The overall gear ratio in a 2 stage speed reduction gear box (with all spur gears) is 12. The input and output shafts of the gear box are collinear. The countershafts which is parallel to the input and output shafts has a gear (Z₂ teeth) and pinion (Z₃ = 15 teeth) to mesh with pinion (Z₁ = 16 teeth) on the input shafts and gear (Z₄ teeth) on the output shafts respectively. It was decided to use a gear ratio of 4 with 3 module in the first stage and 4 module in the second stage.

The centre distance in the second stage is

The sun gear in the figure is driven clockwise at 100 rpm. The ring gear is held stationary. For the number of teeth shown on the gears, the arm rotations at

List $$I$$ (Gear types)
(a) Worm gears
(b) Cross helical gears
(c) Bevel gears
(d) Spur gears

List $$II$$ (Applications)
1. Parallel shafts
2. Non-parallel, intersecting shafts
3. Non-parallel, non intersecting shafts
4. Large speed ratios

The arm OA of an epicylic gear train shown in Fig. revolves counter clockwise about O with an angular velocity of 4 rad/sec. Both gears are of same size. The angular velocity of gear C, if the sun gear B is fixed, is