On the Inverse Dynamics Problem of General Parallel Robots

In the present paper we introduce a general solution of the inverse dynamics problem of any parallel robot including mechanisms with reduced mobility as well as redundant structures. Starting from the Denavit-Hartenberg and physical parameters we derive the robot's dynamics equation using the subsystems method and the Lagrangian formalism. After choosing the minimal coordinates the obtained equations are reduced to the minimal form based on the coordinate partitioning method. A main advantage is that the equations of motion are derived exclusively in an analytical form which allows the implementation into symbolic computation software, e.g. Maple. As a result, we automatically obtain the inverse dynamics solution which can directly be translated to optimized C-code and therefore be used in real-time applications. Several examples demonstrate the effectiveness of the proposed method.