Screw Thread Nomenclature

The Screw Thread Nomenclature Trainer teaches the ISO 261 metric screw thread system through interactive visualization and calculation. The canvas supports two viewing modes: a 2D cross-section that shows the truncated ISO thread profile in detail, and a 3D isometric helix view that visualizes how the thread wraps around the cylinder. Both views update in real time as you change parameters.

The trainer covers nine standard metric thread sizes from M2 to M12 with adjustable pitch (coarse, fine, or custom). All key dimensions are calculated and displayed: major diameter (d), pitch diameter (d₂), minor diameter (d₁), thread depth (h), pitch (P), thread angle (60°), and helix angle (λ). Hover any dimension on the canvas or in the readout cards and the matching element on the other side highlights.

The trainer opens in Explore mode with a 2D cross-section view by default. Use the View toggle in the controls bar to switch between Section and 3D Helix views. Mode tabs (Learn / Explore / Practice / Quiz) sit alongside the view toggle.

To explore: (1) Pick a thread size from the dropdown (e.g., M6). (2) The default coarse pitch is shown. (3) Click a standard pitch preset or drag the pitch slider; you can also use the −/+ stepper or type into the number box. (4) Watch the canvas animate smoothly between pitch values. (5) Toggle individual canvas overlays (Dimensions, Part Labels, Equation, Pitch Line, Grid) using the checkboxes. (6) Open the "Step-by-step Calculation" panel below, or click the floating "Show Calculations" button for a full KaTeX-rendered derivation modal.

Hover any dimension on the canvas (d, d₂, d₁, P, h, 60°, λ) and its readout card highlights. Hover a readout row in the Diameters or Thread Profile panel and the corresponding annotation on the canvas highlights with a tooltip. This bidirectional linking helps you connect terminology with the visual geometry.

Keyboard: use Left/Right arrow keys to navigate Learn-mode lessons, or to step the pitch slider one increment in Explore mode. Right-click the canvas for a context menu (Export PNG, Copy All Values as CSV, Copy Designation, Toggle 3D view, Reset). The Calc FAB at the bottom-right of the canvas opens a step-by-step LaTeX-rendered derivation of every formula in classical mathematical notation.

Click the 3D Helix view button to switch from cross-section to an isometric rendering of the threaded shaft. The view shows a cylinder with the helix path drawn around it, illustrating how a thread is fundamentally a helical ridge. The helix angle λ is visualized directly: steeper helix corresponds to larger pitch (or smaller diameter).

The 3D view auto-rotates slowly and responds to pitch changes — finer pitch tightens the helix wrap and shows more turns over the same axial length. Toggle back to Section view to see the cross-section dimensions. The Equation toggle works in both views.

Learn mode steps you through five lessons: (1) What is a Screw Thread? — with an animated helix unwrap demonstrating the relationship between circumference, pitch, and helix angle. (2) Thread Terminology — crest, root, flank, thread angle. (3) Key Dimensions — an M10 worked example with all formulas. (4) ISO 261 Designations — how to read M8×1.25. (5) Coarse vs Fine — side-by-side M10 comparison.

Navigate using Prev/Next buttons, the progress dots, or Left/Right arrow keys.

Practice mode presents a random thread designation (e.g., M8 × 1.25) and asks you to calculate three dimensions: pitch diameter (d₂), minor diameter (d₁), and thread depth (h). Enter your values to three decimal places and click "Check". The trainer marks each as correct (within 0.002 mm tolerance) or incorrect. Click "New" for a fresh problem.

Quiz mode runs five timed questions where you must calculate a specific dimension (d₂, d₁, h, or λ). After five questions you see your score with a star rating and a per-question review.

• Memorise the three key formulas: d₂ = d − 0.6495P, d₁ = d − 1.0825P, h = 0.5413P. These constants come from the 60° ISO metric thread geometry and 5H/8 truncation.
• The major diameter (d) and thread angle (60°) are always fixed for a given thread size. Only pitch-dependent dimensions change.
• Coarse pitch is the default when no pitch is specified (e.g., M10 means M10 × 1.5). Fine pitch must always be specified explicitly.
• Use the pitch slider in Explore mode to build intuition for how pitch affects thread depth and minor diameter. The canvas animates smoothly, making the relationship visible.
• The helix angle λ increases with pitch and decreases with diameter. It is typically small (2–5°) for standard fastener threads — visible clearly in the 3D Helix view.
• Click "Show Calculations" to see the full derivation in classical mathematical notation (KaTeX).
• Right-click the canvas to export a PNG or copy values to spreadsheet (CSV).