Unit 23: Applied mathematics for engineering
LO1 and 2
Analysis of a cam
Learner activity sheet
A cam is used in engines to periodically open and close inlet valves and exhaust valves. Cams are
mounted on a camshaft which rotates causing the position of the valves to change.
See http://en.wikipedia.org/wiki/Camshaft
You are to read the descriptions below and answer all of the questions in Activities 1, 2 and 3.
The diagram below shows a cam which rotates about the centre of its heel on a camshaft at point O. For
this particular cam, a straight line joins points A and B and is tangential to the circular profile of both the
heel and the nose at those points. A similar line joins points C and D.
You should generalise the dimensions of the cam by replacing the dimensions shown (16, 12 and 14)
with variables r1, r2 and d respectively. Other essential geometry features such as angles and lengths
should also be assigned variable names. Proceed with the analysis below using these variables and
finally replace the variables with their numerical values to obtain the required numerical solutions. It is
recommended that you create a spreadsheet that will allow dimensions to be changed and required
values to be calculated quickly.
Version 1
Activity 1
Calculate the perimeter of the cam.
Activity 2
Calculate the area of the cam.
Activity 3
As the cam rotates about point O, the distance, x mm, between O and a point directly above O depends
upon the angle, θ, at which the cam is rotated. In the diagram above x = 16, but if the cam is rotated 90o
anticlockwise x = 26. For this cam x will vary between 16 and 26 depending upon the angle of rotation.
The cam lift for any angle of rotation is defined as:
Lift = x – heal radius
The diagram below illustrates this.
Lif
x
θ
O
Calculate the lift when:
(i)
θ = 250o
(ii) θ = 45o
Version 1
O
(iii) θ = 80o
(iv) θ = 130o
(v) Sketch a graph of lift against θ for 0o ≤ θ ≤ 360o.
Version 1