内摆线的图形分类与应用研究

Figure Classification and Application Research of Inner Cycloids

短幅外摆线由于处处光滑连续被应用在了摆线针轮减速器的设计上,事实上内摆线比外摆线具有更多的图形特征,当满足一定的几何关系时,内摆线呈现光滑角的正多边形、光滑角的正多角形、尖角的正多角形、多瓣与多角共生图形以及无限不循环图形,这些图形特征在工件加工、图样生成、搅拌作业、高阶停歇机构设计中有着广泛的应用.通过建立行星轮上点的轨迹方程,令一个坐标在一个位置上的一至三阶导数同时等于零,得到了图形分类的基本关系.

Short width outer cycloid has been applied in design of cycloid pin wheel redactor due to its curve everywhere smooth and continuation. In fact inside cycloids have more figure characteristics. Inside cycloids present regular polygons with many sides and smooth angles, regular polygons with many smooth angles, regular polygons with many sides and pointed angles, many petals and many angles symbiotic figures; and infinite no circulation figures when specific geometrical relationships met. These figures have extensive uses in work piece machining, pattern generation, puddling work, and high order intermittent mechanisms designed. Basic relationships on figure classification have been got through building locus equations on the planetary gear and letting one to three ordered differentials of one coordinate on one location simultaneously to be zeros.