THE FINGER TRAP — credits and provenance ======================================== WHAT THIS IS ------------ An independent reimplementation, written from published geometry, of the behaviour of a biaxially braided tube — the object sold as a finger trap, a cable grip, and an orthopaedic finger-traction sleeve. It is not a port, a decompilation or a copy of any existing program. No code, art or data from any other product is present in this bundle. Everything renders from the engine's own helix parameterisation. THE ORIGINAL ------------ The finger trap is a PUBLIC-DOMAIN FOLK OBJECT with no identifiable inventor, no copyright holder and no trademark asserted here. * A one-ended German version, the "Maedchenfaenger" (girl catcher), is documented from at least 1870. * The phrase "finger trap" first appears in an American newspaper in 1900; a variant name with a dated ethnic prefix appears in a 1953 Ohio newspaper advertisement. The device is NOT of Chinese origin. * Documented engineering descendants: orthopaedic finger and arm traction (Austria, 1870), the Vivien Kellems cable grip, parachute-line finger traps, fly-fishing and Indonesian fruit presses. * Source for all of the above: https://en.wikipedia.org/wiki/Finger_trap The neutral descriptive name "The Finger Trap" is used throughout. No manufacturer's brand appears anywhere in this bundle. WHAT DIFFERS FROM THE ORIGINAL OBJECT ------------------------------------- This is a laboratory and a game, not a simulation of a specific manufactured trap. 1. The strands are INEXTENSIBLE. Bamboo and the galvanised steel of a cable grip are close enough; the paper and cotton-tape novelty traps are not. A real paper trap grips LESS than this model at high load, because strand stretch adds compliance in series. 2. There is NO STRAND-STRENGTH LIMIT. The fiercest trap here computes a holding force of about 8.9 kN. A real bamboo braid tears long before that, so for a hard pull the actual escape route is breakage, not slip. The app says so in Help. 3. The finger is a RIGID CYLINDER. A real finger compresses, which changes both its radius and the snugness as the pull rises. 4. The two helix families are BALANCED, so their torques cancel and the trap cannot unscrew. A single-handed spiral wrap would, and is not modelled. 5. The "snugness" W0 is a user parameter in N/m, not a constitutive law. The app does not pretend to know the radial stiffness of woven bamboo. 6. The six named traps, the locking map, the force gauge, the escape game and every control are ORIGINAL to this page. PROVENANCE OF EVERY CONSTANT ---------------------------- Tags: DOCUMENTED (a source states it) / qualified (documented, but of something adjacent) / DERIVED (derived here, proved by the harness) / MEASURED (this build measured it numerically) / RECONSTRUCTED (a plausible value chosen here, sourced to nothing). DOCUMENTED * The device is a "cylindrical, helically wound braid, usually the common biaxial braid", woven from bamboo. -- Wikipedia, finger trap article. * Mechanism: "Pulling the entire braid lengthens and narrows it" by reducing the angle between warp and weft, reducing the circumference. -- same. * Escape: "push the ends toward the middle, which enlarges the openings". -- same. * Origin, dates and engineering uses as listed above. -- same. * Braid kinematics L = b cos(theta), D = b sin(theta)/(n pi), D = D0 sin(theta) with D0 = b/(n pi), where b is the unwound strand length and n the number of times it circles the axis. -- McKibben braid relations, e.g. "Contraction Sensing with Smart Braid McKibben Muscles", https://pmc.ncbi.nlm.nih.gov/articles/PMC5424474/ * The McKibben force law is proportional to (3 cos^2(theta) - 1) and vanishes at "theta = 54.7 degrees", the documented end of contraction. -- same. * Capstan (Euler-Eytelwein) equation T_load = T_hold e^(mu phi); its stated validity conditions are inextensibility and no flexural rigidity, and "the force gain is independent of the radius of the cylinder". Attributed to Euler (1769) and Eytelwein (1808). -- https://en.wikipedia.org/wiki/Capstan_equation * Friction angle theta = arctan(mu_s). -- https://en.wikipedia.org/wiki/Friction (The trap's criterion does NOT compare against this angle; see DERIVED below.) qualified * Lu Dingjie, You Zhong, Liu Zhuangjian, Lu Guoxing, a paper on the geometry and mechanics of the finger trap, Extreme Mechanics Letters vol. 71, 2024, article 102200. Bibliographic record confirmed independently on J-GLOBAL (202402269533797788) and NASA ADS (bibcode 2024ExML...7102200L). The publisher's page returns 403 to an unauthenticated fetch, so ONLY THE ABSTRACT was read. Two claims are taken from it and both are marked qualified: that the straps "undergo reconfiguration" (i.e. the inextensible idealisation is the literature's own), and that "the linear axial force transforms into an exponential force". The exponential derived independently in this build is in contact LENGTH, not in applied force. * The industry term for the same effect on cable grips is the "trellis effect". Source is a vendor buying guide, not a refereed one. * Coefficient of friction of human skin spans 0.12 to 0.74 depending on material and skin site. -- a review of skin-textile tribology, https://pmc.ncbi.nlm.nih.gov/articles/PMC8948776/ . It is a range across many textiles, not a bamboo-on-finger measurement. DERIVED (each proved in tools-harness.js against an independent oracle) * Invariant b^2 = L^2 + (n pi D)^2 -- the helix unrolled flat. * Widest tube at tan^2(theta) = 2, i.e. arctan(sqrt 2) = 54.735610317245 degrees; largest lateral area at exactly 45 degrees. * Inward line load from braid tension: W = (T/R) tan^2(theta). * Holding force Fmax = W0 R cot^2(theta) (e^Lambda - 1), Lambda = mu ell tan^2(theta)/R. * Release push Prelease = W0 R cot^2(theta), and the exact identity Fmax / Prelease = e^Lambda - 1, so pushing beats pulling precisely when Lambda > ln 2. * Locking criterion: hold iff mu (ell/R) tan^2(theta) > ln(1 + F* tan^2(theta)/(W0 R)). * The zero-snugness case is DEGENERATE: Fmax is identically zero for every braid angle and every friction coefficient. Reported as a non-result, not hidden. RECONSTRUCTED (no physical trap was measured; all six traps' dimensions are of this kind) * Strand length b = 0.196 m and n = 3 turns for the novelty traps; b = 0.377 m, n = 4 for the cable grip. Chosen so the braid angle a real finger forces lands near 55-60 degrees. * Finger radii 6.0 / 8.5 / 9.0 mm; cable radius 12 mm. * Snugness W0 of 15 / 300 / 800 / 2000 N/m (contact pressures of roughly 0.3 / 5.6 / 14 / 27 kPa). * Default friction 0.40, mid-range of the documented 0.12-0.74 skin span. * A determined two-handed pull taken as 100 N, used only to sort traps into "you can pull free" and "you cannot". MEASURED (numbers produced by this build's harness; see the Findings tab, which prints them straight out of the harness output rather than from anything typed by hand) * Every figure on the Findings tab, including all convergence tables. VERIFICATION ------------ tools-harness.js engine assertions, with four independent oracles tools-harness-page.js asset, wiring, CSP and figure-consistency checks on the bundle tools-smoke.js headless-Chrome play-through with pixel and console assertions tools-mutants.js mutation sweep over the engine BUILT WITH ---------- No third-party code of any kind. No CDN, no external script, stylesheet, font or image. The renderer, the engine, the harnesses and the icons were all written for this bundle. The icons and social card are generated by tools-images.py (Pillow) from the engine's own helix geometry. LICENCE ------- MIT, see LICENSE.txt. The finger trap itself is public domain.