Dynamic response and chaotic behavior of a controllable flexible robot

Abstract

AbstractFlexible robots with controllable mechanisms have advantages over common tandem robots in vibration magnitude, residual vibration time, working speed, and efficiency. However, abnormal vibration can sometimes occur, affecting their operation. Traditionally only simple mechanisms are considered in studying abnormal vibration, omitting reference to important chaotic phenomena caused by the flexibility of the mechanism rod. In order to better understand the causes of abnormal vibration, our work takes a controllable flexible robot with a complex series-parallel mechanism as a research object and uses a combination of Lagrangian and finite element methods to establish its nonlinear elastic dynamics. The effectiveness of the model is verified by comparing the calculated frequency with the frequency measured in a test. The time-domain diagram, phase diagram, Poincaré map, maximum Lyapunov exponent, and bifurcation diagram of the elastic motion of the robot wrist are studied, and the chaotic phenomena in the system are identified through the phase diagram, Poincaré map, the maximum Lyapunov exponent, and the bifurcation diagram. The relationship between the parameters of the robot motion and the maximum Lyapunov exponent is discussed, including trajectory angular speed and radius. The results show that chaotic behavior exists in the controllable flexible robot and that trajectory angular speed and radius all have an influence on the chaotic motion. Our work provides a theoretical basis for further research on the control and optimal design of flexible robot mechanisms.