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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June 2018
Research-Article
Compositional Submanifolds of Prismatic–Universal–Prismatic and Skewed Prismatic–Revolute– Prismatic Kinematic Chains and Their Derived Parallel Mechanisms
Xinsheng Zhang,
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
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
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Pablo López-Custodio,
Pablo López-Custodio
Centre for Robotics Research,
King's College London,
London WC2R 2 LS, UK
e-mail: pablo.lopez-custodio@kcl.ac.uk
King's College London,
London WC2R 2 LS, UK
e-mail: pablo.lopez-custodio@kcl.ac.uk
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Jian S. Dai
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
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
Search for other works by this author on:
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
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
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
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. Jun 2018, 10(3): 031001 (9 pages)
Published Online: March 1, 2018
Article history
Received:
October 12, 2016
Revised:
August 23, 2017
Citation
Zhang, X., López-Custodio, P., and Dai, J. S. (March 1, 2018). "Compositional Submanifolds of Prismatic–Universal–Prismatic and Skewed Prismatic–Revolute– Prismatic Kinematic Chains and Their Derived Parallel Mechanisms." ASME. J. Mechanisms Robotics. June 2018; 10(3): 031001. https://doi.org/10.1115/1.4038218
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