Theory of Machine
The relation between number of links (l) and number of joints (j) in a kinematic chain is

l = j + 4
l = (1/2).(j + 2)
l = (3/4).(j + 3)
l = (2/3).(j + 2)

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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)

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

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