Theory of Machine
When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by (where r = Pitch circle radius of pinion, R = Pitch circle radius of wheel, and φ = Pressure angle)

[(r + R) sinφ]/2
[(r² + R²) sinφ]/2
[(r + R) cosφ]/2
[(r² + R²) cosφ]/2

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Theory of Machine
Two pulleys of radii r₁ and r₂ and at distance x apart are connected by means of an open belt drive. The length of the belt is

π (r₁ - r₂) + (r₁ - r₂)²/x + 2x
π (r₁ + r₂) + (r₁ - r₂)²/x + 2x
π (r₁ + r₂) + (r₁ + r₂)²/x + 2x
π (r₁ - r₂) + (r₁ + r₂)²/x + 2x

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