A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator

[+] Author and Article Information
H. Y. Lee

Department of Mechanical Engineering, Beijing University of Posts and Telecommunications, Beijing 100088, China

C. Woernle

Institute A of Mechanics, University of Stuttgart, Pfaffenwaldring 9, 7000 Stuttgart 80, Germany

M. Hiller

Department of Mechanics, University of Duisburg, Lotharstrasse 21, 4100 Duisburg, Germany

J. Mech. Des 113(4), 481-486 (Dec 01, 1991) (6 pages) doi:10.1115/1.2912808 History: Received October 01, 1990; Online June 02, 2008


The inverse kinematic problem of the general 6R robot manipulator is completely solved by means of a 16th degree polynomial equation in the tangent of the half-angle of a revolute joint. An algorithm is developed to compute the desired joint angles of all possible configurations of the kinematic chain for a given position of the end-effector. Examples for robots with maximal 16 different configurations show that the polynomial degree 16 is the lowest possible for the general 6R robot manipulator. Further, a numerical method for the determination of the boundaries of the workspace and its subspaces with different numbers of configurations is developed. These boundaries indicate the singular positions of the end-effector.

Copyright © 1991 by The American Society of Mechanical Engineers
Topics: Manipulators
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