This simulator models an ideal, rigid, lossless three-planet epicyclic (planetary) gearset — a sun gear, ring gear and carrier — using the Willis relation. Hold the ring, carrier or sun stationary, adjust tooth counts, input speed and torque, and watch the resulting speed ratio, delivered torque and holding reaction develop across the other two members.
• A real-time 3D cutaway workbench of the externally toothed sun gear, three planet gears on carrier pins, internally toothed ring gear, three-arm carrier and a highlighted held-member reaction fixture, plus concentric shaft/bearing supports, with home view, focus-selected-part, full-enclosure/cutaway toggle, exploded view, auto-rotate, expand and show/hide labels controls. • An Equipment laboratory tab with a labeled parts index (sun, planets, ring, carrier, fixture, shafts, console) and click-to-inspect component callouts, plus a live member-speed chart (sun, ring and carrier rpm). • Fixture controls: member held stationary (ring held/sun drives carrier, carrier held/sun drives ring, or sun held/ring drives carrier), sun tooth count (18–36), each planet's tooth count (12–24, with ring teeth Nr = Ns + 2Np derived automatically), input shaft speed (0–180 rpm) and ideal input torque (0–50 N·m). • Playback controls: start/stop motion at the four selectable model speeds shared with the workbench. • A Curves & measurements tab with two live charts (sun/ring/carrier speed; input vs. output power), the underlying model equations (Willis relation, planet spin, held-member speed ratios, torque/power balance) and snapshot readouts for fourteen metrics including signed speed ratio and external holding reaction. • An Experiments tab with four guided fixtures (ring-held reduction, carrier-held reversal, sun-held drive, different tooth set) and a Model verification bench that runs independent deterministic checks against a fresh model without disturbing your live trial, plus a timestamped event log and a copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz with reset, and a written model-scope statement with a referenced technical background link.
A planetary gearset has three coaxial members — sun, ring and carrier — related by the Willis relation: Ns·ωs + Nr·ωr = (Ns + Nr)·ωc. Because this single equation ties all three angular speeds together, fixing any one member's speed (usually to zero, by holding it stationary) leaves a determinate speed relationship between the remaining two.
Holding the ring gives a speed reduction set by carrier/sun = Ns/(Ns+Nr); holding the carrier reverses direction between sun and ring, ωr/ωs = −Ns/Nr; holding the sun gives carrier/ring = Nr/(Ns+Nr). The simulator's four guided experiments walk through all three held-member modes plus an alternate tooth set so you can see each ratio arise directly from tooth counts.
A planet gear's absolute spin speed is not the same as the carrier's rotation — it also spins about its own pin axis in response to meshing with the moving sun, following ωplanet = ωc − (Ns/Np)(ωs − ωc). With ideal lossless gears, input power always equals output power (Pin = Pout), and the stationary held member carries a reaction torque even though it does zero work, since power is torque times angular speed and its speed is zero.
This is an ideal, rigid, lossless spur-gear kinematic and static-torque-balance model with three equally spaced planets and steady input speed. It excludes backlash, elastic deflection, bearing friction, transient clutch dynamics and detailed involute tooth-contact or stress analysis — gear teeth are schematic profiles, not manufacturing involutes, and torque values at zero speed are ideal static ratios rather than a dynamic stall analysis.
Not generally. A planet gear both spins about its own pin and orbits with the carrier; its spin speed is set by the sun mesh relative to the moving carrier, following ωplanet = ωc − (Ns/Np)(ωs − ωc), so spin and orbit are genuinely different motions.
Yes. Power equals torque times angular speed, and the held member's angular speed is zero, so it can carry a reaction torque — the holding torque — while transferring zero power. Only the sun, ring and carrier that are actually rotating exchange power.
Ring teeth are derived automatically as Nr = Ns + 2·Np, the pitch-closure condition that lets the sun, planets and ring mesh consistently. You set sun and planet tooth counts directly; the simulator computes the matching ring count.
No. It is an ideal, rigid, lossless kinematic and static torque-balance model with schematic gear-tooth profiles rather than manufacturing involutes. It excludes backlash, elastic deflection, bearing friction and transient clutch dynamics, so it should not be used for stress or tolerance analysis.