Screw algebra based kinematics analysis and its uses in reconfiguration recognition of mechanisms

• Main Author: Zhang, Xinsheng
• Other Authors: Iliopoulos, Costas ; Dai, Jian
• Published: King's College London (University of London) 2018
• Subjects: 004
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.739994

Reconfigurable mechanisms can change their motion branches or topologies when constraint singularity occurs, and this phenomenon of reconfiguration leads to bifurcation or multi-furcation of mechanisms. Recognising reconfiguration in mechanisms and identifying the corresponding geometrical constraints remain unsolved in the field of mechanism theory and have raised much interest of investigation from 1990s. This dissertation uses the properties of screw algebra and Lie algebra to establish a method of modelling and detecting bifurcation and multi-furcation in reconfigurable mechanisms at singularity configurations. Based on the fundamentals of the screw algebra, this method establishes an algebraic way of modelling the kinematics of mechanisms and the variations of screw systems in which the screws have the same pitch. The screw algebra based method is extended to the scope of Lie group, where this dissertation uses compositional manifolds to explore the feasible finite displacements of reconfigurable mechanisms. The dissertation starts from investigating the screw dependency based on α- and β-planes generating hyperquadrics in the 5-dimensional projective space. Projective geometry and matrix operation are adopted towards the situation where a non-zero pitch is involved in a screw system. Screw systems are related to hyperquadrics in five-dimensional projective space by constructing projective transformations. Following the screw dependency investigation based on screw algebra, this dissertation examines high-order kinematic analysis of mechanisms by implementing a recursive method of Lie bracket computation of screws and such a method provides a compact description for kinematic models of mechanisms with integrating the bilinear form representation of kinematic constraints of a derivative queer-square mechanism. This method allows local analysis of mechanisms at any configurations including singularity configurations. Specifically, the research integrates the coefficient matrix of first-order kinematic analysis and the bilinear form matrix of second-order kinematic analysis which makes it possible to identify geometrical constraints when dealing with complex mechanisms. The dissertation then explores the relationship between screw algebra and Lie group. In such a way, the method of identifying finite displacements in reconfigurable mechanisms is investigated. The research explored the traditional PRP kinematic chain producing the planar motion subgroup SE(2) to a relatively generic kinematic chain in which the prismatic-joint direction is not necessary to be perpendicular to the revolute-joint axis, and revealed the equivalent displacement manifold, leading to the discovery of a pseudo-helical motion with a variable pitch of the particular PRP chain. Throughout the dissertation, the screw algebra based approach of kinematics analysis of mechanisms is proven effective and compact in representing screw-system variations, kinematic constraint modelling of mechanisms at singularity configuration, computational submanifolds analysis of mechanisms, Jabobian matrix construction of reconfigurable mechanisms, and recognition of motion branches using these fundamental theoretical tools. This thesis investigates the properties of screw systems within the context of screw algebra and applies the screw algebra based kinematics to modelling and motion-branch recognising of reconfigurable mechanisms.