An over drive for a vehicle consists of an epicyclic gear train as shown in the figure, with compound planets B-C. B has 15 teeth and meshes with an annuius A which has 60 teeth. C has 20 teeth and meshes with the sunwheel D which is fixed. The annulus is keyed to the propeller shaft Y which rotates at 740 rad/sec. The spider which carries the pins upon which the planets revolve, is driven directly from main gear box by shaft X, this shaft being relatively free to rotate with respect to wheel D. Find the speed of shaft X, When all the teeth have the same module. -

Na = 740 rad/s = 7047 rpm

Nd = 0

Also, Tb + Td + Tc = Ta

Td = Ta-Tc-Tb = 60-20-15 = 25

From table

M+N = 0 -------------- (i)

-MTd/Tc x Tb/Ta +N = 7047

-M25/20 x 15/60 +N = 7047

-0.3125M + N = 7047 ------------------- (ii)

Solving (i) and ( ii)

M = -5369

N = 5369

As the shaft X is relatively free to rotate, when Nd = 0, It will rotate at the speed same as that of the arm.

Hence,

Speed of X = Narm = N = 5369 rpm