How to draw an involute for a circle | Length of the string is greater than the circumference

Описание: This video illustrates how to construct an involute for a given circle.

Example – Length of the string is greater than circumference of the circleTrace the path of end point of a string, length of 160 mm, when it is wound around a circle of 42 mm diameterCircumference of the circle = πd = 132 mmLength of the string = 160 mm

An involute is a type of curve that is generated by tracing a point on a string as it unwinds from another shape, typically a circle. Imagine tying a string to the edge of a circular object and then unwinding it while keeping the string taut. The path traced by the end of the string as it unwinds forms an involute.
The involute also defined as the path of a point on a straight line which rolls without slip along the circumference of a cylinder.

Key Characteristics of an Involute:
1. Base Curve: The shape (often a circle) from which the string unwinds is called the base curve.
2. Perpendicular Tangents: At any point on the involute, the tangent to the curve is perpendicular to the radius of the base circle at the point where the string was last touching the circle.
3. Gear Design: Involutes are crucial in the design of gears. The teeth of involute gears mesh smoothly, ensuring a constant transmission ratio, which is important for efficient power transmission.
The mathematical representation of an involute of a circle involves parametric equations, where the parameter typically relates to the angle of unwinding.