Posture keeing property of the bicycle with twin gimbal mechanism using gyroscopic moment effect

Abstract

Gyro actuator is often used for the posture control of systems which cannot be supported on a fixed ground. The gyroscopic moment makes preccesion movement of the gimbal mechanism and its effect depends on the rotating speed of the wheel. In this paper, the accurate dynamic model is derived for bicycle with twin gimbal mechanism considering ups and downs of the ground, which causes the disturbance to the bicycle. It turns out that the effect of the undulations of the ground is cancelled if the rotating speed of the wheels of the twin gimbal are exact the same. Then the stability of this model without feedback control is discussed. This model has fourth order characteristic polynomial and the characteristic roots for the first and the second modes are derived through lower order approximation. The first mode is unstable and the second mode is stable if there is a viscous friction in the gimbal rotation axis bearing. Simulation and experimental results show that the parameters should be designed so that the amplitude ratio of the gimbal pitch angle with regard to the cart roll angle for the first mode may become small to keep the posture of the bicycle for a longer time. This analysis method can be used for a simple feedback control system of the bicycle to evaluate the design parameters of the mechanism and control.

Keywords

• bicycle
• posture keeing
• gyroscopic moment
• unstability
• amplitude ratio