Affiliation:
1. General Motors R&D Center, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055
Abstract
Spherical linkages, having rotational joints whose axes coincide in a common center point, are sometimes used in multi-degree-of-freedom robot manipulators and in one-degree-of-freedom mechanisms. The forward kinematics of parallel-link robots, the inverse kinematics of serial-link robots and the input/output motion of single-degree-of-freedom mechanisms are all problems in displacement analysis. In this article, loop equations are formulated and solved for the displacement analysis of all spherical mechanisms up to three loops. We show how to solve each mechanism type using either a formulation in terms of rotation matrices or quaternions. In either formulation, the solution method is a modification of Sylvester’s elimination method, leading directly to numerical calculation via standard eigenvalue routines.
Subject
Computer Graphics and Computer-Aided Design,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
Reference20 articles.
1. Nielsen, J., and Roth, B., 1999, “Solving the Input/Output Problem for Planar Mechanisms,” ASME J. Mech. Des., 121(2), pp. 206–211.
2. Wampler, C. W.
, 1999, “Solving the Kinematics of Planar Mechanisms,” ASME J. Mech. Des., 121(3), pp. 387–391.
3. Wampler, C. W.
, 2001, “Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation,” ASME J. Mech. Des., 123(3), pp. 382–387.
4. Duffy, J., 1980, Analysis of Mechanisms and Robot Manipulators, Halsted Press, John Wiley and Sons, New York.
5. Kline, M., 1972, Mathematical Thought From Ancient to Modern Times, Vol. 1, Oxford University Press, Oxford, UK.
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