Gear Tooth Involute Function Derivation Conversion from degrees to radians:

..

180 .

180 .

Radius of Curvature at Point “A” (an arbitrary point):

. Where:

, "A" " "

is an arc length of the “string” unwound from the basic circle and therefore it can be written as:

ρA ΘA

3602πR

πΘAR180

2πR circumference of the base circle ΘA angle deg. The same equation can be expressed in radians:

ρA ΘAR ΘA ρA

R

ΘA angle rad.

Substituting Radius of Curvature at Point “A” equation:

ΘA

.

R

And,

tan ρA

R ΘA

Also, ΘA

Therefore:

Gear Tooth Involute Function tan

angle rad. angle deg. angle rad.