Abstract: A bi-directional pen plotter includes two pen stables and a pen holder located between the two pen stables for snatching a pen from either pen stable and for inserting a pen into either pen stable. There are four distinct stops to the motion of the pen holder at each pen stable depending on the four possible combinations of pen locations. Measuring the relative distances travelled by the pen holder in an initialization procedure the positions of all of the pens in the system may be determined uniquely.