CAM & FOLLOWER:-( Part-3) Radial Cam Tutorial

CAM & FOLLOWER:-( Part-3) :- Radial Cam with Knife Edge Follower Tutorial:

⇒Construction of Cam Profile for a Radial Cam :-

In order to draw the cam profile for a radial cam, first of all the displacement diagram for the given motion of the follower is drawn. Then by constructing the follower in its proper position at each angular position, the profile of the working surface of the cam is drawn.

In constructing the cam profile, the principle of kinematic inversion is used, i.e. the cam is imagined to be stationary and the follower is allowed to rotate in the opposite direction to the cam rotation. 

The construction of cam profiles for different types of follower with different types of motions are discussed in the following examples. 

Q. A cam is to give the following motion to a knife-edged follower : 

     1. Outstroke during 60° of cam rotation ; 

     2. Dwell for the next 30° of cam rotation ; 

     3. Return stroke during next 60° of cam rotation, and 

    4. Dwell for the remaining 210° of cam rotation.

The stroke of the follower is 40 mm and the minimum radius of the cam is 50 mm. The follower moves with uniform velocity during both the outstroke and return strokes. Draw the profile of the cam when 

(a) the axis of the follower passes through the axis of the cam shaft, and

(b) the axis of the follower is offset by 20 mm from the axis of the cam shaft.

Sol.

Construction:-

Fig 2.1  

First of all, the displacement diagram, as shown in Fig. 2.1, is drawn as discussed in the following steps :-

1. Draw a horizontal line AX = 360° to some suitable scale. On this line, mark AS = 60° to represent out stroke of the follower, ST = 30° to represent dwell, TP = 60° to represent return stroke and PX = 210° to represent dwell. 

2. Draw vertical line AY equal to the stroke of the follower (i.e. 40 mm) and complete the rectangle as shown in Fig. 2.1. 

3. Divide the angular displacement during outstroke and return stroke into any equal number of even parts (say six) and draw vertical lines through each point. 

4. Since the follower moves with uniform velocity during outstroke and return stroke, therefore the displacement diagram consists of straight lines. Join AG and HP. 

5. The complete displacement diagram is shown by AGHPX in Fig. 2.1. 

(a) Profile of the cam when the axis of follower passes through the axis of cam shaft :-

The profile of the cam when the axis of the follower passes through the axis of the cam shaft, as shown in Fig. 2.2, is drawn as discussed in the following steps :-

Fig 2.2

1. Draw a base circle with radius equal to the minimum radius of the cam (i.e. 50 mm) with O as centre. 

2. Since the axis of the follower passes through the axis of the cam shaft, therefore mark trace point A, as shown in Fig. 2.2. 

3. From OA, mark angle AOS = 60° to represent out stroke, angle SOT = 30° to represent dwell and angle TOP = 60° to represent return stroke. 

4. Divide the angular displacements during out stroke and return stroke (i.e. angle AOS and angle TOP) into the same number of equal even parts as in displacement diagram. 

5. Join the points 1, 2, 3 ...etc. and 0′,1′, 2′, 3′ ,  ... etc. with centre O and produce beyond the base circle as shown in Fig. 2.2.

6. Now set off 1B, 2C, 3D ... etc. and 0′H,1′J ... etc. from the displacement diagram. 

7. Join the points A, B, C,... M, N, P with a smooth curve. The curve AGHPA is the complete profile of the cam.

NOTE :- The points B, C, D .... L, M, N may also be obtained as follows : 

1. Mark AY = 40 mm on the axis of the follower, and set of Ab, Ac, Ad... etc. equal to the distances 1B, 2C, 3D... etc. as in displacement diagram.

2. From the centre of the cam O, draw arcs with radii Ob, Oc, Od etc. The arcs intersect the produced lines O1, O2... etc. at B, C, D ... L, M, N. 

(b) Profile of the cam when the axis of the follower is offset by 20 mm from the axis of the cam shaft :-

The profile of the cam when the axis of the follower is offset from the axis of the cam shaft, as shown in Fig. 2.3, is drawn as discussed in the following steps :-

Fig

1. Draw a base circle with radius equal to the minimum radius of the cam (i.e. 50 mm) with O as centre. 

2. Draw the axis of the follower at a distance of 20 mm from the axis of the cam, which intersects the base circle at A. 

3. Join AO and draw an offset circle of radius 20 mm with centre O. 

4. From OA, mark angle AOS = 60° to represent outstroke, angle SOT = 30° to represent dwell and angle TOP = 60° to represent return stroke.

5. Divide the angular displacement during outstroke and return stroke (i.e. angle AOS and angle TOP) into the same number of equal even parts as in displacement diagram. 

6. Now from the points 1, 2, 3 ... etc. and 0,1,2,3 ′′′′... etc. on the base circle, draw tangents to the offset circle and produce these tangents beyond the base circle as shown in Fig. 2.3. 

7. Now set off 1B, 2C, 3D ... etc. and  0′H,1′J ... etc. from the displacement diagram. 8. Join the points A, B, C ...M, N, P with a smooth curve. The curve AGHPA is the complete profile of the cam.

Credit (Resources):- Theory of machine by Khurmi & Gupta.

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