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 a 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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March 2004
Technical Papers
Advances in Polynomial Continuation for Solving Problems in Kinematics
Andrew J. Sommese,
Andrew J. Sommese
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618
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Jan Verschelde,
Jan Verschelde
Department of Mathematics, Statistics, and Computer Science, 851 S. Morgan St. (MC 249) University of Illinois at Chicago, Chicago, IL 60607-7045
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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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Andrew J. Sommese
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618
Jan Verschelde
Department of Mathematics, Statistics, and Computer Science, 851 S. Morgan St. (MC 249) University of Illinois at Chicago, Chicago, IL 60607-7045
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 February 2003. Associate Editor: C. Mavroidis.
J. Mech. Des. Mar 2004, 126(2): 262-268 (7 pages)
Published Online: May 5, 2004
Article history
Received:
July 1, 2002
Revised:
February 1, 2003
Online:
May 5, 2004
Citation
Sommese, A. J., Verschelde, J., and Wampler, C. W. (May 5, 2004). "Advances in Polynomial Continuation for Solving Problems in Kinematics ." ASME. J. Mech. Des. March 2004; 126(2): 262–268. https://doi.org/10.1115/1.1649965
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