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The science
Meshing gears
Two gears of the same module m mesh when their pitch circles touch: the centre distance is a = m (N1 + N2)/2 and the pitch-circle speeds are equal, so ω2/ω1 = -N1/N2 (the minus sign: opposite rotation). Along a chain the ratios multiply.
Torque and power
The tooth force F acts at the pitch radius, so torque scales the other way: T2 = T1 (N2/N1) η with mesh efficiency η (typically 0.95 to 0.99 per spur mesh). Power P = T ω drops by η at every mesh, so a gear k meshes away from the input gets at most ηk of the power.
Checks
The first check turns the input three times and compares the distance travelled at the pitch circle of both gears of every mesh. The second compares the drawn centre distances with the formula. The third closes the power balance over the whole tree.
Simplifications
Ideal rigid spur gears with straight-sided trapezoid teeth (not true involutes), no backlash, no friction beyond the constant mesh efficiency, no shaft inertia. Same eight-gear tree as the 3D scene.
What to try
- Make the leaf gear G7 smaller: its speed rises and the torque it can deliver drops.
- Lower the mesh efficiency and see which leaf loses most (the one deepest in the tree).
- Raise the load on G5 and watch the input torque needed.