Solving Sets of Nonlinear Equations for the Design and Analysis of Mechanical Systems

在本研究项目中，为求解一组用于机械系统设计和分析的非线性方程提供了理论基础。这种方法可以对所有可能的解进行快速的数值测定。拥有所有可能的解决方案的主要优点是，设计优化可以简单地通过从备选解决方案中选择最佳方案来执行。对于具有符号系数的方程，该方法产生一个数学模型，可以从中推导出理论进展。系统方程的解用表示为特征矩阵或多项式的文字系数的物理系统参数来表示。然而，这些结果是在分析和设计链接机构的背景下产生的，例如，串联关节机械手，它们适用于各种各样的工程问题。* * * / /

In this research project, a theoretical basis is developed for the solution of a set of nonlinear equations which are used for the design and analysis of mechanical systems. The approach allows a rapid numerical determination of all possible solutions. The main advantage of having all possible solutions is that design optimization can be performed simply by selecting the best from amongst alternative solutions. For equations with symbolic coefficients, the method yields a mathematical model from which theoretical advances can be derived. The solutions of the system equations are formulated with physical system parameters expressed as literal coefficients of a characteristic matrix or polynomial. Whereas the results are generated in the context of analysis and design of linked mechanisms, e. g., a serial jointed manipulator, they are applicable to a wide variety of engineering problems.*** //