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.