The Straightedge

A planar linkage — fixed pivots, rigid rods, pin-joints — turned by a crank. The Peaucellier–Lipkin (1864) was the first to convert pure rotation into a mathematically exact straight line, by circle inversion. Drive the crank and watch the pen draw.

Linkage

Crank angle

Speed

Long bar L — the two equal arms from the pivot O

Rhombus side ℓ — the four equal bars (must be < L)

Crank a

Coupler offset (pen position on the coupler)

Trace

Play

Presets

Skin

The pen sits where the rhombus closes. O is the fixed pivot; the small crank spins the joint Q on a circle that passes through O — and its circle-inverse P rides a perfectly straight rail. Skins change only colour & material, never the geometry.