Performance Analysis Based On Geometry Algebra And Study On Dynamic Characteristics Of 3-UPU Parallel Mechanism

In recent years,the theoretical and experimental research of limited-DOF parallel mechanism is an important research direction and frontier technology in the field of robot.Compared with the 6-DOF parallel mechanism,the limited-DOF parallel mechanism has both constraint space and freedom space due to its structural constraints.Therefore,many properties of the limited-DOF parallel mechanism are related to the form of constraints.In this paper,the performance of 3-UPU parallel mechanism is analyzed by combining the characteristics of motion / force and geometric algebra,aiming to solve the difficult problems of limited-DOF parallel mechanism by combining the computational advantages of geometric algebra.Finally,the dynamic characteristics of the mechanism are analyzed by simulation,and the results of modal,harmonic response and transient kinematics are obtained.The main work is as follows:Taking the 3-UPU parallel mechanism as the research object,the symbolic expression of the motion space of the moving platform is obtained by means of constraint summation.In this method,through the mapping relationship between the motion space and the force space in the screw theory,combined with the expression of the screw in geometric algebra,the expressions of the allowable motion subspace and the binding force subspace at the end of the branch chain are obtained.Using this method to analyze the degree of freedom of the mechanism simplifies the calculation process,and the analysis process can be applied to the singularity analysis.A modeling method of position forward solution based on conformal geometry algebra is proposed.This method obtains the coordinate expression of each point of the moving platform by constructing the geometric entity through the geometric outer product,and obtains the forward position solution of the mechanism by combining the structural features with the trigonometric function.In order to test the performance changes of speed and acceleration in the process of mechanism movement,the simulation of the mechanism is carried out to get the speed fluctuation range when the mechanism is started and the results are obtained.There will be no large fluctuation caused by speed and acceleration in the process of mechanism movement.Finally,the workspace of the mechanism is obtained by polar coordinate search and inverse position solution.Combined with the constraint characteristics and the transfer characteristics in singular configuration,the singularity is defined as constraint singularity and transfer singularity.The lower the index value is,the closer it is to the singular configuration of the mechanism.The stiffness of the mechanism is studied by means of finite element simulation.Firstly,the finite element model of the mechanism is constructed,and the deformation,stress and strain nephogram of the mechanism under the initial configuration are obtained by simulation.Through the analysis,the weak parts of the mechanism are obtained,which provides reference data for the optimization of the mechanism and the improvement of the motion accuracy.Through modal analysis,the natural frequencies and mode shapes of the moving platform at four different heights are obtained.The results show that the natural frequencies of the first three modes are low,and the mechanism needs to be further optimized;The sensitive frequency of the mechanism is obtained by harmonic response analysis,which is of great significance to avoid resonance and fault diagnosis.Then the transient dynamic analysis is carried out to obtain the deformation and transient response of the mechanism under impact load of different heights.It is concluded that the mechanism should avoid the moving platform working in a high position as far as possible,so as to maintain the good dynamic characteristics of the mechanism.