Unwinding a taut string from a unit circle makes its free end trace an involute. The straight portion remains tangent to the circle, and its length equals the arc length already unwound.将绷紧的细线从单位圆上逐渐展开，自由端就描出渐开线。展开后的直线段始终与圆相切，其长度等于已经展开的圆弧长度。
The gold point is the tangency point, and the green point is the free end. The tangent segment length increases as , even though the circle radius stays one.金色点是切点，绿色点是自由端。圆的半径始终为一，而切线段长度随 增加。