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

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Theory of Machine
In the below figure, PC is the connecting rod and OC is the crank making an angle θ with the line of stroke PO and rotates with uniform angular velocity at ω rad/s. The Klien's acceleration diagram for determining the acceleration of the piston P is shown by quadrilateral CQNO, if N coincides with O, then

Acceleration of the piston P is maximum and its velocity is zero
Acceleration and velocity of the piston P is zero
Acceleration of the piston P is zero and its velocity is maximum
Acceleration and velocity of the piston P is maximum

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