期刊名称：International Journal of Advanced Robotic Systems
印刷版ISSN：1729-8806
电子版ISSN：1729-8814
出版年度：2013
卷号：10
DOI：10.5772/56136
语种：English
出版社：SAGE Publications
摘要：Machine tools based on a Stewart platform are considered the machine tools of the 21st century. Difficult problems exist in the design philosophy, of which forward displacement analysis is the most fundamental. Its mathematical model is a kind of strongly nonlinear multivariable equation set with unique characteristics and a high level of difficulty. Different variable numbers and different solving speeds can be obtained through using different methods to establish the model of forward displacement analysis. The damped least-square method based on chaos anti-control for solving displacement analysis of the general 6-6-type parallel mechanism was built up through the rotation transformation matrix R , translation vector P and the constraint conditions of the rod length. The Euler equations describing the rotational dynamics of a rigid body with principle axes at the centre of mass were converted to a chaotic system by using chaos anti-control, and chaotic sequences were produced using the chaos system. Combining the characteristics of the chaotic sequence with the damped least-square method, all real solutions of forward displacement in nonlinear equations were found. A numerical example shows that the new method has some interesting features, such as fast convergence and the capability of acquiring all real solutions, and comparisons with other methods prove its effectiveness and validity.
关键词：Chaos Anti-Control; Parallel Mechanism; Damped Least Square Method; Nonlinear Equations
