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Solving the Forward Kinematic Problem of 4-DOF Parallel Mechanisms (3T1R) With Identical Limb Structures and Revolute Actuators Using the Linear Implicitization Algorithm

[+] Author Affiliations
Mehdi Tale Masouleh, Clément Gosselin

Université Laval, Québec, QC, Canada

Dominic R. Walter, Manfred Husty

University of Innsbruck, Innsbruck, Austria

Paper No. DETC2011-47884, pp. 969-978; 10 pages
doi:10.1115/DETC2011-47884
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5483-9
  • Copyright © 2011 by ASME

abstract

This paper investigates the forward kinematic problem of 4-DOF parallel mechanisms with revolute actuators and identical limb structures and performing a three translations and one rotation motion pattern. The general architecture of all the mechanisms under study in this paper originates from the type synthesis performed for 4-DOF parallel mechanisms with identical limb structures. The mathematical framework used in this paper is based on algebraic geometry where the forward kinematics and constraint expressions are explored in a seven-dimensional kinematic space by means of the so-called Study parameters (dual quaternions). In this paper, the algorithm applied for obtaining the forward kinematic and constraint expressions is based on a recent and novel approach, called linear implicitization algorithm, which is based on solving systematically a system of linear equations to determine the coefficients of the non-linear constraint equations. This paper presents also an example of a 4-DOF parallel mechanism.

Copyright © 2011 by ASME

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