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RESEARCH PAPERS: Robotics Papers

A Study of the Jacobian Matrix of Serial Manipulators

[+] Author and Article Information
K. J. Waldron, Shih-Liang Wang, S. J. Bolin

Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43210

J. Mech., Trans., and Automation 107(2), 230-237 (Jun 01, 1985) (8 pages) doi:10.1115/1.3258714 History: Received July 10, 1984; Online November 19, 2009

Abstract

Inversion of the Jacobian matrix is the critical step in rate decomposition which is used to solve the so-called “inverse kinematics” problem of robotics. This is the problem of achieving a coordinated motion relative to the fixed reference frame. In this paper a general methodology is presented for formulation and manipulation of the Jacobian matrix. The formulation is closely tied to the geometry of the system and lends itself to simplification using appropriate coordinate transformations. This is of great importance since it gives a systematic approach to the derivation of efficient, analytical inverses. The method is also applied to the examination of geometrically singular positions. Several important general results relating to the structure of the singularity field are deducible from the structure of the algebraic system.

Copyright © 1985 by ASME
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