Theory of Machine
The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity ω₁ rad/s in the clockwise direction and the link OB turns with angular velocity ω₂ rad/s in the clockwise direction, then the rubbing velocity at the pin joint O is (where r = Radius of the pin at O)

ω₁.ω₂.r
(ω₁ - ω₂)r
(ω₁ + ω₂)r
(ω₁ - ω₂)2r

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Theory of Machine
The inversion of a mechanism is

Obtained by reversing the input and output motion
Turning its upside down
Changing of a higher pair to a lower pair
Obtained by fixing different links in a kinematic chain

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Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

(l₁ + l₂ + l₃)/3
l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴
l₁ + l₂ + l₃
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³

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Theory of Machine
Angle of descent of cam is defined as the angle

Through which the cam rotates during the period in which the follower remains in the highest 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
During which the follower returns to its initial position

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