snap-fits

name	snap-fits
description	Cantilever and annular snap-fit design - beam length and taper, permissible strain per material, undercut, insertion and return angles, catch clearance, FDM orientation.
triggers	["snap","snap-fit","snapfit","cantilever","clip","latch","hook","lid","catch","undercut","retention"]
version	1.0.0
license	Apache-2.0
author	AgentCAD core
requires	[]

A snap-fit holds a position by elastically deflecting a beam past an undercut and letting it spring back. Everything else follows from one number: the material's permissible strain. Size the beam from that, spend part of it on the undercut, and the joint works; guess the undercut and the hook either snaps off (too deep) or falls open (too shallow). Use this skill whenever a lid, cover, clip, latch or press-together housing has to assemble without fasteners. Do not use a snap to carry a sustained load — plastics creep, and a beam held deflected loses most of its retention in weeks; use a screw (enclosures) or a press fit (fits-and-clearances) for that. Do not use one for a seal (the lip does the sealing, the snap only holds it shut), and think twice about hundreds of open/close cycles in PLA.

Size the beam before you draw anything

Rectangular cantilever, width b, thickness t at the root, free length L, permissible strain ε (a fraction, not a percent).

• L ≥ 5·t, and 5–10 is the useful range. Below 5 the slender-beam equations overpredict the deflection you can get (root rotation and shear stop being negligible); above ~10 the beam is floppy and the retention force disappears.
• Taper the thickness 1:2 root→tip. Constant section puts all the strain at the root; a beam tapering t → t/2 strains almost uniformly and takes 64 % more deflection at the same root strain and the same force.

Permissible tip deflection (Bayer/BASF snap-fit manuals):

beam	permissible deflection y
constant section t	y = ε·L² / (1.5·t)
thickness tapered t → t/2	y = 1.64 · ε·L² / (1.5·t)
width tapered b → b/4	y = 1.28 · ε·L² / (1.5·t)

ε·L²/(1.5·t) and 2·ε·L²/(3·t) are the same expression — both are the constant-section formula. The taper is the 1.64 factor, never a rewrite of the denominator; a source calling ε·L²/(1.5·t) the tapered formula has dropped it. Invert to audit an existing hook: ε = 1.5·y·t / (1.64·L²).

Deflection force at the root and the force you feel on assembly:

• P = b·t²·E·ε / (6·L) — the taper does not change this: the root section sets the force, the taper only buys deflection.
• W = P·(μ + tan α) / (1 − μ·tan α) — α is the lead angle (below), μ ≈ 0.3 for plastic on plastic (0.2 for PP/POM, 0.4 for a dry rough printed surface).

Worked: PLA, ε 1.2 %, t 2 mm, L 12 mm, b 12 mm, E ≈ 3300 MPa → y = 1.64·0.012·144/(1.5·2) = 0.94 mm, undercut 0.66 mm, P = 26 N, W ≈ 28 N per hook at α = 30°. Two hooks = ~56 N to close the lid: firm, one-handed, right.

Permissible strain by material

Full table with a source per row: tables/material_strain.json.

material	ε one-time	design value	note
PLA	1.0–1.5 %	1.2 %	stiff, notch-sensitive — long beam, small undercut
PETG	2.5–3 %	3 %	best printed default: ductile, forgiving
ABS	4–6 %	4 %	the classic moulded snap resin
PA (nylon)	4–6 %	6 %	value is dry-as-moulded
PP	6–8 %	8 %	highest of the commodity resins
PC	3–4 %	4 %	tough but very notch-sensitive

Deratings that are not optional: halve for a joint opened and closed repeatedly; halve again outside ~0–40 °C; take 50–70 % of the value for FDM even when the layers lie in the bending plane, and 30 % when they do not (see below). Glass fill cuts permissible strain hard (a 30 % GF nylon is nearer 1.5 % than 6 %) — never reuse an unfilled number for a filled grade.

The undercut rule

undercut ≤ y_perm is the hard limit — the beam must deflect by the full undercut to assemble. Design to undercut ≈ 0.7·y_perm so tolerance, temperature and the ramp's own elasticity have somewhere to go. Then clamp:

• undercut ≥ 0.3 mm on a printed part, or the layer/tolerance noise (±0.15 mm typical) eats the retention. If 0.7·y_perm < 0.3 mm the beam is too short or too thick — lengthen L (deflection goes as L²) before you thin t.
• undercut ≤ 0.8·t_tip, or the nose is a spike that shears off.
• undercut ≤ the catch wall thickness, minus 0.3 mm.

Free space behind the beam must be at least y_perm + 0.3 mm, or the beam bottoms out on the wall before the hook clears and you snap the root.

Insertion and return angles, and the catch

Both angles are measured from the insertion axis (the direction of assembly), so 90° is a shoulder square to the pull.

joint	insertion α	return β	behaviour
permanent	30°	90°	square shoulder — only releases if you push the beam aside by hand
releasable	30°	45°	pulling cams the beam out

α below 20° makes a long fragile ramp; above 45° the insertion force nearly doubles (tan 60° = 1.73). A permanent joint needs a release tab if it is ever to be serviced: extend the beam past the nose by ≥ 3 mm so a fingernail or a screwdriver can push it clear.

The mating catch — a window, a ledge or a groove in the other part:

• depth in the pull direction ≥ undercut + 0.1–0.2 mm, so the hook seats without preload. A preloaded shoulder creeps and the joint loosens.
• 0.2–0.3 mm clearance per side around the beam (FDM); 0.1 mm for SLA/CNC. fits-and-clearances has the process table.
• take rattle out with the lip or a gasket, never by preloading the snap.
• a through window makes engagement visible and audible; a blind ledge needs undercut + 0.8 mm of material left behind it.

Annular (ring) snaps

A full 360° ring snapped over a shaft or into a bore strains in hoop, not in bending. Stretching a ring of diameter d over an interference y grows its circumference by π·y, so ε = y/d and

y_max = ε_perm · d

PP at 8 % on a 20 mm boss allows 1.6 mm of undercut; PLA at 1.2 % allows 0.24 mm — which is why full rings belong to compliant resins (PP, PE, TPU) and almost never to PLA. Notes that decide the design:

• if both parts flex, they share the interference; a rigid shaft in a compliant hub puts all of it in the hub.
• a ring is far stiffer than a cantilever, so the assembly force is large even when the strain is legal — check W before choosing one.
• slot it. Three to six slots turn the ring into cantilever fingers; each finger then follows the cantilever math with b = its arc width. This is the right answer for FDM and for any stiff resin, and it is far easier to print than a continuous undercut.
• DuPont's handbook has geometry factors refining y_max for a thick hub.

FDM: orientation is the whole game

• Put the beam in the layer plane. A hook printed with its axis vertical loads the layer bonds straight in tension at the root, where strain to failure is 30–50 % of the in-plane value. This is the single most common cause of a snapped hook. Print the lid flat with the beams pointing sideways, or split the part.
• Root fillet r ≥ 0.5·t. A sharp root is a stress concentration of 2–3× and is exactly where every beam breaks; at r/t = 0.5 the factor is down near 1.2. The fillet stiffens the root slightly, so do not count it as free length — measure L from the end of the fillet.
• The β = 90° retention face is a 90° overhang of depth undercut. Up to ~0.6 mm it bridges cleanly; deeper, flip the part so the ramp is the overhang, or chamfer the shoulder to 45° (which also makes it releasable — decide, do not discover).
• Elephant foot spreads the first layer 0.1–0.2 mm: a nose printed on the bed loses its clearance. Chamfer 0.4 mm on bed-side edges.
• Keep t a whole multiple of the extrusion width (2.0 mm at a 0.4 nozzle = 5 lines) so the beam is solid perimeters and not sparse infill.

More process rules: fdm-design-rules. The mating housing: enclosures.

Building it in build123d

Working part: snippets/cantilever_lid.py — a parametric lid with two opposed tapered hooks that derives its undercut from the material's strain. The order of operations matters:

1. plate, 2. plate corner fillets, 3. the beams, 4. the noses,
2. the root fillet last.

from math import radians, tan

TAPER_GAIN = 1.64          # t -> t/2 taper

def hook_sizes(eps, t_root, beam_l, insert_deg, requested):
    beam_l = max(beam_l, 5.0 * t_root)
    y_perm = TAPER_GAIN * eps * beam_l ** 2 / (1.5 * t_root)
    undercut = max(min(requested, 0.70 * y_perm, 0.8 * (t_root / 2)), 0.15)
    rise = undercut / tan(radians(insert_deg))   # lead-in ramp height
    return beam_l, y_perm, undercut, rise

Traps, each of which has cost somebody a rebuild:

• part.edges().filter_by(Axis.Z) for the plate corners catches the beams' vertical outer edges too. Fillet the plate before the beams exist.
• Taper with loft() between two rectangles, not extrude(taper=…) — the taper argument draws in on all four sides, and you want the outer face flat because it carries the nose.
• Start the beam root inside the plate (0.5–1 mm). Two exactly coplanar touching faces are a degenerate boolean; an overlap always fuses.
• Select the root-fillet edges by an explicit band in both X and Y — group_by(Axis.Z)[0] hands you the plate's whole underside perimeter. Then use safe_fillet, which searches the radius down instead of failing (selectors-and-occt-failures).
• A beam that never reached the plate fuses successfully as a second solid. Assert it: check_that(lambda part, m: len(part.solids()) == 1, name="one_solid") (design-specs). n_solids in the build metrics is the same evidence.
• Clamp β at 88° before tan — tan(90°) gives a zero-height sliver face that OCCT will happily turn into an invalid solid.

Checklist

• L ≥ 5·t, thickness tapered t → t/2.
• y_perm computed from the material's ε, derated for FDM and cycles.
• 0.3 mm ≤ undercut ≤ 0.7·y_perm and ≤ 0.8·t_tip.
• Free space behind the beam ≥ y_perm + 0.3 mm.
• Catch depth = undercut + 0.1–0.2 mm; 0.2–0.3 mm side clearance.
• α = 30°; β = 90° (permanent, with a release tab) or 45° (releasable).
• Root fillet r ≥ 0.5·t; beam axis in the layer plane.
• Assembly force W per hook × hook count is a force a hand can apply.
• Build reports one solid, is_valid, no dropped features.

Sources

• Bayer MaterialScience (now Covestro), Snap-Fit Joints for Plastics — A Design Manual (1998): cantilever deflection formulas, the 1.64 / 1.28 taper factors, permissible-strain table, the mating-force equation.
• BASF Corporation, Snap-Fit Design Manual: the same beam equations and permissible strains, independently published.
• DuPont, General Design Principles for DuPont Engineering Polymers, Module I — cantilever and cylindrical (annular) snap-fit sections, hub/shaft geometry factors.
• G. Erhard, Designing with Plastics (Hanser, 2006): permissible strain, notch sensitivity, creep under sustained deflection.
• NatureWorks Ingeo 3D-printing grade technical data sheets (4043D, 3D850) and Eastman Chemical copolyester (Eastar, Amphora 3D) technical data sheets, ISO 527 tensile data — the basis for the derated PLA and PETG rows.