Transcript ME321 - Kinematics and Dynamics of Machines Design Process

ME321
Kinematics and Dynamics of
Machines
Steve Lambert
Mechanical Engineering,
U of Waterloo
7/21/2015
Gear Trains
There are three general classifications for gear trains:
Simple
Gear Train
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Compound
Gear Train
Planetary
Gear Train
Simple Gear Trains
Speed Ratios:
V = -2r2 = 3r3
r3
N3
 2 n2

 
 3 n3
r2
N2
V
N 3 For external
n2

n3
N 2 gears
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n2 N 3

n3 N 2
For internal
gears
Compound Gears
3
2
5
4
n2 n2 n4  N 3  N 5  N 3 N 5
 
 

  
n5 n3 n5  N 2  N 4  N 2 N 4
ndriver product of number of teethon driven gears

ndriven product of number of teethon driver gears
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Planetary Gear Trains
ring
planet
‘Simple’ planetary gear
trains have two degrees of
freedom
i.e., we must specify two
inputs
sun
arm
In a planetary (or epicyclic) gear train, one of the axes
rotates around another axis
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Planetary Gear Trains
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Formula Method
5
3
Start with relative velocity analysis
with respect to the arm
for two gears
 24   21   41   2   4
34  31   41  3   4
2
4
Divide these two equations to get
the final formula
 24  2   4

34 3   4
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Formula Method
 LA  L   A

 FA  F   A
The term on the lefthand-side of the
equation is the
velocity with respect
to the arm, and can
always be calculated
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Subscripts:
L - Last gear
F - First Gear
A - Arm
The terms of the right hand side
of the equation represent three
absolute velocities
Given 2, the third can always
be calculated