Robots , Chain , Design
Commentary by Dr. Valentin Fuster
2006;():1067-1078. doi:10.1115/DETC2006-99070.

This contribution presents a comprehensive theory for the type synthesis of fully parallel platforms. The theory deals with both types of platforms, 6 D.O.F. parallel platforms and lower mobility platforms. The theory is based on an analysis of the subsets and subgroups of the Euclidean group, SE(3). It is likely that the theory can be also developed based on an analysis of the subspaces and subalgebras of the Lie algebra, se(3), of the Euclidean group, SE(3).

Topics: Lie algebras
Commentary by Dr. Valentin Fuster
2006;():1079-1086. doi:10.1115/DETC2006-99087.

Nonlinear equations arise from the synthesis of linkages. Newton’s method is one of the most accessible and easiest to implement of the iterative root-finding algorithms for these equations. As a discrete deterministic dynamical system, Newton’s method contains subsystems which have highly random motion. In a so-called chaotic zone, there is a rapid interchange between the basins of attraction for each root of the equation. Choosing initial points from such chaotic zone, one can obtain a certain number of roots or possible all of them under the Newton’s method. In this paper, how to locate the chaotic zones is addressed following the global analysis of real Newton’s method. It is show that there exist four chaotic zones for a general 4th degree polynomial. As an example, the equation derived from exact synthesis for five positions is solved.

Commentary by Dr. Valentin Fuster
2006;():1087-1094. doi:10.1115/DETC2006-99088.

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

Topics: Robots
Commentary by Dr. Valentin Fuster
2006;():1095-1105. doi:10.1115/DETC2006-99089.

Based on the new viewpoint of structural decomposion that any multi-loop mechanism are made up of by a series of ordered single opened chains(SOCs), a new method for kinematic analysis of parallel manipulators, i.e, the SOCs modular method has been presented in the paper. The new method has the following features: (1) The dimensions of sets of the nonlinear kinematic analysis equations are reduced to the minimum, and the kinematic analysis equation often contains only one unknown variable for most parallel manipulators generally applied now. Accordingly, all the real solutions to forward kinematics problem of parallel mechanisms can be easily obtained by using one-dimension searching algorithm; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas; (3) Compared with homotopy continuation method, it has higher computing efficiency.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2006;():1107-1115. doi:10.1115/DETC2006-99094.

The importance of finding singular configurations (singularities) of mechanisms has become clear since the interest of the scientific community for parallel architectures arose. Regarding the singularity analysis, the main interest has been devoted to architectures with more-than-one degree of freedom (dof) without realizing that one-dof mechanisms are commonly used and deserve the same attention. This paper addresses the singularity analysis of one-dof planar mechanisms. A general method for implementing this analysis will be presented. The presented method relies on the possibility of giving geometric conditions for any type of singularity. It can be used to generate systems of equations to solve either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2006;():1117-1122. doi:10.1115/DETC2006-99124.

This paper unveils line-geometric foundations of finite displacement screw systems, with an emphasis on incompletely specified displacement of points. Linear line complexes are basic entities used in this research. Bisecting linear line complexes arising from finite displacements are proved to be subject to a reciprocal condition if a new definition of pitch of finite screws is defined. This definition was the one used to formulate finite screw systems. The relations among intersections of linear line complexes, screw systems, and varieties of lines are established in order to investigate finite screw systems. A novel treatment of point displacements allows us to visualize finite screw systems when they are formed by intersecting linear line complexes. This paper provides geometric insights into finite displacement screws and presents a new framework for the unification of finite and infinitesimal kinematics.

Topics: Screws , Geometry
Commentary by Dr. Valentin Fuster
2006;():1123-1130. doi:10.1115/DETC2006-99153.

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much if not all of the previous work in this area has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. An elegant geometric method is developed based on line geometry that can be considered as a generalization of the classical Reuleaux’s method used in 2D kinematics. The case of over determined system is also considered a linear solution is presented based on least squares method.

Topics: Geometry
Commentary by Dr. Valentin Fuster
2006;():1131-1145. doi:10.1115/DETC2006-99275.

In the last five years Prof. Shai has developed a comprehensive theory of the duality among different areas of engineering science, in particular between mechanisms and trusses. In this contribution, it is shown a different approach that, in the opinion of the authors, generalize the approach presented by Prof. Shai and clear some misconceptions.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2006;():1147-1153. doi:10.1115/DETC2006-99300.

A mechanism that encounters a certain change in the number of links or degree of freedom during operation will also result the variation of the topological structure in every stage. Since the mechanisms with variable chain in different stages during operation have different topologies, but the applications of this kind of mechanisms are very extensively. And this also result the complications of representation of the topology thoroughly. Mechanisms with variable chain now always been represented by graph according to the topology of each stage, but hardly represent by using a formula. We would like to propose an approach to develop the function for representing the mechanism with variable chain that focus on the sequential movement, and help the representation of the operation not only by the graph but also by the function. According to the operation of the mechanisms with variable chain, the movement of the mechanisms can be classified into parallel system movement and sequential system movement. Parallel movement mechanisms are the mechanisms operate more than one links in the same time when giving an input; and when we give an input that can operate just only one link and effect and transfer the movement of the next one step by step, we can call this kind of mechanisms as sequential mechanisms. In this work we apply composite function for represent the movement of each stage, and also verified the representation by applying it on the existed examples.

Topics: Chain , Mechanisms
Commentary by Dr. Valentin Fuster
2006;():1155-1168. doi:10.1115/DETC2006-99321.

Low-degree-of-freedom (Low-DOF) parallel manipulators (PMs) have drawn extensive interest, particularly in type synthesis in which two main approaches were established in the reciprocal screw system theory and Lie group theory. This paper aims at proposing a new type synthesis method to complementing the above methods. For this purpose, the concept of the DOF characteristic matrix, originated from displacement subgroup and displacement submanifold, is proposed. A new but general approach based on the atlas of DOF Characteristic Matrix is addressed for both exhaustive classification and type synthesis of low-DOF PMs. Compared to the method based on Lie group, the proposed approach is prone to construct an orthogonal structure and easy to realize the complete classification and exhaustive enumeration of a class of low-DOF PM. In order to verify the effectiveness of the proposed method, type synthesis of Translational PMs (TPMs) particularly in ones with an orthogonal structure is performed, resulting in some novel orthogonal TPMs.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2006;():1169-1175. doi:10.1115/DETC2006-99338.

We present a new tool used to design and simulate parallel robots in their environments. Explicit kinematic equations, for a given architecture, are generated automatically. The user has the choice of specifying, among all the variables, the input and the output of the mechanism. We also present a method to generate a path of the end effector and to detect singularities along the generated path.

Commentary by Dr. Valentin Fuster
2006;():1177-1184. doi:10.1115/DETC2006-99340.

A study about mobility and workspace of a 3-5R translational parallel spatial mechanism that has three symmetric limbs is presented. Mobility analysis based on the screw theory and numerical calculations were carried out to show if the proposed mechanism enabled the pure translational motion of a platform. The size and shape of workspace of the mechanism were also evaluated.

Commentary by Dr. Valentin Fuster
2006;():1185-1192. doi:10.1115/DETC2006-99386.

Three kinds of new discontinuously movable (DM) spatial 7-link mechanisms named hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6R1P DM mechanisms are synthesized by combining planar and spherical 4R trivial chains. Their discontinuous mobility is explained using the Lie group algebraic properties of the displacement set. In addition, the same given spatial arrangement of joints can be linked in two ways thus constituting two distinct chains with a quite different mobility. One chain has two global degrees of freedom (dofs), which disobey the general Grubler-Kutzbach mobility criterion. The other chain exhibits a singular pose, which is a bifurcation towards two distinct working modes of one-dof mobility. As a result, the set of relative motions between any two specific links is not a manifold but consists of the union of displacement 1-dimensional manifolds.

Topics: Mechanisms
Commentary by Dr. Valentin Fuster
2006;():1193-1198. doi:10.1115/DETC2006-99613.

In this paper we present a solution to the inverse kinematics problem for serial manipulator of general geometry. Using only seven equations which are consisted of Duffy’s four kinematical equations containing only three angles and three corresponding angles’ sincos identical equations instead of traditional fourteen equations, we reduce the inverse kinematics problem of the general 6R manipulator to a univariate polynomial with minimum degree based on Groebner-Sylvester method. From that, a conclusion can be drawn that the maximum number of the solutions is sixteen, generally. Also the mathematics mechanization method used in this paper can be extended to solve the other mechanism problem involving nonlinear equations symbolically.

Commentary by Dr. Valentin Fuster
2006;():1199-1208. doi:10.1115/DETC2006-99649.

This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. The paper brings together the kinematics of planar robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Through the use of planar quaternions, it is shown that the problem of synthesizing the Cartesian rational motion of a planar 2R arm can be reduced to that of circular interpolations in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a planar 3R arm can be reduced to that of circular interpolation in one plane and constrained spline interpolation in a circular ring. Due to the limitation of circular interpolation, only C1 continuous rational motions are generated. For applications that require C2 continuous motions, the paper presents a joint-space based method for generating a C2 continuous motion that approximates a given C1 rational motion of the end link.

Commentary by Dr. Valentin Fuster
2006;():1209-1221. doi:10.1115/DETC2006-99650.

This paper deals with the problem of synthesizing piecewise rational spherical motions of an object that satisfies the kinematic constraints imposed by a spherical robot arm with revolute joints. The paper brings together the kinematics of spherical robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Using quaternion kinematics of spherical arms, it is shown that the problem of synthesizing the Cartesian rational motion of a 2R arm can be reduced to that of circular interpolation in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a spherical 3R arm can be reduced to that of constrained spline interpolation in two separate planes. Due to the limitation of circular interpolation, for spherical 2R robot arm, only C1 continuous rational motions are generated. In this case, for applications that require C2 continuous motions, the paper presents a method for generating a C2 continuous joint motion that approximates a given C1 rational motion of the end-effector. For spherical 3R arm, C2 continuous rational motions are generated exactly.

Commentary by Dr. Valentin Fuster
2006;():1223-1228. doi:10.1115/DETC2006-99673.

A kinematic analysis method that determines roll center of a planar half-car kinematic model with variable tread width is proposed. For this, a half-car model whose wheels are assumed to be connected to the ground by revolute and prismatic joints are constructed, and instantaneous centers of the wheels with respect to the ground of the model is estimated by poles of the wheels with respect to the ground for small roll displacement. Then, the theorem of three centers is applied to determine the locus of roll center of the half-car model. Using the proposed analysis method, roll displacement of vehicle body, wheel angle variation, wheel contact point variation, and centrodes of relative motion between vehicle body and the ground, which is the locus of roll center, can be calculated.

Topics: Wheels
Commentary by Dr. Valentin Fuster
2006;():1229-1237. doi:10.1115/DETC2006-99677.

The goal of this paper is to demonstrate that the Modified Grübler-Kutzbach Criterion when combined with a simple procedure for determining the reciprocal screws offers a direct and simple method for analysing highly complex mechanisms including the over-constrained parallel manipulators. Since the scalar product of screws is not dependent on the choice of the origin, one can quickly obtain a simple expression of screws by selecting an appropriate coordinate system. In such simple expression, the coordinates of a screw would include 0 or 1, and thus greatly simplifies the procedure for determine the number of constraints in a mechanism. Seven rules have been presented to help simplify the analysis process. The advocated approach makes it possible to determine, within minutes, the mobility of a highly complex mechanism by using a pencil and a paper. Many over-constrained mechanisms, including three parallel mechanisms, are presented as examples.

Topics: Screws
Commentary by Dr. Valentin Fuster
2006;():1239-1248. doi:10.1115/DETC2006-99695.

The displacement analysis of open and closed kinematic chains is based on polynomial equations whose variables are functions of relative joint displacements. The objective of this paper is to investigate new and interesting properties of the transformations between the canonical cosine-sine polynomials and the even degree tan-half angle polynomials associated with displacement kinematics. Using a homogeneous coordinate formulation, it is shown that the coefficients of the polynomials are linearly related by a projective transformation whose elements can be defined recursively. The canonical cosine-sine polynomial is then transformed to a cosine or a sine polynomial which can be rooted by usual techniques. However, all real roots are bracketed between −1 and +1 which can have numerical advantages over a corresponding tan-half angle polynomial for which the entire real axis must be searched. It is also demonstrated how polynomial solutions corresponding to circular points at infinity in the tan-half angle, which are typically introduced as extraneous roots via algebraic elimination, may be easily factored out by the transformation to the cosine-sine formulation.

Commentary by Dr. Valentin Fuster
2006;():1249-1255. doi:10.1115/DETC2006-99754.

The Generalized Lever is a new tool in gear train representation. It extends the traditional concept of a lever representation of a planetary gear set to one that includes negative lever ratios. This allows an exhaustive permutation of the nodes of a lever, thereby leading to all possible topological arrangements of a planetary gear train. Consequently, we achieve a compact representation of large families of planetary gear trains, which would otherwise have to be dealt with on a case-by-case basis.

Commentary by Dr. Valentin Fuster

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