The Stewart platform is a six-degree-of-freedom, in-parallel linkage. It is used in automotive and flight simulators, positioning tables for assembly and robotic applications, and various other applications requiring linkages with high structural stiffness. It consists of a base link, a coupler link, and six adjustable-length legs supporting the coupler link. Each leg consists of a prismatic joint with ball-joint connections to the base and coupler, respectively. The forward kinematics problem for the Stewart platform may be stated as follows: given the values of the six prismatic joint displacement inputs to the linkage, compute the position and orientation of the coupler link. This problem may be set up as a system of nonlinear multivariate polynomial equations. We solve this problem using a numerical technique known as polynomial continuation. We show that for Stewart platforms of general geometry (i.e., platforms in which the linkage parameters are arbitrary complex numbers) this problem has 40 distinct solutions.
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June 1993
Research Papers
The Stewart Platform of General Geometry Has 40 Configurations
M. Raghavan
M. Raghavan
Power Systems Research Department, General Motors Research Laboratories, 30500 Mound Road, Warren, MI 48090–9055
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M. Raghavan
Power Systems Research Department, General Motors Research Laboratories, 30500 Mound Road, Warren, MI 48090–9055
J. Mech. Des. Jun 1993, 115(2): 277-282 (6 pages)
Published Online: June 1, 1993
Article history
Received:
May 1, 1991
Online:
June 2, 2008
Citation
Raghavan, M. (June 1, 1993). "The Stewart Platform of General Geometry Has 40 Configurations." ASME. J. Mech. Des. June 1993; 115(2): 277–282. https://doi.org/10.1115/1.2919188
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