Planar Motion Synthesis Using an Approximate Bi-Invariant Metric

[+] Author and Article Information
P. Larochelle

Florida Institute of Technology, Melbourne, FL 32901

J. M. McCarthy

University of California-Irvine, Irvine, CA 92717

J. Mech. Des 117(4), 646-651 (Dec 01, 1995) (6 pages) doi:10.1115/1.2826735 History: Received April 01, 1994; Revised August 01, 1994; Online December 11, 2007


In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of spherical displacements. The optimal linkage is obtained by minimizing this distance for each of the n goal positions.

Copyright ┬ę 1995 by The American Society of Mechanical Engineers
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