Research Papers

Compositional Submanifolds of Prismatic–Universal–Prismatic and Skewed Prismatic–Revolute– Prismatic Kinematic Chains and Their Derived Parallel Mechanisms

[+] Author and Article Information
Xinsheng Zhang

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

Pablo López-Custodio

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

Jian S. Dai

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

Manuscript received October 12, 2016; final manuscript received August 23, 2017; published online March 1, 2018. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 10(3), 031001 (Mar 01, 2018) (9 pages) Paper No: JMR-16-1303; doi: 10.1115/1.4038218 History: Received October 12, 2016; Revised August 23, 2017

The kinematic chains that generate the planar motion group in which the prismatic-joint direction is always perpendicular to the revolute-joint axis have shown their effectiveness in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the standard prismatic–revolute–prismatic (PRP) kinematic chain generating the planar motion group to a relatively generic case, in which one of the prismatic joint-directions is not necessarily perpendicular to the revolute-joint axis, leading to the discovery of a pseudo-helical motion with a variable pitch in a kinematic chain. The displacement of such a PRP chain generates a submanifold of the Schoenflies motion subgroup. This paper investigates for the first time this type of motion that is the variable-pitched pseudo-planar motion described by the above submanifold. Following the extraction of a helical motion from this skewed PRP kinematic chain, this paper investigates the bifurcated motion in a 3-prismatic–universal–prismatic (PUP) parallel mechanism by changing the active geometrical constraint in its configuration space. The method used in this contribution simplifies the analysis of such a parallel mechanism without resorting to an in-depth geometrical analysis and screw theory. Further, a parallel platform which can generate this skewed PRP type of motion is presented. An experimental test setup is based on a three-dimensional (3D) printed prototype of the 3-PUP parallel mechanism to detect the variable-pitched translation of the helical motion.

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Grahic Jump Location
Fig. 1

PRP chain and the related submanifolds

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Fig. 2

Geometrical structures of the PRP chain with a tilting angle and the PRH chain: (a) PRP chain with a tilting angle α and (b) PRH kinematic chain

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Fig. 3

The 3-DOF PRP-Schoenflies parallel mechanism

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Fig. 4

The PRP chain extracted from pivoting limb that is limb 1 and its equivalent revolute–prismatic–revolute chain

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Fig. 5

The Lie subgroups in limb 1

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Fig. 6

The PRP chain with a tilting angle extracted from limb 2

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Fig. 7

Feasible displacements in motion branch A: (a) home configuration (see Sec. 8); (b), (c) from the test setup in Sec. 7, the platform are performing pure rotation, without any translation along x- and y-axis

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Fig. 8

Feasible displacements in motion branch B: (a) home configuration (see Sec. 8); (b), (c) the photos only illustrate the rotation of the platform, and the translation of the helical motion is to be detected in Sec. 7

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Fig. 9

Bifurcated motion and constraint singularity in the 3-PUP

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Fig. 10

The experimental environment for detecting the translation of the helical motion



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