Analytical Fully-Recursive Sensitivity Analysis for Multibody Dynamic Chain Systems

This paper presents a novel fully recursive method, a direct differentiation based approach, which facilitates first-order sensitivityanalysis in optimal design problems involving multibody dynamic systems. A state space O(n) dynamic analysis algorithm based on avelocity space projection method, as promoted by Kane [18], forms the foundation of the underlying formulation. This algorithm cansignificantly reduce the massive number of mathematical and associated computational operations involved in explicitly generatingand solving the sensitivity equations. This benefit is particularly evident for systems involving a combination of many state variablesand design parameters. The development presented in this paper focuses on chain systems to illustrate the recursive nature of thealgorithm. The computational efficiency and solution accuracy of the presented algorithm are investigated through the proceduresapplication to the simulation and design sensitivity determination of spatial chain systems involving 2, 4, 6, ..., 24 degrees offreedom, as well as a simple planar double pendulum.