6/6-SPS型Stewart机构奇异轨迹性质识别的Z截面法

对6／6-SPS型Stewart并联机构的奇异轨迹的性质进行识别。基于Stewart并联机构奇异轨迹的解析表达式,推导出了该并联机构在相互平行的Z截面上的奇异轨迹。结果表明：6／6-SPS型Stewart并联机构在相互平行的Z截面上的奇异轨迹总是一个二次多项式其包括四对相交直线、一条抛物线及双曲线束。但是,当机构的上、下平台不平行时,机构在空间中的奇异轨迹又是一个不可分解的三次多项式。

Property Identification of the Singular Loci of the 6/6-SPS Stewart Manipulator by Using the Cross-Section of Z-plane

This paper studied the problem of identifying the property of the singular loci of the 6/6-SPS Stewart manipulators. Based on the analytical expression that represents the singular loci of the manipulator for a constant orientation, a quadratic expression that represents the singular loci of the manipulator in parallel Z-planes was derived, and further the property of the singular loci was identified. It shows that the singular loci of the manipulator in parallel Z-planes are all quadratic expressions, which contain infinite hyperbolas, four pairs of intersecting straight lines and a parabola. So it can be concluded that when the moving platform is not parallel to the base one, the singular locus equation of the manipulator in three-dimensional space is a special irresolvable polynomial expression of 3-degree, whose cross sections in parallel Z-planes contain a parabola, four pairs of intersecting straight lines and infinite hyperbolas.