The following are the important dimensions and geometries concerned with toothed gear:
Pitch Circle :
Pitch circle is the apparent circle that two gears can be taken like smooth cylinders rolling without friction.
Addendum Circle :
Addendum circle is the outer most profile circle of a gear. Addendum is the radial distance between the pitch circle and the addendum circle.
Dedendum Circle :
Dedendum circle is the inner most profile circle. Dedendum is the radial distance between the pitch circle and the dedendum circle.
Clearance is the radial distance from top of the tooth to the bottom of the tooth space in the mating gear.
Backlash is the tangential space between teeth of mating gears at pitch circles.
Full Depth :
Full depth is sum of the addendum and the dedendum.
Face Width :
Face width is length of tooth parallel to axes.
Diametral Pitch :
Diametral pitch (p) is the number of teeth per unit volume.
p = (Number of Teeth) / (Diameter of Pitch circle)
Circular Pitch :
Circular pitch is the space in pitch circle used by each teeth.
Gear Ratio :
Gear ratio is numbers of teeth of larger gear to smaller gear.
Pressure Line :
Pressure line is the common normal at the point of contact of mating gears along which the driving tooth exerts force on the driven tooth.
Pressure Angle :
Pressure angle is the angle between the pressure line and common tangent to pitch circles. It is also called angle of obliquity. high pressure angle requires wider base and stronger teeth.
Pitch Angle :
Pitch angle is the angle captured by a tooth.
Pitch angle = 360/T
Contact Ratio :
Contact ratio is angle of angle of action and pitch angle.
Path of Approach :
Path of approach is the distance along the pressure line traveled by the contact point from the point of engagement to the pitch point.
Path of Recess :
Path of recess is the distance traveled along the pressure line by the contact point from the pitch point to the path of disengagement.
Path of Contact :
Patch of contact is the sum of path of approach and path of recess.
Arc of Approach :
Arc of approach is the distance traveled by a point on either pitch circle of the two wheels from the point of engagement to the pitch.
Arc of Recess :
Arc of recess is the distance traveled by a point on either pitch circle of the two wheels from the point to the point of disengagement.
Arc of Contact :
Arc of contact is the distance traveled by a point on either pitch circle of the two wheels during the period of contact of a pair of teeth.
Angle of Action :
Angle of action is the angle turned by a gear during arc of contact.