Sewn signatures, capstan thread tension, a screw press and the swelling spine. Drag to orbit, wheel or pinch to zoom. Use the bar on the scene to pick signatures, cover and gold tooling, then press Start binding.
Each button recomputes the whole book for a range of values.
The science
Thread tension (capstan equation). Each time the thread wraps a cord by an angle θ, friction holds back part of the pull: T = T0 e−μθ. With μ = 0.25 and one half-turn (π) per cord, three cords leave only about 9 % of the pull at the far end, which is why binders pull the thread tight at every station. The breaking load is σbA with A = πd²/4.
Pressing. A screw press turns a torque M into a force F = 2πηM/lead (the screw is mostly friction, η about 0.2). The pressure p = F/A squeezes the stack of leaves. A paper stack is soft at first and stiffens: we use the empirical law h/h0 = 1 − a ln(1 + p/p0) (a = 0.045, p0 = 20 kPa), whose tangent modulus is E = (p0/a)(1 + p/p0).
Spine swell. The paper compresses but the thread does not, so each sewn signature adds about one thread diameter to the spine only. Spine S − fore-edge F grows with the number of signatures, giving a wedge of half-angle ψ = atan((S−F)/2w). Binders “round and back” the spine into a circle of chord S and half-angle φ: R = S/(2 sin φ).
Alignment. Each signature is knocked up (jogged) by hand with an error of standard deviation (1 − q)·1.5 mm, plus a systematic drift from the tension difference between the first and last cord divided by a grip stiffness of 8 kN/m. The fore-edge must be trimmed by the spread of the offsets.
Honest simplifications. Material constants are typical values for 90 to 100 g/m² paper and linen thread, not measurements. The thread fills the spine with exactly one diameter per signature. Glue, board hinges and paste-down are not modelled. Thickness on screen is exaggerated 4 times so the stitches are visible; every number is real. This is a virtual workshop for understanding mechanics, not a bench manual: sharp tools and presses injure real hands.
Made with Blender · Three.js. Educational only.