Algebraic Method:

This method is depending on the relative motion among the two associated members. Angular velocity of gear S = angular velocity of S relative to arm a + angular velocity of a.

That is

ω_s = ω_sa + ω_a

or,

N _s  = N _sa   + N _a                                  . . . (10.5)

here, N _s , N _sa , and N_a are speeds of respective members in rpm.

From equations (10.5)

N _sa= N _s  - N _a                                                                          . . . (10.6)

likewise,

N _pa = N_a  - N _p                                                 . . . (10.7)

From equations (10.6) & (10.7)

                . . . (10.8)

 As,

or,

                  . . . (10.9)

In equation (10.9), left hand side is the train value. Substituting known quantities, unknown quantity can be estimated.