Analytical dynamic model for planar close-chain linkages with alterable length and inertia parameters based on parallel calculation

Abstract

Analytical dynamic model based on the sub model of links and a parallel algorithm for planar close-chain mechanisms, in which lengths and inertia parameters of links can be changed, is established based on Kane dynamic equation and numeric-symbolic approach. The influence of lengths and mass of driving links on driving force/torque are also studied. The close vector is applied in the kinematical analysis of planar close-chain mechanisms and expressions of velocity and acceleration of links are derived. Real-time code of matrix elements of each sub model, in which lengths and inertia parameters of links as well as generalized coordinates are expressed as symbols, the other variables as numeral, are derived off-line. Then the total driving force/torque of planar close-chain mechanisms are obtained by piled add. An optimization method of real-time code based on the parallel algorithm of sub model of links is proposed. The procedures of dynamic modeling and real-time code optimization can be performed off-line, and parallel calculation structure is adopted, therefore on-line calculation time can be reduced greatly, which is of advantage to real-time control of mechanisms. The examples of dynamic simulation are given for illustration.