Each gear meshes with the next at their shared pitch circle, so the tangential (pitch-line) speed must match at the contact point: ωi·ri = ωi+1·ri+1. Since pitch radius is proportional to tooth count (r = module·N/2) for gears sharing a module, this collapses to the classic gear-ratio law, applied link by link along the whole train:
ω(i+1) = ω(i) · N(i) / N(i+1) (driven RPM = driver RPM × driver teeth / driven teeth)
direction(i+1) = −direction(i) (external meshed gears always counter-rotate)
T(i+1) = T(i) · (N(i+1)/N(i)) · η (torque scales opposite to speed; η = per-mesh efficiency)
P(i+1) = T(i+1) · ω(i+1) = P(i) · η (power is conserved except for the modeled mesh loss)
Turn the input RPM or any tooth-count slider and every downstream gear's speed, direction and torque updates instantly from these equations — a small gear driving a large one always trades speed for torque, and a large gear driving a small one trades torque for speed, exactly as in a real clockwork train.
- Direction — alternates gear to gear (green = clockwise, amber = counter-clockwise), because two external gears in mesh must rotate opposite ways or their teeth would collide.
- Torque — inversely tied to the RPM ratio so that power in ≈ power out, minus the small loss set by the mesh-efficiency slider.
- Tooth profile — each gear is drawn with real addendum/dedendum tooth geometry (not a plain circle), so mesh spacing visibly matches the pitch radius.