Machine Design — Cheat Sheet
Gears, belts, shafts, bearings, springs, keys — the transmission formulas.
Gears (metric module)
| Pitch diameter | d = m·N |
| Ratio | i = N₂ / N₁ |
| Centre distance | C = m(N₁ + N₂) / 2 |
| Outside diameter | d_o = m(N + 2) |
Belts
| Speed ratio | i = D₂ / D₁ |
| Open belt length | L = 2C + π(D₁+D₂)/2 + (D₂−D₁)²/4C |
Shafts
| Shear (solid) | τ = 16T / πd³ |
| Twist | θ = TL / GJ |
| Power | T[N·m] = 9550·kW / rpm |
Bearings & springs
| Rating life | L₁₀ = (C/P)ᵖ (p = 3 ball, 10/3 roller) |
| Spring rate | k = Gd⁴ / (8D³N_a) |
| Spring stress | τ = K_w·8FD / πd³, C = D/d |
Keys & power
| Key force | F = 2T / d |
| Key shear | τ = F / (w·L) |
| Rotational power | P = T·ω = 2πnT / 60 |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.