Lecture 13

Mechanics of Machines MBB2072

Lecture 13Mark Ovinis

dwell

rise

rise

rise

fall

fall

fall

fall

dwell

dwell

Overview Cam Motion Cam in an Engine Valve Categories of Cam & Cam Followers Prescribed Follower Motion Follower Motion Scheme Cam Design: Graphical Method Cam Design: Analytical Method Pressure Angle Geneva Mechanism

Geneva MechanismThe Geneva drive is a mechanism that translates a continuous rotation into an intermittent rotary motion.

It is an intermittent gear where the drive wheel has a pin that reaches into a slot of the driven wheel and thereby advances it by one step.

The drive wheel also has a raised circular blocking disc that locks the driven wheel in position between steps.

Follower Motion Scheme Constant Velocity Constant Acceleration Harmonic Motion Cycloidal Motion

Influence of Cam ShapeShape of cam

Follower acceleration

Stress VibrationFollower

Force

Follower shape

Follower position

Cam Shapes

Constant Velocity

Rise distance H

Time period for rise T

Time, t

t

s

vTH

dtdsv

Constant velocity

throughout the follower rise.

Impractical for machines to

change velocity instantly (infinite

acceleration) at start and end of

rise.

Constant Velocityv

a

THv

Infinite acceleration implies infinite force. Might be practical for low

cam speed applications where

the force magnitudes in

starting and ending the rise do not

affect performance.

Constant Acceleration

THv 2

max

Rise distance H

s

v Constant acceleration to reach

vmax and then constant

deceleration to a stop.

Also called parabolic motion

Constant Acceleration

THv 2

max

THv 2

max

THv 2

max

2

4THa

THv 2

max

2

4THa

Abrupt change in acceleration at the

middle and end of rise. These will cause

undesirable inertial force and thus

vibration.Only suitable for low

cam speed.

Generating Displacement Diagram Graphically

for Constant Acceleration Follower Motion Scheme

Example 9-4A cam drive is required for a mechanism that feeds papers into a printing press. The cam follower must rise outwards 1.0 in. with constant acceleration for 1.7 s,dwell for 0.8 s, fall 0.5 in. with constant acceleration in 0.8 s, dwell for 0.3 s, fall 0.5 in. with constant acceleration in 0.8 s and then repeat the sequence. Determine the required speed of the cam and graphically plot a follower displacement diagram.

Follower MotionRise 1.0 in.

1.7 s 139.1°

Dwell 0.8 s 65.5°Fall 0.5 in. 0.8 s 65.5°Dwell 0.3 s 24.5°Fall 0.5 in. 0.8 s 65.5°One cycle 4.4 s 360°Cam speed = 1 rev/4.4 s = 13.6 rpm

Constant Acceleration

Constant Acceleration

Constant Acceleration

0 1.7 Time (s)

0.85

1.0

0.5

Follo

wer d

ispla

cem

ent

(in.)

Constant Acceleration Rise

0 1. 7

Time (s)

1.0

0.5

Follo

wer d

ispla

cem

ent

(in.)

3. 4 4.4

2 2.55

Harmonic Motion

THv2max

s

v

Harmonic MotionTHv2max

2

2

max 2THa

2

2

min 2THa

Generating Displacement Diagram Graphically

for Harmonic Follower Motion Scheme

Follower Motion (Q9-7)Rise 2.0 in.

1.0 s 102.9°

Dwell 0.5 s 51.4°Fall 2 in. 1 s 102.9

°Dwell 1 s 102.9

°One cycle 3.5 s 360°Cam speed = 1 rev/3.5 s = 17.1 rpm

Harmonic Rise

Harmonic Fall

0 1. 0

Time (s)

2.0

1.0

Follo

wer d

ispla

cem

ent

(in.)

3. 0 2.0

0 1. 0

Time (s)

2.0

1.0

Follo

wer d

ispla

cem

ent

(in.)

3. 0 2.0

Cycloidal Motion

THv 2

max

Cycloidal MotionTHv 2

max

2min2THa

2max2THa

No sudden change in

acceleration at the end of

cycle.

Generating Displacement Diagram Graphically

for Cycloidal Follower Motion Scheme

Displacement CurvesCon-Vel Con-Acc

Harmonic

Cycloidal

Velocity CurvesCon-Vel Con-Acc

Harmonic

Cycloidal

Acceleration CurvesCon-Vel Con-Acc

Harmonic

Cycloidal

Comparison of Motion Schemes

Cons Veloc

Cons Accel Harmoni

cCycloi

d

Less forces on the followerSmoother motion, less vibration

Likely to be more difficult and costlier cam design & manufacturing

More suitable for higher cam speed

9-6 9-8 9-37

TutorialTut Week 9•7-26•7-36

Tut Week 10

Assignment

9-5 9-44

Assignment 4 To be submitted by

Friday, 6 April 2012

6-25: Windshield Wiper Velocity Analysis7-27: Compressor Linkage Acceleration Analysis7-57: Lift Mechanism Acceleration AnalysisDue 5pm Friday 30 March 2012.

Assignment 3