Research on theoretical analysis of a one-degree-of-freedom vibration system in which the moment of inertia is a function of time

Abstract

In order for a work robot to immediately start working after positioning and stopping, it is necessary to suppress free vibrations that occur when the robot stops. In the case of 1-degree-of-freedom vibration of a constant coefficient system, free vibration can be suppressed using the input shaping method in which the duration of the excitation force during acceleration and deceleration is a multiple of the natural period. However, in the case of a robot that turns while changing its posture, the moment of inertia is a function of time, so there is a problem that the period is not constant. Therefore, we express the moment of inertia as a function of time and derive a theoretical impulse response by applying the Sturm-Liouville type differential equation solving method.