Post on 30-Aug-2014
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