Machinery's Handbook, 31st Edition
Planetary Gearing
2291
Ratios of Planetary or Epicyclic Gearing D = rotation of driver per revolution of follower or driven member F = rotation of follower or driven member per revolution of driver. (In Fig. 1 through Fig. 4, F = rota tion of planet type follower about its axis.) A = size of driving gear (use either number of teeth or pitch diameter). Note: When follower derives its motion both from A and from a secondary driving member, A = size of initial driving gear, and formula gives speed relationship between A and follower. B = size of driven gear or follower (use either pitch diameter or number of teeth) C = size of fixed gear (use either pitch diameter or number of teeth) x = size of planet gear as shown by diagram (use either pitch diameter or number of teeth) y = size of planet gear as shown by diagram (use either pitch diameter or number of teeth) z = size of secondary or auxiliary driving gear , when follower derives its motion from two driving members S = rotation of secondary driver , per revolution of initial driver . S is negative when secondary and initial drivers rotate in opposite directions. (Formulas in which S is used give speed relationship between follower and the initial driver.) Note: In all cases, if D is known, F = 1 ÷ D , or, if F is known, D = 1 ÷ F .
Follower
Follower
Follower
B
B
C
Driver
Driver
C
Driver
Fixed
Fixed
Fixed
Fig. 1. F B C = 1+
Fig. 2. F B C 1 = −
Fig. 3. F B C =
Follower
x
x
y
Driver
C
y
E
Driver
B
C
B
Follower
Fixed
Driver
Follower
Fixed
Fixed
Fig. 4. cos F E B C = +
Fig. 5. F y B x C 1 # # = +
Fig. 6. F x B y C 1 # # = +
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