基于同源机构构造的一类自运动机构综合及其比例尺度特征

Synthesis of a Type of Self-motion Mechanisms and the Dimensional Characteristic of Ratio Based on the Construction of Cognates

以一类动静平台均为等边三角形的6-SS型自运动机构为研究对象,从同源机构构造的视角探究该类机构的综合以及尺度特征。根据末端构件存在的转动、移动特征,建立空间单环SSC机构的共形几何代数模型,分析其运动参数与尺寸参数之间的映射关系;基于该机构在最高位置处的垂直投影,构造了具有相同映射关系的一簇3-SS/C机构,揭示了等边三角形平台的6-SS型自运动机构的同源构成本质以及所需满足的位形条件。根据机构簇存在的尺寸转换关系,设计给定的3-SS/C机构的同源机构,分析并得出平台设计点满足的几何规律,提出了6-SS型自运动机构综合的几何化方法;进一步基于所得出的几何规律,揭示了该类机构的比例尺度特征,Griffis-Duffy平台为该类机构的特例。该项研究在丰富同源机构种类的同时,也为包含比例尺度特征的机器人机构拓扑结构设计提供了一个崭新视角。

The research focuses on the 6-SS type self-motion mechanisms with regular triangle platforms. From the viewpoint of the construction of cognates, the synthesis and the dimensional characteristic are studied. Based on the characteristics of rotation and translation, the conformal geometric algebra model of a spatial SSC mechanism is established, and the mapping relationship between the kinematic parameters and dimensions is analyzed. According to the perpendicular projection of the SSC mechanism at the highest position, a cluster of 3-SS/C mechanisms with the same mapping relationship as SSC mechanism is proposed. Then the construction essence of the 6-SS type self-motion mechanisms with regular triangle platforms based on cognates and configuration conditions are revealed. Through the dimensional transformation of the 3-SS/C mechanism cluster, the cognate mechanism of a known 3-SS/C mechanism is designed, and the geometric regularity of the designed point is expressed. The geometric method for the mechanism synthesis is proposed. Furthermore, the ratio of dimensions in this type of mechanisms is deducted based on the obtained geometric regularity. The research not only yields up the variety of cognate mechanisms, but also provides a new viewpoint for topological structure synthesis of robot mechanisms regarding to the dimensional characteristic of ratio.