Abstract
First, screw theory, product of exponential formulas and Jacobian matrix are introduced. Then definitions are given about active force wrench, inertial force wrench, partial velocity twist, generalized active force, and generalized inertial force according to screw theory. After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.
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References
Gong Zhenbang, Wang Qinque, Qian Jinwu,et al., Mechanical Design for Robots[M]. Publishing House of Electronics Industry, Beijing, 1995, 132–190 (in Chinese).
Richard M Murray, Li Zexiang, Sastry S Shankar.A Mathematical Introduction to Robotic Manipulation [M]. Xu Weiliang, Qing Ruiming (transls). China Mechanical Industry Press, Beijing, 1998, 11–101 (Chinese Version).
Brockett R W, Stokes A, Park F. A geometrical formulation of the dynamical equations describing kinematic chains[A]. In: IEEE Robotics and Automation Society (ed).IEEE International Conference on Robotics and Automation[C]. IEEE Computer Society Press, USA, 1993, 637–641.
Park F C. Computational aspects of the product of exponentials formula for robot kinematics[J].IEEE Transactions on Automatic Control, 1994,39(3): 643–647.
Chen Wenliang.Analytical Mechanics[M]. Shanghai Jiaotong University Press, Shanghai, 1991 (in Chinese).
Greenwood D T.Classical Dynamics[M]. Xu Weiliang, Qing Ruiming (transls). Science Press, Beijing, 1982 (Chinese Version).
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Wu-fa, L., Zhen-bang, G. & Qin-que, W. Investigation on Kane dynamic equations based on screw theory for open-chain manipulators. Appl Math Mech 26, 627–635 (2005). https://doi.org/10.1007/BF02466337
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DOI: https://doi.org/10.1007/BF02466337