Geometrical method to determine the reciprocal screws and applications to parallel manipulators

  • Authors:

  • Jianguo Zhao;Bing Li;Xiaojun Yang;Hongjian Yu

  • Affiliations:

  • Department of electrical and computer engineering, michigan state university, mi 48824, usa;Shenzhen graduate school, harbin institute of technology, shenzhen 518055, p.r. china and state key laboratory of robotics and system (hit), harbin 150001, p.r. china;Shenzhen graduate school, harbin institute of technology, shenzhen 518055, p.r. china;Shenzhen graduate school, harbin institute of technology, shenzhen 518055, p.r. china

  • Venue:
  • Robotica
  • Year:
  • 2009

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Abstract

Screw theory has demonstrated its wide applications in robot kinematics and statics. We aim to propose an intuitive geometrical approach to obtain the reciprocal screws for a given screw system. Compared with the traditional Plücker coordinate method, the new approach is free from algebraic manipulation and can be used to obtain the reciprocal screws just by inspecting the structure of manipulator. The approach is based on three observations that describe the geometrical relation for zero pitch screw and infinite pitch screw. Based on the observations, the reciprocal screw systems of several common kinematic elements are analyzed, including usual kinematic pairs and chains. We also demonstrate usefulness of the geometrical approach by a variety of applications in mobility analysis, Jacobian formulation, and singularity analysis for parallel manipulator. This new approach can facilitate the parallel manipulator design process and provide sufficient insights for existing manipulators.