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Gear Trains and Planetary Systems in Mechanical Engineering

Learn the three classifications of gear trains: Compound, Simple, and Planetary. Understand speed ratios and design principles for compound gears and planetary gear trains. Discover the formula method for analyzing relative velocities in gear systems.

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Gear Trains and Planetary Systems in Mechanical Engineering

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  1. ME321 Kinematics and Dynamics of Machines Steve Lambert Mechanical Engineering, U of Waterloo

  2. Gear Trains There are three general classifications for gear trains: Compound Gear Train Simple Gear Train Planetary Gear Train

  3. V Simple Gear Trains Speed Ratios: V = -2r2 = 3r3 For internal gears For external gears

  4. 3 5 2 4 Compound Gears

  5. ring planet sun arm Planetary Gear Trains ‘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

  6. Planetary Gear Trains

  7. 5 3 2 4 Formula Method Start with relative velocity analysis with respect to the arm for two gears Divide these two equations to get the final formula

  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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