Machine Design
Castle nut is a locking device in which

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
A slot is cut partly is middle of nut and then slot reduced by tightening a screw
One smaller nut is tightened over main nut and main nut tightened against smaller one by loosening, creating friction jamming

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Machine Design
In a band and block brake, the ratio of tensions on the tight and slack sides of band is given by (where μ = Coefficient of friction between the blocks and the drum, θ = Semi-angle of each block subtending at the centre of drum, and n = Number of blocks)

T₁/T₂ = (μθ)n
T₁/T₂ = [(1 - μ tanθ)/ (1 + μ tanθ)]n
T₁/T₂ = μθ × n
T₁/T₂ = [(1 + μ tanθ)/ (1 - μ tanθ)]n

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