Research On The Non-Linear Dynamic Characteristics Of Planar Under-Actuated 2R Manipulator Actuated By PMSM

Non-linear systems extensively exist in real world. The research on various complicated phenomenon arising from these systems lead the non-linear science booming, and created several kinds of theories, such as dissipativity structure theory, synergetics, catastrophe theory, chaos and fractal theory.Mechatronics, as a new trend of mechanical engineering, is composed of sub-systems, such as the actuators and mechanisms. The aim of this study is to explore the dynamic characteristics of mechatronics under the circumstance that each sub-system is nonlinear, and there exist some fixed points, periodic motion and chaotic motion.The subject of this study is the system with a planar under-actuated 2R manipulator actuated by permanent magnet synchronous motor (PMSM). The mainly research work and conclusions are listed as following.1. The dynamic behaviors of planar under-actuated 2R manipulator system are studied. The analytical model is established by Lagrange Equation and Runge-Kutta method is employed to solve the dynamic equations. The effects of parameters on the dynamic behaviors of the mechanism are revealed by means of time series, power spectra, maximum Liapunov exponents and bifurcation diagram. The results show that the motion of the mechanism may be periodic or chaotic depending on the combination of the parameters of the mechanism, and the style of the bifurcation may be changed due to the different parameters.2. For the PMSM part dynamics studying, the analytical model of the motor is developed according to the basic principles of electromagnetics and dynamics, and the analysis is carried out after the transformation of time and dimensions. Runge-Kutta method is also employed to solve the dynamic equations. It is shown by the results that fixed point, periodic motion and chaotic motion all can arise from the system of PMSM.3. The dynamic characteristics of integral system of planar under-actuated 2R manipulator actuated by PMSM are studied with the same procedure and method as that adopted in analysis of the mechanism and PMSM. The results show it is impossible to infer the behaviors of the system simply by the behaviors of sub-system because the coupling between the motor and the mechanism is very strong.4. A scheme to control the motion of the 2R manipulator system by adjusting the parameter of the motor is proposed.