Planetary Gear Set Simulator

One simple planetary gear set Updated November 2026 Free, no sign-up

Simulator

Example simple planetary gear set, face view, with a band and three clutchesBandSun holdingclutchCarrier holdingclutchLocking clutch
  • Sun gear
  • Planet carrier
  • Ring gear

Computed for this example gearset (sun 30, ring 72, planets 21 teeth), ignoring friction losses. Not a figure for any real transmission.

Drive, hold and lock

Pick the input member, then hold one member or lock two together. The strip under the drawing shows how each member turns.

This is a study simulation for trade exams, not a test or repair procedure. Figures are computed for this example gearset and example unit, ignoring friction losses, and are not figures for any real transmission.

Drive, hold and lock the members of an example planetary gear set to see its ratio and torque, then find a slipping band or clutch from test readings.

This free simulator animates an example simple planetary gear set: a sun gear, three planet gears on a carrier and a ring gear, with a band and three clutches that hold or lock the members. It fits the transmission topics of the 421A Heavy Duty Equipment Technician and 310S Automotive Service Technician Red Seal exams. It is a simplified teaching model of ideal gears with no friction losses, so every figure on screen is computed for this example gearset, not taken from any real transmission.

How a simple planetary gear set works

The three members and what each can do

A simple planetary gear set has three members: the sun gear in the centre, the ring gear around the outside with its teeth on the inside, and the planet carrier. The planet gears turn on pins in the carrier and mesh with the sun gear and the ring gear at the same time. Drive one member and hold another, and the third is the output; the simulator marks each member as input, held or output. With nothing held and nothing locked, the set has nothing to push against, so the output is not driven and no torque is transmitted: that is neutral. Lock any two members together and all three turn as one at input speed, a 1.00:1 direct drive in which the planets do not turn on their pins. Holding a member while two members are locked together leaves nothing that can turn, so the set cannot move.

Working out the ratio

The speeds follow one relation: sun teeth times sun speed, plus ring teeth times ring speed, equals the two tooth counts added together times carrier speed, with a turn the opposite way counted as negative. With the ring held and the sun driving, the sun turns 1 + ring teeth ÷ sun teeth times for each carrier turn, which is 1 + 72 ÷ 30 = 3.40 in this example. In a simple set with one member held and none locked, holding the carrier reverses the output, and taking the output from the carrier reduces speed. With one member held and none locked, driving the carrier gives an overdrive, with the output turning faster than the input. The number of planet gears does not appear in the relation, so it does not change the ratio.

Torque and the held member

Ignoring friction losses, output torque equals input torque times the ratio, so a 3.40:1 reduction gives 3.40 times the input torque at the output. The holding device carries the reaction torque that balances the input and output torques: with the ring held and the sun driving, that is 2.40 times the input torque. When the output turns the opposite way, the reaction is the input and output torques added together, so a held carrier takes 3.40 times the input torque with the sun driving. That reaction grows with the load, so a weakened band or clutch may still hold a light load and slip under a heavy one. In direct drive the locking clutch carries torque between the locked members, so a worn or weakly applied clutch can slip there under a heavy load too.

Bands, clutches and line pressure

In automatic transmissions the members are held or locked by bands and multi-disc clutches, applied by hydraulic pressure that the pump supplies. The pump and the main regulator make line pressure, which feeds every apply circuit. A band wraps the outside of a drum and is tightened by a hydraulic piston called a servo. A clutch squeezes a stack of plates together: with one set of plates tied to the case it holds a member, and between two turning parts it drives them or locks them together. Each range applies its own set of bands and clutches, called elements, and the apply chart in the service information shows which ones.

Finding a slipping element

The example unit in Find the fault drives the sun and takes the output from the carrier: in Low a band holds the ring, and in Direct a locking clutch locks the sun to the ring. When an element slips, input speed rises while output speed does not follow, and the speed check compares the two. Trouble in some ranges usually points to an element those ranges apply and the working ranges do not, while trouble in every driving range usually points to something they share, such as line pressure. Apply pressure low in one circuit, with line pressure normal, usually points to a leak in that circuit. Line pressure low in every range usually points to the supply, such as the pump, the main regulator or a clogged filter. Line pressure low in one range and normal in the others usually points to a leak in a circuit that range applies. Slip under a heavy load with every pressure normal usually points to worn friction material, which lowers the torque the element can hold. In this example unit, read each apply port in the range that applies it. In the other ranges that element is released, so its port reads no pressure even on a healthy unit.

The six combinations in this example

These are the six ways to drive one member and hold another, computed for this example gearset with a sun of 30 teeth and a ring of 72, ignoring friction losses.

HeldInputOutputOutput turns per input turnRatioKind
RingSunCarrier0.29, same direction3.40:1Reduction
RingCarrierSun3.40, same direction0.29:1Overdrive
SunRingCarrier0.71, same direction1.42:1Reduction
SunCarrierRing1.42, same direction0.71:1Overdrive
CarrierSunRing0.42, opposite direction2.40:1Reverse reduction
CarrierRingSun2.40, opposite direction0.42:1Reverse overdrive

Ratio means input speed divided by output speed; above 1.00:1 is a reduction, and below it is an overdrive.

Parts of the gear set

Sun gear

What it is: The gear in the centre of the set, with its teeth on the outside.

What it does: It can be the input, the held member or the output; with the ring held and the sun driving, the set gives its largest reduction.

In this drawing: In this example gearset it has 30 teeth, and a stripe marks it so its turning can be followed.

Planet gears

What it is: Gears that sit between the sun gear and the ring gear and mesh with both at the same time.

What it does: They pass torque among the sun, the ring and the carrier, and they turn on their pins whenever the members turn at different speeds.

In this drawing: This example gearset has three, each with 21 teeth; the number of planet gears does not change the ratio.

Planet carrier

What it is: The frame that holds the pins the planet gears turn on.

What it does: With one member held and none locked, taking the output from it reduces speed, driving it gives an overdrive, and holding it reverses the output.

In this drawing: It is drawn as a plate joining the three pins, with an arm that marks its position.

Ring gear

What it is: The outer gear, with its teeth cut on the inside.

What it does: With the sun driving and the output taken from the carrier, holding the ring gives a reduction.

In this drawing: In this example gearset it has 72 teeth, cut in a drum, and a notch on the drum marks its position.

Band

What it is: A strap with a friction lining that wraps the outside of a drum.

What it does: A hydraulic piston called a servo tightens it to hold the drum still; released, it lets the drum turn.

In this drawing: It wraps the ring gear drum; in Operate it is drawn solid and close when applied, dashed and apart when released.

Holding clutch

What it is: A multi-disc clutch with one set of plates tied to the case.

What it does: Applied by hydraulic pressure, it holds its member still.

In this drawing: The drawing has one for the sun gear and one for the carrier; in Operate the plates touch when applied and stand apart when released.

Locking clutch

What it is: A multi-disc clutch between two members.

What it does: Applied with no member held, it locks the two members together, and the whole set turns as one at 1.00:1.

In this drawing: In Find the fault it locks the sun to the ring for Direct; in Operate any two members can be locked.

Fault-finding table

FaultSymptomWhat to testWhat you would seeCause
Band lining wornDirect is normal; in Low the unit drives a light load but slips under a heavy load.Speed check in Low under a heavy load, then the band apply port in Low and the line pressure.In this example unit, a slip in Low under a heavy load, with band apply pressure normal and line pressure normal.Band lining worn
Band apply piston seal leakingDirect is normal; in Low the unit drives a light load but slips under a heavy load.Band apply port in Low, and the line pressure.In this example unit, band apply pressure below normal in Low, with line pressure normal.Band apply piston seal leaking
Band not applying (no apply pressure reaches it)No drive in Low; Direct is normal.Speed check in Low, then the band apply port in Low.In this example unit, no drive in Low and no band apply pressure in Low; with the output stopped, the ring turns 0.42 times per input turn, opposite direction.Band not applying (no apply pressure reaches it)
Locking clutch friction wornLow is normal; in Direct the unit drives a light load but slips under a heavy load.Speed check in Direct under a heavy load, then the clutch apply port in Direct and the line pressure.In this example unit, a slip in Direct under a heavy load, with clutch apply pressure normal and line pressure normal.Locking clutch friction worn
Locking clutch piston seal leakingLow is normal; in Direct the unit drives a light load but slips under a heavy load.Clutch apply port in Direct, and the line pressure.In this example unit, clutch apply pressure below normal in Direct, with line pressure normal.Locking clutch piston seal leaking
Locking clutch not applying (no apply pressure reaches it)No drive in Direct; Low is normal.Speed check in Direct, then the clutch apply port in Direct.In this example unit, no drive in Direct and no clutch apply pressure in Direct; with the output stopped, the ring turns 0.42 times per input turn, opposite direction.Locking clutch not applying (no apply pressure reaches it)
Low line pressure from the supply (pump or main regulator)Under a heavy load the unit slips in both Low and Direct; with a light load both ranges drive.Line pressure, then the band apply port in Low or the clutch apply port in Direct.In this example unit, line pressure low, with apply pressure below normal at the band in Low and at the clutch in Direct.Low line pressure from the supply (pump or main regulator)
Band lining worn: why, and how to tell it apart

Why

Worn lining lowers the torque the band can hold, so it holds the smaller reaction of a light load and slips under the larger one, even with normal apply pressure.

How to tell it apart

A leaking band piston gives the same slip with band apply pressure below normal; a supply fault gives low line pressure and a slip in Direct as well.

Band apply piston seal leaking: why, and how to tell it apart

Why

Fluid escaping past the piston seal lowers the pressure that applies the band, so it clamps less firmly and slips under a heavy load.

How to tell it apart

Worn lining gives the same slip with normal band apply pressure; a supply fault makes the line pressure low as well.

Band not applying (no apply pressure reaches it): why, and how to tell it apart

Why

With no apply pressure the band never tightens, so nothing holds the ring and the set stays in neutral in Low.

How to tell it apart

A worn or leaking band still drives a light load in Low; this one drives no load at all.

Locking clutch friction worn: why, and how to tell it apart

Why

Worn friction plates lower the torque the clutch can carry, so under a heavy load the sun and ring turn at different speeds.

How to tell it apart

A leaking clutch piston gives the same slip with clutch apply pressure below normal; a supply fault gives low line pressure and a slip in Low as well.

Locking clutch piston seal leaking: why, and how to tell it apart

Why

Fluid escaping past the piston seal lowers the clamping pressure on the plates, so the clutch slips under a heavy load.

How to tell it apart

Worn plates give the same slip with normal clutch apply pressure; a supply fault makes the line pressure low as well.

Locking clutch not applying (no apply pressure reaches it): why, and how to tell it apart

Why

With the clutch not applied and the band released, nothing holds or locks a member, so the set is in neutral in Direct.

How to tell it apart

A worn or leaking clutch still drives a light load in Direct; this one drives no load at all.

Low line pressure from the supply (pump or main regulator): why, and how to tell it apart

Why

The band and the clutch are fed by the same line pressure, so low pump output, a faulty main regulator or a clogged filter weakens both.

How to tell it apart

In this example unit, a fault in one element affects the range that applies it and leaves the line pressure normal.

About this simulator

The gear set and the two-range unit are generic and do not copy any real product. On a real unit, pressure and stall tests follow the service information for that transmission, with the fluid at operating temperature. Rotating and moving parts are an entanglement hazard: keep clear of them during a running test, and use lockout when work needs the energy controlled.

Sources: university mechanism-theory course notes and an engineering teaching site on epicyclic gear trains, transmission trade-magazine technical articles, and CCOHS guidance on working around machinery.

Use this simulator in a class

Paste this code into a class page or a course site such as Moodle or D2L to show the simulator there. It is free to use for teaching, with the link back kept.

Open the full page: how it works and free practice questions

Frequently asked questions

What happens when two members of a planetary gear set are locked together?

With no member held, all three members turn as one at input speed, a 1.00:1 direct drive, and the planet gears do not turn on their pins.

What happens when no member is held and none are locked together?

With nothing held and nothing locked, the set has nothing to push against, so the output is not driven and no torque is transmitted: the set is in neutral. Locking two members together instead gives direct drive.

Does the number of planet gears change the ratio?

No. The speed relation uses the sun and ring tooth counts and has no term for the number of planets.

How does one planetary gear set give reverse?

In a simple planetary gear set, hold the carrier and drive the sun or the ring: the planets then turn on fixed pins and the output turns the opposite way. In this example, the sun driving with the carrier held gives a 2.40:1 reverse reduction.

Why can a worn band or clutch hold a light load but slip under a heavy one?

The torque a band or clutch must carry rises with the load, so a weakened one can still hold the smaller torque of a light load but slips once the torque is more than it can hold.

Which trades is this simulator for?

It fits the transmission topics of the 421A Heavy Duty Equipment Technician and 310S Automotive Service Technician exams. More simulators are listed on the trade simulators page.