The Finger Trap

What this is

A finger trap is a braided tube. Pull its ends and it gets longer and thinner, so it clamps whatever is inside. This page reproduces that from geometry, then asks the question the toy is famous for and answers it with a number.

“The harder you pull, the tighter it grips, so pulling can never free you.”

The first half is true and the second does not follow. The squeeze the braid applies is exactly proportional to the pull — W = W₀ + T·tan²θ/R, linear in the tension T — so it never outgrows the pull, and the applied force cancels out of the escape question altogether. What is left is finite:

Set the snugness W₀ to zero — a braid with friction but no interference — and F_max is zero for every braid angle and every friction coefficient. The braid multiplies snugness; it cannot create it. A trap that is loose on a thin finger cannot be made to grip by pulling on it, however hard, and the simulator on the Findings tab slides one off under a pull of -.

What was checked, and against what

• The kinematics DOCUMENTED are the McKibben braid relations, L = b cos θ and D = b sin θ / (nπ). They are checked here against a polyline helix whose length is a chord sum and whose radius is found by bisection — an oracle that is never shown either formula.
• The widest tube sits at arctan√2 = -°. A golden-section maximiser handed only the numerically measured volume, and never told what to look for, returns it to - degrees. The same maximiser on lateral area returns 45°, a different angle, which is why one fixed point would not have been enough.
• The squeeze law DERIVED is checked against discrete polygon statics on a closed helix — vector sums, no curvature formula.
• The holding force DERIVED is checked against a dynamic Coulomb simulator: springs, masses, friction impulses, a stick test. It contains no exponential and no differential equation, and it agrees to - relative.
• The critical braid angle is located twice — once as the root of a transcendental equation, once by bisecting the simulator's own hold/escape verdict. They agree to - degrees.

What the model does not include

• Strand stretch. Bamboo and steel are inextensible enough; the paper and cotton-tape traps sold as novelties are not. Stretch adds compliance in series and makes a real paper trap grip less than this model at high load.
• Strand strength. There is no failure criterion here. The fiercest shipped trap computes a holding force of -; long before you reach that, a real bamboo braid tears. For a hard pull, breaking is the escape route, not slipping.
• A soft finger. The finger is a rigid cylinder. A real one compresses, which changes both R and the snugness as you pull.
• Twist. The two helix families are balanced, so their torques cancel and the trap does not unscrew. A single-handed spiral wrap would, and is not modelled.

Credit

The finger trap is a public-domain folk object with no single inventor. A one-ended German version, the Mädchenfänger, is documented from at least 1870; “finger trap” appears in an American newspaper in 1900, and a variant name with a dated ethnic prefix in a 1953 Ohio advertisement; the device is not of Chinese origin. The same braid is sold as a cable grip (the Vivien Kellems grip), as orthopaedic finger traction, and as the finger trap that secures parachute lines.

This is an independent reimplementation written from the documented geometry. It is not a copy of any program. Full provenance — every constant, its tag and its source — is in CREDITS.txt. The controls, the six named traps, the locking map and the escape game are original to this page; no physical trap was measured, so all dimensions are marked RECONSTRUCTED.

Everything here runs in your browser. There is no account, no server call and no model: the numbers are computed on the page each time you move a slider.