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

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

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Theory of Machine
Open pairs are those which have

Elements of pairs not held together mechanically
Point or line contact between the two elements when in motion
Surface contact between the two elements when in motion
Two elements that permit relative motion

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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, centre of gravity of the cam and cam speed
Total lift, total angle of lift, minimum radius of 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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