# Involute Curve / Engineering Curve – Engineering Drawing

**Definition**: It is a curve traced out by an end of a piece of thread unwound from a circle or a polygon. the thread being kept tight.** or**

It is a curve traced out by a point in a straight line which rolls without slipping along a circle or a polygon.

**Example 1 – Involute Curve**

**Draw an involute of a circle of 50 mm diameter. Also, draw a normal and tangent to it at a point 100 mm from the centre of the circle.**

#### Procedure:

- Draw a circle of 50 mm diameter and divide it into 12 equal parts and mark them as 1′, 2′, … 12′.
- Draw a line of length equal to the circumference of circle as 𝛑d = 𝛑 * 50 = 157.14 mm and tangent to the circle. Divide this line into 12 equal parts and mark them as 1, 2, …, 12.
- Draw tangents to the circle at points 1′, 2′, … 12′ in the direction of position of string during wounding operation.
- On tangents to the circle at points 1′, 2′, …. 12′ take length equal to the arc length 1P, 2P, …., 12P to mark points P1, P2, ….. P12 respectively.
- Join points P, P1, P2,….P12 by a smooth curve to get involute of a circle as shown in the figure.
- Now, to draw normal and tangent to the involute at an point M on it (which is obtained on a curve 100 mm from the centre of the circle) join M with the centre of the circle. With that line as diameter draw a semicircle cutting the circle of involute at point N. Join N with M to get normal and draw right angle to this normal at point M to get tangent TQ.

**Example 2 – Involute Curve**

**Draw a circle with diameter AB equal to 65 mm. Draw a line AC tangent to the circle at A and of length 135 mm. Trace the path of end A of the line AC when it rolls on circle without slipping.**

**Name the curve. Draw a normal and tangent to the curve at a point 100 mm from the centre of the circle.**

#### Procedure :-

- Draw a circle of 65 mm diameter and divide it into 12 equal parts and mark them as 1′, 2′, … 12′.

- Draw a line of length equal to the circumference of circle as 𝛑d = 𝛑 * 65 = 204.29 mm and tangent to the circle. Divide this line into 12 equal parts and mark them as 1, 2, …, 12.

- Mark a position of point C on this tangent line such that AC = 135 mm. Observe that the C is a point lying inside the circumference length of tangent line.

- Draw tangents to the circle at points 1′, 2′, … in the direction of position of string during unwinding operation.

- On the tangents at points 1′, 2′, .. take length equal to the arc length A-1, A-2, … to mark points A1, A2 … respectively.

- Join points A, A1, A2, … in sequence by a smooth curve to get required involute.

- Now, to draw normal and tangent to the involute at an point M on it (which is obtained on a curve 100 mm from the centre of the circle) join M with the centre of the circle. With that line as diameter draw a semicircle cutting the circle of involute at point N. Join N with M to get normal and draw right angle to this normal at point M to get tangent TQ.