一种新型并联机床的奇异位形解析

Close Form Solution to Singularity Configuration of A New Type Parallel Machine Tool

提出了一种以空间三自由度并联机构作为主进给机构的并联机床新结构。建立了并联机床主进给机构位置分析的输入输出方程,推导了奇异位形判别的解析表达式。该判别式在形式上为多项式代数方程,在推导过程中引入数值-符号处理技术,得到了多项式代数方程中每一系数元素的数值-符号形式的解析表达式。主进给机构的奇异位形的集合为参数空间的曲面片,得到了奇异曲面方程及奇异曲面的截面曲线图。

A new type parallel machine tool, which utilizes a 3dof spatial parallel mechanism as main feed machanism, is proposed in this paper. The input-output equation of displacement analysis for the main feed mechanism of parallel machine tool is established. An analytical expression for determining singularity configuration which is a polynomial equation is set, and the numeric-symbolic manipulating technique is introduced in the paper. Analytical expressions of numeric-symbolic form for each coefficient of the ploynomial equation are derived. The section curve graph of a singularity surface is drawn. A numerical example of singularity configuration analysis is given for illustration.