Engineering Curves Helix

1. Helix Curve
By
Prof. A.J.More
Department of Engineering Sciences
SlideNo-1Prof.A.J.More AISSMS's IOIT Pune

2. Contents
• Define- Helix
• Helix on cylinder
• Helix on Cone
• Applications of Helix
Prof.A.J.More AISSMS's IOIT Pune SlideNo-2

3. Helix
• IT IS A CURVE GENERATED BY A POINT WHICH
MOVES AROUND THE SURFACE OF A RIGHT
CIRCULAR
• CYLINDER / CONE AND AT THE SAME TIME
ADVANCES IN AXIAL DIRECTION
• AT A SPEED BEARING A CONSTANT RATIO TO THE
SPPED OF ROTATION.
Prof.A.J.More AISSMS's IOIT Pune SlideNo-3

4. Helix on Cylinder
• It is curve generated by a point which moves around the surface of a right circular
cylinder and at same time advances in the axial direction at a speed which bears
constant ratio to the speed or rotation.
Prof.A.J.More AISSMS's IOIT Pune SlideNo-4

5. 1
2
3
4
5
6
7
8
P
P1
P
P2
P3
P4
P5
P6
P7
P8
1
2
3
4
5
6
7
HELIX
(UPON A CYLINDER)
PROBLEM: Draw a helix of one convolution, upon a cylinder.
Given 80 mm pitch and 50 mm diameter of a cylinder.
(The axial advance during one complete revolution is called
The pitch of the helix)
SOLUTION:
Draw projections of a cylinder.
Divide circle and axis in to same no. of equal parts. ( 8 )
Name those as shown.
Mark initial position of point ‘P’
Mark various positions of P as shown in animation.
Join all points by smooth possible curve.
Make upper half dotted, as it is going behind the solid
and hence will not be seen from front side.
SlideNo-5Prof.A.J.More AISSMS's IOIT Pune

6. It is a surface generated by moving a Straight line keeping one
of its end fixed & other end makes a closed curve.
What is Cone ?
If the base/closed curve is a
polygon, we get a pyramid.
If the base/closed curve is a circle,
we get a cone.
The closed curve is known as base.
The fixed point is known as vertex or apex.
Vertex/Apex
90º
Base

7. If axis of cone is not perpendicular to
base, it is called as oblique cone.
The line joins vertex/ apex to the
circumference of a cone is known as
generator.
If axes is perpendicular to base, it is called as right circular cone.
Generator
Cone Axis
The line joins apex to the center of base is called axis.
90º
Base
Vertex/Apex

8. P
1
2
3
4
5
6
7
P
P1
P2
P3
P4
P5
P6
P7
P8
P1
P2
P3
P4
P5P6
P7
P8
X Y
HELIX
(UPON A CONE)PROBLEM: Draw a helix of one convolution, upon a cone,
diameter of base 70 mm, axis 90 mm and 90 mm pitch.
(The axial advance during one complete revolution is called
The pitch of the helix)
SOLUTION:
Draw projections of a cone
Divide circle and axis in to same no. of equal parts. ( 8 )
Name those as shown.
Mark initial position of point ‘P’
Mark various positions of P as shown in animation.
Join all points by smooth possible curve.
Make upper half dotted, as it is going behind the solid
and hence will not be seen from front side.
SlideNo-8Prof.A.J.More AISSMS's IOIT Pune

9. Prof.A.J.More AISSMS's IOIT Pune SlideNo-9

10. Prof.A.J.More AISSMS's IOIT Pune SlideNo-10
Applications:
•Helical Stair case
•External and internal threads
•Worm
•Shape of Springs
•Helical grooved cam for automation

11. Prof.A.J.More AISSMS's IOIT Pune SlideNo-11

12. Thank You
SlideNo-12Prof.A.J.More AISSMS's IOIT Pune