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doneI've built the gear pair: a 20-tooth pinion driving a 47-tooth wheel on two parallel shafts, with a base plate and two bearing blocks per shaft. It builds with 19 parts, and its overall size is 257 × 146.5 × 179 mm, which matches the size I worked out by hand. I rendered it and checked it at both ends of every input range.
**Geometry**
- **Gears:** each is a flat tooth outline pushed out to the 25 mm face width. The tooth flanks are true involutes running from the root circle to the tip circle.
- On the pinion, the root circle (52.5 mm) is smaller than the base circle (56.4 mm), so each flank runs straight out from the root to the base circle before the involute starts.
- On the wheel, the root circle is larger than the base circle, so the involute starts right at the root.
- **Mesh and motion:** the shafts run horizontally, 100.5 mm apart, with the wheel shaft at the same height as the pinion's. At a pinion angle of 0, a pinion tooth sits centred in a wheel tooth space on the line between the shafts. The wheel turns by minus the pinion angle × 20/47, so the teeth stay in mesh at every angle.
- **Other parts:** each gear has a hub boss on one side and a shaft that runs through two blocks with bronze bearing rings. The base plate has four corner bolt heads. The shaft and hub sizes scale with the root diameters.
**Results at the default inputs**
| Result | Value |
|---|---|
| Gear ratio | 2.35 |
| Pitch diameters (pinion / wheel) | 60 / 141 mm |
| Base diameters | 56.38 / 132.50 mm |
| Tip diameters | 66 / 147 mm |
| Root diameters | 52.5 / 133.5 mm |
| Centre distance | 100.5 mm |
| Circular pitch | 9.425 mm |
| Base pitch | 8.856 mm |
| Transverse contact ratio | 1.65 |
| Pitch-line velocity | 9.42 m/s |
| Tangential force | 4000 N |
| Radial force | 1456 N |
| Normal force | 4257 N |
| Output torque | 282 N·m |
| Output speed | 1276.6 rpm |
| Power | 37.7 kW |
| No-undercut tooth count | 17.10 exactly, so 18 teeth |
Each result is its own value in the model, labelled with its unit.
**Inputs you can change in the Inputs panel**
| Input | Range |
|---|---|
| Module | 1.5 to 6 mm |
| Pinion teeth | 12 to 40 |
| Wheel teeth | 25 to 120 |
| Pressure angle | 14.5°, 20° or 25° |
| Face width | 10 to 60 mm |
| Input torque | 10 to 500 N·m |
| Input speed | 100 to 6000 rpm |
| Pinion angle (moves the gears) | −360° to 360° |
**Limits**
- **Tooth shape:** the teeth are standard full-depth teeth, the root is drawn as straight lines between points rather than a rounded fillet, and there is no backlash.
- **No undercut:** pinions below the no-undercut count (18 teeth at 20°) are still drawn with full involutes; the model reports the count but doesn't reshape the teeth.
- **No real bores:** Gendl can't cut one solid out of another, so the shafts just pass through the hubs and bearing blocks.
- **No losses:** output torque assumes no friction losses.
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textBearing-block boxes aren't leaves (they have a child), so I'll make the block body its own child.
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promptA pair of involute spur gears in mesh on two parallel shafts, a single reduction stage. Parts: pinion and wheel, each an extruded outline with true involute tooth flanks between root and tip circles, a hub boss and a shaft stub on each, and a base plate carrying two bearing blocks per shaft. Inputs: module 3 mm, pinion teeth 20, wheel teeth 47, pressure angle 20 degrees, face width 25 mm, input torque 120 N m, input speed 3000 rpm, and the STATE input pinion-angle-deg. The wheel turns by minus the pinion angle times z1/z2, phased so that a pinion tooth sits in a wheel tooth space on the line of centres and the teeth stay in mesh at every angle. Compute: gear ratio, pitch diameters, centre distance, base, tip and root diameters, circular pitch, base pitch, transverse contact ratio from the tip and base radii, pitch-line velocity in m/s, tangential, radial and normal tooth forces in N, output torque and speed, transmitted power in kW, and the smallest tooth count free of undercut at this pressure angle, 2 / sin^2(alpha).
(This prompt was written by Claude, Anthropic's AI model, as one entry in a catalog of simulative models of automotive systems.) House brief: key dimensions and operating values are root inputs with input-controls (ranges the model holds at); STATE inputs must really move the parts; each result named above is a computed-slot of MODEL with a doc string giving its unit; simplified but recognisable geometry, about 15 to 80 leaves; colours only from Gendl's own table, hyphenated: :steel-blue, :slate-gray, :dim-gray, :silver, :brass, :copper, :bronze, :firebrick, :goldenrod, :orange, :red, :black, :dark-olive-green.
noteSession 6e07a85b6637 opened for an external agent.