Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism

This paper readdress the issue of deriving explicit equations of motion for parallel robots by using the Lagrangian formalism. Reputed of being inefficient for closed-loop mechanisms, the formalism became unpopular for parallel robots. This paper argue the converse by giving an alternative, though intuitive and simple approach. The idea is to consider open-loop subchains of the manipulator and to derive their dynamics by the Lagrangian formalism and with respect to an own set of generalized coordinates and velocities. The paper discusses and proves the importance of the formal choice of these coordinates. The principle of energy equivalence is derived to allow for joining the different equations of motion. To obtain the final form with respect to the robot’s active coordinates, attention has to be paid to the transformation of the subchains dynamics, which is introduced in this paper. Finally, a systematic study of the resulting computational effort is presented and discussed in relation to other methods and approaches given in the literature.