What is profile shift in gears and when is it used?

Profile shift (x coefficient) modifies gear tooth geometry by shifting the cutting tool during manufacturing. Positive shift (+x) strengthens teeth (thicker at root), reduces undercut in small gears (<17 teeth for 20deg pressure angle), but increases tip interference risk. Negative shift (-x) weakens teeth but allows closer center distances. Sum of profile shifts (x1+x2) determines center distance modification: delta_a = m.(x1+x2).cos(alpha)/cos(alpha'). Use balanced shifts (x1 = x2) to maintain sliding velocity balance. Applications: avoiding undercut, matching non-standard center distances, optimizing specific sliding, and improving load distribution.