Theory of Machine
In a circular arc cam with roller follower, the acceleration in any position of the lift will depend only upon

Total lift, total angle of lift, minimum radius of cam and cam speed
Mass of cam follower linkage, spring stiffness and cam speed
Total lift, centre of gravity of the cam and cam speed
Radius of circular arc, cam speed, location of centre of circular arc and roller diameter

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

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