3 UPS-RPR Parallel Mechanism Static Stiffness Optimization Design

In recent years,the parallel mechanism is more and more widely used in all kind of fields.The parallel mechanism of less degrees of freedom with its topology structure,not only has the advantages of parallel mechanism,but also the driver is relatively less than parallel mechanism of the six degrees,and the control is simpler.So these advantages further expand its application fields.Researches on it are of great significance.In this dissertation,a 3UPS-RPR parallel mechanism is presented,and the kinematics,statics and stiff'ness of the mechanism are studied.The following works have been accomplished:Firstly.introduce the structure of the 3UPS-RPR parallel mechanism.The freedoms of this mechanism are calculated by Kutzbach-Grubler formulation.The Euller matrix of the mechanism is constructed.The kinematic inverse solution equation of the mechanism is established by combining the exponential product formula.On the basis of the inverse kinematic solution obtain the working space of this mechanism;The complete Jacobian matrix of the mechanism is solved based on the screw theory.Based on the principle of virtual work.the mapping between the force screw in the joint space and the operation space is established.The relationship between the evalution index and the geometrical parameters of the mechanism is analyzed,all these analysises lay foundation for the optimal design of the mechanism.On the basis of the jacobian matrix of whole deformation using principle of virtual work,in the case of thinking of the elastic deformation caused by constraints.the stiffness matrix of the end of all branched chains are constructed.Based on this,the static stiffness model of the 3UPS-RPR parallel mechanism is established.Stiffness distributions at the workspace are gained through the simulation.According to the principle of orthogonal transformation,stiffness matrix will be converted diagonal matrix in the mainly stiffness direction and determine the direction of the principal stiffness which lay foundation for the application of this mechanism.Stiffness and force transfer performance as the optimization goal,and genetic algorithm is used to multiple parameters optimization,organization optimization,By comparing the performance index before and after optimization,find that using the optimized structure parameters to enhance the both aspects performance.