Dynamic analysis of an axially moving robot manipulator supported by bearings

In this study, a robot manipulator is modelled as a cantilever beam, which moves in an axial direction, has a lumped mass at the end, and is supported by intermediate springs. Considering the tip mass and intermediate springs in the modeling, we derive the equations of motion in which the rigid-body motion is coupled with the flexible motions, and then analyze the transverse vibrations of the beam. Furthermore, we study the tip mass effects on the natural frequencies and the corresponding mode shapes. The natural frequency loci veering is analyzed for variations in the tip mass and the spring position/stiffness. In addition, we investigate the exchange and localization of modes around these veering regions as well as the parameter effects on the mode shapes. Using a Short-time Fourier transform (STFT), the relationship between the dynamic characteristics and dynamic responses are described. It is found that the dynamic characteristics of the beam are dependent on the veering distance. It is also shown via dynamic responses that the mode exchanges occur when a veering distance is close.