以拓展矢性复数对RSSR机构进行运动分析

从空间机构的分析与综合的角度提出解决三维空间矢量分析的一种新的数学工具—拓展矢性复数。拓展矢性复数与四元数等其他用于空间机构分析与综合的数学方法差别在于拓展矢性复数不仅满足乘法交换率,同时具有明确几何表示和影射关系,可以表示三维空间中两矢量的夹角和矢量绕各个坐标轴的旋转及绕任意空间单位矢量的旋转。以拓展矢性复数对RSSR机构进行运动分析,说明了拓展矢性复数是解决空间机构问题的一种新的数学方法。

Motion Analysis of RSSR Mechanism by Expanding Vector Complex Number

From the viewpoint of analyzing and synthesizing of space mechanism, presents a new mathematical toolexpanded vector complex number, to solve the problem of vector analysis of three - dimensional space. The difference between expanded vector complex number and the mathematical tools which apply other analyzing and synthesizing methods to the space mechanism, such as quatemion, is the expanded vector complex number not only meets the commutative property of multiplication, but also has definite geometric expression and mapping relationship. The expanded vector complex number could expediently express the intersection angle of two vectors in the three - dimensional space and the rotation of vector to the coordinate axes, as well as the rotation of vector to the unit vector of random space. The expanded vector complex number is applied to analyze the motion of RSSR mechanism and the result shows that the expanded vector complex number is an effective new method to solve the problem of space mechanism.