Kinematics of Machines

1. Lecture by
Mr. B. B. Sangame
Assistant Professor
Department of Mechanical Engineering
Theory of Machines-I

2. A cam is a rotating machine element which gives reciprocating or oscillating
motion to another element known as follower.
The cam and the follower have a line contact and constitute a higher pair.
The cams are usually rotated at uniform speed by a shaft, but the follower
motion is predetermined
Introduction
Classification of Followers
1. According to the surface in contact.
(a) Knife edge follower. (b) Roller follower.

3. (c) Flat faced or
mushroom follower.
(d) Spherical faced follower
2. According to the motion of the follower. :
(a) Reciprocating or translating follower.
(b) Oscillating or rotating
follower.
The followers as shown in Fig. (a) to (d) are all
reciprocating or translating followers.
The follower, as shown in Fig (e), is
an oscillating or rotating follower.

4. 3. According to the path of motion of the follower.
(a) Radial follower. When the motion of the follower is along an axis passing through the centre of the cam, it
is known as radial follower. The followers, as shown in Fig. (a) to (e), are all radial followers.
(b) Off-set follower.

5. Classification of Cams
1. Radial or disc cam. In radial cams, the follower reciprocates or oscillates in a direction
perpendicular to the cam axis.
2. Cylindrical cam. In cylindrical cams, the follower reciprocates or oscillates in a direction
parallel to the cam axis. The follower rides in a groove at its cylindrical surface.

6. Terms Used in Radial Cams
1. Base circle.
2. Trace point.
3. Pressure angle.
4. Pitch point.
5. Pitch circle.
6. Pitch curve.
7. Prime circle.
8. Lift or stroke.

7. The follower, during its travel, may have one of the following motions.
1. Uniform velocity,
2. Simple harmonic motion,
3. Uniform acceleration and retardation, and
4. Cycloidal motion.
Motion of the Follower

8. Displacement, Velocity and Acceleration Diagrams when the
Follower Moves with Uniform Velocity

9. Displacement, Velocity and Acceleration Diagrams when the
Follower Moves with Simple Harmonic Motion (SHM)
Let S = Stroke of the follower,
θO and θR = Angular displacement of the cam
during out stroke and return stroke of the
follower respectively, in radians, and
ω = Angular velocity of the cam in rad/s.
velocity of the follower on the outstroke,
𝑉𝑜 =
πωS
2θO
velocity of the follower on the return
stroke,
𝑉𝑅 =
πωS
2θR
Maximum acceleration of the follower on
the outstroke,
𝑎𝑜 =
π2ω2S
2(θO)2
Maximum acceleration of the follower on the
return stroke
𝑎𝑅 =
π2ω2S
2(θR)2

10. Displacement, Velocity and Acceleration Diagrams when the
Follower Moves with Uniform Acceleration and Retardation
Let S = Stroke of the follower,
θO and θR = Angular displacement of the cam
during out stroke and return stroke of the
follower respectively, in radians, and
ω = Angular velocity of the cam in rad/s.
velocity of the follower on the outstroke,
𝑉𝑜 =
2ωS
θO
velocity of the follower on the return
stroke,
𝑉𝑅 =
2ωS
θR
Maximum acceleration of the follower on
the outstroke,
𝑎𝑜 =
4ω2S
(θO)2
Maximum acceleration of the follower on the
return stroke
𝑎𝑅 =
4ω2S
(θR)2

11. Displacement, Velocity and Acceleration Diagrams when the
Follower Moves with Cycloidal Motion
Let S = Stroke of the follower,
θO and θR = Angular displacement of the cam
during out stroke and return stroke of the
follower respectively, in radians, and
ω = Angular velocity of the cam in rad/s.
velocity of the follower on the outstroke,
𝑉𝑜 =
2ωS
θO
velocity of the follower on the return
stroke,
𝑉𝑅 =
2ωS
θR
Maximum acceleration of the follower on
the outstroke,
𝑎𝑜 =
2πω2S
(θO)2
Maximum acceleration of the follower on the
return stroke
𝑎𝑅 =
2πω2S
(θR)2