Turn blue knob A to enter increment of polar angle DA

Turn orange knob R to enter increment of radius DR

The X scale shows increment along the X axis: DX = DR.cos(DA)

The Y scale shows increment along the Y axis: DY = DR.sin(DA)

A pin of the pink rack slides in slots of sliders X and Y.

Two slider-crank mechanisms ensure rotation angles of orange knob and yellow gear equal.

The inverse opration (Cartesian coortinades to polar coordtinades) is possible.