Characterisation of parallel kinematic machines based on structural workspaces

In this paper, we present the static and dynamic structural characterisation of a low-mobility parallel kinematic manipulator, involving analysis of its stiffness and vibrational dynamic behaviour. The study starts by building numerical models of the behaviour of the manipulator to be compared to experimental measurements from a prototype. For the case study, we consider a four-degree-of-freedom (x, y, z, θz) manipulator with prismatic actuators designed by the COMPMECH research group at the University of the Basque Country. The characterisation allows the behaviour of the static and dynamic stiffness, as well as the natural frequencies of the manipulator, to be mapped in the manipulator workspace. These maps together with kinematic, static and dynamic constraints lead to the definition of operational, static, dynamic and structural workspaces, respectively. Further, we analyse the modes of the manipulator to determine dynamic displacements, these being key in the performance in the machining tasks for which the robot was designed