Kinematic Modeling And Precision Analysis Of Typical Complex Mechanical Products Based On Meta-action

Based on the meta-action theory,this paper uses the method of multi-body kinematics to abstract and simplify the motion system of complex mechanical products.Then,the kinematic modeling and analysis of complex mechanical products are carried out by combining coordinate transformation method and screw theory,and the motion error modeling method based on meta-action is proposed,which provides theoretical and methodological references for the research of motion and precision of complex mechanical products.The main research contents are as follows:(1)Kinematic modeling and error analysis of the meta-actions and meta-action chains.By using the method of error transfer digraph and coordinate matrix transformation,this paper analyzes the error transfer process in and between the metaaction assembly units,and constructs the error transfer mathematical models.By analyzing the motion process of a single action-action,considering the influence of geometric and assembly errors on the motion performance,the key errors are mapped into the motion parameters,and the complete motion equation of the meta-action is established.Then,according to the motion transfer and coupling relationships,the kinematic model of a meta-action chain is deduced.At the same time,the formation mechanism of motion parameter error of various kinds of element actions is analyzed,and the error evaluation index parameters can be determined.(2)Kinematic modeling and analysis of a series complex mechanical system.In this chapter,the meta-action theory and multi-body kinematics theory are used to abstract and simplify the motion systems of complex mechanical products.The main research object is the mechanical products represented by industrial robots,which only have one motion output to perform tasks.Based on the structural decomposition of "function-motionaction"(FMA),the structure models of multi-body systems(MBS)are constructed.According to the FMA-MBS structure models,kinematic analysis can be carried out from the action layer,the motion layer and the motion system layer.Then,the general mathematical model of the motion chain(motion axis)is expressed in the form of screw index matrix by using screw method,and the expression of the motion mathematical model of joint and mechanical system can be further derived.According to the motion and constraint relationships of each component of the system,the spinor index product of the complex mechanical motion system with multiple degrees of freedom is constructed in the form of product of exponential(POE).(3)Research on kinematics and accuracy of parallel complex mechanical systems.This chapter analyzes the machining motion system of multi-axis CNC machine tools,which consists of several sub motion systems.It constructs the FMA-MBS structure model,kinematics model and three error models of the machine tools.The cutter and workpiece subsystems can be regarded as two independent single complex mechanical motion systems,and its kinematic model can be obtained by the modeling method in Chapter 3.The motion error of a machine tool is the comprehensive result of all the metaactions’ errors.The kinematic models of the subsystems can represent the kinematic accuracy through differential transformation and matrix substitution.Then,the evaluation model of the machining error is derived based on the relationships between the movements and the spatial structures.The mathematical model of the whole machine tool’s machining error is obtained by synthesizing the motion errors of the cutter and workpiece motion systems.An example of a CNC controlled 5-axis machining center is presented to verify our new modeling method.