For many mechanical systems, including nearly all robotic manipulators, the set of possible configurations that the links may assume can be described by a system of polynomial equations. Thus, solving such systems is central to many problems in analyzing the motion of a mechanism or in designing a mechanism to achieve a desired motion. This paper describes techniques, based on polynomial continuation, for numerically solving such systems. Whereas in the past, these techniques were focused on finding isolated roots, we now address the treatment of systems having higher-dimensional solution sets. Special attention is given to cases of exceptional mechanisms, which have an higher degree of freedom of motion than predicted by their mobility. In fact, such mechanisms often have several disjoint assembly modes, and the degree of freedom of motion is not necessarily the same in each mode. Our algorithms identify all such assembly modes, determine their dimension and degree, and give sample points on each.
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ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 29–October 2, 2002
Montreal, Quebec, Canada
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-3653-3
PROCEEDINGS PAPER
Advances in Polynomial Continuation for Solving Problems in Kinematics Available to Purchase
Andrew J. Sommese,
Andrew J. Sommese
University of Notre Dame, Notre Dame, IN
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Jan Verschelde,
Jan Verschelde
University of Illinois at Chicago, Chicago, IL
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Charles W. Wampler
Charles W. Wampler
General Motors R&D Center, Warren, MI
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Andrew J. Sommese
University of Notre Dame, Notre Dame, IN
Jan Verschelde
University of Illinois at Chicago, Chicago, IL
Charles W. Wampler
General Motors R&D Center, Warren, MI
Paper No:
DETC2002/MECH-34254, pp. 481-488; 8 pages
Published Online:
June 18, 2008
Citation
Sommese, AJ, Verschelde, J, & Wampler, CW. "Advances in Polynomial Continuation for Solving Problems in Kinematics." Proceedings of the ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 27th Biennial Mechanisms and Robotics Conference. Montreal, Quebec, Canada. September 29–October 2, 2002. pp. 481-488. ASME. https://doi.org/10.1115/DETC2002/MECH-34254
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