On the Effects of the Operating Speed on the Dynamic Behavior of Manipulators With Rigid Links

The effect of tile operating speed on the dynamic behavior of robot manipulators is determined by examining the potential resonant energy transfer to a robot manipulator system during its motion by the different harmonics of the actuating torques (forces). The potential resonant energy transfer (hereafter called the energy transfer), particularly by the higher harmonics present in the actuating torques, is of considerable interest since they represent one of the main sources of vibration and control problems in such systems. For a given trajectory pattern, the ratios of the total energy transfer by the non-trajectory and the “higher” harmonics of the actuating torques to the total energy input to the system are determined. Here, the higher harmonics refers to the harmonics with frequencies above the highest frequency of the trajectory harmonics. It is shown that in the absence of gravity, for the class of nonlinear dynamics systems represented by the rigid link robot manipulators, the ratios are independent of the speed of operation. For a given path geometry, the relative magnitude of the individual energy transfer is, however, dependent on the positioning of the path within the workspace of the manipulator and the pattern of motion. In the presence of gravity, as the operating speed is increased, the ratios tend to their no gravity values. The application of the developed method to manipulator synthesis and path and trajectory planning for minimal system susceptibility to vibrational excitation, and a number of related topics of interest are discussed.