Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator

[+] Author and Article Information
Waseem A. Khan

Centre for Intelligent Machines, McGill University, Montréal, Québec Canada H3A 2A7wakhan@cim.mcgill.ca

Venkat N. Krovi1

Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260

Subir K. Saha

Department of Mechanical Engineering, IIT Delhi, New Delhi, India

Jorge Angeles

Centre for Intelligent Machines, McGill University, Montréal, Québec Canada H3A 2A7

See 23 for a more detailed discussion of the type of singularities.


Corresponding author.

J. Dyn. Sys., Meas., Control 127(4), 529-536 (Nov 30, 2004) (8 pages) doi:10.1115/1.2098890 History: Received November 23, 2003; Revised November 30, 2004

We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 4

Desired trajectory and required driving torques

Grahic Jump Location
Figure 3

Three-DOF Planar parallel manipulator used in the example

Grahic Jump Location
Figure 2

3-DOF Planar parallel manipulator

Grahic Jump Location
Figure 1

Two bodies connected by a kinematic pair



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