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Synthesis and Construction of a Family of One-DOF Highly Overconstrained Deployable Polyhedral Mechanisms (DPMs)

[+] Author Affiliations
Guowu Wei, Jian Dai

King’s College London, London, UK

Paper No. DETC2012-70918, pp. 615-626; 12 pages
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4503-5
  • Copyright © 2012 by ASME


This paper presents a family of one-DOF highly overconstrained regular and semi-regular deployable polyhedral mechanisms (DPMs) that perform radially reciprocating motion. Based on two fundamental kinematic chains with radially reciprocating motion, i.e. the PRRP chain and a novel plane/semi-plane-symmetric spatial eight-bar linkage, two methods, i.e. the virtual-axis-based (VAB) method and the virtual-centre-based (VCB) method are proposed for the synthesis of the family of regular and semi-regular DPMs. Procedure and principle for synthesizing the mechanisms are presented and selected DPMs are constructed based on the five regular Platonic polyhedrons and the semi-regular Archimedean polyhedrons, Prism polyhedrons and Johnson polyhedrons. Mobility of the mechanisms is then analysed and verified using screw-loop equation method and degree of overconstraint of the mechanisms are investigated by combing the Euler’s formula for polyhedrons and the Grübler-Kutzbach formula for mobility analysis of linkages.

Copyright © 2012 by ASME



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