The following data refer to two meshing involute gears of \(20^{\circ}\) pressure angle: Number of teeth on pinion \(=20\), speed ratio \(=2\), speed of pinion \(=250 \mathrm{rpm}\), module \(=12 \mathrm{~mm}\)

The addendum of each wheel is such that the path of approach and path of recess on each side are half of the maximum possible length. Calculate

(a) addendum for both the wheels, (b)the length of arc of contact, and

(c) the maximum possible sliding velocity approach and recess.