Abstract：High nonlinearity and coupling were shown from the dynamic characteristics of dual-arm cooperating manipulators because of the constrained relationship brought by desired task. Therefore, it was difficult to establish dynamical equation with traditional Lagrange equation. Aimed at the dynamics modeling of dual-arm cooperating planar manipulators, a generalized dynamical equation of multi-link planar manipulators was established and proved with traditional Lagrange equation. Then the additional torque and dynamical equation of dual-arm cooperating planar manipulators subject to some desired trajectory were acquired based on the famous Udwadia-Kalaba equation in analytical mechanics field and the above-mentioned generalized dynamical equation of multi-link planar manipulators. The new approach overcomes the disadvantage of obtaining dynamical equation from traditional Lagrange equation by Lagrange multiplier. The stimulation results of the varying law of the joint angles and the motion path of the bar prove that the dynamical equation established by this method conforms to the matter of fact.
刘佳, 刘荣. 双臂协调机械手动力学建模的新方法[J]. 北京航空航天大学学报, 2016, 42(9): 1903-1910.
LIU Jia, LIU Rong. New approach for dynamics modeling of dual-arm cooperating manipulators. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2016, 42(9): 1903-1910.
[1] 熊有伦.机器人技术基础[M].15版.武汉:华中科技大学出版社,1996:89-91.XIONG Y L.Fundamentals of robot techniques[M].15th ed. Wuhan:Huazhong University of Science and Technology Press,1996:89-91(in Chinese).
[2] SANCHEZ-SANCHEZ P,ARTEAGA-PEREZ M A.Simplied methodology for obtaining the dynamic model of robot manipulators[J].International Journal of Advanced Robotic Systems,2012,9(6):700-709.
[3] TARN T J,BEJCZY A K,XUN X.Design of dynamic control of two cooperating robot arms:Closed chain formulation[C]//IEEE International Conference on Robotics and Automation.Piscataway,NJ:IEEE Press,1987,4:7-13.
[4] NAKAMURA J,GHOUDOUSSI M.Dynamics computation of closed-link robot mechanisms with non-redundant and redundant actuators[J].IEEE Transactions on Robotics and Automation,1989,5(3):294-302.
[5] LUH J Y S,ZHENG Y F.Computation of input generalized forces for robots with closed kinematic chain mechanisms[J].IEEE Journal on Robotics and Automation,1985,1(2):95-103.
[6] SMITH D A.Reaction force analysis in generalized machine systems[J].Journal of Manufacturing Science and Engineering,1973,95(2):617-623.
[7] WANG L C T,MING J K.Dynamic load-carrying capacity and inverse dynamics of multiple cooperating robotic manipulators[J].IEEE Transactions on Robotics and Automation,1994,10(1):71-77.
[8] UDWADIA F E,KALABA R E.A new perspective on constrained motion[J].Mathematical and Physical Sciences,1992,439(1906):407-410.
[9] UDWADIA F E,SCHUTTE A D.Equations of motion for general constrained systems in Lagrangian mechanics[J].Acta Mechanica,2010,213(1-2):111-129.
[10] UDWADIA F E,KALABA R E.Explicit equations of motion for mechanical systems with nonideal constraints[J].Journal of Applied Mechanics,2001,68(3):462-467.
[11] UDWADIA F E,KALABA R E.On constrained motion[J].Applied Mathematics and Computation,2005,164(2):313-320.
[12] UDWADIA F E,WANICHANON T.Control of uncertain nonlinear multi-body mechanical systems[J].Journal of Applied Mechanics,2013,81(4):1-11.
[13] UDWADIA F E,WANICHANON T,HANCHEOL C.Methodology for satellite formation-keeping in the presence of system uncertainties[J].Journal of Guidance Control and Dynamics,2014,37:1611-1624.
[14] SCHUTTE A D,UDWADIA F E.New approach to the modeling of complex multi-body dynamical systems[J].Journal of Applied Mechanics,2010,78(2):856-875.
[15] HUANG J,CHEN Y H,ZHONG Z H.Udwadia-Kalaba approach for parallel manipulator dynamics[J].Journal of Dynamic Systems,Measurement,and Control,2013,135(6):1012-1030.
[16] ZHAO H,ZHEN S C,CHEN Y H.Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory[J].Chinese Journal of Mechanical Engineering,2013,26(5):839-850.
2016, Vol. 42 
