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

Gear Trains There are three general classifications for gear trains: Compound Gear Train Simple Gear Train Planetary Gear Train 11/20/2018

Simple Gear Trains Speed Ratios: V = -2r2 = 3r3 V For external gears For internal gears 11/20/2018

Compound Gears 2 3 4 5 11/20/2018

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 11/20/2018

Planetary Gear Trains 11/20/2018

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 11/20/2018

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 11/20/2018