Configuration Synthesis And Analysis Of 3-DOF Parallel Mechanism Based On Lie Group Theory

Due to the advantages of large stiffness,high precision and compact structure,parallel mechanisms are more and more widely used.But as a typical representative of"knowledge-intensive" institutions,topological design of parallel mechanism is the most challenging in the design of mechanical products and the most can reflect the core content of original traits and inventiveness,so for the parallel mechanism synthetically theory research,not only to improve the mechanical product design,innovation and competitiveness also has the very vital significance,but also can enrich the existing theories,so as to make the theory instruction practice more convenient.Because the configuration synthesis problem of parallel mechanism is very challenging,the existing configuration synthesis theory either cannot use the analytical method to study the configuration synthesis problem of parallel mechanism,or the existing method is too complicated,which makes the calculation very difficult.Therefore,based on the matrix Lie group,this Theses proposes an algebraic analytic method for configuration synthesis of parallel mechanisms with finite motion.Then,the kinematics and error accuracy of 3-RRR parallel mechanism are analyzed based on the Lie group,so as to form a relatively complete configuration synthesis and analysis method.The content of this paper consists of the following aspects:In the aspect of configuration synthesis of parallel mechanism,it is p proposes an algebraic analytic method for configuration synthesis of parallel mechanisms with finite motion.through the expansion of the basis,the resulting branched chain twist ?Mi is called the augmented type of the end-effector twist ?M,so these augmented type twist will constitute the standard branched chain twist ?Mi.these augmented twist ??se(3)are mapped to e???SE(3)by exponential mapping,thus describing the motion of the parallel mechanism at the finite motion level.Then,through the matrix Lie group e???SE(3),the equivalent replacement of types or exchange of kinematic pairs is carried out for each kinematic pairs generating finite motion.Therefore,six principles for the configuration synthesis of branched chains are given by using matrix lie groups,and these six principles are applied to the motion equivalent transformation of these branched chains with finite motion,so as to obtain the motion equivalent branch chains of augmented branched chains.The topological configuration of parallel mechanism is obtained by the intersection operation of these branch chains.Based on the configuration synthesis method proposed in chapter 2,a total of 72 kinds of parallel mechanisms branched chains with three rotational degrees of freedom?404 kinds of parallel mechanisms branched chains with two rotational degrees of freedom and one translational degree of freedom,and 90 kinds of parallel mechanisms branched chains with three translational degrees of freedom are synthesized.Because it is found that a parallel mechanism with two degrees of translational and one degree of rotational freedom can be derived from a parallel mechanism with three degrees of rotational freedom,it is only necessary to study a parallel mechanism with three degrees of rotational freedom.The kinematics model of 3-RRR parallel mechanism was established by using lie group theory,and then the velocity and acceleration of 3-RRR parallel mechanism were analyzed.Finally,the correctness of the model was verified by simulation analysis based on matlab and creo.Then,based on the above model and the method proposed by Meng and Li,the error model of 3-RRR parallel mechanism was established by using the Lie group theory to calculate and analysis the pose error of the end-effector.