Arc of Contact in Involutes Gears:

While point of contact moves along with the path of contact. Above Given figure shows path of contact CD for gears 1 and 2 while motion is transmitted. Below given figure illustrates movement of tooth of gear 1 from starting of contact at C until the ending of contact at D. While point of contact is at C the involutes profile of the tooth is at location GH. A point P′ on this profile is at pitch circle. Whereas point of contact is at P its layout is JK. At the ending of engagement at D, the profile takes the position DL along with a point on pitch circle at P″. Hence, the arc of contact is P′ P P″.

Arc of contact, P′ P P″ = Arc of approach P′P + Arc of recess PP″

Arc of approach, P′P = ω₁ r × Time of approach (t_a)

Arc of recess, P′P = ω₁ r × time of recess (t_r)

. . . (9.4)