Jacquard Loom Shed

What is modelled

A Jacquard head lets each warp thread be raised on its own. A row of the card strip is a 16-bit instruction: a punched hole lets a hook be lifted, a blank holds it down. When the shed opens, a raised thread is pulled up by h at the heddle eye while the cloth fell stays put, so its length grows from L to the hypotenuse and the yarn tension rises. The shed timing and the diamond, wave and twill programmes are those of the 3D page; the yarn stiffness and tension scale are assumed values.

Equations

• Thread length s = sqrt(L2 + h2), extension δ = s - L, strain δ/L.
• Tension T = T0 + EA δ / L with EA = 40 N (assumed cotton-like yarn) and T₀ = 0.015 N x tension setting.
• Lifting work per thread W = ∫ T (y/s) dy = T0δ + EA δ2/(2L).
• Shed angle atan(h / L); cloth speed rpm x pick spacing.

Checks run in the page

• Polyline length of the lifted thread against the hypotenuse.
• Numerical lifting work against the closed form.
• Hook counts by rows and by columns, and the longest float of plain weave and twill.
• A 60 s stepping of the cycle phase against rpm x pitch.

Honest simplifications

Linear elastic yarn, a symmetric shed that lifts raised threads by half the shed height, no friction in the heddles, no beat-up force and no yarn crimp. The yarn stiffness and the tension scale are illustrative, not machine calibration.

• Press Fast and slack and watch the tension graph: a short heddle distance and a tall shed pull the thread hard.
• Press Plain weave and then Long twill floats, and compare the longest float figures.
• Raise the shed height and see peak tension grow faster than linearly when the distance is short.