The epicyclic gear train has _____ degrees of freedom

Explanation

Degree of freedom(DOF) – Degree of freedom of plane mechanism is defined as the number of inputs or independent co-ordinates needed to define the configuration or position of all the links of mechanism with respect to a fixed link.

Kutzback equation of degree of freedom,

DOF = 3 × (L – 1) – 2j – h

Where L = number of links in the mechanism, j = Binary joint or lower pair, h = higher Pair

DOF of the epicyclic gear train

L = 4

j = 3   Between ( 1 and 2, 1 and 4, 3and 4)

h = 1  Between 2 and 3

DOF = 3 × (4 – 1) – 2 × 3 – 1 = 2

Alternate Method

Degree of freedom is the number of inputs required to produce a unique output.

In Epicyclic gear train, there are two inputs required to produce a unique output i.e. one at arm and other at sun gear or at ring gear.

Input 1:

If sun is fixed, then input is given to Ring gear Or If ring gear is fixed, then input is given to sun gear.

Input 2:

Input is given to Arm.

Hence, (3) is the correct answer.