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.
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January 2004
Technical Papers
Displacement Analysis of Spherical Mechanisms Having Three or Fewer Loops
Charles W. Wampler
Charles W. Wampler
General Motors R&D Center, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055
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Charles W. Wampler
General Motors R&D Center, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 2002; revised June 2003. Associate Editor: C. Mavroidis.
J. Mech. Des. Jan 2004, 126(1): 93-100 (8 pages)
Published Online: March 11, 2004
Article history
Received:
July 1, 2002
Revised:
June 1, 2003
Online:
March 11, 2004
Citation
Wampler, C. W. (March 11, 2004). "Displacement Analysis of Spherical Mechanisms Having Three or Fewer Loops ." ASME. J. Mech. Des. January 2004; 126(1): 93–100. https://doi.org/10.1115/1.1637653
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