1Five minutes to a first drive

1. Open the app. A single 15-tooth, module 2 spur gear is the driver (#1). It is always the root of the train.
2. Add New puts a second gear on it, meshing. Select it in the Gears list and set Number of teeth (N): the ratio in the list updates as you type.
3. Turn the connection. Connection properties · Direction swings the child around its parent; the centre distance stays correct.
4. Press Space (or Start/Stop). The train turns at the drive speed. Drag the dot on tooth 0 to turn it by hand when stopped.
5. Check the numbers. Info (top right, or I) opens the data box: diameters, contact ratio, working pressure angle, tooth forces.
6. Export. Select a gear → DXF selected for cutting, STL for printing. SVG all gives a drawing of the whole train.

Everything is saved in the browser as you work. Save writes a .gg file; Copy share URL puts the whole design in a link.

2How a design is put together

The train is a tree. Every object hangs off one parent by a connection:

• Gear (mesh): the two mesh; the centre distance follows from the teeth, module and profile shift, and the direction is yours to choose.
• Axle: the child sits on the same shaft: same centre, same speed, new layer.

A layer is one shaft line. Visibility · Same layer shows only the layer of the selection, which is how you work on a multi-stage box. The 3D view shows the layers one above the other, as STEP export stacks them, and there Visibility hides what it dims in 2D.

Ratios come out of the tree: the Gears list shows each object's ratio to drive 1 and its rpm, signed by direction (the info box spells out ↺ CCW / ↻ CW).

What can connect to what

A rack cannot be the driver. Type buttons that would break an existing connection are disabled and say why.

3The stage

100% means real size on screen at 96 dpi: hold a caliper to the screen and the pitch diameter is right. The bottom right corner always shows the current scale.

Overlays (Display section): gear guides (root, base, reference and tip circles), gear labels, centre marks, curve types (involute / trochoid / tip / root drawn in different colours), Bézier nodes for the selected object and its neighbours, and the line of action with live contact points. The same section holds Lost motion, which is a simulation setting rather than an overlay (§6.2). The 3D view draws the guides, labels, centre marks and the line of action too: the line of action of every mesh on show, over everything, on the top face the two gears share. Curve types and Bézier nodes are 2D only.

Labels are written in one size across the design, so the big wheels and the small ones read alike: the largest size every wheel has room for, but never less than half of what the roomiest wheel could take. A wheel with no room even for that gets a smaller text of its own, and one tiny wheel never shrinks all the others. No letter takes more than 8° of the circle it is written on, so a small wheel's label keeps to small letters instead of wrapping round its hub in a few big ones. Every label keeps at least a letter's height clear of the teeth, the holes and the edges of a rim; where a wheel has no room for that the text gets smaller, and where it would be under 1.2 mm tall the wheel goes without. The exports and the 3D view use the same sizes.

This manual, while you work. Help (H) shows it in a panel on the stage, where the info box sits, so you can read it with the gears still in front of you and still turning; Esc or Help again puts it away. The manual and the info box share that corner: opening one closes the other. It is this same page, not a copy, so everything in it works there: the contents, the § links, the figures. The panel's bar names the chapter you are reading, and it is a menu of all of them: choose one and the manual goes there. The link at the top right of the bar, open in new window, hands it to a tab of its own at that chapter and puts the panel away; Shift-click Help does the same without opening the panel first. On a page of its own the manual's contents are a column on the left, always there, with the chapter you are reading marked in it; on a narrow screen they are a button in the corner that names that chapter and opens the list. Below about 1000 px of window there is no room for it beside the gears, so Help opens the page instead; widen the window and the panel comes back if that is how you left it. The website opens without the manual and the info box; the desktop app opens them as you left them.

4Designing gears

4.1Spur gear

Geometry follows the standard rack: addendum 1·m, dedendum 1.25·m, so root clearance is 0.25·m. The flank is a true involute; the fillet is the trochoid the generating rack's tip corner traces, so undercut appears exactly where a hobbed gear would have it, which is also why the app can warn about it rather than guess.

The info box reports reference, base, tip and root diameters, the diameter where the involute starts (Involute starts Ø: below this the flank is fillet, not involute), circular pitch, Béziers per tooth and the worst fit error of the curve fit (§9).

4.2Internal (ring) gear

Same parameters plus Rim thickness (material outside the roots); teeth run from 12 to 400. Rules the app enforces or warns about:

• The ring needs at least one more tooth than the largest gear meshing with it (hard limit), and 8 more to avoid interference in practice (warning).
• Pinion tips hit the bottom of the ring's tooth spaces means the pair as drawn would not assemble: raise the ring's teeth, lower the pinion's, or shift the profiles.
• Where a space closes up before the root (high pressure angle or shift), its two flanks run on to meet in a V, involute all the way, instead of crossing. Only where the meshing pinion's tips would reach into that V (a very high pressure angle) is its bottom cut back along the tips' path, as a pinion-type cutter would cut it.
• Seen from a meshing pinion, each corner of the ring's tips sweeps a loop past the pinion's teeth. With many teeth between them, or a low pressure angle, that loop dips a few micrometres into the fillet at the foot of the pinion's teeth, just below where its involute starts. The ring's tip circle is then moved out just far enough for the corners to clear the fillets (a few hundredths of a module); the flanks mesh as before.

Ring gears take screw holes in the rim (§7).

4.3Rack

Teeth, Module, Pressure angle, Body height (material below the roots), and Display:

• Fade: a window of rack fades out past the contacts (drawing style).
• Cut: the same window with hard ends.
• Length: a finite rack of Teeth teeth that travels; when it runs past the end it wraps by whole teeth so it never leaves the screen.

Contact distance places a rack child along its parent's rack, measured from the parent's contact point. The info box gives the rack's travel in mm/min at the current speed, the number you need for a feed calculation.

In the exports the rack is a piece of whole teeth. In Fade and Cut mode the piece follows the animation and jumps back one tooth each tooth of travel; export in Length mode when you want a definite bar.

4.4Planetary set

Sun gear (SN), Planet gears (PN), Ring gear (RN), Number of planets, Auto profile shift, Backlash, Ring rim, and the roles.

Two rules govern the set, both checked live:

• Teeth: RN = SN + 2 · PN, or the planets cannot mesh with both sun and ring.
• Assembly: (SN + RN) / n must be a whole number, or the planets cannot be spaced equally. The app then places them on the nearest valid tooth positions and warns.

Planetary setup gives each member a role: Input (driven by the parent), Fixed, Drive (its own drive: a differential), Output (children hang off it). The ratio follows: with the ring fixed, carrier / sun = SN / (SN + RN); the info box always shows the actual Output / input ratio for the roles you chose.

Auto profile shift applies the no-undercut shift to the sun and planets and balances the ring to keep both meshes right; the info box lists the three shifts used. Contact ratios for sun–planet and planet–ring are listed separately: check both.

The carrier is drawn as thin dashed arms; select the set to dimension them (radius of the planet axes and the angles between the arms).

4.5Chain wheel set

Pick an ISO 606 / ANSI chain (04C, 05B, 06B, 06C, 08A, 08B, 10A, 12A, 16A) and the two tooth counts. For a bigger or smaller chain than these, pick Custom pitch and set Chain pitch (p) (1–100 mm): the roller, plates, pins and widths follow the pitch in the proportions of the ANSI roller chains, so the sprockets are cut for that chain's rollers. The tooth form is the simplified ISO 606 profile: roller seat radius ri = 0.505·d1 + 0.069·∛d1, seating angle (140 − 90/N)°, flank radius re = 0.008·d1·(N² + 180), tip between the standard minimum and maximum.

Wheel distance (D) is a target: the real distance in brackets is the nearest one that gives a whole, even number of links (so the chain closes with the same link types). The info box gives the link count, the chain length and both pitch diameters.

The chain also decides how the sprocket is built. A sprocket has to run between the chain's inner plates, so its toothed body is not a face width you choose: it is the ISO 606 tooth width for the chain you picked: 0.93·b1 up to 12.7 mm pitch and 0.95·b1 above, where b1 is the width between the plates. The app fixes it, states it in the 3D properties and in the info box, and gives you the two things that really are yours:

• Tooth chamfer: what lets the chain roll on and off instead of catching a square corner. It is a shallow cone turned onto the outer edge of the wheel: it starts where the roller seats end and the tooth flanks begin, and sinks towards the tips at the angle you give (Auto = 10°, a workshop chamfer), so the tips lose the most and the seats the rollers sit in keep their full width. It changes the solid only: the 2D outline, and the SVG and DXF exports, stay the flat profile you would cut.
• Hub: the collar around the bore, per sprocket: None, One side (flush with the teeth on the other face, as most machined sprockets are) or Both sides. Its width is the whole width of the wheel at the hub and can never be less than the body; its diameter is capped by what the chain plates clear where they wrap onto the wheel, p·cot(π/N) − 1 − h₂ (ISO 606); the field shows that limit, and a hub asked to be fatter is trimmed to it with a . A hub too small to leave material around its own bore is left out and reported.

Holes and screw holes are set as usual (§7): the ones that fit inside the hub are bored through it, giving the grub screw or the shaft a proper length of grip, and any outside it go through the body alone. The hub is drawn as a thin circle in 2D, and comes out in the STL and OBJ solids; in SVG and DXF it lands in the optional guides layer, because a flat-cut part has no hub.

In the 3D view the chain itself is drawn: outer and inner links in turn, with their rollers and pins, wrapping both sprockets and running as the set turns, which is also the easiest way to see whether a hub is too fat for the plates to pass over. Every size of a link is that chain's own (plate depths, roller and pin diameters, and the width over the plates), in 2D as in 3D, so a roller always fits the seat the sprocket is cut with.

4.6Belt wheel set

Presets: GT2 2 mm and 3 mm, HTD 3M / 5M / 8M, T5, T10, and a flat belt. Choose the two tooth counts; Wheel distance is again a target, snapped to a whole number of belt teeth. The info box gives the belt tooth count, the pitch length and both pitch diameters: the numbers you order a belt with.

Sprockets and pulleys are always spur; there is no helical option for them.

4.7Tooth profiles: involute, cycloidal, clock

Two different things share the word cycloidal. This section is about the shape of a gear's teeth, the Tooth profile of a spur gear, a ring gear or a rack. The Cycloidal Drive, a whole reducer with pins and a lobed disc, is a part type of its own (§4.8).

Tooth profile has three settings, shared like the module by everything that meshes together:

• Involute (the default): what every other section of this manual describes, with a pressure angle and a profile shift.
• Cycloidal: exact cycloids. A circle rolling round the outside of the pitch circle traces the addendum (an epicycloid), the same circle rolling inside traces the dedendum (a hypocycloid). Gears whose flanks are traced by the same circle are conjugate, so the whole group shares one Rolling circle Ø, and any two of them mesh, either way round, ring gears and racks included. The curves are fitted to the same curve precision as the involutes (§9).
• Clock: clock wheels and pinions after BS 978 Part 2, as Hugh Sparks wrote it up and Rainer Hessmer's Cycloidal Gear Builder draws it. Radial flanks below the pitch circle, the addendum one arc on each side; the bigger gear of a pair is the wheel (teeth half a pitch wide, an ogival tip 0.95 of its pointed height), the smaller the pinion (thinner leaves, rounded by a table of leaf counts: high ogival up to 7, medium ogival for 8 and 9, round from 10). Clock teeth are for gear pairs: a group with a ring gear or a rack in it gets cycloidal teeth instead, and the button says why.

The rolling circle. As wide as a gear's pitch radius, it gives that gear straight radial flanks; narrower, flanks that widen towards the root (a stronger tooth); wider, flanks that lean in (a warning says so). Auto makes it as wide as the smallest gear's pitch radius, the clockmaker's choice, and narrow enough for every ring gear in the group: inside a ring the circle may be at most the difference of the two pitch radii, or the teeth interfere.

What changes with the profile:

• The centre distance is always m · (N₁ + N₂) / 2: cycloidal teeth have no profile shift, and they only mesh at exactly that distance.
• The pressure angle is not one number: 0° at the pitch point, growing to the ends of the path of contact. The info box gives the range and the mean, and the loads (§10) use the mean.
• Line of action draws the path of contact as it really is for these teeth: two arcs of the rolling circle, crossing at the pitch point.
• Curve types colours the epicycloids blue and the hypocycloids violet; a clock tooth's arcs are blue too.
• The label reads CYCLOIDAL or CLOCK where an involute gear's reads its pressure angle.
• Clock arcs only approximate conjugate flanks (that is the standard: it is made for a wheel driving a pinion). The app works out, for each clock pair, how far the pinion may take its play up before a flank touches at any phase of the mesh, and takes up only that much: the teeth never overlap, and at some phases the pinion floats a hair off its wheel, as in a real clock train. Two clock gears of the same size are a wheel (the parent) and a pinion (the child).
• Lost motion (§6.2) works as it does for involute teeth: with cycloidal teeth the gap is your Backlash; a clock pinion brings its own, its leaves being thinner than half a pitch, so a clock train waits on a turn back even with Backlash at 0.

4.8Cycloidal drive

A cycloidal reducer in one part: a ring of Pins (N) round the housing, a disc with one lobe fewer rolling inside them on an eccentric, and output pins that run in holes in the disc and take its slow turn off without the wobble. With the eccentric as the input and the pin ring held, the output turns once for every N − 1 turns of the input, the other way round: 1:11 with 12 pins, in a single stage.

The Holes & shaft joints section has the input shaft's hole (through the eccentric, at the axis) and screw holes in the housing.

The disc's edge is the path a pin centre takes, seen from the disc, moved in by the pin radius: an epitrochoid, fitted to the curve precision like everything else. Every pin touches an ideal disc all the time, but only half of them carry the load: Line of action marks those pins and draws their lines of force, which all run through one point, the pitch point, e · N out along the eccentric. The info line counts the loaded pins; the info box gives the members' speeds and torques (they are in the fixed ratio 1 : N − 1 : −N, eccentric : disc : ring), the disc's size and a rough force per loaded pin.

The sizes hang together, and the panel keeps them sound: change one and the others come along as far as they have to. The eccentricity is held under the most the pins allow, which is the least of three limits:

• e × N under the pin circle's radius, or the disc's edge has cusps.
• The lobes curving no tighter than the pins: thick pins on a small, very eccentric drive would fold the disc's edge over itself (undercut). The panel keeps a little margin.
• The lobes swinging clear of the housing between the pins: the disc reaches pin circle/2 + 2e − pin radius from the axis, which must stay inside the pins' outer edge. Thin pins hold the eccentricity down.

A file or a script that sets a drive past them is drawn at the limit, with a warning.

The children of a cycloidal drive sit on its output. In 3D and in the exports it is five parts on one layer: housing, (pins,) disc, eccentric and output pins. A real drive often has two discs half a turn apart, to balance it; the app draws one.

4.9Gear pump

An internal gear pump in one part, like the oil pump of an automatic gearbox: a pinion on the shaft that drives it, inside a ring gear with a few teeth more. The ring turns in a bore of the pump's body, set off from the pinion by the centre distance, the same way as the pinion and pinion teeth / ring teeth as fast. The body itself is yours to design (in your CAD program): the app makes the gears, the crescent and the ports. Where the teeth come out of mesh the spaces between them open and draw oil in through the inlet port; they carry it round on either side of the crescent, the fixed separator that fills the gap between the two tip circles, and squeeze it out of the outlet port where they go back into mesh.

A gerotor does without the crescent: its ring has only one tooth more than the pinion, and every one of its teeth keeps touching the pinion. The chambers between neighbouring teeth grow on one side of the mesh and shrink on the other, and the ports, placed where the chambers are smallest and largest, do the rest.

Changing the tooth form brings that form's own teeth (11 / 13 gearbox teeth, 13 / 17 involute, 6 / 7 gerotor with its sizes); the module (a gerotor's own: see below), the crescent and the ports stay as they were.

Teeth chooses the tooth form:

• Gearbox (a new pump's): the teeth of a gearbox oil pump. The ring sets the shape: its spaces are cut by a straight-flanked cutter the size of the pinion, which leaves them with long flat bottoms, slightly rounded corners and flanks that curve into the ring's flat tips. The pinion is cut to fit the ring: its teeth are the room the ring's teeth leave as the two turn, so their flanks are the exact opposite of the ring's, their tips are cut flat where the ring's bottoms would be without the Clearance, and their roots are cut as much deeper than the ring's tips reach. With no involute to keep to the teeth stay big, and two teeth apart is enough (11 and 13, as most gearbox pumps have them).
• Involute: an involute pinion and ring gear, with a pressure angle and profile shifts. The ring's spaces are the room the pinion sweeps as the two turn (swept by a pinion 0.25 modules taller, for the usual clearance at the bottoms): involute where the two are conjugate, and dug, or the ring's tips cut back along the pinion's path, where only a few teeth apart its tips reach further.
• Gerotor: round lobes on a ring with one tooth more than the pinion, and the pinion their exact mate. Its controls are its own (below).

The Holes & shaft joints section has the pinion's shaft hole (a spline fits a gearbox pump's hub).

Gerotor. The ring's teeth are round lobes, their centres on the Lobe circle. Seen from the ring the pinion moves exactly as a cycloidal drive's disc moves in its pins (§4.8), so it is made the same way: the path of the lobes' centres (an epitrochoid) moved in by the lobe radius. Every lobe touches it at once, along a line through the pitch point. Between the lobes the ring's valleys follow what the pinion's tips sweep, the Valley clearance out, with rounded corners where they meet the lobes. Its sizes are in mm, as you would measure them on a gerotor, and they hang together as a cycloidal drive's do: new teeth or another lobe circle keep the pump's shape (eccentricity × ring teeth / lobe circle radius), and the eccentricity stays under what the lobes allow.

Involute teeth only a few apart. A pinion inside a ring with only a few teeth more would hit the ring's tips well after the mesh: the tooth tips meet as the pinion rolls round. The app cuts the ring the way a shaper cutter the size of the pinion would: it rolls the pinion a whole turn inside the ring and takes back every tip it would hit, to its path. The note under Rim thickness and the info box say when it has, and where the flanks now start. The pinion and the ring never overlap, and the ring's flanks stay involute where they work. What may run short is the contact: the info box gives the contact ratio, and a warning comes under 1. A bigger pressure angle (25 to 30°) or a tooth more on the ring brings it back. Gearbox teeth have none of this: their pinion is cut from the room the ring leaves to begin with.

What it pumps. The info box gives the displacement per turn of the pinion and the flow at its speed, from where the teeth touch: what goes out is what the teeth on both sides of the line of contact sweep. For involute teeth the app works it out exactly and averages it over one tooth; for gearbox teeth it takes the teeth as touching at the pitch point, where the two pitch circles roll. A gerotor's is exact: it follows one chamber from smallest to largest, from the touches on its two lobes, and the pinion turns once while pinion teeth chambers fill. At the set Pressure the pinion needs pressure × displacement / 2π of torque; the loads (§10) also say what pressure the torque it gets could hold. The pump passes its torque on to whatever sits on its shaft.

Line of action shows where the pinion and the ring touch: for involute teeth the line of action, for gearbox teeth the path of contact, a curve from the line of centres out to where the pinion's tips leave the ring's flanks, with the contacts running along it (none while the ring floats in the backlash), on the stage and in the 3D view. A gerotor shows it as a cycloidal drive does: the lobes that turn the ring, and their lines of force, all through the pitch point. The info line counts the pairs. The ports are drawn dashed over the gears.

The children of a pump sit on its pinion's shaft. In 3D and in the exports it is four parts on one layer: the ring, the crescent, the pinion and the port plate under them. The port plate is the part of the pump's body the ports go through: a disc as wide as the ring, with the inlet and outlet ports cut out of it, ready to be the face the gears run against. Its width is set in the 3D view's properties (Port plate width, under the gears' Face width); Auto makes it half as thick as the gears. The pinion's shaft goes through it too, in a round bore (the shaft turns there): as wide as the pinion's hole for a round, flatted or keyed shaft, as wide as the hole reaches for a hex or a spline, none when the pinion has no hole. A gerotor has three parts: no crescent.

4.10Non-circular gear pair

Two gears that are not round, in one part: the driver on the part's own shaft and the follower beside it, at the distance its shape needs. They roll on each other like any pair, but the follower's speed changes as they turn: an elliptical pair runs the follower slow, then fast, twice a turn of an ellipse each way; a nautilus pair speeds up all the way round. Such gears give a press a slow working stroke and a quick return, make an oval flow meter count, or simply turn in a way round gears can't.

The app draws the driver's pitch curve (dashed, as a round gear's pitch circle) from the shape, works out the follower's so the two roll without slipping and close after a whole number of lobes, and cuts both with the same rack rolling along each curve: the teeth mesh at every turn, as an involute pair does (on a circle it gives exactly the spur gear). The size comes from the teeth: the driver's pitch curve is teeth × π × module long.

Shape:

• Elliptic: Lobes 1 is an ellipse turning on its focus (its twin as the follower: the classic elliptical pair), 2 an oval turning on its centre, 3 a rounded triangle, and so on. Eccentricity says how far from round (0 is a circle), up to what the teeth can follow (below). Changing the lobes keeps the steepness: the eccentricity follows.
• Eccentric: a round gear turning on a point off its centre (Pivot offset, a share of its radius); the follower is not round.
• Nautilus: two log spirals. Growth is the largest pitch radius over the smallest. Teeth: All round turns all the way round, a straight step joining the spiral's ends, where the teeth hand over and the follower's speed jumps. Teeth: Sector (Gear Generator Pro) is a toothed sector of the angle you give (Sector), which can only swing: choosing it (or changing it) turns drive 1 back and forth just across the sector (Back & forth, §14.5) and starts it from the sector's start. Turned on past the sector's ends, by hand or with Back & forth off, the driver leaves the follower behind, as real ones would. Swing to fit does it again after you change drive 1's speed.
• Custom: a shape you draw (below).

The note under the fields gives the centre distance and how much slower and faster than the driver the follower turns; the info box adds the pitch radii, the steepest push and the contact ratio, and the loads the follower's torque, which changes as they turn.

How far a shape can go. The teeth set the limits. Where the pitch curve bends tighter than the teeth are deep the roots fold, and in a tight hollow the tips do; where the curve leans far from square to the line of centres the teeth push sideways, and past 60° (pressure angle and lean together) the pair jams. So Eccentricity, Pivot offset and Growth go no further than the teeth, the lobes and the pressure angle allow: the note under the field says how far and why, and when you change the teeth, the lobes or the pressure angle the shape comes back within it. The stage marks the stretches that come close on the pitch curves (Gear guides on): amber where it is steep, red where it can't work (a drawn shape can go there). More teeth (with a smaller module, the same size) or a gentler shape cures both. Where a hollow meets a sharp bend the tips of one gear could reach the roots of the other, as a ring gear's can reach its pinion's: the app cuts those tips back, and says so if that is not enough.

What rides on the pair goes on the follower's shaft and turns with it. A gear there, and the train after it, speed up and slow down with the follower: the list and the info box give its speed as a range (and the speed now), and the loads are worked out where it runs slowest and its torque is largest. Another non-circular pair there makes two in series (a recipe in §12). To put something on the driver's shaft, add it to the part the pair sits on, on the same axle. Turning a gear past the pair by its marker works as anywhere else, and with Lost motion on its gaps are crossed as the follower turns.

Spur only: a helix would not mesh, as the ratio changes along the face. In 3D and in the exports it is two parts, the driver and the follower, with their pitch curves as guides in SVG and DXF.

Drawing a shape (Gear Generator Pro). Edit shape on the stage (under the pair's properties) turns the shape into points on the driver's pitch curve, freezes the animation and dims the pair:

• drag a point: both pitch curves follow as you drag, the follower at its new place, the stretches that go too far marked red and amber; hold still a moment and the teeth are drawn too. Letting go keeps about as many teeth as fit round the new curve (a multiple of the lobes). One drag is one undo;
• the points of one lobe are the solid ones; the hollow ones are their copies on the other lobes (and, with Mirror, on the lobe's other half): dragging a copy moves its point;
• double-click the curve for a new point (the shape stays as it is until you drag it); Delete takes the selected point away, or Alt-click it;
• Mirror makes the lobe symmetric about its middle (one point for both halves), or lets each half go its own way; Lobes (in the panel) repeats the lobe more or fewer times;
• Esc or Done closes the editor. It shares the stage with neither the info box nor the manual: it closes them when it opens, and opening either of them closes it.

A drawn shape opens in every Gear Generator and turns and exports there; only Pro draws it.

A nautilus pair has no editor: its spiral jumps at the step (or ends, as a sector) and the editor draws whole lobes. Its Draw: line says so; choose Elliptic or Eccentric and edit that.

5Profile shift and undercut

Profile shift moves the cutting rack in or out by x·m:

• Positive shift on a small pinion removes undercut, thickens the root and raises the tooth; it also pushes the pair apart (the working pressure angle rises).
• Negative shift brings a pair closer together than the standard centre distance.
• A pair keeps meshing at the centre distance the app computes from both shifts; it is never the naive m(N₁+N₂)/2 unless both shifts are zero.

No undercut uses x ≥ 1 − N·sin²α / 2. The warning Undercut: consider a profile shift appears only when the undercut actually eats into the involute (the involute start radius is more than 2 % above the base circle): a hair of undercut on a large gear is not flagged.

Watch the contact ratio while shifting: below 1 the pair loses contact between teeth, and the app marks it in red in the info box and warns in the list.

6Backlash and lost motion

6.1What backlash does here

Backlash is a circumferential value in millimetres, entered per gear (and once per planetary set, where it is shared by both meshes). Each flank of the gear is thinned by half of it, so a pair with 0.2 mm on each gear has 0.4 mm of circumferential play.

What the app does with it:

• The teeth are really thinner: it is in the outlines, the DXF, the STL, everything.
• The driven member takes the gap up, so the flanks that carry the load touch and the trailing flanks show the gap. This holds for external pairs, internal meshes and both meshes of a planetary set.
• Direction matters. Reverse the drive (Rev) or drag a gear the other way by its marker and the contact moves to the other flank, as it does in a real drive.
• So does where you push. Turning the train by a wheel in the middle of it makes that wheel the source: it drives the gears after it in the usual way, but it also back-drives everything between it and the first gear, so those meshes take their play up on the opposite flank, again as in a real drive when you turn an output shaft by hand.

6.2Lost motion: the dead band, simulated

Backlash on a drawing is a number per mesh. What you actually feel at a shaft is lost motion: the angle the input can turn, after a reversal, before the output moves at all. It is the sum of every mesh's play referred through the ratios, and it is what decides whether a positioning drive can repeat a move, whether a reversing load will hammer, and how much of a servo's resolution a gearbox throws away.

Lost motion (Display · Lost motion, on by default) simulates it properly rather than drawing it. Each mesh is a dead band: the driven wheel is pushed by one flank, and when the driver reverses it stands still until the other flank comes round to it. Reverse the drive (Rev) and watch a three-gear train: the first gear turns alone; the second waits out its gap, then starts; only then does the third begin to wait out its own. The delays add up down the train, one mesh at a time, exactly as the real one does.

Reading your design's lost motion off the screen. Freeze the animation, then take the output wheel by its first-tooth marker and turn it in the direction that unloads it. It will turn freely while the gaps close one after another, and the input gear will not move at all: the angle the output covers before the input twitches is the lost motion of your train, referred to the output shaft. Turn it back the other way and the whole train follows instantly, because those flanks are already touching. That asymmetry is real, and it is the same thing you feel with a shaft between your fingers.

Other things the simulation shows you:

• No contact means no contact. While a mesh sits inside its gap neither flank is touching, so its contact dots disappear and the info line counts it as 0 tooth pairs in contact. The line of action stays drawn: that is where the teeth will meet. Over a reversal you can watch contact leave one flank, vanish, and arrive on the other.
• Where you push matters. Turning the train by a wheel in the middle makes that wheel the source: the wheels after it follow through their own gaps, and the wheels between it and the drive are back-driven through theirs, one at a time, before the drive itself moves.
• It does not drift. However long the animation runs, and however many reversals, a mesh that has been driven one way sits exactly on its flank again: the state is pinned, not integrated.
• A pump turned by its ring drives its pinion through the play: the ring's flanks push, and the contacts and the line of action move over to them, as when the pinion drives the other way.

Switch it off to compare, or to read the exact meshing position of a train under load: the take-up then closes the whole gap the instant the direction changes, as a drawing would show it.

What is not in it: torsional windup of shafts and teeth, friction, inertia (a free wheel does not coast through its gap; it waits to be pushed), bearing and keyway clearance, and chain or belt slack. The number you read off is the geometric lost motion of the gearing alone, which is the part you can do something about while designing the teeth.

One simplification: a planetary set takes its two meshes (sun–planet and planet–ring) up together rather than one after the other, so a set behaves as a single dead band of the size of both. The total is right; only the order within the set is not.

6.3Choosing a value

Circumferential, total per mesh:

Backlash is not the same as the root clearance (0.25·m, always present) and not the same as the centre-distance tolerance; if you widen the centre distance instead, use a positive shift rather than thinning the teeth.

7Holes, joints and screw holes

Per wheel (Holes & shaft joints):

Shaft joints. The LEGO axle and the three splines are cut with a Clearance on every side of the profile: 0.1 mm unless you set it, about right for a printed part; 0 gives the nominal size. The note under a spline says what is drawn.

• LEGO axle: the cross of a LEGO Technic axle, its arms ending on the circle the axle turns in. Corner radius rounds the four inside corners, which a printer leaves round anyway and where the axle has small fillets of its own. LEGO® and Technic™ are trademarks of the LEGO Group, which does not sponsor, authorise or endorse Gear Generator; the hole is only sized to take their axles.
• Spline, straight (ISO 14): the hub of a straight-sided spline shaft, centred on its minor Ø. Size lists the light and medium series as n × d × D with the spline width B; Custom takes your own.
• Spline, involute (DIN 5480): the hub (N) of an involute spline, 30° pressure angle: its tips on dB − 2m, its roots on dB + 0.2m, its spaces as wide as the shaft's teeth (the shaft's profile shift, which the note shows). Size lists common sizes as reference Ø × module × teeth; Custom takes a reference Ø and module, and the teeth as the standard has them (Auto) or your own.
• Servo spline: the output shaft of a hobby servo (25T Futaba and MG996R, 24T Hitec, 23T JR, 21T SG90 and other micro servos, 20T), as fine pointed serrations. Servo splines are not standardised and makers differ, so the sizes are typical ones: print a test piece and adjust the clearance, or take Custom (teeth, outer Ø, tooth depth).

Screw holes are a bolt circle: number of holes, bolt circle radius, hole diameter, and a rotation for the first hole (shown once there is a hole). On a ring gear they sit in the rim.

The app will not produce a part that cannot exist:

• A hole that would break into the teeth, into the centre hole or into its neighbour is left out, and the reason appears as in the list and in the info box.
• The same for a centre hole larger than the wheel allows.
• The limit is the tooth roots less 0.8 · module, with at least 0.8 mm of material between holes. If a hole is dropped, either shrink it, move the bolt circle, or give the wheel more material (a bigger rim on a ring, more teeth on a gear).

The other bores are drawn at their nominal size: add your own fit allowance (H7/h6 as your process needs, or 0.1 – 0.3 mm for printed parts).

8Tooth form in 3D: helical, double helical, herringbone

Press 3D to enter the 3D settings view. It shows the whole setup as solids, the layers one above the other as STEP export stands them, and holds the settings that only exist in 3D. Visibility works as in 2D, except that what it leaves out is hidden rather than dimmed: All, the selection's layer (Same layer), or the selection alone (Object). As in 2D, changing it leaves the view where it is; Fit (double-click) fits what is on show. Clicking empty space deselects and keeps the layer or the object on show. Back from 2D, the 3D view is where you left it. The Gears list is there to select from; adding, removing and clearing wait for the 2D view, where a new gear's teeth, module and connection are set:

A chain wheel set has no face width to set: the chain fixes the toothed body, and the panel says how wide it is and why. Its 3D section holds the tooth chamfer and the two hubs instead (§4.5).

Module and pressure angle are normal values. A helix angle converts them into the transverse plane the profile is cut in:

m_t = m_n / cos β        tan α_t = tan α_n / cos β        x_t = x_n · cos β

So the 2D outline, every diameter and every centre distance grow by 1 / cos β. The panel shows a line saying so, and the info box lists the transverse module and transverse pressure angle next to the normal ones you entered. At β = 20°, a 15-tooth m2 gear has D = 31.93 mm, not 30 mm.

What to check in the info box:

• Overlap ratio εβ = b · sin β / (π · m_n). Aim for ≥ 1 if you want the smooth running helical gears are chosen for; below 1 the face is too narrow for the helix angle.
• Axial force Fa = Ft · tan β per mesh, the load your bearings have to take. Double helical and herringbone report balanced instead, because the two halves cancel.
• Hands: for a planetary set the sun carries the set's hand and the planets and ring take the other.

The twist is about the mid-plane, so the section at half the face width is exactly the 2D profile and conjugate partners mesh in every slice. Holes and ring rims stay straight.

9Accuracy

9.1What the curves are

• Involute flanks are fitted with cubic Béziers to a tolerance you set; they are not polylines and not arc approximations.
• Fillets are the true trochoid of the generating rack's tip corner, including undercut.
• Tip and root arcs are circular arcs, in pieces of at most 30° that never stand out of their circle (at most 0.00025 % of the radius inside it); so are round parts such as pins and eccentrics. A hole's arcs may stand as little outside its circle: that only makes it a hair bigger.
• Circles (guides, bores, bolt circles) are exact arcs.

Curve precision (Document section) is the largest distance a Bézier may sit from the exact curve. Default 2 µm; range 0.1 µm – 50 µm. It drives the stage, the SVG, the DXF, the meshes: everything.

The curves keep to the material's side of the exact shape: nowhere do they stand out of a tooth, and nowhere are they more than the curve precision inside it. Parts whose exact outlines touch (a pinion and its ring at the contact, flanks with the backlash taken up) can only come apart by that little in an export, never overlap, so a CAD interference check finds them touching or clear.

The info box reports, per gear:

• Béziers per tooth and the total for the outline;
• Max fit error in µm: the worst actual deviation of the fitted curve from the exact involute for this gear. This is the number to quote when someone asks how accurate the profile is.

At the default setting a typical gear comes out with a handful of segments per flank and a fit error well under a micrometre, smaller than any cutting process will hold.

9.2Accuracy of each export

Exports carry marks, labels and guides according to the Display checkboxes, on their own layers/groups, so you can switch them off for a cutting file and on for a drawing.

A STEP file (AP214, millimetres) opens in any CAD program as solids you can edit, measure and machine: every part is a named body of its own. STEP – All Gears places them as they stand on the stage, in the pose of the animation, so they mesh; the layers stand one above the other, a millimetre apart, and clear of a chain running on the layer below, as the 3D view shows them. STEP – Selected exports a gear on its own axes, centred on the origin, and a planetary set or a chain or belt drive as it stands. Racks, rings, holes, helical, herringbone and double helical teeth all come out as solids; chains and belts do not.

The All Gears exports (SVG, DXF and STEP) hold the gears of the stage only. Gear Generator Pro's 3D gear pairs are not among them: a pair is exported on its own, while it is selected (§14.1).

9.3What is verified, and how

The geometry is covered by an automated test suite (run with npm test), not judged by eye:

• No overlap: every kind of pair (spur, cycloidal and clock teeth, ring gears, racks, planetary sets, the cycloidal drive, the three pump tooth forms, non-circular pairs) is built and placed as the app does it, turned both ways through its mesh, and checked with the curves themselves: nothing reaches into its mate by more than 2 nanometres, the check's own resolution, at 2 µm and at 0.5 µm curve precision.
• Backlash take-up: with 0.4 mm of backlash the outlines pass within ~1 µm of the contact points the line of action predicts: the load side really touches, in both directions, and whichever wheel of the train the hand turns (including the meshes that then run backwards).
• Lost motion: the wait is exactly the width of the gap and not a hair more, it passes down a train mesh by mesh, no teeth dig in anywhere along the crossing, and the state neither widens nor drifts after hundreds of reversals: a long run one way puts every mesh back on its flank to the last digit.
• Ring gears: the outline never crosses itself over a wide sweep of pressure angles and shifts, and the pinion always clears the space bottoms.
• Solids: every tooth form (spur, helical, double helical, herringbone) on gears with keyways, on rings and on racks comes out as a closed 2-manifold with the expected volume; helical partners are checked slice by slice.
• Sprockets: every chain, a wide range of tooth counts and each kind of hub give a closed solid of the volume the body, the hub and the holes add up to; every vertex of a chamfered wheel is shown to lie on the cone the chamfer angle describes, with the roller seats at full width; a hole on the hub is bored through it and one outside it is not; and the chain links come out closed, alternating and one pitch apart along the path.
• Units and I/O: unit maths, .gg round trips, share links and Gear Generator 2 import.

9.4What the app does not compute

It is a geometry and kinematics tool. It does not do:

• strength, stress, Lewis/AGMA/ISO 6336 ratings, or material selection;
• efficiency, friction or losses: all torques are ideal (power in = power out);
• lubrication, temperature, noise, or dynamic effects;
• tolerance stack-ups, fits, or manufacturing allowances (kerf, shrinkage, over-extrusion);
• bevel, worm, hypoid or non-circular gears;
• chain wear, elongation or the sag of a long span; the chain is drawn at its nominal pitch, running on the pitch polygon, and the links are rigid.

Treat its numbers as exact geometry, and your own engineering judgement as the rest.

10Loads and forces

Set the input on drive 1: Torque (N·m) or Power (W); the line under it shows both. Load flows down the tree, split at branches by Load share (Auto divides equally).

The info box, per object, gives:

• Torque and Power at that object;
• Tooth forces with each neighbour: tangential Ft, radial Fr = Ft·tan α_w, axial Fa = Ft·tan β (helical), and the resultant normal force Fn, the load for a bearing calculation;
• Chain / belt tension and an approximate shaft load (twice the tension);
• Planetary: sun, carrier and ring torques and the force per planet mesh.

Working pressure angle α_w is used, not the nominal one, so shifted pairs give the right force directions.

Planetary sets with a second drive. The three member torques are in fixed ratios Ts : Tr : Tc = 1 : RN/SN : −(1 + RN/SN), so only one load can be set: drive 1's. A second drive's load box is read-only and shows what its member must supply, labelled Coupled to Drive 1. A member held at 0 rpm carries torque but no power: that is correct, not a bug.

11Warnings

Every warning appears as next to the object in the Gears list, with the text in the info box.

12Recipes

A two-stage reducer. Driver 15 T → mesh a 45 T (3:1). Select the 45 T, Add New, set the new gear's connection to Axle: it is now the second shaft. Mesh another gear on that, 15 T → 60 T (4:1). The list shows 12:1 overall. Use Visibility · Same layer to work on one shaft at a time.

A planetary gearbox. Add a planetary set. Sun 12, planet 9, ring 30 (30 = 12 + 2×9 ✓, (12+30)/3 = 14 ✓ for 3 planets). Roles: sun Input, ring Fixed, carrier Output → ratio 1 : 3.5. Check both contact ratios in the info box, then set Auto profile shift if the sun is small.

Rack and pinion travel. Mesh a rack on a gear. The info box gives travel in mm/min at the drive speed; travel per revolution = π · m · N. Export in Length mode to get a definite bar.

A printed helical pair. Design the pair in 2D first (the numbers are normal module values). Press 3D, choose Helical, set β = 15–20° and a face width of at least π·m / sin β to keep εβ ≥ 1. Add 0.2 – 0.3 mm of backlash for FDM. Export both gears as STL: they are closed solids, no repair needed.

Laser-cut plate gears. Keep the tooth form spur. Add backlash equal to your kerf plus a little (0.15 – 0.25 mm typical). Switch off labels and guides in Display, then DXF selected per part, or DXF all for a nested sheet.

A sprocket you can fit to a shaft. Add a chain wheel set and pick your chain: the toothed body is now as wide as that chain allows, which on a small pitch is only a few millimetres, not enough to grip a shaft. Press 3D, set the primary wheel's Hub to One side, and give it a width that suits the shaft (a bore's worth of grip is a fair rule) and a diameter within the limit the field shows. Back in 2D, put the bore and a couple of screw holes on a bolt circle that stays inside the hub (the note under the screw holes says how far that reaches), so the screws are drilled through the full hub. STL selected exports the sprocket as one closed solid, chamfered teeth, hub and all. The flat SVG or DXF of the same wheel is the plain profile, as it must be: a laser has no way to cut a hub.

Oval gears for a flow meter. Add a Non-circular Gear Pair, Elliptic, Lobes 2, Follower lobes 2: two ovals turning on their centres, the classic oval-gear meter. Give the driver an odd number of teeth a lobe (the field says how many) and both gears are the same part. An eccentricity of 0.2 to 0.3 keeps the steepness under 45°.

A slow stroke and a quick return. Elliptic with 1 lobe: the follower turns slowly while the driver's far end drives it and fast while its near end does. The note gives the speed range; raise the eccentricity for more, and watch the steepness in the info box.

A shaft that speeds up and slows down between two steady ones. Add a Non-circular Gear Pair (Elliptic, 1 lobe), select it and Add New another one with the same shape, lobes, eccentricity and teeth: it goes on the first one's follower. The second pair undoes the first: its follower turns steadily at the drive's speed, while the shaft between them runs slow and fast twice a turn (the list shows its range). A tool on that middle shaft works at a changing speed while the machine's input and output stay even. It holds for 3 lobes too; with 2 the output still varies.

Measuring the lost motion of a train. Enter the backlash you can really hold on every gear, leave Lost motion on, and press Freeze. Note where the last gear's tooth-0 dot sits, then drag that dot in the direction that unloads the train: it turns freely, mesh after mesh, while the first gear stands still. The moment the first gear twitches, stop: the angle the output has covered is the lost motion of the whole train at the output shaft (§6.2). Halve a mesh's backlash, or move the big ratio nearer the output, and repeat to see what it buys you.

13Files, sharing and compatibility

• .gg: the whole document as JSON. Save / Open…. Older files are upgraded silently, and .gg3 files from the first web versions open too.
• Share URL: the entire design compressed into the link; nothing is stored on a server.
• Gear Generator 2: Import URL… reads a GG2 share link; Open… reads a GG2 .gg file (the same extension: the two are told apart by what is inside). GG2 chains map to the nearest preset.
• Autosave: your work is kept in the browser between sessions.
• The view is kept with the document: 2D or 3D, where the stage was panned and zoomed to, and the 3D view's turn, tilt and zoom. The page reloaded, the desktop app started again or a .gg file opened, you see what you saw when you left it. A share link opens fitted to the stage, as before.
• Export passes: exports are gated by a time-limited pass: without one the Export section lists the formats a pass downloads, and Get an export pass opens the store; with one the export buttons are there and the panel shows the time left. A pass works in three browsers at a time: in another one, choose Already paid? in the store and enter the 6-digit code it e-mails to the address you bought the pass with (or open the e-mail's link there). The same sheet sells the Gear Generator 3 Desktop App (45 EUR): a lifetime license that works offline, on macOS (Apple silicon and Intel), Windows and Linux, on 3 computers per license, every export included, with free minor updates and the next major version at a reduced upgrade price. Its license key comes by e-mail, with the link to the download page. The desktop build has no store.

The desktop app (Mac, Windows, Linux) works from its menus instead of the panel's Document, Export and Display sections: File › New, Open…, Close, Save, Save As…, Import › Share Link… (a GG3 or GG2 link), Export › SVG / DXF / STEP / STL / OBJ, Copy Share Link; Edit › Undo, Redo; View › 2D / 3D, the zooms, the info box, the display settings, the unit system and the colour theme; Help › the manual, in a window of its own. Double-click a .gg file to open it. A Gear Generator 2 file is converted to the new format the first time you save it, after asking (Save As… keeps the original). Closing or quitting asks about unsaved changes, and the last document is there again the next time the app starts. The app bought on geargenerator.com asks once for the e-mail address and license key from the purchase e-mail; a key works on three computers for each license bought with it, and License… moves it to another one (deactivate it there first: a computer past the key's number is turned away). A team buys several licenses on one key, so everyone registers with the same e-mail address and key, and License… › Add computers… adds more to it later. Once registered, the app works offline. The Mac App Store edition needs no key.

When a new version is out, the app says so: at most once a day, as it starts, it asks geargenerator.com, sending only its name and version number. Download opens the download page in the browser, Later asks again tomorrow, and Skip This Version stays quiet until the next one. Check for Updates… (in the Gear Generator menu on the Mac, under Help elsewhere) asks at once. Without an internet connection nothing is asked, and nothing changes.

14Gear Generator Pro: 3D gears, web views and drawings

Gear Generator Pro is the desktop app with three things more:

• 3D gear pairs: worm gears, bevel gears and screw gears, whose axes cross, so a flat drawing can't show them.
• Web views: views of your setup for your own website, in 2D or 3D, still or turning. The website needs one script and one line of HTML for each web view.
• Back and forth: a drive that turns one way and then the other, eased at every turn (§14.5).

Pro is a separate app with its own license; a Gear Generator license does not open it, but a Pro license opens both.

14.13D gear pairs

The 3D Gears section of the panel, just below the Gears section, keeps gears whose axes cross. Each entry is a pair of two wheels that turn together and connect to nothing else:

• Worm gear: a worm and its wheel, the axes crossed at 90°. Every turn of the worm moves the wheel on by one tooth per start, so the ratio is large (30 teeth, 1 start: 30:1). With a small lead angle the wheel can't drive the worm back (self-locking).
• Bevel gear: two toothed cones, the axes meeting at the shaft angle (90° unless you change it; equal teeth make mitre gears). The teeth are Straight or Spiral, with a spiral angle and the pinion's hand. An Offset moves the pinion's axis past the gear's, which makes the pair a hypoid.
• Spider gear: a differential's spider and side gear, the axes meeting at the shaft angle (90° in most differentials, any angle from 30° to 150°; less where the bigger gear's pitch cone would pass 80° or its tip cone 85°, which few teeth reach sooner: the panel says how far). They are straight bevel gears with the backs of differential gears: both backs on one sphere round the apex, where the gears seat in the case. The spider turns on its cross pin, and the side gear has a hub, its journal in the case.
• Screw gear: two helical gears on axes crossed at 90°. Their helix angles add up to 90°, and both have the same hand.

The section works like the Gears section:

• Add New makes a pair of the kind chosen last. Remove takes the selected pair away, and Clear takes them all. A web view that shows a pair goes with it: the app names those web views and asks first. Undo brings back the pair and its web views together.
• Click a pair in the list to select it: - the view goes 3D and shows the pair in place of the gear's layer; - the gear's sections step aside for 3D gear type (Worm, Bevel, Spider, Screw) and the pair's properties.
• One thing is selected at a time. Selecting a gear lets the pair go, and so does going back to 2D (2D, Esc). Selecting a pair lets the gear go.
• The main drive turns the pair, as it turns the gears: its Speed in the Animation section, Start/Stop, Freeze and Reset. - It drives the first wheel: the worm, the pinion, the spider, gear 1. That wheel is shown as selected. - The other wheel follows at the ratio of the teeth. - The info line counts both wheels' turns, and the line under the properties gives both wheels' rpm.
• The wheels carry what the gears carry, switched by the same Display settings: - labels, guide circles, centre marks; - a first tooth marker on a flat face of each wheel (a bevel gear's toe, its pinion's back, a spider gear's toe, a worm's end). A toe too narrow for the label (a spider round a big pin) still takes a smaller marker.
• While the animation is stopped, drag a first tooth marker to turn the pair by hand; this turns the main drive. Let go while it is moving and the pair keeps turning, slowing to a stop.
• A self-locking worm can't be turned by its wheel. That is a worm whose lead angle is within the friction angle, about 5.7° (a single-start worm ten modules across); the line under its properties says so. Turned by hand, its wheel only crosses the backlash and stops at the thread, and without backlash it doesn't move. Every other pair turns from either wheel.
• Backlash plays as it does between gears (§6.2): - With Display · Lost motion on, the gap is a dead zone. Reverse the drive, or the hand on a marker, and the other wheel stands still until the gap is crossed. - A hand on the second wheel's marker makes that wheel the source: it pushes the driver through the gap. - With Lost motion off, the gap is taken up at once, on the side the motion loads.
• A web view can show a pair (§14.2): select the pair, then Add New in Web Views. Selecting a pair while a web view is selected puts the pair in that web view, as selecting a gear would.
• Line of action (Display): where the teeth touch, over everything, in the accent colour. - Screw gears, and a worm with a cylindrical wheel: a straight line through the pitch point, along the flanks' normal. - A worm with a throated wheel: the line of action in the wheel's mid-plane. - Bevel and spider gears: arcs of the plane of action on the spheres of the heel and the toe.

Each runs between where the teeth come into contact and where they leave it, for the flanks the drive loads now; it changes sides when the drive turns back.

• The info box (I) shows the selected pair: - both wheels' sizes; - how they mesh: the sliding speed at the pitch point, the efficiency (friction μ 0.1), the backlash; - what they carry with Drive 1's load: both torques, the power in and out, and each wheel's tangential, axial and radial tooth force. A spiral bevel pinion's thrust is shown towards or away from the apex, and it flips when the drive turns the other way.
• Exporting a pair (File › Export): while a pair is selected, the exports are the pair's, and say so. - STEP – 3D Gear Pair… exports it as it meshes: both wheels in place, at the angle the animation has turned them to, as solids fitted through the wheels' slices within the curve precision. - STL – 3D Gear Pair… and OBJ – 3D Gear Pair… export each wheel laid out to print: standing on its axis, a bevel gear on its back, a spider gear on its toe (on its back if only that end is cut flat). - PDF Drawing – 3D Gear Pair… is the installation drawing of the pair (§14.7): the pair from above, isometric, in four views, then each wheel on its own sheet (a bevel or spider gear standing on its back, its teeth up, as the pair's gear stands). Bevel and spider gears show the angle between their axes, and each wheel's distance from the apex to its back (the mounting distance) and its width; a worm or screw pair shows the distance between the axes (in the top view, out beside the wheels); every wheel its width along its axis and its outer diameter, a worm with shaft ends its threaded length inside its whole length too (its own sheet also gives the shafts' diameter). A table gives where each axis passes and which way, the shaft, the outer diameter and where the wheel's faces are along it. The tooth data (first sheet, four views, each wheel's sheet) starts with the module and pressure angle. A worm pair's is complete: the axial module and pressure angle (the wheel's transverse ones), the normal ones, the lead angle and hand; each wheel's sheet adds its own diameters (reference, tip, root, base), the worm's profile (ZI, involute helicoid), axial pitch, lead, threaded length and shafts, the wheel's helix angle, face width (a throated wheel's throat, outer diameter and throat radius), its mate and the centre distance. The drilling templates are the views that show an axis end on: the top view for the wheel, the side view for a worm. - The All Gears exports are greyed out then, and so are SVG and DXF: a pair is not one of the stage's gears, and not a flat drawing. Select a gear, or go back to 2D, to export the gears of the stage.
• Pairs are saved with the document in its .gg file, and undo works on them as on every change.

The properties:

• Module and Pressure angle: - worm gear: the worm's axial module, which is the wheel's transverse module; - bevel and spider gears: at the large end of the teeth (the heel); - screw gear: the normal module, the same on both gears.
• Teeth of each wheel. A worm also has Worm starts: the number of threads, 1 to 6.
• Worm gear: - the worm's diameter (pitch diameter), hand and threaded length; - the shaft past both ends of the thread (length 0: none); - the wheel's face width, and the Wheel: Cylindrical or Throated.
• Bevel gear: - the shaft angle; - the face width, measured along the cone, at most 45% of the cone distance; - the teeth (Straight, or Spiral with its angle and hand); - the Offset.
• Spider gear: - the shaft angle: between the spider's axis and the side gear's; - the face width, as a bevel gear's; - each gear's toe: Spherical, or Flat: cut square to the axis through the pitch circle at the toe, so the teeth's ends and the face lie in one plane (as on many cast or printed spider gears) and the face width along the pitch cone stays as set; - each gear's back cut: how far in from the top of its back (on the side gear: where the sphere meets the hub) the back is cut off flat, square to the axis; 0 keeps the sphere. A shallow cut flattens the sphere; a deeper one cuts the teeth's heel ends off where they cross the plane. A cut only ever takes material away, and goes no deeper than leaves a tenth of the face at the teeth's roots (the panel says so). The hub stands its length out of the cut back. Flat ends print well. The spider is lifted to stay clear of the ground as it turns; - the spider's Pin Ø (the cross pin it turns on), the side gear bore, and the side gear's hub: its diameter, and how far it stands out of the round back (either 0: none). A hub has to be wider than the bore and fit inside the heel's root circle; a pin, a bore or a hub the gear can't take is left out, and the panel says how big it may be.
• Screw gear: - gear 1's helix angle, 25° to 50° (gear 2 has the rest of the 90°); - the hand of both; - each gear's face width.
• Bores of both wheels. 0 means none, and a bore too big for its wheel is left out.
• Backlash: for a worm gear it comes off the wheel's teeth (measured at its pitch circle); for the others, half comes off each gear (a bevel pair's at the heel). The pair then plays it as described above.

The line under the properties gives the ratio, the centre distance (or, for bevel and spider gears, the pitch cones and the cone distance, which is the radius of a spider pair's round backs), and the other sizes worth knowing.

How exact the pairs are:

• Bevel gears are cut as the gears are (§5), with a crown gear (a flat bevel gear) in the rack's place: - their flanks are spherical involutes, so the two gears mesh on every sphere around the apex; - the crown gear's tip corner rounds every tooth's root and undercuts the foot of a pinion with few teeth, as the rack undercuts a small gear. A bevel gear is undercut at the same tooth count as its equivalent spur gear (N / cos δ teeth). - A spiral is logarithmic: the same spiral angle along the whole face. - Spider gears are straight bevel gears made the same way. Their backs are exact spheres: the heel ends of the teeth lie on the same sphere, so the whole back is one round face. A flat toe or a back cut ends every flank exactly where it meets the plane (the flanks are lines through the apex).
• Screw gears are involute helical gears, cut by the rack as every gear.
• The worm is an involute helicoid. Its wheel is one of two kinds: - Cylindrical: an involute helical gear. The two are crossed helical gears and touch at a point, as most printed worm wheels do. - Throated: cut by the worm itself, as a hob cuts it, slice by slice across the face. Its teeth wrap round the worm in a throat and touch it along a line. The throat sits a quarter module clear of the worm's root, and the outer diameter is one module over the tip diameter. The face can be no wider than 1.8 × (worm radius − module); a wider one is made that wide, and the panel says so.
• The tests check that the two wheels of every kind never overlap as they turn, down to 6-tooth pinions at 14.5°, and that every wheel is a closed solid whose faces never cross, at the extremes below too.
• With an offset, the pinion is fitted to the gear in the middle of the face, and both gears' teeth are made a little thinner so that they clear. The pair looks like a hypoid but is not generated as one: print it to look at, not to carry a load.
• At the extremes a bevel pair is made as near to what you asked as a solid can be, and every export is made from that: - With the shaft angle so wide that a pitch cone opens past 90°, that gear is an internal bevel gear: its teeth point inwards, as a ring gear's do. No crown gear can cut one, so its tooth foot is shaped as a ring's (§4.2): the involute, a fillet, then the root. - To reach the offset the pinion turns 25° at most; the teeth would be too thin past that. A larger offset is taken as far as that goes: the panel says so, and the info box gives the offset reached. - A pinion with few teeth at a small pressure angle, with much backlash or a large offset, can be thinned through at the narrow neck its undercut leaves. It is then thinned only as far as leaves the neck a tenth of a module wide, so it has a little less backlash than asked. A neck narrower than the tooth's top makes the tip pointier instead. - The teeth are never made coarser than a hundredth of the module, so a small module keeps its detail. - STEP fits its surfaces through the same slices, within the curve precision: the same solids, with smooth faces instead of facets. Checked in OpenCascade at these extremes too: each wheel one valid, closed solid, its volume within a fraction of a percent of the slices'.

14.2Web views in the panel

The Web Views section, at the end of the panel, works like the Gears section:

• Add New makes a web view of what the stage shows now.
• Remove takes the selected one away, and Clear takes them all.
• The list below shows every web view kept with the document; click one to select it, and click it again (or press Esc) to let it go.
• Websites: opens your websites, with their themes and site keys (§14.4).

Web views are saved with the document in its .gg file, and undo works on them as on every change to the document.

14.3Framing a web view

While a web view is selected, the stage shows its crop box: a box of the web view's size in the middle of the stage, dimmed around it. Over it, in white, are the web view's name and size (view-1 640×480 px) from its left edge, and a lock at its right edge (straight after the text, when the text is wider than the box). Under it a line says that changes to the view are made to the web view, with Close at its right edge: Close (or Esc) lets the web view go, and the stage is the editor's again. What the box frames is the web view:

• Arrange the setup under the box as always: pan and zoom in 2D, orbit in 3D. Fit (F, double-click) fits the setup into the box. The web view keeps the framing as soon as the view settles.
• The lock fixes the framing: while it is closed nothing zooms, pans or turns the view, not even Fit. Clicking a gear still selects it.
• Resizing the window (or anything that changes the stage's size) moves and scales the box, and the view follows it: the box keeps showing what it framed.
• The look of the stage is kept too: the display settings (grid, guides, labels, centre marks, curve types, line of action), the selected object with its centre distances, and the Visibility filter. A web view shows a selection as the editor does. A 3D web view shows what the 3D view shows: the layers stacked, and only what Visibility leaves on show. With a 3D gear pair selected, the web view shows the pair (§14.1), turned by the main drive as in the app.
• The box is shown at its real size when it fits between the stage tools and the info line: one pixel of it is one pixel on the website. A bigger box is shown scaled down, and says by how much; the web view is still made at its own size.
• Drag the box's handles to resize it. It stays centred and grows on both sides at once; Shift keeps its shape at a corner.

The gear's own property sections step aside, and Web View properties take their place:

• Name: how the web view is known in the document (and to npx ggview inject, §14.4).
• Width, Height: in pixels, from 64 to 2560; or a Size preset.
• Motion: Still (the train in the pose it is in when the web view is copied) or Animated: the animation's own Start and Stop. Choosing Still stops the animation, Animated starts it; Start / Stop with the web view selected switches it the other way round. Selecting a web view starts or stops the animation as it moves. An animated web view turns as the drives turn on the stage: at their speed, back and forth if they are (§14.5). Each web view keeps its own: a drive's Speed and Back & forth changed while a web view is selected are that web view's, and selecting another one sets the drives as that one keeps them. What the stage shows is what the website will.
• Snippet: the form of the HTML: HTML, data-* (valid HTML, which some site builders need), or WordPress (a [ggview …] shortcode).
• Website: whose theme and site key the preview and the script use.
• Web page: Copy puts the web view's snippet on the clipboard, to paste where it goes; Preview shows it as the website will.
• Website files: ggview.js… saves the website's script, with its theme and site key in it (one for all its web views); Preview page… saves every web view of the document on one page, to open from the disk.

14.4On the website

<script src="/ggview.js" defer></script>
<div class="ggview" width="640" height="200" content="1.…"></div>

The page loads the script once and has one <div> per web view. The script:

• draws each web view at its width, or smaller where the page is narrower;
• turns only the web views on screen, and stops altogether when none are;
• leaves the mouse wheel and touch to the page;
• shows a still picture to visitors who ask their system for less motion.

Websites. Websites: in the Web Views section (or Web Views › Websites… in the menu) lists your websites. For each one you give:

• its name;
• its domains (each covers its subdomains too, so example.com covers www.example.com);
• the theme of all its web views: Auto (light, or dark when the visitor's system is), Light, Blueprint or Dark;
• whether the background is transparent.

Get key asks geargenerator.com for the website's site key. This needs the registered Pro license and an internet connection. The key goes into its ggview.js.

How many domains. A Gear Generator Pro license has site keys for 3 domains; a domain pack (1, 10 or 100 domains, one-time) adds more, for good. Each domain covers its subdomains. The Websites sheet's Domains box says how many your license has used and has left, and which they are. Buy more domains… there opens the packs' page in the browser with your license's e-mail address filled in: the domains go to the license registered to it.

• A domain counts from its first key on, for good. A key on a website keeps working without asking geargenerator.com, so taking a domain off your list doesn't give its place back.
• Keys for a domain already counted are free, any time: a new ggview.js, other domains with it, or coming back to it later.

The badge. Without a valid key for the page's domain, a web view still shows, with a small Made with Gear Generator badge in its corner, in Gear Generator's own lettering (smaller in a narrow web view). The browser's console says why. On your own computer (localhost, *.test, a page opened from the disk) any valid key will do, so a site can be tried before it goes up. To see it, use Preview with no website chosen.

What counts is the site in the visitor's address bar. A web view in a site builder's HTML block counts as your site. Your page framed by another site counts as that site, and shows the badge there.

3D gear pairs on the website need a ggview.js saved by this version of the app or later. An older one leaves the web view empty and says in the browser's console that it needs updating: save the website's ggview.js… again. A browser without WebGL 2 can't show a pair (the console says so); every other web view still shows there. A web view of a part with a LEGO axle or spline hole (§7) needs a ggview.js saved by this version or later as well.

The theme. A website's CSS can fine-tune its theme with the same colours the app uses, for example .ggview { --stroke: #333; --gear-fill: #eee; --screen: transparent; }.

Other ways in:

• The npm package @geargenerator/ggview gives frameworks and bundlers the script as a module.
• npx ggview init (from that package) writes a website's ggview.js.
• npx ggview inject fills <div class="ggview" data-src="gears/drive.gg#banner"> from the web views saved in a .gg file, after a static site is built.
• The WordPress plugin takes the site key and the theme in Settings › Gear Generator, and the [ggview …] shortcode in posts and pages.

14.5Back and forth

Every drive has a Back & forth line between its Speed and its Load:

• the switch (On / Off);
• how long it turns each way, in seconds;
• the easing: how much of each run is spent speeding up and slowing down. At 0 % it turns round at once; at 100 % it swings smoothly, at full speed only in the middle of each run.

The drive's speed is the most it reaches. Everything the drive turns follows: the gears, the 3D gear pairs, the web views on a website. With Lost motion on, the backlash is crossed at every turn, as by hand. It is kept with the document, and every web view keeps its own (§14.3).

14.6AI Assistant

An AI app can design in the open document: Claude Desktop, Claude Code, Cursor, or any other app that takes an MCP server. Ask it for "a 1:60 reduction in module 1, under 120 mm", "a planetary set for 5:1", or "a worm pair 30:1, exported as STEP to my desktop". You watch it work, and each of its changes is one step of Undo.

It finds tooth counts for a ratio with the app's own solver, adds and changes parts, and checks the design for the same warnings you see, and for parts that run into each other. It also looks at a picture of the design and fixes what it finds. It can save the design and export it where you ask, but never over a file unless it says so.

Setting it up

1. In Gear Generator Pro, choose Help › AI Assistant…, then Turn On. The line under the introduction says whether the assistant is On or Off, and what it is doing: waiting for an AI app, or which one is connected.
2. Click Set up an AI app… and connect your AI app: - Claude Desktop: click Install in Claude Desktop…, and confirm in Claude Desktop's install dialog. That's all. If you move Gear Generator Pro to another folder, install it again. If you'd rather set it up by hand, copy the entry for claude_desktop_config.json (Settings › Developer › Edit Config) and restart Claude. Don't use both. - Claude Code: the claude mcp add … command. - Other apps: a local MCP server, which is Gear Generator Pro itself, started with --mcp.

The first time the AI uses a tool, Gear Generator Pro starts if it isn't running. Opening the AI app alone doesn't start it. A round AI badge in the info line shows that an AI app is connected; it pulses while the app is changing the design.

What it can and can't do

• It works on the open design only, and you can undo every change it makes.
• It writes only Gear Generator documents and exports (.gg, SVG, DXF, STEP, STL, OBJ, the PDF drawing), where it names them.
• It opens only the Gear Generator documents it is asked to open. If the open design has unsaved changes, you are asked first.
• Turn it off in the same sheet. The AI app then gets a message saying the assistant is off.

14.7Installation drawing (PDF)

The installation drawing is for making the housing the gears go in. Select a part and choose File › Export › PDF Drawing – Selected Layer…: the drawing shows every part on that part's layer (a gear on another's axle is a layer up, and has a drawing of its own). Choose the paper (A4, A3, Letter or Tabloid, the last one is remembered) and whether to add the drilling templates, then Save PDF….

• The sheets: first the layer seen from above, alone, with its holes; then the layer in an isometric view, with a table of which sheet each part is on; then every part on a sheet of its own (identical planets share one), seen along its own axis (the top view), from the front and isometrically, with its shaft, diameter, width and the sizes the info box gives; last the drilling templates. The parts' views are in first-angle projection for a metric design and third-angle for an imperial one (the symbol is in the title block). Each sheet has the largest standard scale that fits (2:1, 1:1, 1:2, 1:5…); the isometric view may have its own, written under it.
• Nothing is written over a part: a value whose place would be on one is led out by a thin line, a dot where it starts, to the free space round the parts.
• The holes: every centre a wheel turns on is a hole, lettered A, B, C… The top view gives the distance between every two holes whose wheels mesh (or a chain's or belt's two wheels), along the line between them, and at every hole where such lines meet, the angle between each two neighbouring lines; the first line from hole A also gets its angle to the horizontal, so that the layout's turn is fixed. Holes that nothing on the layer ties together get the same from the nearest hole of the rest. A planetary set's planets stand on a circle round the sun: it is drawn with its radius, and the angles between all the planets are given (they turn with the carrier, so no distances and no angle to the horizontal). Each part's outer diameter has a leader (one for parts of a size: "3× Ø23.39"), and the overall width and height are dimensioned outside the view (as the parts sweep them: the tip circles); each part's sheet gives its face width and its bore. The table beside the view gives each hole's X and Y from hole A, the shaft (the part's bore: size the housing's hole for the shaft, a bushing or a bearing), the outer diameter to keep clear, the face width and the parts on it, then the centre distances (with each line's angle to the horizontal) and the angles between them. A ring gear's screws are listed with it; planets are marked as turning with the carrier: they are not holes in the housing.
• A cycloidal drive also shows the circle its pins stand on and the output pins' circle, each with its radius and the pins' count and diameter, the eccentric's offset from the shaft (e) and the eccentric's diameter. Its parts' sheets: the housing with its pins (dashed when they stand out of the housing), their circle's radius, their diameter, the angle between two of them and the radius of the pockets' bottom; the disc with its centre hole and the output pins' holes (their circle's radius, their diameter, the angle between two); the eccentric with the distance between its two centre lines, the shaft's and its round's (e); the output pins with their circle's radius, their diameter and the angle between two.
• A gear pump has two holes: the pinion's shaft and the ring's centre (the body's bore), with the distance between them and the pinion's and the ring's pitch diameters. Its parts' sheets: the ring, with the depth of its spaces from the pitch circle to their bottoms; the crescent and the port plate (its diameter, the ring's, and the bore for the pinion's shaft, round the pinion's centre), each with the two circles it or its ports lie between (dashed: the ring's round the ring's centre, the pinion's round the pinion's, the centre distance apart), their radii and the angles round the ring's centre (the crescent's span, each port's start and end from the line through the two centres); and the pinion. A gerotor's ring sheet shows its lobes as a cycloidal drive's housing shows its pins: dashed, their circle's radius, their diameter and the angle between two, and the radius its valleys reach.
• A rack shows its pitch line (a chain line, named: where its gears' pitch circles roll) and, for every gear on it, the distance from the gear's hole to the pitch line and to the rack's back, which the rack runs on: the back places the rack's guide in the housing. Both are drawn beside the gear, out along the rack (only the pitch line's when the next gear leaves room for one, along the gear's own centre line when it leaves none) and listed under RACKS. The rack's own sheet shows it turned round, its teeth towards the front view, with its pitch line; beside the top view are its back's distance to the teeth's root and to the pitch line, and its overall height. A rack too long to be drawn readably whole is drawn interrupted: its first and last three teeth with break lines between them, its length dimension still the whole rack's; the isometric view shows all of it.
• A part's sheet: its top view gives the outer diameter, the bore and the pitch circle's diameter; a part with screw holes also shows the circle they stand on, its diameter with how many holes of what size ("Ø31.78 (6× Ø4)"), and the angle between two neighbouring holes. The front view gives the face width. The column lists what the info box (I) gives about the part's size (diameters, pitch, centre distances, the chain or belt, the helix…).
• The drilling templates: the views that show holes end on are printed again at 1:1, each hole with its coordinates and size. Print them at 100 % (actual size, not "fit to page") and check the 100 mm bar. A layout bigger than the paper is split over pages that overlap: lay them over each other, the crosses on the crosses.
• The parts are drawn as cut, real teeth and all, the hidden lines left out, in thin lines. Pitch circles and centre lines are chain lines, a bore inside a part a dashed line; a chain or belt shows its pitch line in the top view. The views' names, the letters and the dimensions are written in Gear Generator's own stroke font.
• With a 3D gear pair selected, PDF Drawing – 3D Gear Pair… draws the pair (§14.1).
• The AI Assistant makes the same drawing (export as pdf, §14.6).

15Reference card