Cam Design

CAM DESIGN

Chapter 8

Introduction

Terminology

• Type of Follower Motion

– Rotating follower

Terminology

• Type of Follower Motion

– Translating follower

Terminology

• Type of Joint Closure

– Force

Terminology

• Type of Joint Closure

– Form

Terminology

• Type of Follower

– Flat-faced – Roller

Terminology

• Type of Follower

– Mushroom

Terminology

• Type of Cam

– Radial

• Previous Figures

– Axial

Terminology

• Type of Motion Constrains

– Critical Extreme Position (CEP)

– Critical Path Motion (CPM)

• Type of Motion Program

– RF: rise-fall

– RFD: rise-fall-dwell

– RDFD: rise-dwell-fall-dwell

SVAJ Diagrams

Double-Dwell Cam

Double-Dwell Cam

• Example 8.1 A Bad Cam!

– Consider the following cam design CEP

specification• dwell at zero displacement for 90 degrees

• rise 1 in (25 mm) in 90 degrees

• dwell at 1 in (25 mm) for 90 degrees

• fall 1 in (25 mm) in 90 degrees

• cam 2π rad/sec

Double-Dwell Cam

Double-Dwell Cam

• Fundamental Law of Cam Design

– The cam function must be continuous

through the first and second derivatives

of displacement across the entire

interval (360 degrees)

• The jerk function must be finite across the

entire interval

• Functions

– Simple Harmonic Motion (SHM)

– Cycloidal Displacement

Double-Dwell Cam

– Combine

» Constant Acceleration

» Trapezoidal Acceleration

» Modified Trapezoidal Acceleration

» Modified Sinusoidal Acceleration

– Sine-Constant-Cosine-Acceleration (SCCA)

– Polynomials

Double-Dwell Cam

– Simple Harmonic Motion (SHM)

sin2

cos2

sin2

cos12

3

3

2

2

hj

ha

hv

hs

Double-Dwell Cam

– Cycloidal Displacement

• Start with the acceleration function (sine

wave)

2sin2

1

2cos1

2cos4

2sin2

3

2

2

hs

hv

hj

ha

Double-Dwell Cam

– Combined Functions

• Constant Acceleration

Double-Dwell Cam

– Combined Functions

• Trapezoidal Acceleration

Double-Dwell Cam

– Combined Functions

• Modified Trapezoidal Acceleration

Double-Dwell Cam

– Combined Functions

• Modified Trapezoidal Acceleration

Double-Dwell Cam

– Combined Functions

• Modified Sinunusoidal Acceleration

Double-Dwell Cam

– Combined Functions

• Modified Sinunusoidal Acceleration

Double-Dwell Cam

– Sine-Constant-Cosine-Constant (SCCA)

• A family of acceleration functions that includes

constant acceleration, simple harmonic, modified

trapezoid, modified sine, and cycloidal curves.

• Expression for the functions within each zone are

given in pages 413-415

Double-Dwell Cam

– Sine-Constant-Cosine-Constant (SCCA)

Double-Dwell Cam

– Comparison of five cam acceleration program

• Acceleration

Double-Dwell Cam

– Comparison of five cam acceleration program

• jerk

Double-Dwell Cam

– Comparison of five cam acceleration program

• velocity

Double-Dwell Cam

– Comparison of three cam acceleration program

• displacement

Double-Dwell Cam

– Polynomial Functions

• 3-4-5 Polynomial

n

nxCxCxCxCxCxCCs 5

5

4

4

3

3

2

210

5

5

4

4

3

3

2

210

CCCCCCs

4

5

3

4

2

321 5432

CCCCCv

3

5

2

432 201262

CCCCa

sBC' thefrom found are s' C

zero are ,, 210 CCC

Double-Dwell Cam

– Polynomial Functions

• 4-5 -6-7 Polynomial7

7

6

6

5

5

4

4

3

3

2

210

CCCCCCCCs

6

7

5

6

4

5

3

4

2

321 765432

CCCCCCCv

5

7

4

6

3

5

2

432 4230201262

CCCCCCa

sBC' thefrom found are s' C

zero are ,,, 3210 CCCC

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Single-dwell cam specifications

• rise: 1 in (25.4mm) in 90 degrees

• fall: 1 in (25.4mm) in 90 degrees

• dwell: at zero displacement for 180

degrees(low dwell)

• cam ω: 15 rad/sec

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Cycloidal Motion

2sin2

1

2cos1

2cos4

2sin2

3

2

2

hs

hv

hj

ha

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Double Harmonic

:rise for the

2sin2sin2

2coscos2

2sin2

1sin

2

2cos14

1cos1

2

3

3

2

2

hj

ha

hv

hs

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Double Harmonic

:fall for the

2sin2sin2

2coscos2

2sin2

1sin

2

2cos14

1cos1

2

3

3

2

2

hj

ha

hv

hs

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Double Harmonic

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Polynomials

• Minimize the number of segments (2)

• Minimize the number of boundary conditions

• Redefine the CEP specifications

• rise-fall: 1 in (25.4 mm) in 90° and fall 1 in

90° for a total of 180° (low dwell)

• dwell: at zero displacement for 180°

• Cam ω: 15 rad/sec

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Polynomials

• Boundary Conditions

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Polynomials

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Polynomials (Asymmetrical)

• Redefine the CEP specifications

• rise-fall: 1 in (25.4 mm) in 45° and fall 1 in

135° for a total of 180° (low dwell)

• dwell: at zero displacement for 180°

• Cam ω: 15 rad/sec

• Two segments( Different order, 6 &7)

• Three segments (segment with the smaller

acceleration)

Single Dwell Cam Design

• Rise-Fall-Dwell (RFD)

– Polynomials (Asymmetrical)

Critical Path Motion

• Most common application is for

constant velocity motion

– intermittent

– continuous

– Typical problem

• Accelerate the follower from zero to 10

in/sec

• Maintain a constant velocity of 10

in/sec for 0.5 sec

Critical Path Motion

– Typical problem

• decelerate the follower to zero velocity

• return the follower to start

position

• cycle time exactly 1 sec

Critical Path Motion

Critical Path Motion

Sizing

• Major factor that affect cam size

– Pressure angle

– Radius of curvature

– Base circle radius (flat)

• The smallest circle that can be drawn tangent

to the physical cam surface

– Prime circle radius (roller or curved)

• The smallest circle that can be drawn tangent

to the locus of the centerline of the follower

Sizing

Sizing

• Pressure angle

– The angle between

the direction of

motion (velocity) of

the follower and the

direction of the axis

of transmission

• Between 0° and 30°

Sizing

• Pressure angle

– Eccentricity

• Perpendicular

distance between

the follower’s axis

of motion and the

center of the cam

• The distance b to

the instant center is

equal to the velocity

of the follower

sbVI

4,2

vb

Sizing

• Pressure angle

– Prime Circle

Radius

22arctan

PRs

v

Sizing

• Pressure angle

– Overturning –

Translating Flat-

Faced Follower

Sizing

• Radius of Curvature (Roller)

– No matter how complicated a curve’s

shape may be, nor how high the

degree of the describing function, it

will have a instantaneous radius of

curvature

– Concerns

• Large radius

Sizing

• Radius of Curvature (Roller)

– Concerns

• Undercutting

Sizing

• Radius of Curvature (Roller)

– The rule of thumb is to keep the

absolute value of the minimum radius

of curvature of the cam pitch curve 2

to 3 times as large as the radius of

the follower

fRmin

sRavsR

vsR

PP

Ppitch

22

2/322

2

Sizing

• Radius of

Curvature (Flat)

sRjx bA R

vx

minmax vvfacewidth

minmin asRb

Contour; Cam

cossin vsRr b sincos vsRq b