Dynamics Modelling of Hexaslides using the Decoupled Natural Orthogonal Complement Matrices

In this paper, dynamic model of a class of parallel systems, namely, the hexaslides, is proposed. The model developed is based on the concept the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere. The dynamic model of hexslides, though complex due to the existence of multi-loop kinematic chains, is required for actuator power estimation, computed-torque control, optimum tool trajectory generation, etc. The use of DeNOC offers many physical interpretations, recursive algorithms, and parallel computations. Using the proposed dynamic model, a parallel inverse dynamics algorithm has been presented to compute the actuator forces. This is useful to choose suitable motors for an application. An illustration is provided using an existing machine tool based on hexaslides, namely, the HexaM, while it is carrying out a circular contouring. Secondly, the effect of leg and slider inertias is also studied, which clearly suggests that neither of these can be neglected while finding the actuator forces.