Planar Motion Synthesis Using an Approximate Bi-Invariant Metric-Reference-Cited by-同舟云学术

Planar Motion Synthesis Using an Approximate Bi-Invariant Metric

Published:1995-12-01 Issue:4 Volume:117 Page:646-651
ISSN:1050-0472
Container-title:Journal of Mechanical Design
language:en
Short-container-title:

Author:

Larochelle P.¹,McCarthy J. M.²

Affiliation:

1. Florida Institute of Technology, Melbourne, FL 32901

2. University of California-Irvine, Irvine, CA 92717

Abstract

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.

Publisher

ASME International

Subject

Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials

Link

http://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/117/4/646/5582946/646_1.pdf

Reference10 articles.

1. Bodduluri M. , and McCarthyJ. M., 1992, “Finite Position Synthesis Using the Image Curve of a Spherical Four Bar Motion,” ASME JOURNAL OF MECHANICAL DESIGN, Vol. 114, March, pp. 55–60.

2. Duffy J. , 1990, “The Fallacy of Modern Hybrid Control Theory that is Based Upon ‘Orthogonal Complements’ of Twists and Wrench Spaces,” (editorial) Journal of Robotic Systems, Vol. 7, No. 2, pp. 139–144.

3. Erdman, A., 1992, The First 40 Years of Modern Kinematics, John Wiley and Sons.

4. Hamilton, W. R., 1969, Elements of Quarternions, (reprinted) Chelsea Press.

5. Kazerounian, K., and Rastegar, J., 1992, “Object Norms: A Class of Coordinate and Metric Independent Norms for Displacements,” Proc. of the 1992 ASME Design Technical Conferences, Flexible Mechanisms, Dynamics, and Analysis, DE-Vol. 47, pp. 271–275, September.

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