The closed-form motion equation of redundant actuation parallel robot with joint friction: an application of the Udwadia–Kalaba approach
- 28 Downloads
The closed-form motion equation of the redundant actuation parallel robot with joint friction is established by an extended application of the Udwadia–Kalaba modeling. Based on the cascading nature of the Udwadia–Kalaba equation, the motion equation of the parallel robot is obtained in a hierarchical manner. The redundant actuation parallel robot is segmented into several leg subsystems, which are connected by the kinematic constraints. The constraint forces between the subsystems can be calculated by the Udwadia–Kalaba equation. In virtue of the derived constraint forces, the explicit joints friction models, described by Coulomb friction and Stribeck friction, are formulated separately. There are no auxiliary variables (such as Lagrange multipliers or pseudo-generalized speeds) needed in the method. The established dynamic modeling technique evades the curse of dimensionality when dealing with Moore–Penrose inverse. A 2-DOF redundant actuation parallel robot is chosen to demonstrate the method.
KeywordsParallel robot Motion equation Udwadia–Kalaba equation Joint friction
Ruiying Zhao is supported by National Natural Science Foundation of China (Grant No. 51605038) and Natural Science Basic Research Plan in Shaanxi Province of China (No. 2017JQ5034). Muxuan Pan is supported by Fundamental Research Funds for Central Universities (No. NJ20160020).
- 7.Li, T.M., Jia, S., Wu, J.: Dynamic model of a 3-DOF redundantly actuated parallel manipulator. Int. J. Adv. Rob. Syst. 13(5), 1–12 (2016)Google Scholar
- 11.Yen, P.L., Lai, C.C.: Dynamic modeling and control of a 3-DOF Cartesian parallel manipulator. IEEE/ASME Trans. Mechatron. 9(3), 390–398 (2009)Google Scholar
- 12.Yiu, Y.K., Cheng, H., Xiong, Z.H., Liu, G.F., Li, Z.X.: On the dynamics of parallel manipulators. In: Proceedings of the 2001 IEEE International Conference on Robotics and Automation, vol. 4, pp. 3766–3711 (2001)Google Scholar
- 13.Abedloo, E., Molaei, A., Taghirad, H.D.: Closed-Form Dynamic Formulation of Spherical Parallel Manipulators by Gibbs–Appell Method. RSI/ISM International Conference on Robotics and Mechatronics. https://doi.org/10.1109/ICRoM.2014.6990964
- 17.Carbonari, L., Battistelli, M., Callegari, M., Palpacelli, M.: Dynamic modelling of a 3-CPU parallel robot via screw theory. Int. J. Mech. Sci. 4(1), 185–197 (2013)Google Scholar
- 23.Shang, W.W., Cong, S., Zhang, Y.X.: Nonlinear friction compensation of a 2-DOF planar parallel manipulator. IEEE/ASME Trans. Mechatron. 18(7), 340–346 (2008)Google Scholar
- 30.Udwadia, F.E., Phohomsiri, P.: Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics. Proc. Math. Phys. Sci. 462, 2097C2117 (2006)Google Scholar
- 34.Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley, New York (2006)Google Scholar