JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year MECHANICAL TECHNOLOGY Previous Question Paper (March - 2022 - R15)

Cam mechanisms are used to convert rotary motion into reciprocating or oscillating motion of a follower. The motion of the follower is determined by the profile of the cam. The primary types of follower motions are:

1. Uniform Velocity Motion: The follower moves at a constant velocity. The displacement diagram is a straight line. This motion results in infinite acceleration at the beginning and end of the stroke, causing severe vibrations and wear, making it unsuitable for high-speed applications.

2. Simple Harmonic Motion (SHM): The follower moves with the velocity of a point projected from a circle onto its diameter. The displacement diagram is a sine curve. This motion provides smooth acceleration and deceleration, making it suitable for moderate-speed applications.

3. Uniform Acceleration and Retardation Motion: The follower accelerates uniformly for the first half of the stroke and decelerates uniformly for the second half. The displacement diagram is parabolic. This motion is ideal for high-speed cams as it minimizes the shock and impact forces.

4. Cycloidal Motion: The follower displacement follows a cycloid curve. This motion provides the smoothest operation with zero acceleration at both the start and end of the stroke, making it the preferred choice for high-speed, high-precision machinery to minimize vibration and noise.

Diagrams would typically show the displacement (y-axis) versus the cam rotation angle (x-axis) for each motion type. The uniform velocity graph is a straight diagonal line; SHM is a smooth sinusoidal wave; uniform acceleration/retardation is a series of parabolic arcs; and cycloidal motion is a smooth curve derived from a circle rolling along a straight line.

Given data: Minimum radius of cam (r_min) = 25 mm, Roller radius (r_r) = 3.75 mm, Base circle radius (r_b) = r_min + r_r = 28.75 mm, Lift (L) = 28 mm, Angle of ascent (θ_a) = 60° (π/3 rad), Angle of descent (θ_d) = 90° (π/2 rad), Speed (N) = 200 rpm, Angular velocity (ω) = 2πN/60 = 20.94 rad/s.

1. Kinematic Calculations:

For uniform acceleration and deceleration, maximum velocity (v_max) = 2Lω / θ, and maximum acceleration (a_max) = 4Lω² / θ².

Outstroke (Ascent):

Return stroke (Descent):

2. Cam Profile Construction Steps:

1. Draw the base circle with radius 28.75 mm and the prime circle with radius 25 mm.
2. Mark the starting position of the follower at 0°. Divide the ascent angle (60°) into 6 equal parts and the descent angle (90°) into 6 equal parts.
3. Calculate displacement (s) for each division using the parabolic motion formula: s = 2L(θ/θ₀)² for the first half and s = L - 2L(1 - θ/θ₀)² for the second half.
4. Plot these displacements radially outward from the prime circle.
5. Draw circles of radius 3.75 mm (roller radius) at each displacement point.
6. Draw a smooth tangent curve touching the top of all roller circles to obtain the cam profile.