# Helix Drawing / Helix Construction – Engineering Drawing

## Helix Drawing

Helix is a space curve that is generated by a point moving uniformly on the surface of a cylinder or cone. There are two types of helix.

(i) Helix on cylinder.

(ii) Helix on cone.

## Helix on a Cylinder – Helix Drawing

**Definition:**It is the curve that is generated by a point which moves around the surface of a right circular cylinder and at the same time advances in the axial direction at a speed which bears a constant ratio to the speed of rotation.

Example: A point is moving around the surface of the cylinder of 30 mm diameter at uniform speed and at the same time, it advances in the direction of axis by 40 mm also with uniform speed. Draw the path of moving point and name the curve.

#### Procedure :-

- Draw plan and elevation of cylinder of diameter 30 mm and having 40 mm as the length of axis as shown.
- Draw a development of lateral surface of cylinder, which is a rectangle of width equal to circumference of circular base of cylinder and height equal to the axis length of the cylinder.
- Divide circle (plan) into 12 equal parts and mark them 1, 2, 3, … 12.
- Divide circumference length in development into 12 equal parts and also mark them as 1, 2, … 12.
- Join diagonal of rectangle in development to represent Helix as a straight line in the development.
- Draw vertical lines parallel to the axis of cylinder from 1, 2, … 12 in development to intersect straight line helix in development as shown. From these, intersection points, horizontal lines parallel to the base of cylinder are drawn to intersect elevation of a cylinder at points 1′, 2′, … 12′.
- Transfer intersection points at diagonal of rectangle from development to elevation of a cylinder as shown, to get smooth curve named as Helix in elevation. Half of the helix will be full and half of it will be dotted.

## Helix on a cone – Helix Drawing

**Definition:**It is the curve generated by a point which moves around the surface of a right-circular cone and at the same time advances in the direction of axis at a speed which bears a constant ratio to the speed of rotation.

**Example:**A right angle triangle of two sides 45 mm and 60 mm and hypotenuse 75 mm is rotating around side 60 mm as shown in the figure. A point P is moving from the bottom most position to the highest position on hypotenuse while the triangle completes one revolution. Both the movements are uniform. Draw the path of the point P in elevation and plan. Name the curve of plan and curve of elevation.

#### Procedure :-

- Draw the plan and elevation of a right angle triangle by OAB and O’A’B’ respectively as shown.
- Draw a circle with centre O and radius of OB length.
- Divide the circle into 12 equal parts and obtain various positions of plate in plan and obtain corresponding elevation.
- curve traced by the point P in the plan is spiral and in an elevation is a helix as shown.