摘要
基于Groebner基法和计算机符号处理技术,对三自由度并联机床的位置正解问题进行了符号求解。该法通过对变量排序,建立多项式对的集合,求SP多项式,约简等运算,将一组非线性方程组化简为同价的三角化方程组,得到了封闭形式的解析解;导出了雅可比矩阵,引入了符号处理技术,并且对该并联机床的可操作性进行了分析,给出了具体数值实例。
Symbolic solutions for direct displacement analysis of a three-DOF spatial parallel machine tool are proposed based on Groebner base method and computer symbolic manipulating technique. A set of nonlinear polynomial equations are transformed into a set of equivalent triangularization equations by using the following operations: ordering of variables, forming all pairs of polynomials, finding S-polynomial, and reduction etc. The analytical solutions in the closed form are obtained. The Jacobian matrix is derived,and symbolic technique is introduced into the procedure of derivation of Jacobian matrix.The manipulability of the parallel machine tool is investigated.Two numerical examples are given for illustration.
出处
《机械科学与技术》
CSCD
北大核心
2005年第5期616-619,共4页
Mechanical Science and Technology for Aerospace Engineering
基金
国家自然科学基金项目(50375104)
四川省重点学科项目(SZD425231)资助
关键词
并联机床
位置分析
GROEBNER基
可操作性
计算机符号处理技术
Parallel machine tool
Direct displacement analysis
Groebner base
Manipulability
Computer symbolic manipulating technique
