Theory of Machine
Whitworth quick return mechanism is obtained by inversion of

Five link mechanism
Kinematic chain
Slider crank mechanism
Roller cam mechanism

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Theory of Machine
The magnitude of velocities of the points on a rigid link is

Inversely proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center
Inversely proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center

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

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