Kinematics And Static Stiffness Modeling And Analysis Of A New Three-degree-of-freedom Parallel Mechanis

This article closely combines the major needs of large structural parts for high-end processing equipment,taking the main mechanism R(RPS&RP)-2UPS three-degree-offreedom parallel mechanism in a new type of five-degree-of-freedom TRIFREE hybrid robot as the object,studying the kinematics and static stiffness parameterized modeling method of the mechanism,as well as the construction method of performance evaluation index deeply,and revealing the change law of the kinematics and stiffness performance of the mechanism with the design parameters.The full text has achieved the following results:In the aspect of kinematics modeling and analysis,based on the structural characteristics of the new three-degree-of-freedom parallel mechanism,the analytical expression of the position inverse solution is derived by the vector method.A forward solution method that can avoid solving the nonlinear equations and obtain the end position from the joint variables of the mechanism is proposed,and then it is used to search for the reachable space boundary of the end point of the mechanism,based on this,the task space and the task space/ mechanism volume ratio were defined,and the relationship between the task space parameters and the mechanism scale parameters was established;The mapping relationship between the speed of the driving branch chain joint and the end point speed is established,and based on the singular value theory,a set of indexes that can be used to evaluate the speed transmission performance of the pose coupling mechanism is proposed.On this basis,the law of the influence of key scale parameters on task space/mechanism volume and speed transmission performance is revealed,and the feasible range of parallel mechanism is obtained by taking speed transmission performance,space utilization and avoiding geometric interference as constraints,Providing a theoretical basis on the kinematics level for the size parameters optimization of the mechanism.In terms of static stiffness modeling,a static stiffness modeling method of parallel mechanisms based on the principle of sub-structure deformation and superposition is proposed.This method can simplify the stiffness modeling of the parallel mechanism to the modeling of the flexibility matrix of each sub-structure,which can effectively solve the problem of static stiffness modeling of the parallel mechanism with complex structure and the total deformation of the end cannot be obtained directly.In this process,the concept of a narrow flexibility matrix was proposed to solve the problem that the branch chain stiffness matrix is not full of rank.When modeling the stiffness of each component,a U-pair static stiffness modeling method that considers the boundary conditions of the rotational degree of freedom,and a stiffness modeling method of variable cross-section members based on 3 nodes and 2 elements are respectively proposed,which can improve the accuracy of the stiffness modeling of parts.The built stiffness model explicitly expresses the mapping relationship between the dimensions and structural parameters of various parts and the static stiffness of the whole machine,which can provide a strong theoretical basis for the detailed design and optimization of the subsequent mechanical structure.In terms of static stiffness analysis and optimization,first of all,using the knowledge of structural mechanics,the relationship between the structural parameters of each component and its stiffness characteristics is obtained,and then a parameterized stiffness model of the whole machine is established.,and its correctness is verified by the finite element method under typical poses.Secondly,the performance index that can evaluate the linear stiffness characteristics and angular stiffness characteristics of the whole machine is proposed,and then the influence law of the dimension parameters and the section parameters of the parts on the stiffness performance of the whole machine is revealed;Based on the sensitivity analysis of the stiffness of the whole machine to the stiffness of each part,complete the optimized design of each part,taking the cross-section parameters of the lead screw and the telescopic rod as an example,the optimization design method of the structural parameters based on the optimal static stiffness performance is given in detail.The result shows that the design method proposed in this paper effectively improves the stiffness performance of the whole machine.