Cam Design

What is a Cam and Follower? A cam is a rotating or sliding piece in a mechanical linkage used especially in

transforming rotary motion into linear motion or vice-versa A follower is a link or

linkage train that is constrained to move in translation or in rotation (oscillation)

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.

+/- : Cam-Follower? + : Easy to design

+ : The cam-follower train is a degenerate form of a pure fourbar linkage

(oscillation) or four-bar slider-crank (translation). The variable link length feature

makes it a flexible and useful function generator.

+ : Where a stroke starts & ends at a dwell,

especially for intermittent motion.

Equivalence: pin-joint 4-bar linkage Equivalence: Slider-crank 4-bar linkage

- : Difficult and expensive to make

Examples & Basic terminology

Rise : part of the cycle that pushes the follower up (away from cam center)

Return/Fall : part of the cycle that brings the follower down (towards the cam center)

Dwell : part of the cycle where the follower is stationary (no output despite input)

What are Cams Used For?

Valve actuation in IC engines

Motion control in machinery

Force generation

Precise positioning

Event timing

Base circle (BC): Smallest circle that is:

centered at the cams center of rotation, tangent to the cam profile

Terminology

Trace point: Reference point on the follower that represents its motion

# Center of the roller # Tip of the knife edge

Prime circle (PmC): Smallest circle that is

centered at the cams center of rotation,tangent to the pitch curve

Pitch curve: Path of the

TP relative to the cam

Pressure angle: Angle b/w the normal to the pitch curve at any point and the line of motion of the follower.

measures the steepness of the cam profile normal to the pitch curve is the line along which the normal reaction (Rn) acts, and pressure angle tells us what part of that force (Rn cos) is used in moving the follower

Pitch point: The point on the pitch curve having the maximum pressure angle

Terminology

Lift/Throw: Maximum displacement of the follower from the base circle

Terminology

The angle covered by the cam:

for the follower to rise from its lowest (A) to highest (B) position: Angle of Ascent (1)for the follower to fall from its highest (C) to lowest (D) position: Angle of Descent (3) where the follower remains at rest at its highest position: Angle of Dwell (2: different from 4)

Angle of Action: Angle of Ascent + Dwell + Descent

Types of Cam Motion Programs

Double-

Dwell

(RDFD)

Single-Dwell or

Rise-Fall-Dwell (RFD)

No-Dwell or Rise-Fall (RF)

Type of Motion Constraints

Critical Extreme Position (CEP)

End points of the follower motion are critical & hence, specified.

Path between endpoints is not critical & hence, not specified.

Designer has greater freedom to choose the cam functions which control the motion b/w extremes.

The motion programs RF; RFD; and RDFD, refer to the CEP case of motion constraint.

Critical Path Motion (CPM)

The path between endpoints is critical

Displacements and its derivatives- velocities, etc. may be specified

Endpoints usually also critical

The Fundamental Law of Cam Design

The cam-follower function must:

- Be continuous through the first and second

derivatives of displacement, across the entire

interval of cam rotation (360)

- Be such that the displacement, velocity and

acceleration functions have no discontinuities,

across the entire interval of cam rotation (360).

- Be such that the jerk (derivative of acceleration)

is finite across the entire interval of cam rotation

(360).

Cam design: Role of SVAJ DiagramsThe first task faced by the cam designer is to select the mathematical functions to be

used to define the motion of the follower.

The easiest approach is to linearize the cam, or unwrap it from its shape, and

consider it as a function ploted on the cartesian axes.

S

V

A

J

Cam profile construction: Role of S diagram

Assume that:

The axis of the followerpasses through the cam axis

Cam rotates clockwise

Rise: 60

High dwell: 45

Fall: 90

Low dwell: Rest

1. Circle 50mm dia; angles AOC, COD, DOE for

rise, high-dwell, fall

2. Divide AOC & DOE in same no. of parts: S diag

Mark the radial intersections, as 1-6 & 1-6

3. Mark distances 1-a, 6-f & 1-a6-f,

Equal to corresponding distance as in S diagram.

Cam profile construction: Role of S diagram

Constant Velocity follower (Linear displacement): Unacceptable

Finite velocity

in zero time

Infinite

Acceleration

(inertial forces)

Constant Acceleration follower (Parabolic disp): Unacceptable

Finite Acceleration

In zero time

Infinite Jerk

(inertial forces)

Simple Harmonic Motion for the follower : Unacceptable

Harmonic functions have the property of remaining continuous throughout any number of

differentiations

h Stroke of the follower

Angle turned by the cam during outstroke

Angle turned by the cam in time t: =t

x Lift (displacement) of the follower in time t

Angle turned by the point P on the circumference

of the semicircle in time t

Cam angle: == Angle by P ():

Cam angle: == Angle by P: = /

x= h/2-h/2 cos

Simple Harmonic Motion for the follower : Unacceptable

s =h

21cos

(2.6a)

v =

h

2sin

(2.6b)

a =2

2h

2cos

(2.6c)

j = 3

3h

2sin

(2.6d)

Only Rise

Adjacent

dwell

Divide the semicirclein as many equal parts as

the rise of the follower

Draw horizontal lines fromcircle nodes, locate their

intersections with the vertical

lines at the rise plots

Unacceptable Double-Dwell Functions

Constant velocity (linear displacement)

Constant acceleration (parabolic displacement)

Simple harmonic motion

Some Acceptable Double-Dwell Functions

Cycloidal

Modified Trapezoidal

Modified Sine

Cycloidal Motion of the follower: Acceptable

A cycloid is a curve traced by a point on a circle when the circle rolls on a straight line

(without slipping)

Cycloidal Motion of the follower: Acceptable

A cycloid is a curve traced by a point on a circle when the circle rolls on a straight line

(without slipping)

Cycloidal Motion of the follower: Acceptable

A cycloid is a curve traced by a point on a circle when the circle rolls on a straight line

(without slipping)

Cycloidal Motion of the follower: Acceptable

Ca = 6.28

Cv = 2.00

Cj = 40

Zero slope

Polynomial functions: Cams designed to be acceptable

The general form of a polynomial function is

nth degree polynomial engages n+1 constants

So, if K boundary conditions are known, one can

approximate up to a polynomial of degree K-1

Polynomial functions: Cams designed to be acceptable

Low dwell At zero displacement for 90

Rise 1 unit = 25 mm, in 90

High dwell At 1 unit = 25 mm for 90

Fall 1 unit = 25 mm, in 90

Cam: 2 rad/sec= 1 rev/sec

Design a cam meeting the following design specifications

Global 0 90 180 270 360

Local

Low D 0 1

Rise 0 1

High D 0 1

Fall 0 1

Polynomial functions: Cams designed to be acceptableLow dwell At zero displacement for 90

Rise 1 unit = 25 mm, in 90

High dwell At 1 unit = 25 mm for 90

Fall 1 unit = 25 mm, in 90

Cam: 2 rad/sec= 1 rev/sec

v,a: zero due to dwell

(2 BCs)

s,v,a: zero due to dwell

(3 BCs)

s,v,a: zero due to dwell

(3 BCs)

v,a: zero due to dwell

(2 BCs)s=h=25 (1 BC)

s=0 (1 BC)

Focussing on rise, we have 6 BCs,

implying we can consider a 5th

order polynomial

Polynomial functions: Cams designed to be acceptableLow dwell At zero displacement for 90

Rise 1 unit = 25 mm, in 90

High dwell At 1 unit = 25 mm for 90

Fall 1 unit = 25 mm, in 90

Cam: 2 rad/sec= 1 rev/sec

Rise: BCs

Polynomial functions: Cams designed to be acceptableLow dwell At zero displacement for 90

Rise 1 unit = 25 mm, in 90

High dwell At 1 unit = 25 mm for 90

Fall 1 unit = 25 mm, in 90

Cam: 2 rad/sec= 1 rev/sec

Rise: BCs

Polynomial functions: Cams designed to be acceptableLow dwell At zero displacement for 90

Rise 1 unit = 25 mm, in 90

High dwell At 1 unit = 25 mm for 90

Fall 1 unit = 25 mm, in 90

Cam: 2 rad/sec= 1 rev/sec

3-4-5 polynomial