Modeling of redundant planar parallel manipulators

In this study, a method originally designed for planar open-chain serial manipulators model which is called as a "virtual joint" is extended to model planar parallel manipulators (closed-chain systems). This method describes how the configuration of a robotic chain is generated by fixing either a revolute or a prismatic joint already exist at the same joint and fixed to the ground by appropriate constraint forces which converts the open chain into a closed link loop. Two joints, a revolute and a prismatic are assumed to exist between each link pair. According to the type of the manipulator to simulate, one of the two joints existent is allowed to move while other constrained by appropriately shaped force profiles. Once the model is constructed with this model, it is possible to examine the dynamic behavior of the almost all kinds of multi link planar manipulators. By the proposed method, a set of sub open chain system can be converted into anyone of the planer parallel manipulator type mechanisms and motion equation is properly shaped up to model this particular mechanism. The motion equations are fewer and numerical integration simpler, with fewer tendencies of numerical errors to build up.