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2-UPR&2-RPU冗余并联机构动力学与功耗分析
(四川大学 机械工程学院，四川 成都 610065)
Dynamics and Power Analysis of 2-UPR&2-RPU Redundant Parallel Mechanism
(School of Mechanical Eng., Sichuan Univ., Chengdu 610065, China)

Abstract:A novel 2-UPR&2-RPU parallel mechanism with redundance structure was proposed, which has two rotations and one movement (2R1T) degree of freedom. Based on the screw theory, the degrees of freedom and motion characteristics of the mechanism were analyzed, and the correctness of the analysis was verified by the modified G-K formula. By analyzing the constraints of each branch, the reverse solutions of position was solved by establishing the closed-loop vector equations of each branch. The velocity and acceleration of the mechanism were analyzed by the differential transformation method based on symbolic operation, then the velocity Jacobian matrix and the second order influence coefficient matrixes were obtained. On the basis of this, the Jacobian matrix of each branch was also figured out. The dynamics model of the mechanism was constructed by using the virtual work principle based on the kinematics. For the character that the distribution of the active joints’ drive forces was not unique due to the redundant actuation, the driving force and driving power equation were obtained by the method of 2-norm of driving force. Based on this, a calculation program was written for the constructed mathematical model by using MATLAB, and the constructed kinematics and dynamics model were simulated through specific numerical examples. Finally, in order to verify the correctness of the mathematical model constructed, a virtual prototype of the mechanism was established in ADAMS and simulated under the same conditions. The results were compared with those of MATLAB. The simulation results of both were basically consistent, indicating the correctness of the established mathematical model and showing the max errors of driving force of each rod with 0.091%, 1.83%, 1.04%, 1.40%, respectively. The results showed that under the given motion law, the mechanism does not produce rigid impact. At the beginning and the end of the motion, a certain flexible impact will occur. The driving force of each driving rod changes smoothly during the entire movement, and the total work by the method of 2-norm of the driving force is 1 143.2 J.

LIN Guangchun,LIAO Xunbao,ZHAO Rongkuan,CHEN Shichao.Dynamics and Power Analysis of 2-UPR&2-RPU Redundant Parallel Mechanism[J].Advanced Engineering Sciences,2021,53(1):146-154.