Machine Design
For a bevel gear having the pitch angle θ, the ratio of formative number of teeth (TE) to actual number of teeth (T) is

sinθ cosθ
1/sinθ
1/tanθ
1/cosθ

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Machine Design
The shear stress at a point in a shaft subjected to a torque is

Directly proportional to the applied torque and the polar moment of inertia
Directly proportional to the polar moment of inertia and to the distance of the point from the axis
Inversely proportional to the applied torque and the polar moment of inertia
Directly proportional to the applied torque and inversely proportional to the polar moment of inertia

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Machine Design
Castle nut is a locking device in which

A slot is cut partly is middle of nut and then slot reduced by tightening a screw
Through slots are made at top and a cotter pin is passed through these and a hole in the bolt, and cotter pin spitted and bent in reverse direction at other end
A hard fibre or nylon cotter is recessed in the nut and becomes threaded as the nut is screwed on the bolt causing a tight grip
One smaller nut is tightened over main nut and main nut tightened against smaller one by loosening, creating friction jamming

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