CAMS

Q. 4.1. (a) Define a cam and a follower.

Ans. Cam is a rotating machine part designed to impart reciprocating or oscillating motion to

another part of machine. The part to which motion is given by cart is called followers.

Q 4. 1 (b) Enumerate various types of cams and draw a line diagram of each type

Ans. Two main types of cams are:

(1) Disc or radial cam It shown in fig 4.1, (2) Cylindrical cam It is shown in fig 4.2

Q 4.1. (c) Classify followers depending upon the type of motion.

Ans. (i) Reciprocating follower. Fig. 4.1 Fig. 4.2

(ii) Oscillating follower. Fig. 4.3

Q. 4.1. (d) Classify followers depending upon the axis of motion.

Ans. (i) Radial follower : The axis of follower intersects the axis of cam shaft. Fig. 4.1

(ii) Offset follower : The axis of follower does not intersect the axis of cam shaft. Fig. 4.4

Q. 4.1. (e) Classify followers depending upon the shape of the contacting end.

Ans. (1) Knife edge follower Fig. 4.1

(ii) Roller follower Fig. 4.5

(iii) Flat or mushroom follower Fig. 4.6

(iv) Spherical shaped follower Fig. 4.7

Q. 4.1. (f) Why a roller follower is preferred to knife-edged follower?

Ans. There is a rapid rate at which the knife-edge wears. Therefore roller follower is preferred to

knife-edged follower because there is almost no wear because in case of roller follower the

relative motion is rolling and not of sliding type

Q 4 1 (g) Define cam profile’

Ans. The working contour of a cam which comes into contact with a follower to operate it is

called cam profile. For the cam shown in fig. 4.8, A-B-C-D-A is the cam profile.

Q. 4.1. (h) Define base circle of cam?

Ans. Base circle : It is the smallest circle, drawn from the centre of rotation of a cam,

which forms the part of the cam profile.

Q. 4. 1. (i) Define trace point.

Ans. Trace point: It is the reference point on the follower for the purpose of tracing the cam

profile. It is situated at centre of roller in roller follower and at knife-edge in case of knife-edge

follower.

Q. 4.1. (j) Define prime circle of cam.

Ans. Prime Circle: In case of roller follower the radius of prime circle is equal to the sum of the

base circle radius and the roller radius. In case of knife-edge follower and flat faced follower the

prime circle and base circle are identical.

Q. 4.1. (k) Define pitch curve of cam.

Ans. Pitch curve : It is the curve traced by pitch point if we assume that the cam is stationary and

the follower is moving around the cam.

Q. 4.1. (l) Define pressure angle of cam.

Ans. Pressure angIe: It is the angle between the line of motion of follower and the

normal to the pitch curve.

Q. 4.1. (m) Define pitch point of cam.

Ans. Pitch point: It is that point on the pitch curve at which the pressure angle is maximum.

Q. 4.1. (n) Define pitch circle of cam.

Ans. Pitch circle : It is that circle which has centre at cam centre & passes through

pitch point.

Q. 4.1 (o) Define period, of dwell.

Ans. Period of dwell : It is the period during which the follower remains stationary for some

finite rotation of cam.

Q. 4.1 (p) Define lift of follower.

Ans. Lift or stroke : The maximum travel of follower from the lowest position to the highest

position is called lift or stroke of the follower.

Q. 4.1. (q) What are the different types of motions with which a follower can move?

Ans. (I) Simple harmonic motion.

(ii) Uniform acceleration and uniform retardation motion.

(iii) Uniform velocity i.e. modified uniform velocity motion.

(iv) Cycloidal motion

(v) ‘Any desired motion.

Q. 4.1 (r) List some applications of cam.

Ans. Cams are used in:

(i) Internal combustion engine to open and close the valves.

(ii) Automatic machine tools to give motion to the cutting tool.

(iii) Shoe making machines.

SECTION—B

Q. 4. 2. Derive expressions for displacement, velocity and acc. of follower moving with

SHM and draw these diagrams.

Q. 4.3. Derive expressions for displacement, velocity and acc. of follower which moves with

cycloidal motion and draw these diagrams.

Ans. Let S stroke of follower

= angle through which cam rotates for outstroke of follower.

w = angular speed of cam.

As motion is cycloidal, therefor radius and speed of rolling of an imaginary circle are:

The circle rolls through angle 13 when cam rotates through 0 and point A on circle moves to A.

Q. 4.4. Derive expressions for displacement, velocity and acc. of follower which moves first

with uniform aoc and then with uniform retardation Also draw the displacement, velocity

and acc the diagrams

Q. 4.5. A follower covers out stroke of 36 mm with S.H.M. in 600 rotation of cam. If the

cam speed is 240 rpm, find the max. velocity and max acc. of the follower.

Q. 4.6. A follower moves with uniform acc. and retardation in 60° cam rotation. The cam

speed is 300 rpm and follower stroke is 40 mm. Calculate the max vel. and max acc of

follower.

Q. 4.7 A follower covers stroke of 25 mm with cycloidal motion in 1200 cam rotation Cam

speed is 300 rpm Calculate the maxm velocity and the maxm acc of follower

Q. 4.9 A cam rotatitig clockwise is to give the roller follower of 20 mm diameter the

following motion

(z) Follower to moe outwards 30 mm during 1200 of cam rotation

(ii) Dwell for 60° of cam rotation.

(iii) Return to original position during 90° of cam rotation.

(iv) Dwell for 90° of cam rotation.

The minimumcam is 45 mm and line of stroke is off set 15 mm from the axis of cam. The

displacement of follower is to take place with S.H.M. in outward and return strokes. Draw

the cam profile.

Cam Profile:

Radius of off-set circle = 15 mm.

Draw these two circles.

Draw a vertical tangent to off-set cirde. This is the line of stroke of follower. It meets prime

circle at A.

Joint AO and take OB, OC, OD at 120°, 60° and 90° respectively.

Divide AB and CD rn SIX parts at 1, 2, 5, 4 Draw tangents to off-set circle from these points.

Take I — a equal to I — a of displacement diag. and so on.

With a, h, c h’, a’, D as centre, drawn arcs of radius of roller of follower.

Draw a smooth curve touching the bations of these arcs. This curve represents the cam profile.

Q. 4.10. Draw a neat sketch of tangent cam with roller follower and derive relationship

among its main dimensions.

Ans.

EG and H J are straight flanks. They merge with circular nose at G and H, and with the base

circle at J and F.

The fig. 4.21 shows the follower in the lowest position. When the cam rotates through angle 0,

the line OC will become vertical and follower will get displaced through distance x,

Q 4.12 Write the expressions for maximum velocity and maximum acc, when the roller

follower is at straight flank

Ans From (i) and (ii) of previous question it is clear a that z’ and a increases with 0

When the cam has turned through angle (a. — the roller centre is at M, the displacement is x’ of

roller is x’.

Q. 4.14. In a tangent cam with roller follower, the base circle radius is 25 mm, roller dia 25

mm, angle of ascent 600, lift 12.5 mm, cam shaft speed is 100 rad/s. Determine

(i) The main dimensions of the cam

(ii) The yelloew c. of follower at the beginning of lift

(iii) The velocity and acc of follower at the point where flank merges with circular

nose.

The acc. at the apex of the circular nose,

Q. 4.15. In a tangent cam with roller follower the base circle dia is 90 mm, roller

diameter 40 mm, Angle bctween tagential faces 9Q0, nose circle radius 5 mm and

speed of cam is 120 rpm. Determine the acc. of roller (i) when roller just leave

contact of the flank on its ascent, (ii) when the roller is at its outer end of its lift

Q. 4.16. Derive expressions for velocity and acc. of flat faced follower in contact with

flank of circular arc cam.

Ans. As shown in Fig: 4.23:

When the cam rotates through angle 9about 0, the contact will be at C and the x will be

the displacement of follower

Q. 4.17. Derive expressions for the velocity and aec. of flat-faced follower when in contact

with nose of circular arc cam

Ans Fig 4 24

Wen the cam turns through angle 0 > 4), the contact of follower is at at nose and displacement of

follower is

Q. 4.18 A cam operating a mushroom ended follower has the following dimensions:

Base circle radius 16 5 mm, lift, 725 mm, nose radius 1 6 mm If the total permitted d of

Opening & closing of the valve corresponds to 1100 of cam rotation, determine the flank

radius and maxm. Velocity, acc., and retardation of follower for 900 rpm cam speed.

Ans. Refer to fig. 4.24 and fig. 4.25

Q. 4.19 The following data relates to circular arc cam and flat-faced follower:

Least radius of cam 30 mm, lift 12.5 mm, ascent angle 55°, nose radius 3 mm.

Determine: -

(i) Distance between can centre and nose centre

(ii) Circular flank radius

(iii) Angle of contact on circular flank.

Ans. Refer to fig. 4.23 and fig. 4.24.

Q. 4.20. A circular arc cam operating a mushroom follower has the following particulars:

base circle radius 31.75 mm, nose radus 8 mm, distance between the two centres 40 mm,

semi-angle of action 75°, angle of action on flank 40°, speed 500 rpm.

Calculate:

(i) Flank radius

(ii) Acc. of follower at the beginning of lift, at the end of, lift, at the junction of flank and

nose.

Q. 4.21. Draw the profile of a cam with a flat faced follower as per following specifications

Cam to rotate in anticlockwise direction. Follower to move outward through 3 cm during

1200 of cam rotation. Follower to dwell for 600 of cam rotation. Follower to return to its

initial position during 120° of cam rotation. Follower to dwell for the remaining period of

cam rotation.

The minimum radius of cam is 1.75 cm. The outward and inward strokes are to take place

with uniform (modified) velocity and SHM respectively.

Ans.

1. For displacement diagram, take AD = 1200, BC = 60° and CD = 1200 according to scale and

complete the diagram as fig. 4.25.

2. Draw a circle of minimum radius 1.75 cm as given

3. Let OA is line of stroke.

4. Draw radius OB at 1200 to OA radius in clockwise direction because the cam is to rotate in

anticlockwise direction

5. Similarly draw OC at 60° to radius OB.

6. Draw radius OD at 120° to radius OC.

7. Divide arc AB in four parts.

8. Divide arc CD in six parts as per displacement diagram.

9. Set off the displacement of the follower along the corresponding radial lines Beyond the

minimum radius of circle.

10. At each one of these points draw lines perpendicular to the radial lines.

11. Draw a curve touching all these lines. This curve is the cam profile, as in Fig. 4.26.