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
Angle of ascent of cam is defined as the angle

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

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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 a simplified form of instantaneous center method
Enables determination of Cariole’s component
Is based on acceleration diagram

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

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