Dynamic performances analysis of hybrid press based on dependent generalized coordinates

A kind of multi-link hybrid press mechanism is brought forth. It adopts three motors as actuations to fulfill the single degree of freedom output of end effector. For hybrid press mechanism, the forward kinematics is usually complicated and its numerical solution is computation-intensive and time-consuming. Therefore, the dynamic model is difficult to build up when it needs to analyze the input function's effect on system dynamic performances. Concept of dependent generalized coordinates is adpoted here and a kind of dynamic modeling method of multi-link hybrid mechanism is presented based on the virtual work principle. The linear and angular displacements of every component can be expressed concisely in the form of dependent generalized coordinates. They are much simpler than that of independent generalized coordinates. Accordingly, linear and angular velocities will be derived by differentiating with respect to displacements. Velocity Jacobian matrix will be simplified under dependent generalized coordinates system and the virtual work principle-based dynamic model will also be simplified accordingly. Then it needs to introduce constraint conditions and multiplier in order to acquire actuation forces. Introduction of the constraints guarantees the real kinetic characteristics of mechanism. In the end, the curves of actuation forces and spherical joints' inner forces variations are presented using Matlab. By comparing with Adams simulation results, validity of the method has been proved.