A Symbolic Analysis of the Minimum Dynamic Parameters for the Closed-Link Manipulator using Computer Algebra Software

This paper presents a symbolic analysis method of the minimum set of dynamic parameters for general closed-link manipulator by means of the computer algebra software. This method allows us to obtain all the minimum dynamic parameters (MDP) explicitly and systematically in most cases. A key step is to determine fundamental functions that are necessary and sufficient to express the coefficient matrix of dynamic parameters. The linear independence of column vectors of the coefficient matrix is tested by using fundamental functions and the dynamic parameters are regrouped based on the linear independency. The paper also discusses a sufficient condition in which the dynamics of the closed-link mechanism can be considered to be equivalent to that of the serial-link mechanism. To illustrate the merits of the new method, the authors also examined the MDP of some closed-link mechanisms, using the computer algebra software called“Maple V.”