pitch_diameter.py

# To calculate the size of a gear:
# The diameter of a gear from its center to its ideal meshing point can be represented as the Pitch Diameter.
# Pitch Diameter = Module * Number of Teeth
# Using this, the ideal distance between two gears can be calculated by finding the sum of both gears’ pitch diameters and dividing them by two.
# centerDistance = (pitchDiameter1 + pitchDiameter2) / 2

# The goal is to input a ratio, and output the number of teeth on each gear considering the distance between them.

MODULE = 1
CENTER_DISTANCE = 60 # mm
TARGET_RATIO = 1 # ratio to be solved for. For calculating compound gear sets, find the nth root for each shaft.
                 # for example, for 2 shafts you would find the square root of your final intended ratio.

def findIdealGearSize(centerDistance, pitchDiameter1):
    idealPitchDiameter = (2 * centerDistance) - pitchDiameter1
    return idealPitchDiameter

ratioFound = False
inputNumberOfTeeth = 1
while not ratioFound:
    pitchDiameter1 = float(MODULE * inputNumberOfTeeth)


    # if not a whole number, discard
    numberOfTeeth2 = findIdealGearSize(CENTER_DISTANCE, pitchDiameter1) / MODULE
    if numberOfTeeth2 < 0:
        print("No solution found; this configuration is impossible.")
        exit()
    if (numberOfTeeth2 % 1) == 0: # if it is a whole number
        ratio = inputNumberOfTeeth / numberOfTeeth2
        if ratio >= TARGET_RATIO:
            ratioFound = True
        else:
            print(f"Tried {inputNumberOfTeeth} teeth on gear 1, gives {int(numberOfTeeth2)} teeth on gear 2 with a ratio of {ratio}:1")
    inputNumberOfTeeth += 1 # increment and try again
inputNumberOfTeeth -= 1
pitchDiameter2 = MODULE * numberOfTeeth2
print(f"Gear 1: {inputNumberOfTeeth} teeth, Pitch Diameter: {pitchDiameter1} mm")
print(f"Gear 2: {int(numberOfTeeth2)} teeth, Pitch Diameter: {pitchDiameter2} mm")
# cleaner look
if(ratio % 1 == 0):
    ratio = int(ratio)
print(f"Ratio: {ratio}:1")