ME321 Kinematics and Dynamics of Machines

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ME321 Kinematics and Dynamics of Machines

• Steve Lambert
• Mechanical Engineering,
• U of Waterloo

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Gears
Spur Gears - Parallel shafts and straight teeth
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Gears
Example internal spur gear
Example rack and pinion
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Helical Gears
Helical gears are smoother and quieter than spur
gears, but are more expensive, are not easily
engaged, and they generate a thrust load
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Bevel Gears
Straight bevel gears
Skew bevel gears
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Hypoid and Worm Gears
Hypoid gear
Worm gear
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Fundamental Law of Gearing
We require a constant velocity ratio. For this to
be possible, the common normal of the contacting
tooth flanks must always pass through the pitch
point.
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Involute Action
Imagine that the gears are replaced by two
cylinders connected by a string This system will
satisfy our fundamental law The path traced by Q
will represent our tooth profile
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Involute Action
These are equivalent. Path traced by point Q is
an Involute.
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Gear Tooth Nomenclature
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Gear Nomenclature
Pitch Circle Circular Pitch Addendum Dedendum Cle
arance Diametral Pitch
Circular Pitch
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Standard Gears
Diametral Pitch
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Interacting Gears

• Centre Distance (r2 r3)
• Contact Ratio
• Interference

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Contact Ratio
Contact ratio is the average number of teeth in
contact CR length of line of action / base
(circle) pitch CR l / BP
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Contact Ratio
CR l / BP, where Line of action l AC-AP
DB-DP
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Interference
Interference occurs if point C falls outside
point D - contact beyond involute profile occurs
if O2C gt O2D where