An automated tape head assembly for a multiple axis tape laying machine includes a tape supply reel and a tape compaction roller. Tape from the supply reel passes through the space between the two independent structures of the supply reel and compaction roller defining a tape path that substantially maintains a zero Gaussian curvature of the tape. The tape path is a curved path referred to as a compliance loop that results from a substantially or partially unrestrained curved path between the supply reel and the compaction roller. This structure allows the compaction roller to shift laterally and vertically with respect to the supply reel while the supply reel is in a fixed position with respect to the tape head assembly generally. This structure also allows the compaction roller to roll, steer, and follow the fiber tape's natural path, all with significant independence from the supply reel.