# A mechanical engineering design notebook — every calculation worked, every choice recorded
Recipe No. 27, Labs and workshops. From The know.sh Cookbook: https://know.sh/cookbook/mech-eng-notebook
Your capstone notebook, done properly: a document for each design problem, every calculation worked step by step with its units, the options side by side with the pick marked, and a working brake caliper to squeeze, so the hydraulic lever you worked by hand moves on the page.
- For: a mechanical engineering student on a capstone design
- You get: a document per design problem, calculations worked, choices recorded
- Time: an evening to set up, then weekly
- Made with: Shelf, Document, Section, Elements, Your AI assistant, Revisions
## How it works
1. **A document per design problem.** Give your assistant the project brief and your lecture notes. Ask for a document per design problem, with sections for the requirement, the assumptions, each calculation, the options and the decision.
2. **Work it by hand, then set it out.** Work each calculation yourself first. Then ask for it as a steps element, one stage per step with the formula, the numbers and the units, and check it line by line against yours.
3. **Put the mechanism beside the numbers.** Ask for a widget element that models the part, such as a caliper with a pedal to press. View source shows its code; its figures should agree with your hand working.
4. **Record every choice, and why.** Ask for the options as a table element with the pick marked, and a decisions element that keeps every choice, including the ones you later replaced.
## Try this prompt
Your assistant, connected to know.sh (Claude, ChatGPT or a local model):
> Using know.sh, add a section to Front brakes called The hydraulic lever, by hand, holding a steps element: one step per stage from pedal to deceleration, for 100 N at the pedal, a 4:1 pedal, a 3:1 booster, a 22 mm master cylinder, a 54 mm piston, μ = 0.4, a 130 mm effective radius, a 0.31 m tyre and a 1,400 kg car. Show every formula with its units.
Your assistant, connected to know.sh (Claude, ChatGPT or a local model):
> Using know.sh, read Front brakes and add to Choosing the caliper a table element of the three calipers with the pick marked, and a decisions element: one decision per choice so far, the reason in figures, the options rejected, and the 48 mm caliper marked as superseded.
## Elements in the specimens
Written as your assistant writes them through the know.sh MCP server. Each reads as plain words until you turn elements on (Account → Elements).
Widget, specimen 1:
```element widget
{
"title": "A disc brake caliper, in section",
"caption": "Drag the pedal and watch the pads close on the disc; switch between a floating and a fixed caliper, wear the pads down, and step through what happens from pedal to release. Clearances are drawn ten times larger than life; the figures assume a 4:1 pedal, a 22 mm master cylinder, a 0.4 pad coefficient and a 1,400 kg car.",
"height": 720,
"html": "
\n \n\n
\n \n \n
\n \n \n \n
\n
\n\n
\n
Line pressure
0 bar
\n
Clamp force
0 kN
\n
Friction at the pads
0 kN
\n
Brake torque, one wheel
0 N·m
\n
Car
100 km/h
\n
\n \n\n
\n \n Walk through\n \n
\n \n
",
"css": ".brake svg { display: block; width: 100%; height: auto; }\n.brake text { font: 400 11px var(--sans); fill: var(--ink-2); }\n.lab { font-size: 11px; }\n.hatch { stroke: var(--ink-3); stroke-width: 1; }\n.dot { fill: var(--ink-2); }\n.grit { fill: var(--wash); }\n.headfill { fill: var(--ink); }\n.fixed { fill: var(--wash); stroke: var(--ink); stroke-width: 1; }\n.pin { stroke: var(--ink); stroke-width: 3; }\n.body { stroke: var(--ink); stroke-width: 1.5; }\n.fluidbox { stroke: none; }\n.hose { fill: none; stroke: var(--ink); stroke-width: 6; }\n.piston { fill: var(--paper); stroke: var(--ink); stroke-width: 1.5; }\n.seal { fill: var(--ink); }\n.backing { fill: var(--ink); }\n.padface { stroke: var(--ink); stroke-width: 1; }\n.disc { fill: var(--paper); stroke: var(--ink); stroke-width: 1.5; }\n.discface { fill: var(--paper); stroke: var(--ink); stroke-width: 1.5; }\n.hub { fill: var(--wash); stroke: var(--ink); stroke-width: 1; }\n.vent { stroke: var(--ink-3); stroke-width: 1.5; }\n.padarc { stroke: var(--ink); stroke-width: 1; }\n.arrows line, .arrow { stroke: var(--ink); stroke-width: 2; }\n[data-part] { transition: opacity 120ms; }\n.brake.focus [data-part] { opacity: .22; }\n.brake.focus [data-part].on { opacity: 1; }\n.controls { display: grid; grid-template-columns: 1fr 1fr; gap: 10px 24px; margin-top: 10px; font: 400 14px/1.3 var(--sans); }\n.controls label { display: grid; gap: 4px; }\n.controls b { font-weight: 600; font-variant-numeric: tabular-nums; }\n.controls input { width: 100%; accent-color: var(--ink); }\n.switches { grid-column: 1 / -1; display: flex; flex-wrap: wrap; gap: 8px; }\nbutton { font: 500 14px/1 var(--sans); color: var(--ink); background: var(--paper); border: 1px solid var(--ink); border-radius: 0; padding: 10px 12px; min-height: 40px; cursor: pointer; }\nbutton[aria-pressed='true'] { background: var(--ink); color: var(--paper); }\nbutton:focus-visible, input:focus-visible { outline: 2px solid var(--ink); outline-offset: 2px; }\n.figures { display: grid; grid-template-columns: repeat(auto-fit, minmax(128px, 1fr)); gap: 0 18px; margin: 14px 0 0; border-top: 1px solid var(--ink); }\n.figures div { padding: 7px 0; border-bottom: 1px solid var(--rule); }\n.figures dt { font: 400 12.5px/1.3 var(--sans); color: var(--ink-3); }\n.figures dd { margin: 2px 0 0; font: 400 20px/1.2 var(--serif); font-variant-numeric: tabular-nums; }\n.say { min-height: 1.4em; margin: 8px 0 0; font: italic 400 16px/1.45 var(--serif); }\n.walk { display: flex; align-items: center; gap: 12px; margin-top: 14px; padding-top: 10px; border-top: 1px solid var(--rule); font: 400 13px var(--sans); color: var(--ink-3); }\n.walk span { flex: 1; text-align: center; }\n.step { min-height: 3em; margin: 8px 0 0; font: 400 16px/1.5 var(--serif); }\n@media (max-width: 520px) { .controls { grid-template-columns: 1fr; } }\n@media (prefers-reduced-motion: reduce) { [data-part] { transition: none; } }",
"js": "(function () {\n var $ = function (id) { return document.getElementById(id); };\n var root = document.querySelector('.brake');\n\n // Millimetres to drawing units; the running clearance is drawn ten times larger than life.\n var MM = 2.2, CLEAR = 0.15 * 10 * MM, DISC_L = 318, DISC_R = 342, BACK = 6;\n var PEDAL_RATIO = 4, BOOST = 3, MC_BORE = 22, MU = 0.4, R_EFF = 0.13, TYRE_R = 0.31, MASS = 1400, REAR_SHARE = 0.6, GRIP = 9.81;\n var CALIPERS = {\n floating: { name: 'floating', pistonBore: 54, pistons: 1 },\n fixed: { name: 'fixed', pistonBore: 40, pistons: 2 }\n };\n var state = { pedal: 0, wear: 10, kind: 'floating', boost: true, v: 100, step: -1 };\n var area = function (d) { return Math.PI * d * d / 4; };\n\n function physics() {\n var cal = CALIPERS[state.kind];\n var force = state.pedal * PEDAL_RATIO * (state.boost ? BOOST : 1);\n var p = force / area(MC_BORE); // N/mm² = MPa\n var pistonArea = area(cal.pistonBore) * cal.pistons; // per side, mm²\n var clamp = p > 0.05 ? p * pistonArea : 0; // N, on each pad\n var friction = 2 * MU * clamp; // two faces\n var torque = friction * R_EFF; // N·m\n var decel = torque * 2 * (1 + REAR_SHARE) / (TYRE_R * MASS); // m/s², front pair plus a lighter rear pair\n return { p: p, clamp: clamp, friction: friction, torque: torque, decel: decel, locked: decel > GRIP };\n }\n\n function layout(ph) {\n var fixed = state.kind === 'fixed';\n var pad = state.wear * MM, contact = ph.clamp > 0 ? 1 : 0, wearTake = (10 - state.wear) * MM;\n var inFace = DISC_L - CLEAR * (1 - contact); // inner pad's friction face\n var outFace = DISC_R + CLEAR * (1 - contact);\n var padInX = inFace - pad, backInX = padInX - BACK;\n var padOutX = outFace, backOutX = padOutX + pad;\n // A floating body is pulled inboard by as much as the outer pad needs; a fixed body never moves.\n var shift = fixed ? 0 : -(wearTake + CLEAR * contact);\n $('padIn').setAttribute('x', padInX); $('padIn').setAttribute('width', pad);\n $('padInBack').setAttribute('x', backInX);\n $('padOut').setAttribute('x', padOutX); $('padOut').setAttribute('width', pad);\n $('padOutBack').setAttribute('x', backOutX);\n\n var leftWall = 175 + shift, rightWall = backOutX + BACK;\n var pistonX = Math.min(leftWall + 40, backInX - 70);\n $('pistonL').setAttribute('x', pistonX); $('pistonL').setAttribute('width', backInX - pistonX);\n var fluidX = leftWall + 12, fluidW = Math.max(4, pistonX - fluidX);\n $('fluid').setAttribute('x', fluidX); $('fluid').setAttribute('width', fluidW);\n\n var body;\n if (fixed) {\n var rWall = backOutX + BACK + 70;\n $('pistonR').style.display = '';\n $('pistonR').setAttribute('x', backOutX + BACK); $('pistonR').setAttribute('width', rWall - 12 - (backOutX + BACK));\n body = 'M' + leftWall + ' 100 H' + (backInX - 4) + ' V60 H' + (backOutX + BACK + 4) + ' V100 H' + rWall + ' V240 H' + (backOutX + BACK + 4) + ' V230 H' + (backOutX + BACK) + ' V110 H' + (backInX) + ' V230 H' + (backInX - 4) + ' V240 H' + leftWall + ' Z';\n } else {\n $('pistonR').style.display = 'none';\n body = 'M' + leftWall + ' 100 H' + (backInX - 4) + ' V60 H' + (rightWall + 26) + ' V240 H' + rightWall + ' V112 H' + (backInX) + ' V230 H' + (backInX - 4) + ' V240 H' + leftWall + ' Z';\n }\n $('bodyShape').setAttribute('d', body);\n var sealX = pistonX + 18, tilt = contact ? 4 : 0;\n $('sealL').setAttribute('d', 'M' + sealX + ' 134 l8 ' + (-tilt) + ' v6 l-8 ' + tilt + ' z M' + sealX + ' 206 l8 ' + tilt + ' v-6 l-8 ' + (-tilt) + ' z');\n $('sealR').setAttribute('d', fixed ? 'M' + (backOutX + BACK + 40) + ' 134 l-8 ' + (-tilt) + ' v6 l8 ' + tilt + ' z' : '');\n $('hose').setAttribute('d', 'M20 170 H' + (fluidX + 2));\n\n var len = Math.min(70, 8 + ph.clamp / 500);\n var show = ph.clamp > 0 ? '' : 'none';\n $('clampIn').style.display = show; $('clampOut').style.display = show;\n $('clampIn').setAttribute('x1', backInX - len - 8); $('clampIn').setAttribute('x2', backInX - 6);\n $('clampOut').setAttribute('x1', backOutX + BACK + len + 30); $('clampOut').setAttribute('x2', backOutX + BACK + 24);\n $('frictionArrow').style.display = ph.clamp > 0 && state.v > 0 ? '' : 'none';\n }\n\n function fmt(n, d) { return n.toLocaleString('en-GB', { maximumFractionDigits: d, minimumFractionDigits: d }); }\n\n function figures(ph) {\n $('pedalOut').textContent = state.pedal + ' N';\n $('wearOut').textContent = fmt(state.wear, 1).replace('.0', '') + ' mm';\n $('pOut').textContent = fmt(ph.p * 10, 0) + ' bar';\n $('fOut').textContent = fmt(ph.clamp / 1000, 1) + ' kN';\n $('frOut').textContent = fmt(ph.friction / 1000, 1) + ' kN';\n $('tOut').textContent = fmt(ph.torque, 0) + ' N·m';\n $('vOut').textContent = fmt(state.v, 0) + ' km/h';\n var msg = '';\n if (state.v <= 0 && state.pedal > 0) msg = 'Stopped.';\n else if (ph.locked && state.v > 0) msg = 'The brakes ask for ' + fmt(ph.decel / 9.81, 1) + ' g; the tyres give about 1 g. Without ABS the wheels lock and slide.';\n else if (ph.clamp > 0) msg = 'Slowing at ' + fmt(ph.decel / 9.81, 2) + ' g.';\n else if (state.v > 0) msg = 'Rolling. Press the pedal.';\n $('say').textContent = msg;\n }\n\n var STEPS = [\n ['bracket', 'The bracket is bolted to the steering knuckle and never moves. The caliper body rides on two greased slide pins fixed to it.'],\n ['fluid', 'The pedal pushes the master cylinder. Brake fluid does not compress, so the pressure it makes arrives unchanged in the caliper bore: pressure equals force over the master cylinder\\'s area.'],\n ['piston', 'That pressure acts on the piston\\'s much larger face. Clamp force is pressure times piston area, which is where the hydraulic advantage comes from: a 54 mm piston has six times the area of a 22 mm master cylinder bore.'],\n ['body', 'In a floating caliper the piston pushes the inner pad onto the disc; the reaction slides the whole body inboard on its pins, pulling the outer pad against the other face. A fixed caliper has pistons on both sides and its body does not move.'],\n ['pads', 'Both pads rub the disc. Friction is twice (two faces) the pad coefficient times the clamp force, and braking torque is that friction times the effective radius, here 130 mm.'],\n ['seal', 'On release, the square-section seal, twisted as the piston moved, springs back and draws the piston a fraction of a millimetre away from the pad. That is the running clearance; as the pads wear the piston slides further through the seal, and the fluid in the bore makes up the difference.']\n ];\n\n function showStep() {\n var s = state.step;\n root.classList.toggle('focus', s >= 0);\n root.querySelectorAll('[data-part]').forEach(function (el) { el.classList.toggle('on', s >= 0 && el.getAttribute('data-part') === STEPS[s][0]); });\n $('stepNo').textContent = s < 0 ? 'Walk through' : 'Step ' + (s + 1) + ' of ' + STEPS.length;\n $('stepText').textContent = s < 0 ? '' : STEPS[s][1];\n $('prev').disabled = s < 0; $('next').textContent = s === STEPS.length - 1 ? 'Done' : 'Next';\n }\n\n function render() { var ph = physics(); layout(ph); figures(ph); return ph; }\n\n var angle = 0, last = 0;\n (function vents() {\n var g = $('vents'), out = '';\n for (var i = 0; i < 12; i++) { var a = i * Math.PI / 6; out += ''; }\n g.innerHTML = out;\n })();\n\n function tick(t) {\n var dt = Math.min(0.05, (t - last) / 1000 || 0); last = t;\n var ph = physics();\n if (state.v > 0 && ph.clamp > 0) state.v = Math.max(0, state.v - Math.min(ph.decel, GRIP) * dt * 3.6);\n var omega = (state.v / 3.6) / TYRE_R; // rad/s\n angle = (angle + omega * dt * 57.3 * 0.25) % 360; // drawn at a quarter speed, so it can be seen\n $('rotor').setAttribute('transform', 'rotate(' + angle + ')');\n figures(ph);\n requestAnimationFrame(tick);\n }\n\n $('pedal').addEventListener('input', function (e) { state.pedal = Number(e.target.value); render(); });\n $('wear').addEventListener('input', function (e) { state.wear = Number(e.target.value); render(); });\n $('kind').addEventListener('click', function () { state.kind = state.kind = 'fixed' ? 'floating' : 'fixed'; this.setAttribute('aria-pressed', String(state.kind = 'fixed')); render(); });\n $('boost').addEventListener('click', function () { state.boost = !state.boost; this.setAttribute('aria-pressed', String(state.boost)); this.textContent = state.boost ? 'Booster on' : 'Booster off'; render(); });\n $('drive').addEventListener('click', function () { state.v = 100; render(); });\n $('next').addEventListener('click', function () { state.step = state.step >= STEPS.length - 1 ? -1 : state.step + 1; showStep(); });\n $('prev').addEventListener('click', function () { state.step = Math.max(-1, state.step - 1); showStep(); });\n\n render(); showStep(); requestAnimationFrame(tick);\n})();"
}
```
Steps, specimen 2:
```element steps
{
"label": "Worked by hand: 100 N at the pedal",
"steps": [
{
"title": "Pedal to pushrod",
"body": "A 4:1 pedal and a 3:1 booster: 100 N × 4 × 3 = **1,200 N** on the master cylinder."
},
{
"title": "Pushrod to line pressure",
"body": "Bore 22 mm, so *A* = π × 22² / 4 = 380.1 mm². *p* = *F* / *A* = 1,200 N / 380.1 mm² = 3.157 N/mm², which is **3.16 MPa**, or 31.6 bar."
},
{
"title": "Pressure to clamp: the lever",
"body": "The fluid carries the same pressure to a 54 mm piston: 2,290 mm², six times the bore’s area. Clamp = *pA* = 3.157 N/mm² × 2,290 mm² = **7,230 N** on each pad."
},
{
"title": "Clamp to friction",
"body": "Two pad faces rub the disc, each at μ = 0.4: friction = 2μ × clamp = 2 × 0.4 × 7,230 N = **5,784 N**."
},
{
"title": "Friction to torque",
"body": "Acting at the pads’ effective radius: *T* = 5,784 N × 0.130 m = **752 N·m** at each front wheel."
},
{
"title": "Torque to deceleration",
"body": "Each rear gives 0.6 of a front’s torque, so 3.2 fronts’ worth acts at the 0.31 m tyre: *a* = 752 × 3.2 / (0.31 × 1,400) = 5.54 m/s², or **0.565 *g***."
}
]
}
```
Table, specimen 3:
```element table
{
"caption": "Front caliper options, worked for a 1 g stop",
"columns": [
{
"label": "Caliper",
"align": "left"
},
{
"label": "Pedal for 1 g",
"align": "right",
"numeric": true
},
{
"label": "Mass",
"align": "right",
"numeric": true
},
{
"label": "Verdict",
"align": "left"
}
],
"rows": [
[
"Floating, 48 mm",
"224 N",
"2.6 kg",
"Lightest, but 24 N over the limit"
],
[
"Floating, 54 mm",
"177 N",
"3.1 kg",
"Inside the limit, half the fixed price"
],
[
"Fixed, 4 × 40 mm",
"161 N",
"3.8 kg",
"Most margin, 0.7 kg more a corner"
]
],
"pick": 1,
"notes": "Booster working, μ = 0.4. Masses from the suppliers’ catalogues."
}
```
Decisions, specimen 3:
```element decisions
{
"caption": "Front brake decisions, September",
"decisions": [
{
"title": "Front caliper",
"status": "decided",
"date": "2026-09-22",
"choice": "Floating, one 54 mm piston",
"reason": "177 N for a 1 *g* stop, inside the 200 N limit, at half the price of the fixed caliper and 0.7 kg lighter at each corner.",
"alternatives": [
{
"option": "Fixed, four 40 mm pistons"
},
{
"option": "Floating, one 48 mm piston"
}
]
},
{
"title": "Master cylinder bore",
"status": "decided",
"date": "2026-09-19",
"choice": "22 mm",
"reason": "A 20 mm bore gives 21 per cent more pressure for the same push, but needs 21 per cent more pedal travel than the pedal box allows.",
"alternatives": [
{
"option": "20 mm"
}
]
},
{
"title": "Pad compound",
"status": "open",
"choice": "A road compound at μ = 0.4",
"reason": "Waiting for the supplier’s hot friction figures. At μ = 0.35 the pedal force for 1 *g* rises to 202 N, just over the limit."
},
{
"title": "Front caliper, first pass",
"status": "superseded",
"date": "2026-09-15",
"choice": "Floating, one 48 mm piston",
"reason": "Chosen for weight before the pedal force was worked; at 224 N for 1 *g* it failed the requirement.",
"supersededBy": "Front caliper"
}
]
}
```