Gears are toothed machine parts that transmit motion between parallel shafts. There are several types of gears including spur gears, helical gears, bevel gears, herringbone gears, and worm gears. The speed ratio of two gears is equal to the number of teeth on the driven gear divided by the number of teeth on the driving gear. Additional key terms described include the pitch circle, addendum circle, dedendum circle, tooth thickness, space width, backlash, pressure angle, and the law governing tooth shape.

1. Gear is a toothed machine part that meshes with another toothed part to transmit motion or change speed or direction.
Classification of Gears:
Spur gears coupling two parallel shafts
Gear types

2. Herringbone gear Spiral bevel gear
Bevel gear Worm gear
Speed Ratio of Pair of Gears
The speed ratio of a pair of gears may be defined as the ratio of the angular speed of the driving gear to the angular
speed of the driven gear and is equal to the number of teeth on the driven divided by the number of teeth on the driver.
Addendum and Dedendum Circles
Addendum circle is the circle passing through the outer ends of the teeth of a gear.
Dedendum or root circle is the circle passing through the bottom of the spaces.

3. Addendum Distance and Dedendum Distance. Tooth Depth
Addendum distance or, more commonly, the addendum is the radius of the addendum circle minus the radius of the
pitch circle.
Rooth distance or dedendum is the radius of the pitch circle minus the radius of the root circle.
Total tooth depth is the sum of dedendum and addendum.
Working depth is equal to the sum of the addenda of mating gears.
Face and Flank of Tooth. Acting Flank
Face of the tooth or tooth face is that portion of the tooth curve which is outside the pitch circle.
Flank of the tooth is the part of the tooth curve inside the pitch circle.
Acting flank is that part of the flank which comes in contact with the face of the tooth of the other gear.
Face Width of Gear
Face width of the gear is the length of the gear tooth measured along an element of the pitch surface.
Clearance
Clearance is the distance measured on the line of centers between the addendum circle of one gear and the root circle
of the other, when they are in mesh.
Tooth Thickness. Space Width. Backlash
Tooth thickness, T is the width of the tooth (arc distance) measured on the pitch circle.
Space width or tooth space, S is the arc distance between two adjacent teeth measured on the pitch circle.
Backlash, B is the difference between the space width and tooth thickness.
Pitch Circles and Pitch Point

4. The circle D, drawn through P with center S, is the pitch circle of the gear A, and the circle D1 is the pitch circle of gear B.
Note that the pitch point P is the point of tangency on the center line of the pitch circles, which is equivalent to cylinders
in pure rolling contact.
Tooth Thickness. Space Width. Backlash
Tooth thickness, T is the width of the tooth (arc distance) measured on the pitch circle.
Space width, S or tooth space is the arc distance between two adjacent teeth measured on the pitch circle.
Backlash, B is the difference between the space width and tooth thickness.
Circular Pitch
The distance from the center of one tooth to the center of the next tooth, measured on the pitch circle.
Pc = circular pitch, inches; D = pitch circle diameter, inches; T = number of teeth.
Two gears that mesh together must have the same circular pitch.
Diameteral Pitch
Diamteral pitch, sometimes called as pitch number, is the term ordinarily used to designate the tooth size; it is equal to
the number of teeth divided by the diameter of the pitch circle.
Pd = diameteral pitch or pitch number.
Relation between Circular pitch and Diameteral Pitch
From and , we have:
That is, the product of the circular pitch and the diameteral pitch is equal to π.

5. Arc and Angle of Action
Arc of approach is the arc of the pitch circle where the tooth profile cuts the pitch circle when a pair of teeth first comes
in contact until they are in contact the pitch point. cP is the arc of approach on gear 4 and dP the arc of approach on
gear 2. The lengths of the arcs of approach are equal.
Arc of recess is the arc of the pitch circle from contact at the pitch point until where the tooth profile cuts the pitch circle
when the pair of teeth comes out of contact. Pe is the arc of recess on gear 4 and Pf the arc of recess on gear 2. The
lengths of the arcs of recess are equal.
Arc of action consists of the arcs of approach and recess. cPe is the arc action of gear 4 and dPf is the arc of action of
gear 2. The lengths of the arcs of action are equal.
Angle of approach, α subtends the arc of approach.
Angle of recess β, subtends the arc of recess.
Angle of action, Φ subtends the angle arc of action and is equal to the angle of approach plus the angle of recess.
The Path of Contact
Path of contact is the line drawn through all the points at which the teeth touch each other (in this case the line aPb).
Pressure Angle or Obliquity of Action
Pressure angle, θ is the angle between the line drawn through the pitch point perpendicular to the line of centers and
the line drawn from the pitch point to the point where a pair of teeth is in contact.

6. Law Governing the Shape of the Teeth
The line drawn from the pitch point to the point where the teeth are in contact must be perpendicular to a line drawn
through the point of contact tangent to the curves of the teeth; that is, the common normal to the tooth curves at all
points of contact must pass through the pitch point.
The teeth in the full-line position touch each other at a. The line ST is drawn tangent to the two curves at a. The curves
must be made so that this tangent is perpendicular to the line drawn from a to P. Similarly, in the dotted position the
libe VW which is tangent to the curves at their point of contact b must be perpendicular to the line bP.
The profiles of gear teeth may be (1) Conjugate (2) Involute (3) Cycloid, or (4) Combination of (2) and (3). In any case, the
fundamental law stated above must be satisfied.
Reference:
Elements of Mechanisms by V.L. Daughtie and W.H. James © 1954 John Wiley & Sons, Inc.