Ch9 Gears

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Epicyclic or Planetary Gears
- annulus: outer ring gear which meshes with the planet gears
- carrier: movable arm
- 2 DOF
- system requires control of 2 inputs to produce 1 output
- high torque output
- load shared equally across planet gears means longer life for each
- total motion of any gear is sum of motion of arm and motion of gear with respect to arm
- if arm were stationary would get a simple gear train
- => all motion relative to arm is analyzed as simple gear train
Differential Mechanism
- receives 1 input and produces 2 outputs
- designed to drive a pair of wheels with equal torque while allowing them to rotate at different speeds
- a vehicles wheels rotate at different speeds especially when turning corners
- when turning outside wheel rotates faster and inside wheel rotates slower
Fundamental Law of Gearing
- The angular velocity ratio m_v is constant at all positions
- The torque ratio m_T is constant at all positions
- Gear tooth contours on mating teeth must be conjugates (involute curve)
Involute Curve

size of teeth must be the same for gears to mesh