Modeling and simulation of robotic systems with closed kinematic chains using the virtual spring approach

The dynamic simulation of robotic or mechanical systems with closed kinematic chains using the virtual spring approach is presented in this paper. This approach uses virtual springs and dampers to include the kinematic constraints thereby avoiding the solution of differential-algebraic equations. A special advantage of this approach is that it leads to a completely decoupled dynamic model which is ideal for real-time dynamic simulation using multi-processor computers. Examples illustrating the approach are given and include the four-bar mechanism with both rigid and flexible links as well as the six-degree-of-freedom Gough-Stewart platform. Simulation results are given for these mechanisms. The results achieve a good agreement with the results obtained from other conventional approaches.