The mechanism used in a shaping machine is

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.

Z₂ and Z₄ are

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

For a certain engine having an average speed of $$1200$$ rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within $$2$$% about the average speed. The fluctuation of kinetic energy per cycle is found to be $$2$$kJ. What is the least possible mass of the flywheel if its diameter is not exceed $$1$$ m?