Scroll Chuck

What is modelled

A flat Archimedean spiral (scroll) meshes with teeth under three jaws. Turning the scroll moves the jaws radially together, so the bar self-centres. The grip is the thread wedge force minus centrifugal loss at speed.

Equations

• Spiral r = r0 + p phi / (2 pi); jaw travel per scroll turn = pitch p.
• Lead angle lambda = atan(p / 2 pi r); clamp force F = T_s / (3 r tan(lambda + rho)) with rho = atan(mu).
• Efficiency tan(lambda)/tan(lambda + rho); self-locking when lambda < rho.
• Centrifugal loss m r omega^2; holding torque 3 mu F D / 2; cutting torque k_c a f D / 2.

Checks run in the page

• Lead angle formula and the self-locking comparison.
• Jaw travel per scroll and key turn.
• Symmetric jaws sum to zero.
• Thread efficiency from energy balance.

Honest simplifications

Illustrative sizes (scroll contact radius, jaw mass, gear efficiency, specific cutting force) and a single friction coefficient per contact; no jaw tilt, bar bending, backlash or dynamic imbalance. Not a machining safety tool.

• Press High speed: centrifugal force steals grip and the holding torque falls below the cut.
• Press Strong key pull: more clamp force restores the margin.
• Raise the pitch until the lead angle passes the friction angle and the chuck would loosen.