Handling of Constraints in Multibody Systems Dynamics

Abstract

In the preceding chapters, treatment of the generalization of kinematics and the equations of motion was done in the presence of no constraints. In general, we assumed that the system is not subjected to any external condition or forces restricting its global motion, in which case the generalized coordinates are looked upon as the independent coordinates of the system. If a multibody system becomes subjected to a kinematic or geometric condition during the cycle of its motion, the multibody system is said to be constrained. If the dynamical system has n independent generalized coordinates and m constraint equations, the total number of degrees of freedom is given by n — m. In this chapter, we study the dynamics of multibody systems in the presence of constraints and explore various techniques used to develop the proper governing equations of motion. Dynamics of multibody system requires some intuition where one needs to be able to differentiate between an open treelike system and identify the constraints. Conditions that must be imposed on rigid bodies are usually treated through the generalized forces and closed loops, prescribed motions and any geometrical or kinematical constraints are treated through the use of additional constraint equations to be solved together with the equations of motion.