I developed the following graphics to help clarify the location of the origin and orientation of system motor axes. My hope is that these graphics will make it much easier to discuss motion control strategies for the If Then Paint cnc painting machine moving forward. 

The origin of the six axis cnc brush control machine is located at the bottom left corner of the canvas. The paint management system does not have an absolute origin. Instead, it has a home position at the -x, -y, and -z limits of the paint management system axes.  

The arrows point in the positive direction of the depicted axis. All axes have the capability to move in both directions.

The x-axis positive direction is into the paint carousel. When developing the machine movements, it's generally easier to think about machine movements relative to the "tool" (i.e. paint dispenser in this case). Since the bed (i.e. palette) is moving and the tool is stationary, a bed positive movement towards the tool can be thought of instead as a tool positive movement across the bed.