Torsio Engineering
Quick preliminary sizing of mechanical transmissions and fits: from the requirements to the first dimensions for your CAD.
Free, ad-free, runs entirely in the browser.
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📌 Overview
Torsio Engineering (formerly MechCalc) is an open-source web application for preliminary sizing (dimensionamento di massima). It is meant for whoever has to design a gear pair, a belt drive or a shaft-hub fit from scratch and does not know where to start: enter the requirements (power, speed, ratio, center distance, diameter) and get first-attempt dimensions — module and number of teeth, face width, pitch diameters, belt length, tolerance limits — ready to be drawn in CAD and then refined.
It automates the repetitive, iterative hand calculations of machine design, shows the geometry with live SVG sketches and includes 1-click demo presets.
- From requirements to dimensions: the result of every module is a set of quotes to start the CAD model from.
- Classic machine design methods: Hertz / Lewis for gears (course charts for helical factors and Lewis form factor), ISO 286-2 tolerances, ISO 54 module series, ISO 5296 / DIN 7721 belt pitches. Values are preliminary: detailed verification (e.g. ISO 6336 for gears, the belt manufacturer's catalog, FEM) is the next step.
- Validated: the gear module is checked against worked exam problems (see Validation).
- Client-side: every calculation runs in your browser; nothing you enter is sent to a server.
🚀 Core Modules
1. Cylindrical Gears Synthesis & Rating (ISO 54 / Hertz & Lewis)
Solves the full gear pair synthesis problem with strict mounting constraints:
- Synthesis from Theoretical $z_{\min}$: Scans valid tooth combinations starting from the undercut limit:
$$z_{\min} = \left\lceil \frac{2(1 - x_{r1})}{\sin^2 \theta} \right\rceil$$
- Exact Center Distance Closure: Analytically recalculates the helix angle $\alpha$ to close on a fixed mounting distance $i$:
$$\cos \alpha = \frac{m_n (z_1 + z_2 + 2x_{r1})}{2i}$$
- Dual Hertz & Lewis Checks:
- Evaluates pitting resistance at the Hertzian contact limit to determine the required face width factor $\phi$.
- Filters out combinations exceeding tooth root bending limits ($\sigma_L \le 800\text{ MPa}$).
- Helical Correction Factors: $\Phi$, $\Psi$ and $\Gamma_{t1} + \Gamma_{t2}$ are taken from the course chart (digitized from the original vector plot, $\alpha$ = 0–50°, $z$ = 9–100, interpolation in $1/\sqrt{z}$ between the curves).
- Lewis Form Factor from the Course Chart: $y(z', x)$ for profile shifts $x$ = −0.6…+0.6 and equivalent teeth $z' = z/\cos^3\alpha$ = 10–200 (digitized from the chart, interpolated in $\log z'$ and $x$).
- Series 3 Warning System: Detects non-preferred tooling modules (Series 3) and compares them against scalable Series 1/2 alternatives.
- Inverse Rating Mode ($W_{\max}$): Calculates maximum allowable power and torque for existing gear geometry.
2. Synchronous Timing Belts (ISO 5296 / DIN 7721)
- Supported Pitches: GT2 (2 mm), HTD 3M, HTD 5M, HTD 8M, and T5.
- Center Distance Recalculation: Recalculates exact geometric center distance ($C$) following integer commercial belt tooth rounding ($z_b$).
- Kinematic Verification: Computes driver wrap angle $\theta_1$, teeth in mesh ($z_{\text{mesh}}$), tangential tension ($F_t$), and catalog service factors ($c_0, c_1, c_2$).
3. ISO Fits & Tolerances Selector (ISO 286-2)
- H7 Hole-Basis System: Covers diameters from 3 mm to 500 mm (0.118" to 19.68").
- Interactive SVG Visualization: Real-time rendering of tolerance zones relative to the zero line.
- Reverse Lookup Engine: Identifies matching ISO fit classes directly from target clearance or interference values.
- Manufacturing Notes: Provides machining guidelines and recommended surface roughness ($R_a$).
4. Shaft Design: beam model → critical section → fatigue design
The three steps of the classic method, in three tabs:
- 1 · Beam & loads: the shaft of length $L$ on two bearings with up to four elements (spur/helical gears, couplings, generic forces). Points are named as in the course: A and B are the shaft ends, bearings and elements become C, D, E, … from left to right. Gear forces from the torque ($F_t = 2M_t/d$, $F_r = F_t\tan\theta/\cos\alpha$, $F_a = F_t\tan\alpha$, with the couple $F_a,r$); the direction of each force on the shaft is either chosen in the vertical (V) and horizontal (H) plane or derived from where the mating gear is (any angle) and the rotation of the shaft (driven gear: Ft follows the rotation; driving gear: it opposes it; an idler is two meshes at the same x), and previewed in an oblique view of the whole shaft and in an end view of the gear. Each gear or coupling carries a share of the shaft torque (e.g. 50 % when two users split the power) or none (idler gear). Output: reactions, required dynamic load rating of the bearings ($C = R,L^{1/p}$), the life in hours and, with a catalog $C$, the actual life $L = (C/P)^p$, separate diagrams for the vertical plane (forces and $M_v$), the horizontal plane (forces and $M_h$), the resultant $M_f = \sqrt{M_v^2 + M_h^2}$ and the torque, with the values at every named point, and the most stressed section, which is sent to the design step with one click. Optionally, up to four real sections (diameter, shoulder and fillet, keyway) are checked with the beam loads: the critical one is the section with the lowest safety factor, not necessarily the one with the largest moment (e.g. a relief groove next to a gear), and it goes to the Check tab with one click.
- 2 · Design section: finds the minimum diameter $d$ of the critical section from the Goodman line, with every coefficient re-evaluated at the diameter being tried (the "first attempt" iteration done automatically), then rounds it up to the next standard bearing bore and re-checks the section.
- 3 · Check section: safety factors against fatigue and yield for a known $d$, $D$, $r$, plus the maximum load at that diameter (the usual exam question "find the maximum torque / power / load"): all loads scale together, so $X \propto 1/\text{load}$ and the limit is the current load $\times,X/X_{req}$. The same tab gives the fatigue life at the required X (the $\sigma_N$ that closes the Goodman line, then the Wöhler line) and the remaining life with Miner's rule or Manson's double linear rule ($N_{II} = 14,N^{0.6}$) after up to two previous load phases. The yield card also shows a static von Mises check on the peak stresses, for shafts that do not rotate.
- Loads: rotating (alternating) or constant bending, torque from power and speed or direct, constant / pulsating / fully reversed torsion, constant axial force.
5. Structures: 2D finite elements for beams, frames and trusses
Draw the structure on a snapped grid (drag to create a member, click to cycle the support of a node, to add a force or a distributed load, to put a hinge at a member end); the tables below hold the exact coordinates and loads.
- Solver: plane frame elements (Euler-Bernoulli, 3 dof per node), assembly $K = \sum T^{\mathsf T} k, T$, fixed-end forces for uniform loads (vertical or perpendicular to the member), internal hinges by static condensation of the released rotations. A member hinged at both ends keeps only $EA/L$: it is exactly the truss bar of Luigi's notebook (Ottimizzazione peso, torre radio), which this module generalizes.
- Output: reactions, N / V / M diagrams drawn on the structure (moment on the tension side), deformed shape, utilization map.
- Sizing in six families — solid round, round tube (EN 10219), solid rectangle, square hollow section, IPE, HEA (properties from the nominal geometry with fillets, within 0.3 % of the catalogs): discrete fully stressed design, i.e. the notebook's FSD on catalog sections, with $\sigma = |N|/A + |M|/W \le \sigma_s/X$, Euler buckling $N_{cr} = \pi^2 E I_{min}/(\beta L)^2$ and an optional deflection limit; one section per member or one for all. The families are compared by mass, with a dimensioned drawing of each chosen section.
- Notebook comparison: for pure trusses the continuous FSD of the notebook runs too, without and with buckling (solid round, $|\sigma| \le 0.8,\sigma_{cr}$ as in the notebook's gradient method). Radio tower: FSD without buckling 285 kg (9 compressed bars with $\sigma > \sigma_{cr}$); FSD with buckling 1471 kg, every bar verified — close to the 1454 kg of the notebook's gradient method, which leaves 7 bars slightly beyond the 0.8 margin; with catalog tubes and Euler about 525 kg, while IPE sections cannot carry the compressed legs at all.
6. Bolted joints (method of the Elementi Costruttivi delle Macchine notes)
- Friction joint design: tangential force, or torque on a bolt circle ($F = M_t/(D/2)$, at most $\pi D/D_c$ bolts); $T = F/(m_{bolts},m_{int})$, preload $N = T,X/f$; number of bolts from $N/A_{res} = \sigma_s/X$ with $A_{res} = \pi (0.8d)^2/4$ (rounded down only when $X$ drops by ≤ 0.5 %, as in the hand solutions); comparison of every size of the class.
- Tightening torque: $M_s = N,\frac{d_m}{2},\frac{\cos\beta\sin\alpha + f\cos\alpha}{\cos\beta\cos\alpha - f\sin\alpha} + \frac{N}{2},D_m f$, $d_m = 0.9d$, $\tan\alpha = p/(\pi d_m)$, $D_m = (D_c + d)/2$; von Mises with the tightening torsion for information.
- Check from a given torque: preload, transmissible force and torque.
- External axial load: $K_v = E,(\pi d^2/4)/h$, $K_f = E,A_{eq}/h$ (30° cone), $\Delta F_v$, $\Delta F_f$, bolt load, residual clamping force, joint opening, new transmissible torque, optimal preload $P_{am}K_f/(K_v+K_f)$, tightening diagram.
- Power screws (vise, jack): square / trapezoidal / ISO thread, torque, efficiency, self-locking, stresses.
- Strength classes 4.6 … 12.9, ISO coarse threads M4–M64 with the head across-flats $D_c$ of the notes' tables.
⚡ 1-Click Demo Presets
Load fully calculated engineering cases with a single click:
| Preset Name | Description | Key Specs |
|---|
| Helical Gearbox | Industrial reduction with locked center distance | $50\text{ kW}$, $i = 182\text{ mm}$, optimal $(z_1=19, z_2=78)$ |
| Spur Gear Pair | Standard industrial motor reduction | $5.5\text{ kW}$, $1450\text{ rpm}$, ratio $1:2$ |
| Bearing Fit | Precision shaft-to-bearing tolerance | $\varnothing 30\text{ mm}$ (H7/k6) |
| Reducer Shaft | Intermediate shaft of a spur-gear reducer (exam problem): beam, critical section, design | $30\text{ kW}$, $200\text{ rpm}$, $M_f = 1887\text{ N·m}$ at the bearing → $\varnothing 65$ |
🔗 Shareable Links
Every calculation is kept in the page address (module, inputs, modes, language, units, selected optimizer row), so the URL can be bookmarked or sent as it is. The Share button copies it (on phones it opens the system share sheet). Only values that differ from the defaults are written, e.g.:
https://torsio.app/app.html?m=fits&nominalDiameter=30&fitType=H7%2Fk6
Old links to the root (/?m=...) are forwarded to the calculator. The home page links can also open a demo: app.html?demo=transmission.
🛠️ Architecture & Tech Stack
torsio-engineering/
├── index.html # Home page (static, no framework)
├── app.html # Calculator: UI shell, demo presets, translations
├── modules/
│ ├── core/ # Analytical engines: pure functions, no DOM access
│ │ ├── fits-core.js # ISO 286 tolerance tables, fit analysis, reverse lookup
│ │ ├── belts-core.js # Synchronous timing belt sizing logic
│ │ ├── gears-core.js # Hertz/Lewis synthesis, tooth optimizer, W_max rating
│ │ ├── shafts-core.js # Shaft fatigue design: Kt, q, b1, b2, Goodman, bearing bores
│ │ ├── frames-core.js # 2D frame/truss FEM, section catalogs, FSD sizing with buckling
│ │ ├── dxf-core.js # DXF R12 writer, title block, shaft profile proposal, UNI 6604 keys
│ │ └── bolts-core.js # Bolted joints: friction joints, tightening torque, external load, power screws
│ └── ui/ # Read inputs, call the core, render results and SVG
│ ├── fits-ui.js
│ ├── belts-ui.js
│ ├── gears-ui.js
│ ├── shafts-ui.js
│ ├── frames-ui.js # Structures editor (SVG drawing, tables, results)
│ ├── report-frames.js # Calculation report of the Structures module
│ ├── project.js # Project data, project files, title block data
│ ├── dxf-ui.js # DXF export of every module, shaft profile editor
│ ├── bolts-ui.js # Bolted joints module (three tabs, tightening diagram)
│ ├── report-bolts.js # Calculation report of the bolted joints
│ ├── report.js # Calculation reports of each module (A4, KaTeX)
│ ├── report-transmission.js # Complete transmission report: power flow + chapters
│ ├── report-pdf.js # "Download PDF": A4 pages drawn in the browser, no server
│ ├── validate.js # Input rules of every field: invalid values marked, no verdict on them
│ └── share.js # Shareable links: state <-> URL
├── vendor/ # KaTeX and html2canvas (MIT), compiled Tailwind CSS, brand mark
├── tailwind.config.js # Palette and theme of the calculator; tools/build-css.sh compiles vendor/tailwind/app.css
├── tests/
│ ├── validation.test.js # Core vs. worked exam problems (node, no dependencies)
│ ├── browser_test.py # Share links & form behaviour in headless Chromium (Playwright)
│ └── css_check.py # Compiled CSS up to date and covering every class used at run time
└── README.md # Documentation
Each ui/*.js file depends on the matching core/*.js file, so app.html loads the core first.
- Frontend: Pure Vanilla JavaScript (ES6+, classic
<script> files, no bundler) & HTML5
- Styling: Tailwind CSS 3.4, compiled once and committed (
sh tools/build-css.sh with the Tailwind standalone CLI after changing classes; tests/css_check.py tells when it is needed)
- Rendering: Inline Mathematical SVG
🔗 Linked modules
A Continue with these results bar at the bottom of each module carries its results into the next one:
timing belt → gears (driven speed and power), gears → pinion or wheel shaft (power, speed, pitch diameter, helix),
shaft → ISO fit (diameter) and → bolted flange coupling (torque), frames → bolts at each support (shear |Rx|, uplift −Ry).
The target fields are filled in and highlighted, and a banner says where the data came from and what still has to be checked.
📚 Method and validation page
metodo.html (IT/EN) states, module by module, the method, the key formulas, the sources, how many automatic cases check it and where it stops.
novita.html lists the changes version by version, privacy.html says what data the site handles (calculations stay in the browser, cookieless statistics, the Tally form only on request), 404.html is the page for wrong addresses. Fonts (Archivo, IBM Plex Mono, OFL) are served from vendor/fonts, so no page calls Google. Landing pages for search, one per module in English and Italian (/shaft-calculator/, /bolted-joint-calculator/, /frame-truss-calculator/, /it/dimensionamento-albero/, /it/calcolo-bulloni/, /it/calcolo-telaio-traliccio/), are generated by python3 tools/mkguides.py: method, formulas, a worked exam example with the calculator's numbers, limits, FAQ. app.html without a module opens on a start screen with the six stations (modules/ui/start.js).
Shafts can start from a table of quenched and tempered steels (EN 10083-2/-3, +QT, by diameter range: σR = Rm min, σs = Re min, σLF ≈ 0.5·Rm min as an estimate).
🗂️ Projects and CAD export
- Project data (📁 Project): company, project, job number, client, drawn / checked / approved by, revision with history, logo (PNG/JPG/SVG; without one the Torsio mark is used). They are remembered in the browser and printed in the header and in the ISO 7200 style title block of every report (with signature boxes and the revision table) and every DXF.
- Project file (
.torsio.json): the inputs of all five modules plus the project data, saved and reopened in one click; the file name carries job number, project and revision.
- DXF export (📐, AutoCAD R12 ASCII, opens in any CAD; mm, model space 1:1, layers with linetypes, title block scaled around the drawing on A4/A3, scale chosen automatically):
- Shafts: the whole shaft profile, proposed from the calculation — bearing seats at the designed bore, gear seats at the shoulder diameter, collars between seats, UNI 6604 keyways on gear and coupling seats — editable in a table under the shaft module (the profile is kept in links and project files). Fillets at every step, end chamfers, diameters and chain dimensions, keyway top views with $b \times t_1 \times l$, element labels.
- Structures: member axes with section names, nodes, hinges, supports, loads, overall dimensions, and every chosen section outline at real size.
- Gears: tip, pitch and root circles of the pair at the centre distance. Belts: pitch circles and the belt on the pitch line at the exact centre distance.
- Checked with ezdxf (audit: no errors).
📄 Calculation Reports
Complete transmission report: the Report menu can also join several modules in one document. Chapter 1 shows the power flow (motor → belt → gears → shaft → fits) with speed, power and torque of each stage and checks the modules against each other: belt output speed vs. pinion speed, power along the chain, which gear the shaft carries, whether the gear rim under the teeth is thick enough to be keyed on the shaft (≥ 2.5·m, otherwise the pinion is made integral with the shaft), and whether the fit diameter matches the shaft. Then one chapter per module, numbered 2.1, 2.2, … The Complete drive (7.5 kW) demo builds a linked example: motor 7.5 kW at 1450 rpm, HTD 8M belt 28/56, spur pair τ = 1/4 and the pinion shaft.
The Report of this module entry opens a printable A4 calculation report of the active module, saved as PDF from the browser's print dialog. Every report has the design data, the procedure with the formulas and the substituted values, the results with VERIFIED / NOT VERIFIED, the diagrams, the dimensions for CAD (or the drawing callouts), the assumptions and a link that reopens the calculation. Gears: Hertz design of module and face width (or the power capacity of an existing pair), Lewis check, helical factors, optimizer table, tip and root diameters. Belts: pulleys, pitch length and exact centre distance, teeth in mesh, width, ordering designation. Fits: deviations, limit sizes, clearances, machining and roughness, comparison of the H7 fits, drawing callouts. Shafts: design data, shaft layout and gear forces with the force previews, reactions and bearings, V / H / resultant / torque diagrams, critical and real sections, the section design or check with every formula and substituted value, Goodman diagram and sketch, life and maximum load, the dimensions to take into CAD, assumptions, and a link that reopens the same calculation. It is generated entirely in the browser; formulas are typeset (real fractions, roots, subscripts) with KaTeX (MIT), bundled in vendor/katex and loaded only when a report is opened.
✅ Validation
The gear module is checked against worked exam problems of the course Costruzione di Macchine (exam papers 2018–2022, solved by hand): spur and helical $W_{\max}$, Hertz face-width factor $\phi$ in design mode, Lewis stresses and the helical correction factors read from the chart.
| Check | Cases | Max deviation |
|---|
| Hertz, spur gears ($W_{\max}$, $M_{\max}$, $\phi$, $L$, $F_c$) | 9 | 0.7 % |
| Hertz, helical gears ($W_{\max}$ / capacity at the designed face width) | 3 | 1.0 % |
| Lewis bending stress $\sigma_L$, spur and helical (same $y$ as the hand solution) | 5 | 0.7 % |
| Lewis factor $y$ vs. values read by eye from the chart | 5 | 0.021 |
| Helical factors $\Phi$, $\Gamma_t$, $\Psi$ vs. values read by eye from the chart | 11 | 0.02 |
| Shafts: design diameter and safety factors vs. the official solution (exam of 11 April 2003) | 5 | 1.2 % |
| Shafts, beam model: gear forces, reactions, bending moments, bearing $C$ vs. the official and the hand solution | 17 | 0.7 % (1.3 % on a hand-rounded value) |
| Shafts: $K_t$, $q$, $b_1$, $b_2$ vs. values read by eye from the charts | 7 | 0.09 on $K_t$, 0.015 otherwise |
| Shafts, exam of 9 December 2002 (hand solution): beam moments, critical section, shoulder + keyway design ($d$ = 61 mm) | 11 | 1.4 % |
| Shafts, 11 more exams 2004–2023 (hand solutions): beams with overhangs, idler gears and levers, design, maximum torque / power / load, bearings | 198 | 0.5 % with the same coefficients as the hand solution |
| Structures (FEM): closed-form beams (simply supported, fixed-fixed, propped cantilever, continuous, cantilever, Gerber), portal equilibrium | 10 | exact |
| Structures: radio tower of Luigi's notebook — initial stress 132.62 MPa, FSD weight 284.96 kg in 27 iterations; FSD with buckling vs. the notebook's gradient result | 7 | 0.01 % (1.2 % vs. the gradient) |
The factor deviations are reading errors of the hand solutions (e.g. $y$ = 0.32 read for $z$ = 18, where the chart gives 0.341; $K_t$ = 2.5 read where the course formula gives 2.41). For the shoulder $K_t$ the tool uses the course formula $B,(r/d)^a$; checked against the digitized course chart it stays within ±3 %, while values read by eye in the hand solutions differ by up to +14 %. Every other gap in the shaft exams is a hand slip (documented in the test notes). The official shaft solution writes $X$ = 1.91 for the fatigue check, but that value leaves out the torsion term of the Goodman line: with it, the same coefficients give $X$ = 1.82 (still above the required 1.75). Run the suite (no dependencies) with:
node tests/validation.test.js
💻 Running Locally
No dependencies, package managers, or build steps required:
# Clone the repository
git clone https://github.com/Luigi-Frassi/torsio-engineering.git
# Enter project directory
cd torsio-engineering
# Run using Python 3 built-in server
python3 -m http.server 8000
Then visit http://localhost:8000 in your web browser.
🔒 Privacy
- All calculations run in the browser: the values you enter are never sent to a server.
- The site uses Vercel Web Analytics to count page views: no cookies, no cross-site tracking, visitors are counted with an anonymous hash that is discarded after 24 hours, and only aggregated statistics are kept (page, referrer, country, browser, device type).
- Shareable links carry the calculation in the address; before a page view is sent, a filter removes everything except the open module (
?m=gears), so your inputs are not recorded.
- No ads, no third-party cookies.
📄 License
This project is open-source and distributed under the MIT License.
