Planetary Gear Operation: Reverse

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Fig 1: Identifying Reverse Gear Planetary Operation

Courtesy of MAZDA MOTORS CORP.

GEAR ROTATION SPEED REFERENCE

Planetary gear	Front
Internal gear	N_R (output)
Planetary carrier	0 (fix)
Sun gear	N_S (input)

Suppose the gear ratio in reverse gear is i_REV ,

Fig 2: Identifying Reverse Gear Ratio Formula (1 Of 2)
Courtesy of MAZDA MOTORS CORP.
From the result of N_C =0 in formula (2), the relation between the gear ratio during reverse movement and the rotation speed of the planetary gear set is indicated in the formula below.
(Z_RF +Z_SF ) 0=Z_RF N_R +Z_SF N_S
Therefore,

Fig 3: Identifying Reverse Gear Ratio Formula (2 Of 2)
Courtesy of MAZDA MOTORS CORP.
As a result, the gear ratio in reverse is 2.272.