Inside the Kuru Toga

Three cams, and the trick is the half tooth

My mental model before reading the patents was wrong in a way that I suspect is common. I assumed the mechanism was a ratchet: a pawl, a spring, a wheel that can only go one way. It is not. There is no pawl anywhere in it, and nothing blocks the rotor from turning backwards.

What is in there is three rings. Two of them are cam formation members fixed to the barrel, one above the other, and each carries a continuous sawtooth cut around its face. Between them sits a rotor, free to turn and free to slide up and down, with sawteeth on both of its ends. The rotor is the only part that moves, and the chuck holding the lead is coupled to it, so whatever the rotor does the lead does too (Izawa et al., US8328446B2, priority 2006; Izawa, Kobayashi and Nakayama, US20100232863A1, from JP2007-278904).

All four toothed faces are cut to the same pitch. The crucial detail is that when one pair of faces is fully meshed, the other pair is sitting exactly half a tooth out of phase. Writing pressure pushes the lead, the chuck and the rotor back against a spring; the rotor's upper teeth meet the upper ring half a tooth off, and the only way they can seat is for the rotor to turn through that half tooth. Lifting the pen lets the spring drive the rotor forward again; now its lower teeth meet the lower ring half a tooth off, and they seat by turning it through the other half. The two ring profiles are mirror images, so although the rotor is being pushed in opposite directions on the two half strokes, both halves turn it the same way round.

One press and one lift is therefore exactly one tooth. A forty tooth engine gives nine degrees, which is where the "forty strokes to a full turn" figure comes from, and the Kuru Toga Advance simply halves the tooth count to twenty and gets eighteen. Teardowns that have counted the teeth agree with the arithmetic (Japan Patent Office, 2019; シャー坊, 2023). Mitsubishi built around five thousand prototypes before the writing feel was judged acceptable, and the production mechanism has twenty two parts, roughly twice an ordinary pencil.

Two consequences follow from the fact that the cycle is driven by pressure and not by distance, and both are easy to feel. A short stroke turns the lead exactly as far as a long one, which is why the count is quoted in strokes of a character rather than in millimetres. And if you never lift the pen, drawing one long unbroken line, the rotor never cycles and the lead never turns at all. Turn off "lift the pen" above and watch the mechanism stop indexing while the pencil keeps writing.

Why a lead that never turns goes wrong

Hold a pencil at a fixed angle and the same side of the lead meets the paper on every stroke. Abrasion takes graphite from that side only, and the paper cuts an oblique face across the cylinder. The geometry is simple enough to write down: a lead of diameter d held at an angle θ to the paper develops an elliptical flat whose long axis is d divided by sin θ. A 0.5 mm lead held at sixty degrees ends up with a flat 0.58 mm long.

Three things go wrong at once, and the patent names all three. The line gets wider, because the contact patch grows from something near a point to the full width of the lead. It gets paler, because the same graphite is spread over more paper. And the leading edge of that flat is a feather thin wedge with almost no cross section, which is the first thing to touch the paper on the next stroke and the first thing to snap.

Turn the lead a little between strokes and the paper cuts a fresh face at a fresh azimuth each time. The material left behind is the intersection of all those cuts, and that intersection is a cone about the lead's own axis. The cone's half angle is not a free parameter: it is exactly the angle you hold the pencil at. Hold it at forty degrees and the lead converges on a forty degree cone, which is a decent point. Hold it at eighty and it converges on an eighty degree cone, which is nearly a flat disc. Hold it truly upright and there is no cone at all, and the rotation buys you precisely nothing, which the simulation will confirm if you push the hold angle to eighty eight.

What the turning is actually worth

This is where I expected the mechanism to look impressive and it did not. The wear view runs Archard's law, which says that at a given load and sliding distance the volume of material removed is fixed, regardless of how large or small the contact patch is. That single assumption is enough, and it has a consequence that is easy to miss: the tip can never converge on a mathematical point, because a point would remove no volume. The steady state is a cone with a small flat at its apex, and the size of that flat is what sets your line width.

So the benefit is a race. Rotation moves the lead to fresh ground; wear digs a flat into whatever ground it is on. Whichever is faster wins, and the outcome is not close to constant:

Press lightly with a hard lead and the engine is transformative. Press hard with a soft one and you wear a flat faster than nine degrees a stroke can turn you off it, and the mechanism gives you nothing at all. The Advance's eighteen degrees does not change the shape the tip converges on, only how fast it gets there, which is worth roughly one row of that table.

Two further results fall out of the simulation that I have not seen stated anywhere. The first is that a standard engine gives you nothing for the first full revolution: for the first forty strokes every cut lands on ground the previous cuts have already flattened, and the line width tracks the fixed lead almost exactly before pulling away. The second is the recovery time. Wear a flat deliberately, then start turning, and it takes about twenty two strokes at nine degrees to get back within ten percent of the turning steady state, and about twelve at eighteen. Mitsubishi's developer describes the Advance as recovering from uneven wear "within a few strokes", which is generous but the right order of magnitude.

Mitsubishi's own published claim is that the faster engine writes about twelve percent finer than the standard one with HB and about seventeen percent finer with 2B, using the same 0.5 mm lead. Those are modest numbers, and they sit comfortably inside the range my simulation produces for plausible wear rates. They are also consistent with the most useful piece of third party evidence I found, which is a reviewer who tried to see the difference with real pencils and real leads and reported that with HB it was hard to tell apart even side by side, with 2B visible but modest.

I think that is the honest summary. The Kuru Toga is doing exactly what it claims, the claim is smaller than the reputation, and the size of the effect is mostly determined by something the pencil has no control over, which is you.

What I could not settle

I have not relied on Mitsubishi's own pages, so every figure I have attributed to the manufacturer arrives second hand, through the Japan Patent Office's magazine, through press releases republished verbatim, or through Japanese stationery journalism quoting the development team. I would treat the nine and eighteen degree figures as solid, since the patent kinematics, the tooth counts from two independent teardowns and the manufacturer's claim all agree, and everything else attributed to uni as one step removed.

Three things I could not pin down at all. The direction the lead turns rests on a single teardown, which reports counter clockwise seen from the tip; I have drawn it that way, but would not stake anything on it. The cushion travel and the tooth height are not numerically specified in either patent, so the millimetre figures in the engine view are my own reconstruction, chosen as the smallest that let the cam ride cleanly. And I found no credible measurement of the angle people actually hold a pencil at, so the sixty degree default is a convention rather than a datum.

The parts around the engine in the 3D view, the chuck, the spring and its seat, the housing and the nose, follow the arrangement the patents describe but are drawn to my own dimensions and finishes, not measured from a pencil.

The parameter I am least sure of is the one the conclusion turns on most: how much graphite a stroke actually removes. That is why it is a slider rather than a constant. If you know of a real measurement, I would like to see it.