Dynamics of an elastic multibody chain: Part C—Recursive dynamics

In multibody dynamics, and particularly in the robotics field, there are essentially two problems to consider: inverse dynamics and simulation dynamics. In the former problem, the desired trajectory is specmed and me necessary control forces and torques must be determined, the latter is the converse problem and the one of greater interest for elastic multibody systems

Just as the formulation of motion equations for multibody systems can take numerous paths, so too can their solution. The 'standard' approach to inverse and simulation dynamics is to write the equations of motion in toto for the entire system. However, the topological nature of chains can be exploited using the notion of recursion. Recursive methods allow the chain to be considered on a body-by-body basis rather than on a 'global$apos; level. The attractive feature of recursive algorithms is their computational cost, which varies linearly with the number of bodies in the chain. Global methods, on the other hand, are typically cubic in the number of coordinates

In this paper, which builds on the foundation of the inaugural paper in this series, we develop a recursive simulation algorithm for chains of general elastic bodies having arbitrary (rotational and/or translational) interbody constraints