To design gears for a screw jack with an initial RPM of 1500 and a final RPM of 100, the gear train must be calculated based on the specified dimensions and ratios. The diameter for the other three gears needs to be determined using the gear tooth numbers and the equation for the train ratio. A minimum of 12 teeth per pinion is recommended to prevent undercutting, while keeping tooth counts below 100 is advised to manage manufacturing costs. Reasonable estimates for tooth numbers should be made based on the required train ratio. Proper calculations and sketches are essential for an effective gear design.