10. 12. 13. find the addendum for each gear wheel, path of contact, are of contact and contact ratio. [Ans. 14 mm; 39 mm; 102.6 mm; 109.3 mm; 4] A 20° involute pinion with 20 teeth drives a gear having 60 teeth. Module is 8 mm and addendum of each gear is 10 mm. 1. State whether interference occurs or not. Give reasons. 2. Find the length of path of approach and are of approach if pinion is the driver. (Ans. Interference does not occur; 25.8 mm, 27.45 mm] A pair of spur wheels with involute teeth is to give a gear ratio of 3 to 1. The arc of approach is not to be less than the circular pitch and the smaller wheel is the driver. The pressure angle is 20°. What is the least number of teeth that can be used on each wheel? What is the addendum of the wheel in terms of the circular pitch? [Ans. 18, 54; 0.382 PJ Two gear wheels mesh externally and are to give a velocity ratio of 3. The teeth are of involute form of module 6. The standard addendum is I module. If the pressure angle is 18° and pinion rotates at 90 r.p.m., find: 1. the number of teeth on each wheel, so that the interference is just avoided, 2. the length of the path of contact, and 3. the maximum velocity of sliding between the teeth. [Ans. 19, 57; 31.5 mm; 213.7 mm/s] A pinion with 24 involute teeth of 150 mm of pitch circle diameter drives a rack. The addendum of the pinion and rack is 6 mm. Find the least pressure angle which can be used if under cutting of the teeth is to be avoided. Using this pressure angle, find the length of the arc of contact and the minimum number of teeth in contact at one time. [Ans. 16.8°; 40 mm ; 2 pairs of teeth] Two shafts, inclined at an angle of 65° and with a least distance between them of 175 mm are to be connected by spiral gears of normal pitch 15 mm to give a reduction ratio 3: 1. Find suitable diam-