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

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Theory of Machine
Angle of ascent of cam is defined as the angle

During which the follower returns to its initial position
Through which the cam rotates during the period in which the follower remains in highest position
Moved by the cam from the instant the follower begins to rise, till it reaches its highest position
Of rotation of the cam for a definite displacement of the follower

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Theory of Machine
The Klein's method of construction for reciprocating engine mechanism

Utilizes a quadrilateral similar to the diagram of mechanism for reciprocating engine
Is based on acceleration diagram
Is a simplified form of instantaneous center method
Enables determination of Cariole’s component

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