渐伸线（involute）(或称渐开线(evolent))和渐屈线（evolute）是曲线的微分几何上互为表里的概念。若曲线A是曲线B的渐伸线，曲线B是曲线A的渐屈线。

在曲在线选一定点S。有一动点P由S出发沿曲线移动，选在P的切在线的Q，使得曲线长SP 和直线段长PQ 相同。渐伸线就是Q的轨迹。

若曲线B有参数方程，其中，曲线A的方程为。

曲线的渐屈线是该曲线每点的曲率中心的集。

若该曲线有参数方程（），则其渐屈线为

每条曲线可有无穷多条渐伸线，但只有一条渐屈线。

In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound. It is a roulette wherein the rolling curve is a straight line containing the generating point. For example, an involute approximates the path followed by a tetherball as the connecting tether is wound around the center pole. If the center pole has a circular cross-section, then the curve is an involute of a circle.