Abstract
An explicit equation of motion for constrained systems, called the Udwadia-Kalaba equation, opens up a new way of dynamic modeling of constrained multibody systems, which is accomplished in a straightforward and novel three-step process. However, constraint violation arises from violation of the lower-order constraint equations because the aforementioned equations incorporate only the acceleration level constraints. There are two methods, Baumgarte stabilization method (BSM) and modified method, are implemented to realize the constraint violation suppression. The comparison of the BSM and the modified method is provided, based on numerical simulations for a sample constrained system that represents a lower limbs rehabilitative robot with continuous passive motion for therapy and rehabilitation. The results of numerical simulation obtained by the modified method are superior to that obtained by BSM, which confirms the numerical effectiveness and accuracy of the explicit solution based on the modified method to the constrained planar multibody systems.
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Recommended by Associate Editor Kyoungchul Kong
Yaru Xu is currently a Ph.D. candidate in the School of Mechanical Engineering and Automation at Beihang University, China. Her research interests are in the area of multibody dynamics and rehabilitative robots.
Rong Liu received his Ph.D. in the School of Mechanical Engineering and Automation from Beihang University, China, in 1996. He is currently a Professor of School of Mechanical Engineering and Automation, Beihang University. His main subjects are multibody dynamics, robotics and MEMS.
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Xu, Y., Liu, R. Dynamic modeling of constrained planar multibody systems: A case of lower limbs rehabilitative robot. J Mech Sci Technol 32, 3389–3394 (2018). https://doi.org/10.1007/s12206-018-0642-6
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DOI: https://doi.org/10.1007/s12206-018-0642-6