Machine Design Calculators: Gears, Shafts, Bearings & Springs

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Machine Design: theory, method, and sources

This mechanical workspace publishes 9 governing equations, 5 stated assumptions, 6 documented boundaries, and 1 source so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

The modules follow a power path through a machine: the source turns, gears or a belt or chain change the speed and torque, bearings and shafts carry the result, and keys, bolts, and threads hold it all together.

Springs, flywheels, cams, the classical machines, and hydraulic actuators cover the remaining ways a design stores, smooths, shapes, or amplifies that motion.

Each module opens with the question it answers, the governing relationship, and the specific thing worth noticing, rather than presenting a bare calculator.

Calculators and topics covered

machine design
gears
bearings
shafts
fasteners
springs
cams
hydraulics
gear ratio calculator
compound gear train
spur gear module pitch diameter
belt tension ratio wrap angle
roller chain sprocket sizing
bearing L10 life calculator

Core equations

\begin{gathered}Ratio = \frac{N_{\mathrm{driven}}}{N_{\mathrm{driver}}}\\\text{torque}\; \text{multiplies}\; as\; \text{speed}\; \text{divides}\end{gathered}

d = m \cdot N,\; \text{base}\; \text{circle} = d \cdot \cos \; \varphi ,\; \text{addendum} = m,\; \text{dedendum} = 1.25 m

\begin{gathered}\frac{T_{1}}{T_{2}} = e^{\mu \theta }\; for\; a\; \text{flat}\; \text{belt}\\a\; V - \text{belt}\; \text{uses}\; the\; \text{same}\; \text{relation}\; \text{with}\; an\; \text{effective}\; \text{coefficient}\; \mu ^{\prime} = \frac{\mu }{\sin \left(\frac{\beta }{2}\right)},\; \frac{\text{giving}\; T_{1}}{T_{2}} = e^{\frac{\mu \theta }{\sin \left(\frac{\beta }{2}\right)}}\end{gathered}

Sprocket\; \text{pitch}\; \text{diameter} = \frac{p}{\sin \left(\frac{\pi }{N}\right)}

L_{10} = \left(\frac{C}{P}\right)^{p}\; \text{million}\; \text{revolutions},\; p = 3\; \text{balls},\; \frac{10}{3}\; \text{rollers}

d = \left[\frac{16 \sqrt{M^{2} + T^{2}}}{\pi \cdot \tau allow}\right]^{\frac{1}{3}}

\tau = \frac{Kw \cdot 8 FD}{\pi d^{3}},\; k = \frac{Gd^{4}}{8 D^{3} Na}

\Delta E = I \cdot \bar{\omega }^{2} \cdot Cs

\begin{gathered}Force = \text{pressure} \times \text{area}\\\text{annulus} = \text{bore} - rod\end{gathered}

Method and assumptions

Assumptions

Steady-state operation at the stated speed and load, with no shock or start-up transient.
Gears are standard full-depth involute profiles running at their theoretical centre distance.
Belt and chain calculations assume an open drive on parallel shafts with no slip beyond the friction limit.
Bearing life uses catalogue dynamic capacity with adequate lubrication and correct mounting.
Shaft, key, and bolt checks are static strength calculations against yield.

Limitations and design boundaries

Shaft sizing is a static check. A rotating shaft under steady bending sees fully reversed stress each revolution and needs a fatigue analysis with stress concentration factors at every shoulder, keyway, and groove.
Gear teeth are proportioned geometrically only. Tooth bending and pitting capacity need the Lewis and Hertzian checks with the full set of AGMA derating factors.
The bolt torque relation uses a nut factor that scatters by roughly ±25 % in practice, so torque control alone cannot deliver accurate preload. Critical joints are tightened by angle or by measured bolt stretch.
Bearing L10 is a fatigue statistic. It does not predict failure from lubrication breakdown, contamination, or misalignment, which cause most bearings to fail in service.
Cam profiles cover the rise only, with no dwell or return, and the follower is assumed rigid with no jump at speed.
Nothing here is a substitute for a design code, a manufacturer catalogue, or review by a licensed engineer.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Standard machine design formulationsThe relationships used are the conventional ones from an introductory machine-design sequence: involute gear proportions, the capstan belt equation, ISO tensile stress area, the basic bearing rating life, the Wahl correction for helical springs, and the standard cam motion curves.

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Gear Ratio Calculator

Calculate gear reduction or overdrive ratio, output speed, torque, pitch-line velocity, and tangential tooth force for a spur-gear pair.