Research On Positive Solution And Mechanics Of 3-RPS Parallel Mechanism

Aiming at the processing requirements of the kind of complex parts’ local sharpening,it is proposed to finish the processing requirements of the parts by using the 3-RPS parallel machine tool.Although parallel prototypes have been developed to enable simple motion,design theory is not yet mature enough.In order to solve the problems of positive solution,stiffness and vibration in parallel machine tools,3-RPS parallel mechanism in parallel machine tool is taken as the research object,and theoretical research of positive solution,statics,dynamics and finite element method are carried out respectively.Firstly,in order to solve the problems of the traditional iterative solution method such as the failure of initial solution and the slow solution,a new hybrid genetic algorithm is proposed to solve the positive kinematics of parallel mechanism.This algorithm can effectively converge to the exact solution by using the effective global search ability of genetic algorithm and the local search ability of quasi-Newton method.The results and simulation show that this algorithm has the advantages of high universality,high precision,good convergence and high solution speed.Secondly,in order to improve the static stiffness performance of the mechanism,the evaluation index and optimization method of the static stiffness of the mechanism are proposed.Based on the Jacobi ratio matrix,the condition number and the global flexibility of the static stiffness matrix,a multi-objective optimization function of the mechanism static stiffness is established.Then the genetic algorithm is used to optimize the size of the mechanism to improve the static stiffness.The examples and simulation results show that the overall static stiffness of the optimized mechanism greatly improves in the working space.Then,in order to establish a complete dynamic model of dynamics,Newton Euler method was chosen as the dynamic modeling method on the basis of the friction of the ball joints,the rotating joints,the ball screws and the accompanying movement of the moving platform.The simplified method of dynamic model is given to improve the real-time control efficiency of the mechanism.MATLAB and Adams simulation verify the correctness of the established dynamic model.Finally,in order to avoid the resonance and reduce the vibration,a three-dimensional solid model of the mechanism was established by PROE,and finite element analysis of the mechanism was carried out by ANSYS Workbench.Through the static analysis,check the strength of the mechanism and find the mechanism stiffness weak link;Through the modal analysis,get the natural frequency and mode of the mechanism,and put forward the method of avoiding the resonance;Through the harmonic response analysis,it is concluded that the mechanism should avoid the sensitive frequency,and ensure that institutions can withstand a variety of harmonic loads of different frequencies,laying a theoretical foundation for the further dynamic design and optimization of the institutions.