Type Synthesis And Transformation Configuration Analysis For Reconfigurable Parallel Mechanisms Based On Lie Group Theory

With development of productivity and the innovation of engineering technology,a mechanism is required to have the function of self restruction and reconfiguration and "one machine with multiple functions" to meet the requirements of complex works.Reconfigurable mechanism has been developed for more than 15 years since the first International Conference on Reconfigurable Mechanisms and Robots,but the principle of mechanism evolution and bifurcation remain to be studied.The purpose of this thesis is to study the bifurcation principle of reconfigurable parallel mechanisms,take controllable singularities as the starting point,use Lie groups and Lie algebras and differential manifolds as the main tools,and take the type synthesis of reconfigurable parallel mechanisms as the main line.The transformation configuration principle of the reconfigurable parallel mechanism is proposed,the principle of mechanism evolution and bifurcation are revealed,and the reconfigurable parallel mechanism that realizes the switching of multiple motion branches is synthesized.The main contents of this thesis are given as follows:(1)Based on the characteristics of motion branch represented by Lie subgroups and submanifolds,according to the case where the intersection of two Lie subgroups or submanifolds is an identity element or a non-identity element,the theory of transformation configuration space for reconfigurable parallel mechanisms is revealed,and the conditions of transformation configuration space are discussed.Under the conditions,a method of constructing transformation configuration space is proposed,which provides a theoretical basis for the reconfigurable parallel mechanism to realize the mutual switching of two motion branches.Then,using the kinematic bond and compositional submanifolds,motion representation of the platform of a reconfigurable parallel mechanism is studied,and the motion principle of a reconfigurable parallel mechanism is revealed.Finally,the conclusions are extended to the case with multiple motion branches.(2)Based on the principle of configuration transformation of submanifold switching,a new method for synthesis of metamorphic parallel mechanisms is proposed to synthesize metamorphic parallel mechanisms to realize the transformation between1R2 T and 2R1 T.Taking the motion generators of Lie subgroup and submanifold as the starting point,using the quotient operation of submanifold as the tool,and the switching principle of submanifold subchains as the guidance,metamorphic joints with motion switching are synthesized.According to the relative position relationship between the rotation axes and links of the metamorphic joint,three metamorphic subchains that can change the motion configuration to realize different motions are synthesized,and the metamorphic parallel mechanism is synthesized to realize the transformation between the 1R2 T and the 2R1 T.By analyzing the motion and constraint relationship between subchains and moving platform,the feasibility of the subgroup and submanifold method to synthesize the metamorphic parallel mechanism is further verified.(3)Based on the theory of transformation configuration space,the bifurcation principle of a reconfigurable parallel mechanism is revealed,the transformation conditions of configuration space are elaborated,the theoretical basis of configuration switching of a reconfigurable parallel mechanism is established.Reconfigurable parallel mechanisms with planar and spherical motion branches are synthesized,which provides guidance method for type synthesis of reconfigurable parallel mechanisms.Based on the motion representation of a reconfigurable parallel mechanism,the switching conditions of motion branches are studied,the common motion of subgroup motion generators is excavated,and the series subchains with spherical and Hooke joint motion links are synthesized by combining the different forms of submanifold generators.Furthermore,reconfigurable parallel mechanisms with equal subchains are synthesized to realize the switching between two motion branches in singular configuration space.(4)Compared with the reconfigurable parallel mechanism with two motion branches,the reconfigurable parallel mechanism with three motion branches has a more complex structure,which makes type synthesis of such mechanisms more difficult.Based on the Lie subgroup and submanifold method,switching conditions of three motion branches are studied,and reconfigurable modular submechanisms are designed.A reconfigurable parallel mechanism with switching between three motion branches SE(2),SO(3)and X(z)is synthesized.First,based on the principle of submanifold configuration switching,two reconfigurable double four-bar modular submechanisms are synthesized to satisfy the conditions of trifurcated motion switching.According to bifurcation characteristics of each reconfigurable double four-bar modular submechanism,the platform of the reconfigurable parallel mechanism can be switched among three motion branches.Second,the reconfigurable double four-bar modular submechanisms are units constituting the reconfigurable series subchain and the reconfigurable parallel mechanism.By changing the configuration of the motion branch of the reconfigurable double four-bar modular submechanisms,the configuration of the reconfigurable series subchain and the reconfigurable parallel mechanism can be transformed.The switching conditions of three motion branches provide a theoretical basis for type synthesis of reconfigurable parallel mechanisms with multi-furcated motion.