Abstract
This paper presents an efficient algorithm for multibody systems with closed loops. In most simulators for analysis of mechanical systems, a dynamic model is made by constraint equations in Cartesian coordinates. However in this way, such modeling requires many variables and long CPU time. As a solution of this problem, we have developed an efficient recursive formulation of dynamics of multibody systems by relative coordinates and partial velocity. The simulation systems based on this algorithm proceeds computation as follows: Firstly, Graph theory is applied to characterize the topology of mechanical systems and cut some joints to open the closed chain systems. Secondly, the computational sequences for formulation is defined along the branches. Finally, an order n(O(n)) algorithm is introduced to reduce the number of arithmetic operation. This algorithm shows that it can successfully solve the equation of motion much faster than Cartesian coordinates formulation.
