Position Kinematics of the Generalized Lobster Arm and Its Series-Parallel Dual

[+] Author and Article Information
V. Murthy, K. J. Waldron

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

J. Mech. Des 114(3), 406-413 (Sep 01, 1992) (8 pages) doi:10.1115/1.2926566 History: Received May 01, 1991; Online June 02, 2008


The generalized lobster arm is a six revolute open kinematic chain with 3 consecutive intersecting pairs of axes. A new solution of the inverse position kinematics problem of this arm which takes advantage of its specific geometry is presented. A comparison is made with the direct position kinematics problem of the series-parallel dual mechanism. The equations governing the two problems show strong similarity and can each be reduced to a sixteenth degree univariate polynomial equation. The dual series-parallel mechanism is the one that exhibits, with the lobster arm, the symmetry that exists between the wrench and the velocity motor. Although the results presented here have intrinsic interest, a more generally important feature is the relationship between the solutions to the inverse kinematics of the serial mechanism and the direct kinematics of the parallel mechanism. Although the series-parallel duality has not been shown to hold in the position domain, except in terms of very general characteristics, it is shown here that the two solutions are of the same degree and have other features in common.

Copyright © 1992 by The American Society of Mechanical Engineers
Topics: Kinematics
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