Screw systems composed of (the sum of) three planar pencils of lines are closely related to the singularity analysis of a number of three-legged parallel manipulators (PMs) in which the passive joints in each leg are a spherical joint and a single-DOF (degree of freedom) kinematic joint or generalized kinematic joint. This paper systematically classifies the screw systems composed of three planar pencils of lines based on the intersection of two planar pencils of lines, the classification of screw systems of order 2, and the reciprocal screw system of the three planar pencils of lines. The classification in this paper is more comprehensive than those in the literature. The above results are illustrated using CAD figures. This work may help readers better understand the geometric characteristics of singular configurations of a number of three-legged parallel manipulators.
Classification of Screw Systems Composed of Three Planar Pencils of Lines for Singularity Analysis of Parallel Mechanisms1
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 8, 2013; final manuscript received November 16, 2013; published online March 6, 2014. Assoc. Editor: Jian S. Dai.
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Kong, X., and Johnson, A. (March 6, 2014). "Classification of Screw Systems Composed of Three Planar Pencils of Lines for Singularity Analysis of Parallel Mechanisms." ASME. J. Mechanisms Robotics. May 2014; 6(2): 021008. https://doi.org/10.1115/1.4026340
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