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Two involute gears in a mesh have a module of 10 mm and the pressure angle is 35°. The larger gear has 45 teeth whereas the pinion has 15 teeth. The addendum is equal to one module. Find the arc of contact.

Two involute gears in a mesh have a module of 10 mm and the pressure angle is 35°. The larger gear has 45 teeth whereas the pinion has 15 teeth. The addendum is equal to one module. Find the arc of contact. Correct Answer 39.626 mm

φ = 35°, t = 15, T = 45, m = 10 mm and addendum = 1 module = 10 mm. r = mt/2 = 75 mm, R = mT/2 = 225 mm ra = r + a = 85 mm, Ra = R + a = 235 mm Path of contact = (Ra2 – R2cos2 φ)0.5 + (ra2 – r2cos2 φ)0.5 – (R + r)sinφ = 32.46 mm Arc of contact = Path of contact/cos φ = 32.46/cos 35° = 39.626 mm.

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