平面连杆机构分析与综合的多项式解

【作者】 牛志纲；

【导师】 张纪元；

【作者基本信息】 上海海运学院 ， 机械设计与理论， 2001， 硕士

【摘要】 本课题来源于交通部科技进步“通达计划”项目—“平面连杆机构分析与综合的类解析解”。 文中概述了机构学研究中常见的线性和非线性数学模型，着重述评了非线性代数方程组的各种解法。特别地，对多项式方程组的消元理论和方法作了较为系统的阐述。针对目前多项式方程组的消元理论和方法中存在的问题和不足，本文提出了基组结式消元法，并用以求解机构学研究中的多解问题。该方法的主要思想是：根据多项式秩的大小选取基组，采用贝左结式消元，用改进型零点集结构式确定零点集，从而只需一次整序就可求得一个多项式方程组的零点集。因此基组结式消元法具有消元工作量较小，消元结果方次较低等优点。这不仅解决了迭代求解机构分析与综合的非线性方程组时所需合适初始点的选取问题，而且较彻底地解决了机构装配构形以及机构综合多方案设计等多解问题。文中还提出了确定机构极限位置和按急回特性设计机构的多项式方法。上述两种方法的提出是本文最主要的理论研究成果。 本文利用基组结式消元法求解了206个平面杆组和平面连杆机构装配构形分析或机构综合问题并编制了基组结式消元法程序。该程序可将含三角函数的机构分析或综合方程组自动地变换成多项式方程组并对多项式方程组进行消元，得到原多项式方程组的多项式解。最后形成了平面连杆机构分析与综合的多项式解软件系统。通过大量计算表明，基组结式消元法的确是切实有效的。另外，作者还对基组结式消元法在两种门座式起重机变幅机构优化设计中的应用做了成功的尝试，并编制了“变幅补偿直臂架门机的优化设计和分析计算”和“平衡滑轮式补偿门机的优化设计和分析计算”软件系统。上述三个软件系统是本文具有重要价值的应用研究成果。更多还原

【Abstract】 This paper bases on the Through Program?project of the Ministry of Communication ~ progression of science and technology, whose name is the similar analytic solution of analysis and synthesis of planar linkages.The paper summarized the common linear and nonlinear mathematics model in the research of mechanism science, focusing on the comment on the methods to solve nonlinear algebraic system of equations. Especially elaborating on the theories and methods of polynomial elimination of system of equations systematically. The paper proposes the elimination by eliminant with aid of basic sets (EEABS), in order to solve the problems in the theories and methods of polynomial system of equations 慹limination at present, and to find the multi-solutions of mechanism science ~ research. The main idea of this method is to choose a set according to the order of polynomials, to eliminate by making use of Bezout eliminant, get zero set from the improved formula about set of zero points, so that a polynomial system of equation ~ set of zero points can be got only by one time arrangement. The EEABS has some advantages such as the workload of eliminating is greatly reduced and the degree of eliminating result is lowered, and so on. The method not only solves the problem of how to choose a suitable initial value that needed in solving nonlinear system of equations on analysis and synthesis of mechanism by iteration method, but also better thoroughly solves the problem of multi-solutions on the assembly configurations of mechanism and multi-scheme about the synthesis of mechanism. In addition, the paper proposes a polynomial method to define the limited position of mechanism and to design a mechanism based on its quick-return characteristic. The foresaid two methods are the most important achievements in the field of theoretic research in this paper.The paper has totally solved 206 problems on the analysis and synthesis of planar links and linkages by the EEABS, and compiled the program of EEABS. The program can automatically turn a system of equations that include triangle functions into polynomial system of equations in the analysis and synthesis of the mechanism, to eliminate and get the polynomial solutions of the original system of equations. The software system of analysis and synthesis of planar linkages is formed at last by author. A great number of calculating results show that EEABS is effective and practicable. In addition, the method has been successfully applied into optimum design of two types of range-changing mechanism of gantry crane and the software systems of optimization design and analytical calculation of straight-arm gantry crane and 憃ptimization design and analytical calculation of balance pulley compensation gantry crane?has been compiled. The above-mentioned three software systems are the most valuable achievements in the field of practical research.更多还原