Research On The Dynamics And Chaotic Motion Of The Under-Actuated 2R Cable-Driven Manipulator

Cable-driven mechanism has been widely used in industrial production and daily life, such as aerospace, weight handling equipment and rehabilitation machinery. As a new indirect driven method, cable-driven is quite different from the traditional direct driven. The under-actuated cable-driven mechanism can not only reduce the number of the driving motors and the cables, but also can avoid the interference between the cables. Therefore, the study of under-actuated cable-driven mechanism has significance in theory and practice.The motion of an under-actuated cable-driven 2R manipulator is studied in this thesis. The uniformity theory and method are employed and some modifications are proposed.The main research work and conclusions of this paper are as follows:1. There are some problems about uniformity theory and method, such as there exist errors in the calculation of Euclidean distance, ambiguity in parameter selection and judgment of chaos, poor performance in chaos judgment. The modification of uniformity method is proposed based on the maximum normalized threshold value. The improvement is arrived at by calculating the multidimensional correlation variable of the system, distinguishing period and chaos by threshold value. The efficiency and validity of the improved method is proved by simulation results of Duffing system. And it also provides a analyzing method for the study of dynamic characteristics and chaos for the under-actuated cable-driven 2R manipulator. The relationship between fractal dimension and uniformity is also discussed. It is shown that they are similar and consistent.2.The dynamic model of under-actuated cable-driven 2R manipulator system is established base on Lagrangian method and the dynamic behavior of the system is analyzed by numerical simulation via MATLAB software. The working process is divided into two stages:one is named applied force to the mechanism when the driving force from the rope is exerted on the bar until the driven bar arrived at a predetermined angle. The other one is named removed the force from the mechanism when the mechanism get rid of all external force except the gravity. It is found that there is abundant nonlinear dynamic phenomenon in the second stage.3.The influence of cable-driven location and driving parameters on the motion of the system is investigated and the edge of chaos of under-actuated cable-driven 2R manipulator is detected. In addition to this, some conclusions are drawn from the evolution of the chaotic motion and periodic motion through the analysis of the local interval parameters. The result shows that the changing of location parameters and driving parameters of cable-driven will cause the changing of the motion state, and periodic motion alternating with chaotic motion. A smaller value of uniformity always means a smaller amount value of the periodic motion. The input energy, power and the ratio of the power and equivalent moment of inertia of under-actuated cable-driven 2R manipulator are also studied. The results show that their periodic and chaotic characteristics stay in step with the mechanism motion periodic and chaotic characteristics, same as period and chaos. The amplitudes of power and the ratio of the power and equivalent moment of inertia in chaos are larger than that of period, which may be explained by that the energy of the system flows quickly while the system is in chaotic motion, and relatively slowly while in periodic motion.The improvement and application of uniformity theory and method enrich the research methods of chaos. The research on dynamic characteristics and chaotic motion of under-actuated cable-driven 2R manipulator lays the foundation for the application and control of the mechanism.