Position and orientation characteristic (POC) equations for topological structure synthesis of serial and parallel mechanisms were proposed in a published paper by the authors. This paper will further prove the correctness and strictness of the theoretical foundation for POC equations and also be a reply to the reviewers of our follow-up papers. The main contents of this paper include: symbolic representation of mechanism topological structure and its invariance, velocity characteristic (VC) set and POC set of link and its invariance, one-to-one correspondence between elements of the VC set and POC set, POC equations for the serial mechanism and 10 corresponding “union” operation rules, and POC equations for the parallel mechanism and 14 corresponding “intersection” operation rules. In addition, the interrelations and differences among three methods (POC set based method, screw theory based method, and displacement subgroup based method) for mechanism topological structure design are concluded.
On the Correctness and Strictness of the Position and Orientation Characteristic Equation for Topological Structure Design of Robot Mechanisms
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received June 19, 2010; final manuscript received February 14, 2013; published online April 23, 2013. Assoc. Editor: Delun Wang.
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Yang, T., Liu, A., Shen, H., Luo, Y., Hang, L., and Shi, Z. (April 23, 2013). "On the Correctness and Strictness of the Position and Orientation Characteristic Equation for Topological Structure Design of Robot Mechanisms." ASME. J. Mechanisms Robotics. May 2013; 5(2): 021009. https://doi.org/10.1115/1.4023871
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