source: norton, design of machinery introduction to cam...

At the end of this video, you should be able to:• Explain what a cam is, how it is used, and the typical types of cams• Identify force closed and form closed followers and explain the

benefits and limitations of each• Describe the primary types of cam motion programs

Introduction to Cam DesignSource: Norton, Design of Machinery

What is a Cam and Follower?Cam: specially shaped part designed to move a follower in a controlled fashionFollower: a link constrained to rotate or translate

• A cam‐follower is a degenerate 4‐bar linkage

Source: Norton, Design of Machinery

What are Cams Used For?

• Valve actuation in IC engines• Motion control in machinery• Force generation• Precise positioning• Event timing

Overhead Valve Overhead Camshaft

Valve Trains

Source: Norton, Cam Design and Manufacturing Handbook

Industrial Cam Trains


Hydraulic Pump Application

Stationary segment

Stationary-axial-track

Radial or plate

Barrel or axial - track

Radial or plate

Radial track

Types of Cams


Types of Followers


Force Closed:

Two Ways to Close Follower Joint

Form Closed: Source: Norton, Design of Machinery

Conjugate Cams


Barrel Cams

Tracked:z

FIGURE 13-13

Ribbed barrel cam with oscillating roller follower

Ribbed:


Rotary Indexers Use Ribbed Barrel Cams

Types of Cam Motion Programs

• No‐Dwell or Rise‐Fall (RF)• Single‐Dwell or Rise‐Fall‐Dwell (RFD)• Double‐Dwell (RDFD)• Multi‐Rise‐Multi‐Dwell‐Multi‐Fall

• Different Motion Programs Needed for Each

A Cam Timing Diagram

FIGURE 2-2

A cam timing diagram

1

0

Motionmm or in

Lowdwell

Highdwell

Rise Fall

1.00.25 0.50 0.750 Time t sec

90 180 270 3600 Cam angle θ deg

SVAJ Diagrams

S

V

A

J

At the end of this video, you should be able to:• Describe the difference between critical extreme position and

critical path motion• Explain how the fundamental law of cam design applies to selecting

an appropriate cam profile• Design double dwell cam profiles using a variety of motion types

Cam Motion Design: Critical Extreme Position


Unwrapping Cam Profile

θ

S - Position


Type of Motion Constraints

• Critical Extreme Position (CEP)– End points of motion are critical– Path between endpoints is not critical

• Critical Path Motion (CPM)– The path between endpoints is critical– Displacements, velocities, etc. may be specified– Endpoints usually also critical

Double Dwell Cam Timing Diagram

FIGURE 2-2

A cam timing diagram

1

0

Motionmm or in

Lowdwell

Highdwell

Rise Fall

1.00.25 0.50 0.750 Time t sec

90 180 270 3600 Cam angle θ deg

Naïve and Poor Cam Design: Constant Velocity

FIGURE 2-3

The s v a j diagrams of a "bad" cam design—pure constant velocity

h

0

s

v

0

90 180 270 3600

a

0

j

0

∞ ∞

∞∞

Lowdwell

HighdwellRise Fall

degθ

degθ

degθ

degθ

∞ 2

(a)

(b)

(c)

(d )

∞ 2

∞ 2 ∞ 2

Constant Acceleration (Parabolic Displacement)?

FIGURE 2-6

Constant acceleration gives infinite jerk

(a) Acceleration

(b) Jerk

Lowdwell

HighdwellRisea

0

j

∞

∞

∞

θ

θ

maxa

mina

0

0 β

0 β

Simple Harmonic Motion (SHM)?

sh

vh

ah

jh

= (2.6a)

= (2.6b)

= (2.6c)

= – (2.6d)

2

3

21

2

2

2

2

3

−⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

cos

sin

cos

sin

π θβ

πβ

π θβ

πβ

π θβ

πβ

π θβ

Norton’s Fundamental Law of Cam Design:The cam-follower function must have continuous

velocity and acceleration across the entire interval, thus making the jerk finite.

Choosing Cam Functions

• They must obey the fundamental law• Lower peak acceleration is better: F = ma• Lower peak velocity lowers KE = 0.5mv2

• Smoother jerk means lower vibrations• Magnitude of jerk is poorly controlled in manufacturing

Acceptable Double Dwell Function:Cycloidal Motion

Acceptable Double Dwell Function:Modified Trapezoidal Acceleration

Acceptable Double Dwell Function:Modified Sine Acceleration

FIGURE 3-13

Minimum boundary conditions for the double-dwell case

(a)

(b)

(c)

(d )

h

0

s

v

0

a

0

j

0

Lowdwell

HighdwellRise Fall

degθ

degθ

degθ

degθβ20 0β1

β20 0β1

β20 0β1

β20 0β1

Polynomial Functionss C C x C x C x C x C x C x C xn

n= + + + + + + + +0 1 22

33

44

55

66 3 19 ( . )

when then(a)

when then

θ

θ β

= = = =

= = = =

0 0 0 0

0 01

; , ,

; , ,

s v a

s h v a

v C C C C C= +⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

12 3 4 51 2 3

2

4

3

5

4

βθβ

θβ

θβ

θβ

(d)

a C C C C= +⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

12 6 12 202 2 3 4

2

5

3

βθβ

θβ

θβ

(e)

s C C C C C C= +⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟0 1 2

2

3

3

4

4

5

5θβ

θβ

θβ

θβ

θβ

(c)

0 0 0

00

0

= + + +=

C

C

(f)

01

0 0

0

1

1

= + + +[ ]=

βC

C

(g)

01

0 0

0

2 2

2

= + + +[ ]=

βC

C

(h)

h C C C= + +3 4 5 (i)

01

3 4 53 4 5= + +[ ]βC C C (j)

01

6 12 202 3 4 5= + +[ ]β

C C C ( )k

C h C h C h3 4 510 15 6= = − =; ; (l)

The 3‐4‐5 and 4‐5‐6‐7 Polynomials3-4-5 Polynomial 4-5-6-7 Polynomial

Comparison of Five Double-Dwell Fcns

At the end of this video, you should be able to:• Describe why a double‐dwell profile is not ideal for a single‐dwell

cam• Construct the boundary conditions for a polynomial cam segment• Solve for the coefficients of a polynomial cam segment

Cam Motion Design: Polynomial Deep Dive

Source: http://nptel.ac.in

Single Dwell Cam Design• Rise: 1 inch in 90°• Fall: 1 inch in 90°• Dwell: 180°360°

2 Double‐Dwell Profiles?

Task: Rise‐Fall‐Dwell

Source: http://nptel.ac.in

0 Cycloidal Rise Cycloidal Fall

source: norton, design of machinery introduction to cam...

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