Constraint-plane-based synthesis and topology variation of a class of metamorphic parallel mechanisms
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DOI 10.1007/s12206-014-0931-7
Constraint-plane-based synthesis and topology variation of a class of metamorphic parallel mechanisms†Dongming Gan1,*, Jian S Dai2, Jorge Dias1,3 and Lakmal Seneviratne1,2 1
Robotics Institute, Khalifa University of Science, Technology & Research,127788, Abu Dhabi, UAE School of Natural and Mathematical Sciences, King’s College London, University of London, London WC2R2LS, UK 3 Institute of Systems and Robotics, University of Coimbra, Faculty of Science and Technology, Coimbra 3000-315, Portugal 2
(Manuscript Received July 10, 2013; Revised May 4, 2014; Accepted June 22, 2014) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract This paper investigates various topologies and mobility of a class of metamorphic parallel mechanisms synthesized with reconfigurable rTPS limbs. Based on the reconfigurable Hooke (rT) joint, the rTPS limb has two phases which result in parallel mechanisms having ability of mobility change. While in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane which is used to demonstrate different topologies of the nrTPS metamorphic parallel mechanisms by investigating various relations (parallel or intersecting) among the n constraint planes (n = 2,3,..,6). Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals mobility and redundant geometric conditions of the mechanism topologies. By altering the limbs into the non-constraint phase without constraint plane, new mechanism phases are deduced with mobility change based on each mechanism topology. Keywords: Constraint plane; Mobility change; Parallel mechanism; Reconfiguration; Topology variation ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction Metamorphic parallel mechanisms (MPMs) [1] are a class of mechanisms that possess adaptability and reconfigurability to change permanent finite mobility based on topological structure change. Metamorphic parallel mechanisms keep the advantages of traditional parallel mechanisms in terms of high load-carrying capacity, good positioning accuracy and low inertia [2] but with reconfiguration by phase changes. Each phase of a metamorphic parallel mechanism is the same with a traditional parallel mechanism. Thus metamorphic parallel mechanisms can replace traditional ones in real applications with benefits of configuration change for workspace requirements and operation mobility change with energy saving. For example, in industri
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