Epicyclic Train (form 5) Mechanism Explained: How It Works, Diagram, Formula & Calculator

The carrier drives and the sun speeds up

The orange carrier moves two blue planet gears around the fixed internal ring. Their inner engagement drives the gold sun. Sun and carrier rotate in the same direction, with the sun turning faster.

At a common module, each planet requires Np=(Nr−Ns)/2 teeth. The animation retains the entered dimensions rather than rounding that result. Fractional, zero or negative planet counts produce an unassembled preview.

Both planet meshes are phased together. Two opposed planets are illustrated; no claim is made about equal load sharing or the number of planets needed for a particular gearbox.

Choose teeth for a step-up ratio

The ring and sun controls let you examine individual tooth-count combinations. Carrier speed is a multiple of a common reference, not an absolute rpm value. The sun result uses the same reference.

For exploration by ratio alone, the form 4 calculator uses the same fixed-ring power flow and automatically generates an illustrative tooth set.

This page does not select a generator, flywheel or motor, and its ideal torque fraction is not a gear capacity rating.

Calculate speed, torque fraction and assembly

With the ring fixed, ωs=(1+Nr/Ns)ωc. The sun/carrier speed factor is 1+Nr/Ns. Ideal power balance gives Ts/Tc=1/(1+Nr/Ns) in magnitude.

The ring reaction magnitude is Tc−Ts. It is not the speed factor minus one multiplied by carrier torque. The fixed ring transmits no mechanical power because its speed is zero.

The required planet teeth are (Nr−Ns)/2. This must be a positive integer for the simple common-module geometry. Tooth outlines use illustrative 25° stub involutes with 0.75-module addendum and simplified roots.

60-tooth ring and 12-tooth sun

Each planet needs (60−12)/2=24 teeth. Step-up is 1+60/12=6:1. A carrier speed of 1× reference gives sun speed 6× and ideal sun torque 1/6 of carrier torque.

For example, ideal 6 N·m carrier input would correspond to 1 N·m sun output and 5 N·m ring reaction. The calculation does not include losses.

A 61-tooth ring with the same 12-tooth sun would require 24.5-tooth planets. The diagram keeps the parts visible but does not present that combination as a running gearbox.

Keep kinematics separate from production design

Correct centre distances and speed ratios do not establish tooth strength, acceptable backlash, bearing life or manufacturability. The example uses two opposed planets and illustrative stub involutes; low-count cases outside its profile checks use pitch circles.

Operating limits, tolerances and wear depend on the specified gears and application. A detailed gearbox requires its own tooth geometry, interference, material, load and bearing calculations.

Form 5 questions

Why do odd tooth-count differences fail?

Half the ring-minus-sun difference must be a whole planet tooth count.

What happens when ring and sun counts are equal?

The required planet has zero teeth, so this simple assembly is impossible.

Is the torque factor a capacity?

No. It is the ideal power-conservation ratio, without strength or loss analysis.

Why does high-speed playback slow down?

The inspection animation limits its fastest visible rotation. All relative member speed ratios remain correct.