This paper investigates two situations in which the forward kinematics of planar parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables , , and satisfy a certain relationship. This degeneracy yields a double root of the characteristic polynomial in , which could be erroneously interpreted as two coalesce assembly modes. However, unlike what arises in nondegenerate cases, this double root yields two sets of solutions for the position coordinates of the platform. In the second situation, we show that the forward kinematics degenerates over the whole joint space if the base and platform triangles are congruent and the platform triangle is rotated by about one of its sides. For these “degenerate” manipulators, which are defined here for the first time, the forward kinematics is reduced to the solution of a third-degree polynomial and a quadratic in sequence. Such manipulators constitute, in turn, a new family of analytic planar manipulators that would be more suitable for industrial applications.
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December 2007
Research Papers
Degeneracy Study of the Forward Kinematics of Planar Parallel Manipulators
P. Wenger,
P. Wenger
Institut de Recherche en Communications et Cybernétique de Nantes
, 1 rue la Noe, BP 92101, 44321 Nantes Cedex 3, France
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D. Chablat,
D. Chablat
Institut de Recherche en Communications et Cybernétique de Nantes
, 1 rue la Noe, BP 92101, 44321 Nantes Cedex 3, France
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M. Zein
M. Zein
Institut de Recherche en Communications et Cybernétique de Nantes
, 1 rue la Noe, BP 92101, 44321 Nantes Cedex 3, France
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P. Wenger
Institut de Recherche en Communications et Cybernétique de Nantes
, 1 rue la Noe, BP 92101, 44321 Nantes Cedex 3, France
D. Chablat
Institut de Recherche en Communications et Cybernétique de Nantes
, 1 rue la Noe, BP 92101, 44321 Nantes Cedex 3, France
M. Zein
Institut de Recherche en Communications et Cybernétique de Nantes
, 1 rue la Noe, BP 92101, 44321 Nantes Cedex 3, FranceJ. Mech. Des. Dec 2007, 129(12): 1265-1268 (4 pages)
Published Online: December 13, 2006
Article history
Received:
September 19, 2006
Revised:
December 13, 2006
Citation
Wenger, P., Chablat, D., and Zein, M. (December 13, 2006). "Degeneracy Study of the Forward Kinematics of Planar Parallel Manipulators." ASME. J. Mech. Des. December 2007; 129(12): 1265–1268. https://doi.org/10.1115/1.2779893
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