Theory of Machine
The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r (sin 2θ/n)
m.ω².r sinθ
m.ω².r cosθ
m.ω².r (cos 2θ/n)

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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
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
Mass of cam follower linkage, spring stiffness and cam speed

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