A generalized recursive formulation for constrained mechanical system dynamics

Recursive formulas have been effective in solving the equations of motion for large scale constrained mechanical systems. However, derivation of the formulas has been limited to individual terms in the equations of motion, such as velocity, acceleration, and generalized forces. The recursive formulas are generalized in this paper. The velocity transformation method is employed to transform the equations of motion from Cartesian to the joint spaces. Computational structure of the equations of motion in the joint space is carefully examined to classify all necessary computational operations into several categories. The generalized recursive formula for each category is then developed and applied whenever such a category of computation is encountered. Since the velocity transformation method yields the equations of motion in a compact form and computational efficiency is achieved by generalized recursive formulas, the proposed method is not only easy to implement but is also efficient. A library of generalized recursive formulas is developed to implement a dynamic analysis algorithm using backward difference formulas (BDF) and the relative generalized coordinates. Numerical examples are given to demonstrate the efficiency of the proposed method.