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 operation (Cartesian coordinates to polar coordinates) is possible.