Theory of Machine
The velocity of sliding of meshing gear teeth is (Where ω₁ and ω₂ are angular velocities of meshing gears and ‘y’ is distance between point of contact and the pitch point)

(ω₁ + ω₂)/y
(ω₁/ω₂) y
(ω₁ + ω₂) y
(ω₁ × ω₂) y

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

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Theory of Machine
In a cam drive with uniform velocity follower, the sharp corners of the displacement diagram are rounded off at the beginning and at the end of each stroke. This is done

Because the uniform velocity motion is a partial parabolic motion
Because of difficulty in manufacturing cam profile
In order to have acceleration in beginning and retardation at the end of stroke within the finite limits
Because of loose contact of follower with cam surface

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