渐开线齿轮的齿形由基圆的渐开线来表示。当一直线沿一圆周作纯滚动时,此直线上的任一固定点就画出一条渐开线。根据其几何性质,渐开线可用直角座标表示为:X/r_b=sinε-εcosε①Z/r_b=cosε+εsinε-1 ②式中r_b—基圆半径,(时);ε—展开角,(弧度);X、Z—渐开线的座标。在上述公式中,由于展开角ε有相同的增量,而由公式计算出的X 及Z 所表示的渐开线之间的弧长则不相等,这在齿轮作图中不便于 The involute gear’s tooth profile is indicated by the involute of the base circle. When a straight line follows a circle as a pure scroll, any fixed point on this line draws an involute. According to its geometric properties, the involute can be expressed in Cartesian coordinates: X / r_b = sinε-εcosε①Z / r_b = cosε + εsinε-1 ② Where r_b-base circle radius, (time); ε-expansion angle, ); X, Z-involute coordinates. In the above formula, the arc length between the involute lines represented by X and Z calculated by the formula is not equal because of the same increment of the expansion angle ε, which is not convenient in the gear drawing