A Generalized Recursive Coordinate Reduction Method for Multibody System Dynamics

Th e method of recursive coordinate reduction (RCR) off ers solutions to the forward problem of multibody dynamics at a cost in which the number of operations is linear in both the number of generalized coordinates, n, and the number of independent algebraic constraints, m (e.g., O(n + m)). However, the RCR is presently restricted in applicabil- ity (albeit broad) and susceptible to formulation singularities. Th is article develops two methods for avoiding formulation singularities as well as a recursive general coupled loop solution that extends the RCR to the complete set of multibody systems. Application of these techniques are further illustrated with a special fi ve-bar linkage. Th e existing RCR coupled with these developments constitute a generalized recursive coordinate reduction method that should be used in place of the traditional "O(n)" constraint technique (truly O(n + nm² + m³)) for superior O(n + m) computational performance.