Known fiber placement machines use a compaction roller to press fiber material onto an application surface. The compaction roller traverses the surface, for example, from the left edge to the right edge, then lifts off of the surface, performs a 180 degree change of direction, is placed back into contact with the surface, and then moves from the right edge back to the left edge. For the purpose of illustration, if the bottom of the fiber that is pressed into contact with the mold is black when the head travels from the left to the right side of the mold, and the top of the fiber is white, when the head travels in the opposite direction from right to left, it is still the black bottom of the fiber that is pressed into contact with mold, and the white top of the fiber that is on top. Material layup time is increased because the head has to perform a 180 degree rotation in order to reverse direction, and the fiber delivery path from the wrist that supports the head to the compaction roller is complicated because the 180 degree rotation of the head at the end of every course twists the fiber delivery path through the wrist and causes dramatic changes in the path length.