• CN: 11-2187/TH
  • ISSN: 0577-6686

›› 2010, Vol. 46 ›› Issue (7): 27-34.

• Article • Previous Articles     Next Articles

Proofs of Existence Conditions for Workspaces of Wire-driven Parallel Robots and a Uniform Solution Strategy for the Workspaces

LIU Xin;QIU Yuanying;SHENG Ying   

  1. Key Laboratory of Electronic Equipment Structure of Ministry of Education, Xidian University
  • Published:2010-04-05

Abstract: The workspaces of incompletely restrained, completely restrained and redundant restrained wire-driven parallel robots are investigated, and a uniform solution strategy for workspaces of the three types of wire-driven parallel robots is put forward. Considering the sameness of unilateralism of acting forces, the convex condition of force-closure grasping for multi-fingered hands is utilized to derive the existence theorem of controllable workspaces of general wire-driven parallel robots. Based on existence theorem, convex set theory, linear algebra theory and projection theorem, general existence conditions of workspaces for the three types of wire-driven parallel robots are presented in the forms of corollaries individually, and the necessity and sufficiency of the existence conditions are proved. The existence conditions indicate that the rank of structure matrices of wire-driven parallel robots should be full, and the projections of column vectors of the structure matrices and those of vectors of the generalized external forces on the normal of the same hyperplane should be equivalent in both size and direction. According to the theorem and corollaries, a uniform solution strategy for the workspaces of the three types of wire-driven parallel robots is proposed. The workspaces of three typical wire-driven parallel robots are obtained and compared by using the proposed strategy.

Key words: Convex set theory, Projection theorem, Uniform solution strategy, Wire-driven parallel robots, Workspace

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