RESEARCH PAPERS: Mechanisms Papers

Analysis of Spatial Open-Loop System by Means of Direction Cosine Transformation Matrices

[+] Author and Article Information
T. C. Yih

Mechanical Engineering Department, Florida International University, The State University of Florida at Miami, Miami, FL 33199

Y. Youm

Department of Mechanical Engineering, The Catholic University of America, Washington, D.C. 20064

J. Mech., Trans., and Automation 111(4), 508-512 (Dec 01, 1989) (5 pages) doi:10.1115/1.3259030 History: Received September 01, 1987; Online November 19, 2009


In this paper, an analytical approach for the displacement analysis of spatial openloop systems by means of direction cosine transformation matrices is presented. Two local coordinate systems at each joint are designated to formulate the direction cosine matrices, in recursive form, of the joint axis and link vector. Elements of the 3×3 direction cosine transformation matrices are computed based on the geometry of successive link elements, the unit vectors of preceding joint axis and link vector, and the cofactors of direction cosine matrix. The analysis using direction cosine matrix method will provide the “exact” joint positions in space. A computer algorithm is developed to investigate the workspaces of spatial n-R open-loop systems that projected onto the X-Y, Y-Z, and Z-X coordinate planes, respectively. Numerical examples for the workspaces of an industrial robot and the human upper extremity are illustrated.

Copyright © 1989 by ASME
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