Part of the gear train for a Lath machine tool is shown. Compound gears 2 and 3 slide on a splined shaft so that gear 3 can mesh with gear 4 or gear 2 can mesh with gear 6. Also, compound gears 14 and 15 slide on a splined shaft so that gear 14 can mesh with gear 16 or gear 15 can mesh with gear 17. the angular velocity ratio for the transmission is given by:

Where ωo = ω16 = ω17 and ωi = ω2 = ω3

a/ What should be the two possibility of y. (2 Marks).
b/ What should be the two possibility of x. (2 Marks).
c/ If gear 3 meshes with gear 4, calculate the two possible spindle speeds for a motor speed of 1800 rpm?
(3 Marks).
d/ Now assume that gear 14 meshes with gear 16, and gear 2 meshes with gear 6.
Calculate the number of tooth N6 of gear 6 if N2=10 tooth and ωo=130 rpm? (3 Marks).