Theory of Machine
In a screw jack, the effort required to lower the load W is given by

P = W tan(φ - α)
P = W cos(α + φ)
P = W tan(α - φ)
P = W tan(α + φ)

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Theory of Machine
The contact ratio is given by

(Length of the arc of contact)/(Circular pitch)
(Length of path of recess)/(Circular pitch)
(Length of the arc of approach)/cosφ
(Length of the path of approach)/(Circular pitch)

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