一、引言世界上最早用来作为齿轮啮合齿廓的曲线是摆线。荷兰学者克理斯坦·惠更斯在创造第一架摆钟(挂钟)时,用了摆线作为齿轮啮合的齿廓(1629年),直到今天为止,它仍旧在各种钟表上应用着。但是由于摆线啮合存在着许多严重的缺点,所以后来就被另一种曲线所代替——由俄罗斯科学院士辽纳尔德,欧拉在1754年所创立的渐伸线制齿轮。这是目前获得最广泛应用的一种齿廓曲线,它具有许多众所周知的优点,也同样存在着 First, the world’s first used as a gear meshing profile curve is cycloid. The Dutch scholar Kristen Huygens used a cycloid as the gear meshing tooth profile (1629) in creating the first pendulum clock, which until today is still used on a variety of timepieces. However, because of the serious shortcomings of the cycloid engagement, it was later replaced by another curve - by the Russian Academy of Sciences Leonard, Euler in 1754 created by the involute gear. This is currently the most widely used profile of a tooth profile with many of the well-known advantages as well as