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讨论了平面四杆机构连杆平面上的Ｂａｌｌ点曲线和Ｂｕｒｍｅｓｔｅｒ点曲线的性质及其求解方法，证明了Ｂａｌｌ点曲线上出现奇点的充要条件是该点为Ｂｕｒｍｅｓｔｅｒ点；连续封闭的Ｂｕｒｍｅｓｔｅｒ点曲线产生奇点的充要条件是该点为六个无限接近位置的Ｂｕｒｍｅｓｔｅｒ点，而且奇点总是成对出现的．绘出了几种平面四杆机构连杆平面上Ｂａｌｌ点曲线及Ｂｕｒｍｅｓｔｅｒ点曲线．为平面机构分析和综合提供了新的理论依据．
The properties of the Ball point curve and the Burmester point curve on the plane of the connecting rod of a planar four-bar mechanism are discussed. It is proved that the necessary and sufficient condition for a singular point on the curve of the Ball point is that the point is a Burmester point; the Burmester point The necessary and sufficient condition for the curve to generate a singularity is that the point is a Burmester point of six infinitely close positions, and the singular points always appear in pairs. Plotting Ball Point Curve and Burmester Point Curve on Connecting Rod Plane of Several Planar Four Bar Mechanism. It provides a new theoretical basis for plane organization analysis and synthesis.