A two-axis polar-coordinate drawing machine that converts mathematical functions and vector art into physical ink drawings at wall scale, driven by NEMA 17 steppers through an Arduino running GRBL.

Problem

Most hobby plotters use Cartesian XY gantries, which scale poorly past roughly A3 because doubling the drawing area means doubling rail length, belt tension, and frame stiffness requirements. Polar-coordinate machines — one rotating arm, one radial slide — scale linearly with arm length and can draw a circle much larger than the machine's footprint. I wanted to build one both because the kinematics problem is interesting and because I wanted a tool that could render Fourier-series curves and parametric equations at sizes where the math becomes physically legible.

Role

Sole designer, fabricator, and firmware configurator.

Approach

Designed the mechanical system in Fusion 360 around two NEMA 17 steppers — one driving the rotating arm through a [NEED: belt ratio or direct drive?], one driving the radial carriage via [NEED: leadscrew, belt, rack-and-pinion?]. Printed the frame, pulleys, and arm structure on a Bambu Lab [NEED: which printer — P1S? X1C?] in PETG for the load-bearing parts and PLA for non-structural covers.

Control runs on an Arduino [NEED: Mega or Uno — check your build notes] with a CNC Shield, flashed with GRBL firmware configured for the polar kinematics. The decision I wrestled with: GRBL assumes Cartesian XY by default, so I either needed to modify the firmware to accept polar G-code directly or keep GRBL stock and preprocess Cartesian input into motor-space commands on the host side before sending. I chose host-side preprocessing. Modifying GRBL would have been the cleaner long-term solution but would have meant forking and maintaining firmware for what is fundamentally a one-off machine; a Python script that converts SVG or function input into per-motor step sequences gave me more flexibility with less risk of bricking the controller between iterations.

Four build phases: mechanical prototype, motor and firmware integration, pen-lift solenoid and path optimization, enclosure and cable management. Currently completing phase [NEED: which phase].

Outcome

[NEED: largest drawing size achieved, drawing time for a reference piece, any specific curves/functions you've plotted that are worth naming]. Physical artifacts hanging in my room.