The below images provide a touch of history of drawing robots as well as a few different designs/materialities to consider.
One of the first ‘turtle’ robots (using 2 wheels centred on a vertical axis) was made at the MIT lab in the 1970s, It was programmable using the LOGO language, and thus called LogoTurtle.
A 3D printed version of LogoTurtle that uses an Arduino. The 3D printed chassis is open sourced. This version is by Josh Burker who is using what looks to be a Lindenmayer system generative algorithm to create tree shapes.
This design also uses 3D printing, but its mechanism uses mechanical gearing techniques. It also offers a simple physical UI.
This design uses laser cut perspex pieces.
A collection of drawing robots on Pinterest
In this example (another popular design) two stepper motors are used to hang( and control) a pen on a vertically hung surface. This design more easily achieves location accuracy.