Spring2011ME320
SolutionstoProblemsinHomework#7
Problem1:
1. A30toothgearhasAGMAstandardfulldepthinvoluteteethwithdiametralpitchof12.Calculatethe
pitchdiameter,circularpitch,addendum,dedendum,tooththickness.
Hint: Use Table 9.1 in the textbook. Also, calc
ME 320 Spring 2016
Practice Problems on Cam-Followers
Page 1 of 4
Problem 1. A disc cam with a roller follower is designed for full cycloidal motion rise segment
1
= ( 2 sin
2
)
1
and full cycloidal motion fall segment = (1 + 2 sin
2
) with
the
following
ME 320 Handout 14
Balancing
April 7, 2016
Centripetal force:
2
=
= 2
Balancing Applications
Crank Shaft
Tires
Ref: dnr.louisiana.gov
Cam Shaft
2
Unbalance
Virtually all machines contain rotating components.
Unbalance: when the center of mass of a rotat
1
ME 320 Mechanisms and Dynamics of Machinery
Review of Math and Dynamics Concepts
Dynamic Force Analysis
Lets define two vectors: R such that R=(RX, RY) and RB such that RB=(RBX, RBY). We wish to take the cross
product.
The cross product is defined as:
ME 320 Handout 9
Week 10
Gears Part 2
Thurs. March 3, 2016
Differential Gears: In automobiles and other wheeled vehicles, the
differential allows the outer drive wheel to rotate faster than the
inner drive wheel during a turn. This is necessary when the v
ME 320 Handout 13
Week 10
March 17, 2016
Equation of motion:
m + + = ()
We require Fc(t) > 0 for cam-follower to remain in contact.
Fc: cam force, contact force of the cam on the follower
Fs: spring force, restoring force that brings follower back to orig
ME 320 Handout 11
Week 9
March 10, 2016
Cam-Followers
Cam-Followers as Fourbar Equivalent Linkages
2
Determining Follower Motions
We want to specify the rise and fall
of the displacement diagram over an
interval, b
s=f(q) for 0 q 2p
Definitions:
s*=displ
ME 320 Handout 12
Week 10
March 15, 2016
Constant breadth cam with reciprocating flat-faced
follower. Ref: Theory of Machines and Mechanism, Oxford
Press 2011.
Base Circle, Prime Circle, and Pitch Curve
Once the SVAJ functions are defined, the next step i
ME 320 Handout 10.5
Week 9
March 10, 2016
Rise or lift: maximum
distance the follower
travels
Cam: rigid body that
rotates or oscillates, input
or driver link
Follower: rigid body that
moves because it is in
contact with the cam,
output or driven link
Ref
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I ?=?> 7- %3u76 Yul/5 P: I01 Glmrs thw,
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7
. SM and A'wectont *QHOQ of. 003? Seer Z "' . 2 ' ?
- \-\ A . .
19an m meter (3me Wu Aw. skr-s W'SEB 329% S
1' " 32%: no . N .2. 31 9 : %4 =
Ref: How Everything Works by Luis Bloomfield
ME 320 Handout 8
Week 7
Gears Part 1
February 23, 2016
Friction Drives, Belts and Chains
V-belt Drive
Synchronous (timing) Belt
Chain Drive
2
Toothed Gear types
Spur and helical
gears are used when
the input an
Page 1 of 2
Example: Graphical Cam Layout
A reciprocating (vertical) follower rises 2.0 cm in 50o with simple harmonic motion, dwells for
40o, rises another 1.0 cm in 50o with simple harmonic motion, dwells for 30o, and returns in 160o
with simple harmoni
ME 320 Handout 4
Week 2
January 21, 2016
Designing Mechanisms
1. Qualitative Synthesis: Creation of potential solutions in the absence of a
well defined algorithm that predicts or configures the solution.
2. Type Synthesis: Define suitable types of mechan
Example: Balancing Linkages
Below is a fourbar linkage. Determine the magnitudes and locations of the balance masses to be
added to Links 2 and 4 so that the mechanism is completely force balanced. * indicates value
prior to balancing for Links 2 and 4.
G
1
ME 320 Mechanisms and Dynamics of Machinery
Review of Math and Dynamics Concepts
Complex Variables
Define imaginary number as = 1. Note that 2 = 1.
Let us examine two complex variables: 1 = 1 + 1 and 2 = 2 + 2 . We note that x is the real part
and y is
ME 320 Handout 6
Cam and Gear under brush
Week 4
February 2, 2016
Inside an Electric Toothbrush
Cam (blue) spins and driven by motor (red). Black crank converts
rotation into translation of brush head (blue and green).
Translation, Rotation, and Complex M
ME 320 Handout 7
Week 5
February 9, 2016
Steam engine wheels use cranks
to convert reciprocating (back
and forth) motion into rotational
motion. You connect the blue
rod to the piston so that as it
moves in and out of the cylinder,
the red wheel rotates.
Planetary Gears driving a Jet Engine. PGTs give
us high torque ratios in a compact space by
using multiple planets.
ME 320 Handout 10
Week 9
Gears Part 3
March 8, 2016
From Mechanical Engineering. ASME 01-135
Planetary Gear Trains Defined
Conventional Gea
Pagelof2
ME 320- In Class Extra Credit Assignment 4/5/16
A mechanism is composed of three links: two slidin blocks and one rigid binary link. Link 1
with mass m1 is moving upwards with due to an upward instantaneous
KNOWN external force F1. Link 2 has len
ME 320: Mechanisms and Dynamics of Machinery Fall 2016
Homework #4
Assigned: Tuesday, 10/4/2016 Due: Friday, 10/7/2016
1. A rigid link 2 illustrated in the figure on the right has an
angular velocity of 24 rad/s cw and an angular
acceleration of 160 rad/s
mm Not 1).
A 30-hom gun was Arm/m Shhdowl (imbaww "Moms 4% 939m
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dcdzmhm 3 4% We"; -
Hu: 05, Que, (.1
Tao-HA J\'\r\'\c.\(\r\l.5 S b = f /2
wahkz on chumsions +0 cfw_my
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ME 320: Mechanisms and Dynamics of Machinery Spring 2017
Solutions to Homework #1
Solution to Problem 1:
(iii)
Joint
A
B
C
D
E
F
G
H
(ii)
Contact Type
Lower Pair
Lower Pair
Higher Pair
Lower Pair
Lower Pair
Lower Pair
Lower Pair
Lower Pair
Pair variable (
ME 320: Mechanisms and Dynamics of Machinery Spring 2017
Solutions to Homework #4
Solution to Problem 1:
1. Acceleration difference between points and on link 2 is given by:
?
?
Scale: 1 = 100 in/s2
+
= +
2. Construct the acceleration polygon choosi
ME 320: Mechanisms and Dynamics of Machinery Spring 2017
Solutions to Homework #2
Solution to Problem 1:
1. Loop closure equation:
?
?
+
=
+
2. Solve the equation graphically choosing a suitable scale factor.
.
1. Position vector of point is R
Th
ME 320: Mechanisms and Dynamics of Machinery Spring 2017
Solutions to Homework #3
Solution to Problem 1:
?
=
+
1. Write the equation for velocity difference between points and :
2. Construct the velocity polygon choosing a suitable scale factor. Firs
ME 320: Mechanisms and Dynamics of Machinery Spring 2017
Solutions to Homework #7
Solution to Problem 1:
Given: Tooth number: N = 30, Diametral Pitch = P = 12 in-1
Pitch Diameter: =
Circular Pitch: =
=
30
12
=
12
Using the equations in Table 7-2:
Addendum
Name: _
(Maximum Points: 30)
ME 320: Mechanisms and Dynamics of Machinery
Mid-Term Exam Spring 2017
Instructions:
1.Readthequestionscarefully,andmanageyourtimeefficientlybyprovidingonlystrictlyrequiredanswers.
2.Writeanswertoeachquestionbelowthequestion.I
ME 320: Mechanisms and Dynamics of Machinery Spring 2017
Solutions to Homework #8
Solution to Problem 1:
Speed Ratio of the gear train: =
#
8
2
= (1) #
Therefore, 8 = (1)4 2 4 5 7 2 =
3 5 6 8
18153316
44333648
(880) = 50 rpm (ccw)
Center distance betwe