Recursive and Symbolic Calculation of the Elastodynamic Model of Flexible Parallel Robots

This paper presents a symbolic and recursive calculation of the elastodynamic model of flexible parallel robots. In order to reduce the computational time required for simulating the elastodynamic behavior of robots, it is necessary to minimize the number of operators in the symbolic expression of the model. Some algorithms have been proposed for the rigid case, for parallel robots with lumped springs or for serial robots with distributed flexibilities. In this paper, we extend the previous works to parallel robots with distributed flexibilities. The generalized Newton–Euler model is used and combined with the principle of virtual powers to minimize the number of operators and intermediate variables. Recursive calculations are proposed for the computation of the Jacobian matrices defining the kinematic constraints in order to decrease the number of operators. The proposed algorithm is used to compute the elastodynamic model of a prototype of a planar parallel robot developed at IRCCyN: the DualEMPS. The computed model is compared both with simulations computed with Adams and with experiments. The validity of the approach in terms of result accuracy and computational time is demonstrated.