On Self-Motions of Planar Stewart-Gough Platforms

Authors

  • Veturia Chiroiu Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, Bucharest 010141, Romania
  • Cornel Brişan The Technical University of Cluj-Napoca, str. Memorandumului nr.28, Cluj-Napoca 400114, Romania
  • Ligia Munteanu Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, Bucharest 010141, Romania
  • Cristian Rugină Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, Bucharest 010141, Romania

DOI:

https://doi.org/10.15377/2409-9821.2021.08.2

Keywords:

Self-motion, Duporcq’s theorem, Borel-Bricard problem, Super-ellipsoid surface, Stewart-Gough platform

Abstract

Given five pairs of attachment points of a planar platform, there exists a sixth point pair so that the resulting planar architecturally singular platform has the same solution for the direct kinematics. This is a consequence of the Prix Vaillant problem posed in 1904 by the French Academy of Science. The theorem discusses the displacements of certain or all points of a rigid body that move on spherical paths. Borel and Bricard awarded the prizes for two papers in this regard, but they did not solve the problem completely. In this paper, the theorem is extended to the elliptic paths in order to determine the displacements of certain or all points of a rigid body that move on super-ellipsoid surfaces. The poof is based on the trajectories of moving points which are intersections of two implicit super-ellipsoid surfaces.

Author Biographies

Veturia Chiroiu, Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, Bucharest 010141, Romania

Dept. of Deformable Media and Ultrasonics

Cornel Brişan, The Technical University of Cluj-Napoca, str. Memorandumului nr.28, Cluj-Napoca 400114, Romania

Faculty of Mechanics, Dept. of Mechatronics and Machine Dynamics

Ligia Munteanu, Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, Bucharest 010141, Romania

Dept. of Deformable Media and Ultrasonics

Cristian Rugină, Institute of Solid Mechanics of Romanian Academy, Ctin Mille 15, Bucharest 010141, Romania

Dept. of Deformable Media and Ultrasonics

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Published

2021-07-13

How to Cite

1.
Chiroiu V, Brişan C, Munteanu L, Rugină C. On Self-Motions of Planar Stewart-Gough Platforms. Int. J. Archit. Eng. Technol. [Internet]. 2021Jul.13 [cited 2021Sep.26];8:14-21. Available from: https://www.avantipublishers.com/jms/index.php/ijaet/article/view/1040

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