Theory of Machine
The velocity of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by (where ω = Angular velocity of the cam shaft)

ω (r₁ + r₂) cosθ cosec2θ
ω (r₁ + r₂) sinθ sec2θ
ω (r₁ r₂) sinθ
ω (r₁ r₂) cosθ

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Theory of Machine
Crowning on pulleys helps

In decreasing the slip of the belt
Increase belt and pulley life
For automatic adjustment of belt position so that belt runs centrally
In increasing velocity ratio

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