Theory of Machine
In a cam drive with uniform velocity follower, the sharp corners of the displacement diagram are rounded off at the beginning and at the end of each stroke. This is done

Because of loose contact of follower with cam surface
Because the uniform velocity motion is a partial parabolic motion
In order to have acceleration in beginning and retardation at the end of stroke within the finite limits
Because of difficulty in manufacturing cam profile

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Theory of Machine
Crowning on pulleys helps

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

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Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ω²r [sin θ + (sin 2θ/n)]
ωr [sin θ + (sin 2θ/n)]
ω²r [cos θ + (cos 2θ/n)]
ωr [cos θ + (cos 2θ/n)]

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