Dynamic Analysis And Simulation Of 3-PRS Parallel Manipulator Based On Screw Theory

Parallel robots have been widely used in fields requiring high rigidity,high precision and large load without large working space.The high-precision control of parallel robots is the key technology for the development of mechanical disciplines.The dynamics analysis provides a theoretical basis for the precise control of parallel robots.It is of great significance to use the appropriate basic theory to establish dynamic models and use modern computers for calculation.Based on the subject of the project team,this paper designs a three-degree-of-freedom 3-PRS parallel robot to complete the task of picking up objects in space.In this paper,the kinematics and dynamics characteristics of the parallel mechanism are analyzed based on the screw theory,and the dynamics model and analysis of the parallel robot with flexible members are carried out.The main research contents are as follows:(1)Establish a solid model of 3-PRS parallel robot and briefly analyze its structure.Introduce the screw theory and the exponential product equation,and establish the inertial coordinate system and the tool coordinate system for the 3-PRS parallel mechanism.Combining the spin theory with the kinematics modeling of the single-branched chain of the parallel mechanism,combined with the coordinate transformation matrix to obtain the kinematics model of the remaining branches,and assembling the kinematics model of the whole machine.Using the traditional mathematical method,the Jacobian matrix of the 3-PRS parallel robot is obtained.Based on the screw theory,the Jacobian matrix of the 3-PRS parallel robot is obtained by using the screw and the motion reverse spiral,and the superiority of the screw theory is compared.The singular configuration of the 3-PRS parallel robot is analyzed by combining the Jacobian matrix obtained by the screw theory.A simulation model of the 3-PRS parallel mechanism was built using the Sim Mechanics tool in MATLAB and calculated.The machine end effector position data obtained by software simulation is compared with the calculated kinematics model to verify the correctness of the model.(2)Introduce the Kane equation combined with the screw theory,and analyze the dynamics research method of the parallel robot.Based on the Kane equation combined with the screw theory,the generalized principal dynamics and generalized inertial force of the3-PRS parallel robot are obtained,and a single-branch dynamic model is established.Using the coordinate transformation matrix,the dynamic model of the remaining branches is established,and the whole machine dynamics model is established.Numerical simulations of established kinetic models were performed using numerical calculation software.Find relevant parameters and analyze them.The 3-PRS parallel manipulator was simulated by Adams software,and the correctness of the model was verified by comparing the mathematical model with the simulation results of the software.(3)The finite element method and Lagrange equation are used to establish the elastic dynamics equation of a 3-PRS parallel robot with flexible members.The flexible members of the parallel robot are divided into elements,the kinetic energy and deformation energy models of the elements are established,the relationship between the elements is analyzed,and the dynamic equations of the elements are established by using Lagrange equation.Based on the analysis of the relationship between the unit and the branch chain,the elastic dynamic equations of the branch chain are assembled according to the kinematic and dynamic constraints of the parallel robot system,and the elastic dynamic equations of the flexible system are obtained.The elastic dynamic equations are programmed by numerical software.The kinematics and dynamics of the 3-PRS parallel robot were analyzed and the relationship between the kinematics and dynamics and the related basic parameters.