1. ME321 Kinematics and Dynamics of Machines
Steve Lambert
Mechanical Engineering,
U of Waterloo
11/20/2018

2. Gear Trains There are three general classifications for gear trains:
Compound Gear Train
Simple Gear Train
Planetary Gear Train
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3. Simple Gear Trains Speed Ratios: V = -2r2 = 3r3 V For external gears
For internal gears
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4. Compound Gears 2 3 4 5
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5. Planetary Gear Trains ring planet
sun
arm
planet
‘Simple’ planetary gear trains have two degrees of freedom
i.e., we must specify two inputs
In a planetary (or epicyclic) gear train, one of the axes rotates around another axis
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6. Planetary Gear Trains
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7. Formula Method Start with relative velocity analysis 5
with respect to the arm
for two gears 5 2 4 3
Divide these two equations to get the final formula
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8. Formula Method Subscripts: L - Last gear F - First Gear A - Arm
The term on the left-hand-side of the equation is the velocity with respect to the arm, and can always be calculated
The terms of the right hand side of the equation represent three absolute velocities
Given 2, the third can always be calculated
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