A body-oriented method for finding a linear form of the dynamic equation of fully parallel robots

In order to identify the dynamic parameters in nonlinear adaptive control the robot's dynamic equation has to be written in a linear form. Many methods have been proposed for serial robots, but for parallel robots, the few solutions proposed so far lead to complicated equations that are not readily usable for real-time implementation. In this paper we propose a new method based on the virtual work principle to find a linear form of the dynamic equation of robots. Compared to other methods, it has the advantage that it does not need to open the closed loop structure into a tree-structure robot. It considers rather each body separately using its Jacobian matrix to project the forces into the joint space of the robot. Thus, simplification can be made at the very beginning of the modeling. This is very efficient when used to model fully parallel robots. As an illustration, the proposed method is applied to the 3dof DELTA parallel robot.