Research On Design Theory And Methodology Of A Class Of 2R1T 3-DOF Parallel Mechanisms

This dissertation deals with the theory and methodology for the kinematic design of a class of 2R1T 3-DOF parallel mechanisms, including Jacobian matrix and performance index, dimensional synthesis, forward kinematics, accuracy analysis and synthesis. The following contributions have been made.The constructing principles of Jacobian matrix are analyzed. Then a general model of full 6×6 Jacobian matrix for sub-6 parallel mechanisms is developed using the constraining conditions, which contains the dimensional information affecting the general errors of the end-effector. Based on such model, the ratio of the limb error onto the platform pose accuracy is proposed to be a performance index by using the characteristics of Rayleigh quotient.By taking 3-U(-|P)S/PU and 3-(-|P)US/PU mechanisms as examples, a methodology for the dimensional synthesis is presented on the basis of the development of the full 6×6 Jacobian matrix. In this method, the performance index is to be optimized in a global sense in conjunction with taking into account a set of appropriate mechanical constraints. Examples are given to illustrate the routine of the optimization. The results show that the 3-PUS/PU mechanism has little better kinematic performance in comparison with the 3-UPS/PU mechanism.Forward kinematics analysis of the 3-U(-|P)S/PU mechanism is carried out using analytical method, compared with that of the 3-PUS/PU mechanism. It shows that the forward kinematics problem of the 3-U(-|P)S/PU mechanism is similar to that of the 3-PUS/PU mechanism in terms of formulation and solution.The error mapping functions of the 3-UPS/PU and 3-PUS/PU mechanisms are formulated which allows the geometric error sources affecting the uncontrollable errors of the movable platform to be identified by using method of vector chain. It can be concluded that the uncontrollable errors of the mobile platform are primarily dominated by the errors of the proper-constraint limb. Based on the error models, the accuracies of the mechanisms are evaluated throughout the task workspace. It shows that for the identical task workspace, the accuracy of the 3-(-|P)US/PU mechanism is little better than that of the 3-U(-|P)S/PU mechanism.The effects of the geometric error sources on the uncontrollable errors of the 3-UPS/PU and 3-PUS/PU mechanisms are discussed by means of the sensitivity analysis. Consequently, a novel approach for accuracy synthesis is presented. Such method can be simply depicted as follows: a mathematical model of optimization for accuracy synthesis is established by taking accuracy of connecting limbs and joints as design variables, a properly simplified sensitivity index as weight and the sum of the weighed design variables as a target function, and making position and pose errors within the design criterion.The accuracy synthesis is carried out using genetic algorithm. It concludes that the 3-U(-|P)S/PU and 3-PUS/PU mechanisms have little difference on the general tolerances of the parts provided that they share identical task workspace.The outcome of this dissertation has provided a complete theoretical package for the development of the 3-UPS/PU and 3-PUS/PU mechanisms. And it's also suitable to the development of some others similar parallel mechanism.