Dynamic response and chaotic behavior of a controllable flexible robot

Abstract

Flexible 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.

Finite Element Model of Kinematic Pair Clearances of Elastic Linkage Mechanisms

“…Note that coordinate arrays ub and U  are only different for the elastic displacement. A coordinate system, 11 1…”

“…References [7] and [8] proposed a finite element (FE) model for a motor based on an investigation of its electromechanical coupling relation and systematically investigated the effects of the electromagnetic parameters of the motor on the dynamic performance of the elastic linkage mechanism. References [9][10][11][12] studied how to improve the dynamic performance of the elastic linkage mechanism by refitting the motor at the joint of the manipulator to the frame. However, KED research has not accounted for the effects of the clearance in kinematic pairs.…”

Chaos intensity: Using Lyapunov exponent and uniformity to judge the intensity of mechanism chaos based on a planar slider–crank mechanism with multi-clearance joints

“…Mechanism chaos exists widely in mechanism systems, such as gear system [1], Camfollower mechanism [2], beam [3], planar mechanism [4,5], under-actuated system [6], spatial parallel mechanism [7], and others [8][9][10]. Usually, most of these phenomena are caused by clearance due to design, manufacture, assemblage processes, and influence of wear [11][12].…”

Structural Optimization Design of a Six-Degrees-of-Freedom Serial Robot with Integrated Topology and Dimensional Parameters

“…Industrial robots are extensively employed in the automotive and electronics industries, as well as in other fields [ 2 , 3 , 4 ]. Serial robots [ 5 , 6 , 7 ] are essential components of robots. The complex parameter coupling and multi-objective design of serial robots have attracted the attention and research of scholars [ 8 , 9 , 10 , 11 ].…”