Dynamic modeling of constrained planar multibody systems: A case of lower limbs rehabilitative robot

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.