A new Method for the Direct Dynamics´ Calculation of Parallel Manipulators

This article presents a new method for the modelling of the direct dynamics of the parallel manipulators. The Lagrangian equations of the first type and Lagrange-D´Alembert formulation are used for the derivation of this method. These methods are presented and discussed. Based on this knowledge a new algorithm is suggested. With this algorithm one can accelerate the computations of the direct dynamics´ equations and at the same time formulate them in small terms, which for the analysis of these equations is an advantage. It is shown, that the methods for the modelling of the dynamics of the serial kinematic chains can be used for the modelling of the parallel manipulators´ direct dynamics without major modifications and additional complex transformations. The structure of the new algorithm will allow the parallel realisation of the dynamics´ calculation. Finally, this method is discussed on the example of a planar parallel manipulator - five-bar