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Technical Briefs

Determining the Number of Inverse Kinematic Solutions of a Constrained Parallel Mechanism Using a Homotopy Algorithm

[+] Author and Article Information
Jeremy T. Newkirk, Michael M. Stanišić

Department of Aerospace and Mechanical Engineering, University of Notre Dame, South Bend, IN 46556

Layne T. Watson

Department of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Mechanisms Robotics 2(2), 024502 (Apr 13, 2010) (5 pages) doi:10.1115/1.4001127 History: Received March 19, 2009; Revised December 07, 2009; Published April 13, 2010; Online April 13, 2010

This paper numerically determines the number of real-valued inverse kinematic solutions to a constrained parallel mechanism composed of three triangular platforms. The base and middle platforms are connected by three fixed-length legs, while the middle and distal platforms are connected by three variable length legs that extend out of the fixed-length legs in a collinear fashion. All legs are connected to the platforms via spherical joints at the corners. This mechanism is intended to replicate the motion of a human shoulder girdle. The constrained parallel mechanism has a multivalued solution to the inverse kinematics problem. A homotopy method was used to numerically compute the inverse kinematic solutions for over 100 cases. Each case was filtered for the number of real-valued solutions. The maximum number of real solutions was found to be 8, but in some cases there were fewer solutions.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Constrained parallel mechanism

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Figure 2

The human shoulder girdle

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Figure 3

Skeleton diagram

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Figure 10

Configuration 7

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Figure 11

Configuration 8

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