Study on Multibody Dynamics for the Holonomic Systems Possessing 1 Degree of Freedom.

Abstract

For the design support tool of multibody mechanical systems, many formulations and numerical calculation methods are proposed. For example, there are DAE methods using the Lagrange multiplier, ODE methods using coordinate partitioning technic, the penalty methods using the constraint error, etc. These methods can be applied to multi-degrees-of-freedom systems, and the generality is high. In the meantime, small mechanical systems possessing a few degree of freedom with holonomic constraints are not little. In such case, it is convenient that there is the formulation in which analysts can easily make computer programs, even if they do not use the expensive softwares of multibody dynamics. In this paper, I propose the new simulation method for multibody systems possessing 1 degree of freedom with holonomic constraints. It is easy to deduce the equation of motion for that systems by using the proposed method. Newton iteration method is used for the numerical calculation. The stabilization methods for holonomic constraint errors like Baumgarte method and penalty methods are not required, because kinematics, dynamics and numerical integrations are analyzed simultaneously. Finally, we show numerical examples to demonstrate effectiveness of this approach.