## CAM & FOLLOWER:-(Part-2):-

### 1. Displacement, Velocity and Acceleration Diagrams when the Follower Moves with Uniform Velocity :-

The displacement, velocity and acceleration diagrams when a knife-edged follower moves with uniform velocity are shown in Fig. 1.o(a), (b) and (c) respectively. The abscissa (base) represents the time (i.e. the number of seconds required for the cam to complete one revolution) or it may represent the angular displacement of the cam in degrees. The ordinate represents the displacement, or velocity or acceleration of the follower. Since the follower moves with uniform velocity during its rise and return stroke, therefore the slope of the displacement curves must be constant. In other words, AB1 and C1D must be straight lines. A little consideration will show that the follower remains at rest during part of the cam rotation. The periods during which the follower remains at rest are known as dwell periods, as shown by lines B1C1 and DE in Fig. 1.0 (a). From Fig. 1.o (c), we see that the acceleration or retardation of the follower at the beginning and at the end of each stroke is infinite. This is due to the fact that the follower is required to start from rest and has to gain a velocity within no time. This is only possible if the acceleration or retardation at the beginning and at the end of each stroke is infinite. These conditions are however, impracticable.

Fig. 1.0 Fig. 1.1 |

In order to have the acceleration and retardation within the finite limits, it is necessary to modify the conditions which govern the motion of the follower. This may be done by rounding off the sharp corners of the displacement diagram at the beginning and at the end of each stroke, as shown in Fig. 1.1 (a). By doing so, the velocity of the follower increases gradually to its maximum value at the beginning of each stroke and decreases gradually to zero at the end of each stroke as shown in Fig. 1.1 (b). The modified displacement, velocity and acceleration diagrams are shown in Fig. 1.1. The round corners of the displacement diagram are usually parabolic curves because the parabolic motion results in a very low acceleration of the follower for a given stroke and cam speed.

### 2. Displacement, Velocity and Acceleration Diagrams when the Follower Moves with Simple Harmonic Motion :-

The displacement, velocity and acceleration diagrams when the follower moves with simple harmonic motion are shown in Fig. 1.2 (a), (b) and (c) respectively. The displacement diagram is drawn as follows :

1. Draw a semi-circle on the follower stroke as diameter.

2. Divide the semi-circle into any number of even equal parts (say eight).

3. Divide the angular displacements of the cam during out stroke and return stroke into the same number of equal parts.

4. The displacement diagram is obtained by projecting the points as shown in Fig. 1.3 (a). The velocity and acceleration diagrams are shown in Fig. 1.3 (b) and (c) respectively. Since the follower moves with a simple harmonic motion, therefore velocity diagram consists of a sine curve and the acceleration diagram is a cosine curve. We see from Fig. 1.3 (b) that the velocity of the follower is zero at the beginning and at the end of its stroke and increases gradually to a maximum at mid-stroke. On the other hand, the acceleration of the follower is maximum at the beginning and at the ends of the stroke and diminishes to zero at mid-stroke.

Fig 1.3 |

### 3. Displacement, Velocity and Acceleration Diagrams when the Follower Moves with Uniform Acceleration and Retardation :-

The displacement, velocity and acceleration diagrams when the follower moves with uniform acceleration and retardation are shown in Fig. 1.4 (a), (b) and (c) respectively. We see that the displacement diagram consists of a parabolic curve and may be drawn as discussed below :

1. Divide the angular displacement of the cam during out stroke ( O θ ) into any even number of equal parts (say eight) and draw vertical lines through these points as shown in Fig.1.4 (a).

2. Divide the stroke of the follower (S) into the same number of equal even parts.

3. Join Aa to intersect the vertical line through point 1 at B. Similarly, obtain the other points C, D etc. as shown in Fig. 1.4 (a). Now join these points to obtain the parabolic curve for the out stroke of the follower.

4. In the similar way as discussed above, the displacement diagram for the follower during return stroke may be drawn. Since the acceleration and retardation are uniform, therefore the velocity varies directly with the time. The velocity diagram is shown in Fig. 1.4(b).

Fig 1.4 |

###

4.Displacement, Velocity and Acceleration Diagrams when the Follower Moves with Cycloidal Motion :-

The displacement, velocity and acceleration diagrams when the follower moves with cycloidal motion are shown in Fig. 1.5(a), (b) and (c) respectively. We know that cycloid is a curve traced by a point on a circle when the circle rolls without slipping on a straight line. In case of cams, this straight line is a stroke of the follower which is translating and the circumference of the rolling circle is equal to the stroke (S) of the follower.

Therefore the radius of the rolling circle is /2 S π . The displacement diagram is drawn as discussed below :

1. Draw a circle of radius /2 S π with A as centre.

2. Divide the circle into any number of equal even parts (say six). Project these points horizontally on the vertical centre line of the circle. These points are shown by a′ and b′ in Fig. 1.5 (a).

3. Divide the angular displacement of the cam during outstroke into the same number of equal even parts as the circle is divided. Draw vertical lines through these points.

4. Join AB which intersects the vertical line through 3′ at c. From a′ draw a line parallel to AB intersecting the vertical lines through 1′ and 2′ at a and b respectively.

5. Similarly, from b′ draw a line parallel to AB intersecting the vertical lines through 4′ and 5′ at d and e respectively.

6. Join the points A a b c d e B by a smooth curve. This is the required cycloidal curve for the follower during outstroke.

Fig 1.5 |

STAY TUNED.

©Mukesh Ch. Joshi

@ joshimukesh410820@gmail.com

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