Power Loom Kinematics

What is modelled

The sley is a slider-crank, so its motion is not quite sinusoidal. The shuttle must cross the reed during a window of the crank turn, which fixes its speed. Opening the shed lengthens each warp thread and raises its tension.

Equations

• Sley position x = r (1 - cos t) + l (1 - sqrt(1 - (r/l)^2 sin^2 t)) and velocity r sin t (1 + (r/l) cos t / sqrt(1 - (r/l)^2 sin^2 t)) per radian.
• Shuttle travel with a smooth step: mean speed W / t_flight, peak 1.5 times the mean.
• Warp length sqrt(L^2 + a^2) + sqrt(d^2 + a^2) for a shed opening a; tension T0 + EA strain.
• Cloth rate picks per minute x 60 / (100 x picks per cm) metres per hour.

Checks run in the page

• Exact sley position against the two-term series and its error bound.
• Analytic velocity against a central difference.
• Shuttle distance and peak-to-mean ratio.
• Warp lengthening against its series and the tension rise.
• Counted picks against the cloth-rate formula.

Honest simplifications

Rigid parts, a 0.45 kg shuttle, heald-to-fell distance 0.45 m, beam-to-heald distance 1.2 m and yarn stiffness EA = 60 N are assumed figures; real looms add reed pivots, picking sticks and shed timing that differ by make.

• Press Too short a flight window: the shuttle must be much faster for the same reed width.
• Press Wide heavy cloth and compare the cloth rate with the fast narrow loom.
• Raise the shed opening and watch the warp tension climb.