On The New Methodology Of Mechanism Design Based On Nonlinear Scince

In 1961, E. Lorenz made an important contribution when he studied nonlinear equations motivated by the turbulence of motion of the atmosphere. He discovered that a small change in initial conditions leads to very different outcomes in a relatively short time. Since then, the study of the nonlinear system has been attracting much attention from scholars and researchers. A new discipline, named nonlinear science, has been shaped to explore and seek the common properties for all kinds of nonlinear phenomena in nature.By now many properties have been found. They are listed as sensitive dependence on the initial conditions, fractals and fragmentation, irregular or aperiodic motion, uncombinations of solutions, and apparently random behavior in a deterministic system, unpredictable long-term behavior and so on.Same as other fields of engineering, mechanism, an important branch of mechanical engineering, has been developing for more than a century along parallel line of fighting with nonlinearity. Nowadays, new discoveries, understanding and approaches may emerge by placing it in the wide scenario of nonlinear science. It is the primary purpose of the present research work.Newton's method is one of the most accessible and easiest to implement of the iterative root-finding algorithms for the nonlinear polynomial equations which arise from mechanism synthesis. As a discrete deterministic dynamical system, Newton's method contains subsystems which have highly random motion. In a so-called chaotic zone, there is a rapid interchange between the basins of attraction for each root of the equation. Choosing initial points from such chaotic zone, one can obtain a certain number of roots or possible all of them under the Newton's method. In this dissertation, how to locate the chaotic zones is addressed. It is show that there exist four chaotic zones for a general 4th degree polynomial with one variation, and in the case of higher dimensional polynomial, there exist a chaotic zone in the neighborhood of singular point of its Jacobian matrix. The location of chaotic zone can be simply determined by some critical values of the polynomial. As examples, the equations derived from exact synthesis for five positions are solved.Neural networks have become a powerful tool to deal with nonlinear problem. For example, BP (Backpropagation) neural network is usually employed to mapping some relations which are too complex to be described by mathematical formula. In this dissertation, the motion of the. coupler link is mapped onto a curve of the image space by kinematic mapping, and can be characterized by the so-called Fourier descriptors. The relationship between the Fourier descriptors and the dimensions of the mechanism is one of such complex relation. BP neural networks are trained to map the relationship. Using these neural networks, the dimensions of the mechanism will be outputted when the Fourier descriptors of the motion of the coupler link are inputted to them. So a new approach for motion synthesis is proposed, which is much applicable to the problem such as that the number of prescribed positions is greater than that a linkage can generate exactly or the prescribed motion is the whole cycle motion of a linkage's couple link. Some relevance aspects are also discussed. Much of the emphasis here is placed on the influence of varying the slope parameter X of the binary sigmoid function to the training process of the neural networks. The results demonstrate that for each value of X the training process may be in different states. They are convergence to a fixed point, finite periodicity, quasiperiodicity and chaos.Three aspects of design for a linkage, namely kinematic design, dynamic design and control design, all are nonlinear. They are conventionally divided and performed in separate steps of design. Such design strategy is known as sequential design. In resent years, a new design strategy, named concurrent design, has been developed for the design of cam and other kind of mechanisms. Nevertheless, what is the difference between the results outcome from different design strategies? To answer this question, the coupling of the three aspects is analyzed, and the mathematical design models for both sequential and concurrent designing of five-bar planer mechanism with hybrid actuators are established. Differential evolution algorithm is utilized to find the optimum solutions of the models. The results prove that the sequential design makes the motion of the mechanism more precise, but the effect of the control system worse. Conversely, the concurrent design makes the effect of control more obvious at the expense of losing the precision of the motion. In addition to these, the chaos-based differential evolution algorithm is studied extensively. It is indicated that the different initial conditions will cause the properties of the algorithm changes, and that the ability of the algorithm to escape from local optimums is more powerful if the initial population is chosen using a chatic map.This research has been funded by National Natural Science Foundation of China. The financial support is gratefully acknowledged.