Treadle Spinning Wheel

What is modelled

The treadle turns the large wheel by a crank and connecting rod. A drive band carries the motion to a small whorl on the flyer, so the flyer spins faster than the wheel in proportion to the radius ratio, less a small band slip. The yarn is drafted at a set speed while the flyer inserts turns, so the twist per centimetre is the flyer turn rate divided by the draft speed. The bobbin turns slightly slower than the flyer, and the speed difference winds the yarn on.

Equations

• Ratio i = Rwheel / rwhorl; flyer speed nf = nw i (1 - s), slip s = 0.035.
• Twist T = nf / (100 v) turns per cm, with draft speed v in m/min.
• Twist angle tan α = π d Tm for yarn diameter d and twist per metre T_m.
• Winding: bobbin lag fraction f = 0.016 + 0.10 b, differential Δ = nf f; implied bobbin diameter D = v / (π Δ).
• Linkage: the crank pin at radius 0.145 m drives a rod of fixed length 1.34 m to a pedal of 1.30 m; the pedal angle is found by bisection so the rod length stays constant.

Checks run in the page

• Ratio and flyer speed against the 3D model file.
• Twist from integrating flyer turns over a length of yarn.
• Rod length constant over a full crank revolution.
• Implied bobbin diameter inside a realistic range.

Honest simplifications

A conceptual drive: the slip is a fixed 3.5 percent, the bobbin brake is a lag fraction rather than a friction torque, the yarn diameter is a constant 1 mm for the twist angle, and the pedal is a stylised side view with no foot loads or wheel inertia. The 3D page itself notes the mechanism is interpretive, not a museum reproduction.

• Press Small whorl: the flyer speeds up and the yarn gets much more twist for the same draft.
• Press Fast draft and see the twist per centimetre fall as the yarn is pulled out faster.
• Watch the rod-length plot: it stays flat because the pedal angle always adjusts.