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research-article

Product submanifold based analysis of kinematic chains and a 3-PUP parallel mechanism

[+] Author and Article Information
Xinsheng Zhang

Key Lab for Mechanism Theory and Equipment Design, International Centre for Advanced Mechanisms and Robotics, Tianjin University, Tianjin Centre for Robotics Research King’s College London London, WC2R 2LS, UK
xinsheng.zhang@kcl.ac.uk

Pablo Lopez-Custodio

Centre for Robotics Research King’s College London London, WC2R 2LS, UK
pablo.lopez-custodio@kcl.ac.uk

Jian S Dai

Chair of Mechanisms and Robotics International Centre for Advanced Mechanisms and Robotics, Tianjin University, Tianjin Centre for Robotics Research King’s College London London, WC2R 2LS, UK
jian.dai@kcl.ac.uk

1Corresponding author.

ASME doi:10.1115/1.4038218 History: Received October 12, 2016; Revised August 23, 2017

Abstract

The kinematic chains that generate the planar motion group with the prismatic-joint direction always perpendicular with the revolute-joint axis in each chain, have shown their effectiveness and manifested the charm in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the traditional PRP kinematic chain generating the planar motion group to a relatively general case, in which one of the prismatic joint-direction is not necessarily perpendicular with the revolute-joint axis, leading to the discovery of a helical motion with a variable pitch in this kinematic chain. The displacements of such PRP chain generate a submanifold of the Schoenflies motions subgroup. This paper investigates for the first time this type of motion. Following the extraction of a helical motion from this PRP kinematic chain, this paper investigates the bifurcated motion in a 3-PUP parallel mechanism by changing the active geometrical constraint in its configuration space. The method used in this contribution simplifies the analysis of such parallel mechanism without resorting to in-depth geometry analysis and screw theory. Further, a parallel platform which can generate this PRP type of motion is presented. An experimental test is set up based on a 3D printed prototype of the 3-PUP parallel mechanism to detect the inconspicuous translation of the helical motion.

Copyright (c) 2017 by ASME
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