mechanism

1. Cams
• A cam is an irregular-shaped mechanical member for transmitting a desired motion to another
element, known as the follower, by direct contact.
• The cam and the follower have a line contact and constitute a higher pair.
• A cam may remain stationary, translate or rotate while the follower may translate or oscillate.
• Usually cams rotate at constant angular speed.
• Cams provide a means of achieving any desired follower motion and are used in many
machine.
• They are widely used for operating the inlet and exhaust valves of internal combustion
engines, and are extensively used in machine tools, mechanical computers, instruments and
many other applications.

2. Classification of Followers
• Followers may be classified based on the following
1. Construction of the surface of contact
2. Type of follower motion
3. Location of line of motion with respect to center of cam

3. classification of followers based on surface of contact
• The classification of followers based on follower surface of contact
a) A knife-edge follower: in such a follower a sharp, knife-edge is in contact with the
cam. Such followers produce excessive cam wear, so they are of little practical use.
b) A roller follower: A cylindrical roller, held by a pin to the follower assembly, is in
contact with the cam. At low speeds pure rolling contact is possible but at high speeds
some sliding can also occur. These types of followers reduce wear of the cam surface at
high peripheral speeds.
c) A flat-faced follower: as the name implies, flat face is in contact with the cam. These
types of followers cause high surface stress and reduce and reduce this stress, the flat
face is modified to a spherical surface with a large radius.

4. • Fig 3.2 cam followers (a) knife-edge follower, (b) roller follower,
(c) flat-faced follower, (d) spherical-faced follower

5. Classification of followers based on type of follower motion
• The classification of followers based on type of follower motion is
represented in fig below.
a) Translatory followers: as the cam rotates, the follower reciprocates in
guides.scillates through a certain angle.
b) Oscillatory followers: for a uniform rotary motion of the cam, the
follower oscillates through a certain angle

6. Classification of followers based on follower line of motion
Fig 3.3 is again used to represent classification of followers based on
follower line of motion.
a) Radial followers: these followers translate along an axis passing through
the cam center of rotation.
b) Off-set followers: the axis of follower movement is displaced from the
cam center of rotation.
c) Oscillating followers: these followers oscillate about the axis of the
follower through a certain angle.

7. Classification of cams
• Cams are classified based on:
a. Cam shape as disc cams, translation cams, cylindrical cams, globoidal cams
b. Follower motion:- dwell-rise-dwell-return, dwell-rise-return-dwell
c. Cam construction as spring or pre-loaded cams and positive return cams.
Pre-loaded cams are cams in which the follower is held in contact by an external force provided by
spring, gravity etc.
In positive return cams no external force is required to keep the cam and the follower in contact.

8. Cam Nomenclature
• Base circle is the smallest circle that can be drawn about the center of cam rotation and through the
cam surface. Its size determines the size of the cam.
• Cam profile: The outer surface of the disc cam.
• Trace point: It is a point on the follower, and its motion describes the movement of the follower. It
is used to generate the pitch curve.
• Pitch curve : The path generated by the trace point as the follower is rotated about a stationery
cam.
• Prime circle: The smallest circle from the cam center through the pitch curve

9. • Pressure angle: The angle between the direction of the follower movement and the normal to the
pitch curve.
• Pitch point: Pitch point corresponds to the point of maximum pressure angle.
• Pitch circle: A circle drawn from the cam center and passes through the pitch point is called Pitch
circle
• Stroke: The greatest distance or angle through which the follower moves or rotates
• Lift or Rise is the maximum travel of the follower from the lowest position to the top most
position.

10. Fig. 3.4 Cam nomenclature

11. Displacement Diagram
• Before a cam profile is determined, the motion of the follower in
accordance to the requirements of the system must be selected.
• The follower motion is indicated on the displacement diagram.
• The displacement diagram has as an abscissa the cam rotation angle, and the
ordinate is the follower travel in millimeters.
• The divisions of the abscissa are identified by the station point numbers.
• These divisions can be in degrees or in seconds.

12. The displacement diagram identifies the following motion characteristics:
The rise: motion of the follower away from the cam center
The dwells: those periods during which the follower is at rest, and
The return: motion of the follower toward the cam center.

13. Types of follower motion
• The first step in the design of a cam curve consists in constructing the associated displacement
diagram.
• The follower motion might be a standard or a custom type.
• Some of the standard motions are : uniform, modified uniform, simple harmonic, parabolic and
cycloidal.
• Ordinarily, a cam will have one or more rises and, generally, as many returns as rises.
• Dwell periods might not be necessary.
• The rises, dwells and returns must suitably be distributed around the periphery of the cam.
• The periods of these occupy the time of one rotation of the cam.

14. Uniform motion
• A follower has uniform motion when its velocity is constant.
• The follower moves through the same distance for each equal interval of time or cam rotation
angle.
• Uniform motion is the simplest possible cam motion, but shock results from the changes in
velocity from 0 to some finite value or vice-versa.
• For this type of follower motion, there occur theoretically infinite accelerations and decelerations
at the beginning and end of the rise and return motions.
• Before the follower starts to rise it is in the dwell position,between the dwell and rise periods there
is an acceleration and it is infinite.
• Thus the forces transmitted are very large and shock and other secondary effects result.

15. Fig. 3.6 (a) follower displacement diagram for uniform motion, (b) follower velocity and
acceleration for uniform motion

16. Modified uniform motion
• The uniform-motion curve is modified to reduce the shock at the beginning and end of the motion.
• A convenient method is to use circular arcs at the beginning and end of the motion which are
tangent to the dwell and rise lines.
Fig 3.7 Follower displacement diagram with modified uniform motion

17. Parabolic motion
• Parabolic motion is a constant acceleration motion.
• For a given cam speed and follower rise, parabolic motion has the lowest or maximum
acceleration.
• Parabolic motion can be modified to include a constant velocity motion between acceleration and
deceleration
• This follower motion is recommended for low or moderate speeds.
• To construct the displacement diagram use even number of time divisions with least number of
division equal to six.
• Through the origin of the displacement diagram, construct any line at any angle to the y-axis or
displacement axis.
• Divide this line into parts proportional to:
• 1, 3, 5, 5, 3, 1 for six divisions
• 1,3,5,7,7,5,3,1 for eight divisions

18. • Connect the last division with the point marked on the displacement axis corresponding to the rise.
• Through the other divisions draw lines parallel to this line to obtain the follower displacement for each
divisions of cam rotation.
• Fig 3.9. (a) Follower displacement with parabolic motion. (b) follower parabolic motion characteristics

19. Simple Harmonic motion
• The simple harmonic motion is obtained graphically by construction a semi-circle on the rise of the
displacement diagram and then dividing the semi circle into as many equal parts as are used for
the time axis (or cam angle).
• Fig 3.9 (a) Follower displacement for parabolic motion
• (b) follower motion characteristics for parabolic motion

20. Cycloidal Motion
• In order to avoid infinite jerk between rise , return and dwell motions, cycloidal motion is often
employed.
• Cycloidal motion is a motion which has a zero acceleration at the beginning and end of the rise.
• A cycloid is defined as the locus of a point on a circle that rolls on a straight line.
• For cam rotation angle the displacement of the cycloidal motion is the rise AC=d, which must be
equal to the circumference of the rolling circle. Thus
2𝜋𝑟 = 𝑑
From which the radius of the rolling circle r is obtained to be
𝑟 =
𝑑
2𝜋

21. • To construct the displacement diagram for the cycloidal motion.
1. Draw a circle with center B
2. The circle is then divided into as many equal parts as used for the cam angle axis.
3. The points on the circle are projected to a vertical line through B as shown on the figure.
Through these points lines are drawn parallel to AB which intersect with vertical lines drawn
through the divisions on the cam angle axis.
4. The intersection points are joined by a smooth curve to give the cycloidal motion displacement.

22. Example 1
1. Draw the displacement diagram for a radial roller follower that rises 50mm from its lowest
position with a simple harmonic motion in 1/3 of a revolution, dwells for 1/12 of a revolution
and then returns to its lowest position in 1/6 of a revolution with simple harmonic motion to
remain at rest for the rest of the revolution. Assume of roller diameter of 20mm, and minimum
cam radius of 25mm. For the above motion of the follower, lay out the cam profile that would
produce the required motion.
Solution
Follower rise d=50mm
Cam angle for the rise motion 𝛽 =
2𝜋
3
rad =1200
Dwell angle =
𝜋
6
=300

23. Cam angle for the return motion 𝛽′
=
𝜋
3
rad =600
Dwell angle after the return motion =
5𝜋
12
rad=1500
The displacement diagram is drawn to a convenient scale. The procedure of construction is as followers.
1) Draw the horizontal straight line OPQRS with a convenient length. Preferably OS= development of
the prime circle. OPQRS= 3600
Divide the line OS into segments where
OP=1200
, cam angle corresponding to the rise of the follower.
PQ=300
, cam angle Corresponding to the dwell of the follower in its lifted position.
QR= 600
, cam angle corresponding to the return of the follower.
RS= 1500
, cam angle corresponding to the dwell of the follower in its lowest position

24. 2) Draw a Vertical line through O equal to the follower rise.
𝑂𝑓′=50mm
3) Divide the cam angle corresponding to the rise and return motions into equal even number of
divisions, in this case six divisions.
We obtain 0,1,2,3,4,5,6 for the rise and 0′
, 1′
, 2′
, 3′
, 4′
, 5′
, 6′
for the return.
4) With 𝑂𝑓′
as diameter draw a semi-circle and divide it into equal divisions, the number being equal
to that in step 3. this locates a, b,c,d,e, and f. project these points on to the vertical lines through 0, 1,
2, etc and 0′, 1′, 2′, etc. the projections give points A,B,C,D,E,F on the rise and 𝐴′, 𝐵′, 𝐶′, 𝐷′, 𝐸′, 𝐹′
on the return.
5) Join points A,B,C,D,E,F by a smooth curve and so also 𝐴′, 𝐵′, 𝐶′, 𝐷′, 𝐸′, 𝐹′ to obtain the
displacement diagram.

25. The cam curve is laid out according to the following procedure of construction.
1) Draw the prime circle with center C and radius CO.
CO is set equal to minimum radius of cam plus radius of roller.
CO= 25+10mm=35mm
2) Draw
Angle OCP =1200 to represent the follower rise,
Angle PCQ= 300 to represent the dwell of the follower in the outermost position
Angle=QCR=600 to represent the return of the follower to its lowest position
Angles OCP and QCR are divide into even number of division to match the number of divisions in
the displacement diagram. In this case there are six divisions.

26. 3) From the displacement diagram, o, 𝑎′
, 𝑏′
, 𝑐′
, 𝑑′
,and 𝑓′
are transferred to a vertical line through
the trace point o and the cam center C. these points are rotated to intersect with the rise divisions and
return divisions at 1′, 2′, 3′, 4′, 5′, 6′ and 7′, 8′, 9′, 10′, 11′, respectively. With these points as
center, draw the position of the roller.
4) Join points 0, 1′, 2′,…. 11′ to obtain the pitch curve. Draw tangent to the roller position of the
roller.