Theory of Machine
The tractive force in a locomotive with two cylinders is given by (where c = Fraction of reciprocating parts per cylinder, m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, and θ = Angle of inclination of crank to the line of stroke)

m.ω².r cosθ
m.ω².r sinθ
m.ω².r (cosθ - sinθ)
(1 - c).m.ω².r (cosθ - sinθ)

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Theory of Machine
Kinematic pairs are those which have

Surface contact between the two elements when in motion
Point or line contact between the two elements when in motion
Two elements that permit relative motion
Elements of pairs not held together mechanically

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

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