Roulette of the fixed axis gear train and its application in machining

The locus equation of the roulette of the fixed axis gear train was formulated in this paper, and its application in machining plane was discussed. The locus equation of the roulette of the simple fixed axis gear train was derived by transforming coordinates first, and some typical figures were demonstrated by computer. The relationships among characteristics and forms of the roulettes and the transmission ratios, mechanism parameter and the original phase angles were investigated. Then the equation of the complicated fixed axis gear trains was set up according to the transmission characteristics of the fixed axis gear trains. And then the equation of transmission ratio for machining plane was deduced by using the referred information. At last, an example is given to simulate the machining process, whose result testifies the above result.