 Gear path of contact

The gear path of contact is the locus of actual tooth-contact points during an engagement. For a conventional external involute pair, its active part is a finite straight segment of the gear line of action. Its endpoints are set by the usable tooth flanks, rather than by the infinite geometric line alone. The part before the gear pitch point is the gear path of approach; the part after it is the gear path of recess in the stated direction of transmission.^[ref]

For a standard noninterfering external pair driven by gear1, let $r_{ai}$ be tip radii, $r_{bi}$ base radii, $r_{wi}$ operating radii and ${\alpha }_w$ the operating pressure angle. When tip circles bound the full usable contact,Adding gives $L=L_{\mathrm{app}}+L_{\mathrm{rec}}$. The two lengths need not be equal even when the gears use the same module and reference angle.

For the original module2,20/40-tooth example at20degree reference angle and60mm standard separation, tip radii22 and42mm give $L_{\mathrm{app}}\approx 5.0586\mathrm{mm}$ and $L_{\mathrm{rec}}\approx 4.5960\mathrm{mm}$. Their sum is $9.6546\mathrm{mm}$; dividing by gear base pitch $5.9043\mathrm{mm}$ gives transverse gear contact ratio about1.6352.

These are distances along the line of contact, not arc lengths traveled around a pitch circle. A shortened or altered flank can reduce the active interval, and interference can invalidate the full tip-limited construction. The labels approach and recess also depend on which direction is being followed. A practical contact inspection therefore needs the profile geometry and transmission direction, not just a sketch of two nominal pitch circles.