Configuration-dependent modal analysis of a Cartesian parallel kinematics manipulator: numerical modeling and experimental validation

In the design optimization of a robot the configuration-dependent modal analysis can be a powerful tool to be exploited when high stiffness and high dynamic performances are concurrently required. In this paper the elastodynamics of a lower-mobility Parallel Kinematic Machine for pure translational motions is analyzed. The vibrational modes and the natural frequencies of the robot are evaluated as functions of the end effector position inside the workspace. A finite element model including kinematic joints is used to perform a series of modal analyses in a grid of points inside the workspace. A polynomial regression gives continuous volume maps of the natural frequencies distributions. The numerical model is validated by comparison with experiments: a modal analysis is conducted on a set of inertance Frequency Response Functions acquired on several points of the machine components as a result of an excitation given by an instrumented hammer. A Natural Frequency Difference analysis validates the model under certain conditions and highlights some critical issues to be focused on in future works.