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)

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

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Theory of Machine
The frictional torque transmitted in a truncated conical pivot bearing, considering uniform wear, is

(1/2). μ W cosec α [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3).μ W cosec α (r₁ + r₂)
(1/2). μ W cosec α (r₁ + r₂)
(2/3). μ W cosec α [(r₁³ - r₂³)/(r₁² - r₂²)]

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