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Two gears in a mesh have 45 teeth each and the module is 5 mm. The pressure angle is given to be φ = 15°. The addendum is equal to 1 module. Find the path of contact.

Two gears in a mesh have 45 teeth each and the module is 5 mm. The pressure angle is given to be φ = 15°. The addendum is equal to 1 module. Find the path of contact. Correct Answer 31.159 mm

φ = 15°, t = T = 45 and m = 5 mm. Addendum = 1 module. R = r = mT/2 = 112.5 mm and Ra = ra = 112.5 + 5 = 117.5 mm Path of contact = (Ra2 – R2cos2 φ)0.5+ (Ra2 – R2cos2 φ)0.5 – (R+r)sin φ= 31.159 mm.

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