Parametric CAD

Why this matters

A camera mount changes often: a new camera means new hole spacing, a different screw means a new clearance hole. Redrawing the shape by hand every time is slow and error-prone. Parametric CAD keeps the design intent in variables and relationships, so changing one value updates the whole shape. The drone knowledge base’s CAD and 3D printing unit and lab L05 use the camera mount as the same example.

Sketches, constraints and degrees of freedom

Every feature starts from a 2D sketch, and each element has degrees of freedom (DOF). The FreeCAD Sketcher guide explains that an unconstrained line has 4 DOF (two end points, 2 each). Adding constraints such as horizontal, point lock and length until the DOF reach zero makes the sketch fully constrained, so the shape does not change unexpectedly when parameters are edited. Use constraints that express intent, such as two equal holes or symmetry about an axis, rather than placing things by eye.

ISO273_MEDIUM = {"M2": 2.4, "M2.5": 2.9, "M3": 3.4, "M4": 4.5}   # mm medium clearance holes
T_MIN, EDGE_FACTOR, DENSITY = 3.0, 2.0, 1.24e-3                   # mm, times the hole size, g/mm³

def mount(pitch, screw="M3", t=3.0, depth=20.0):
    hole = ISO273_MEDIUM[screw]
    edge = EDGE_FACTOR * hole
    width = pitch + 2 * edge
    volume = width * depth * t - 2 * 3.14159 * (hole / 2) ** 2 * t
    ok = t >= T_MIN
    return hole, width, volume * DENSITY, ok

for pitch, screw in ((16, "M2"), (20, "M3"), (25.5, "M3"), (25.5, "M4")):
    hole, width, mass, ok = mount(pitch, screw)
    print(f"pitch {pitch:>4} mm, {screw:<4}: hole {hole} mm, plate width {width:.1f} mm, "
          f"mass {mass:.2f} g, thickness rule {'ok' if ok else 'FAIL'}")

pitch   16 mm, M2  : hole 2.4 mm, plate width 25.6 mm, mass 1.87 g, thickness rule ok
pitch   20 mm, M3  : hole 3.4 mm, plate width 33.6 mm, mass 2.43 g, thickness rule ok
pitch 25.5 mm, M3  : hole 3.4 mm, plate width 39.1 mm, mass 2.84 g, thickness rule ok
pitch 25.5 mm, M4  : hole 4.5 mm, plate width 43.5 mm, mass 3.12 g, thickness rule ok

File formats

• CAD source (such as .FCStd) keeps features, constraints and parameters; it can be edited further and must always be kept.
• STEP (ISO 10303-21) stores exact curved geometry for exchange between CAD programs, without feature history.
• STL stores the surface as triangles. The binary form has an 80-byte header, a 4-byte triangle count and 50 bytes per triangle, and carries no units.
• 3MF (3MF Consortium) stores the mesh with units, colours, materials and print settings.

The knowledge base unit stresses that having only an STL is not the same as having the full design history.

STL resolution

When exporting STL, the program replaces curved surfaces with triangles. The largest distance between the true surface and the triangles is the chord error, or surface deviation (FreeCAD Mesh guide). The smaller it is, the smoother the shape but the bigger the file.

import math

R = 10.0
for s in (0.1, 0.05, 0.01):
    n = math.ceil(math.pi / math.acos(1 - s / R))
    triangles = 2 * n + 2 * (n - 2)            # side wall + top and bottom caps
    size = 84 + 50 * triangles
    print(f"chord error {s:4.2f} mm: {n:>3} segments, {triangles:>3} triangles, binary STL {size:,} bytes")

chord error 0.10 mm:  23 segments,  88 triangles, binary STL 4,484 bytes
chord error 0.05 mm:  32 segments, 124 triangles, binary STL 6,284 bytes
chord error 0.01 mm:  71 segments, 280 triangles, binary STL 14,084 bytes

Module lab

Common mistakes

Summary

• A fully constrained sketch has zero DOF and uses constraints that express design intent.
• A parameter table makes design changes fast and design rules checkable.
• CAD source keeps history, STEP exchanges geometry, and STL and 3MF are for printing.
• Smaller chord error means more triangles and larger files.

Check your understanding

1. How many DOF does an unconstrained circle in a sketch have (centre and radius)?
2. How big is a binary STL file with 1,000 triangles?
3. Which format keeps feature history?
4. A 10 mm radius circle uses 24 segments. What is the chord error?
5. Why keep a STEP file even when you already have an STL?