A symmetrical tangent cam with least radius of \(30 \mathrm{~mm}\) operates a roller follower of \(10 \mathrm{~mm}\) radius.

The angle of ascent is \(60^{\circ}\) and lift is \(20 \mathrm{~mm}\). The speed of cam is \(450 \mathrm{rpm}\). Calculate

(a) distance between cam and nose centres,

(b) nose radius,

(c) angle of contract of cam with straight flank, and

(d) acceleration of follower:

(i) at the beginning of lift,

(ii) where the roller just touches the nose, and

(iii) at the apex of circular nose.