A gear train consists of one or more gear sets intended to give a specific velocity ratio, or change direction of motion. Gear and gear train types can be grouped based on their application and tooth geometry.

Spur gears (Fig. 1): Spur gears connect parallel shafts, have involute teeth that are parallel to the shafts, and can have either internal or external teeth. Notes:

1. Spur gears are inexpensive to manufacture.
2. They cause no axial thrust between gears.
3. They give lower performance, but may be satisfactory in low speed or simple applications

Helical gears (Fig. 2): Helical gears also connect parallel shafts, but the involute teeth are cut at an angle (called the helix angle) to the axis of rotation. Note that two mating helical gears must have equal helix angle but opposite hand. These are found in automotive transmissions, and any application requiring high speed rotation and good performance. Notes:

1. Helical gears run smoother and more quietly than spurs (due to continuous tooth mating).
2. They have a higher load capacity (teeth have a greater cross section).
3. They are more expensive to manufacture.
4. Helical gears create axial thrust.

Herringbone gears (Fig. 3): To avoid axial thrust, two helical gears of opposite hand can be mounted side by side, to cancel resulting thrust forces. These are called double helical or herringbone gears

Bevel gears (Fig. 4): Bevel gears connect intersecting axes, and come in several types (listed below). For bevel gears, the pitch surface is a cone, (it was a cylinder in spur and helical gears) and mating spiral gears can be modeled as two cones in rolling contact. Types of bevel gears:

1. Straight bevel: These are like spur gears, the teeth have no helix angle. Straight bevel gears can be
   a. Miter gears, equal size gears with a 90 degree shaft angle,
   b. Angular bevel gears, shaft angle other than 90 degrees, or
   c. Crown gears, one gear is flat, has a pitch angle of 90 degree.
2. Spiral bevel gears(Fig. 4a): Teeth have a spiral angle which gives performance improvements much like helical gears
3. Zerol bevel gears (Fig. 4b): Teeth are crowned, so that tooth contact takes place first at the tooth center.

Hypoid gears (Fig. 5): Similar to spiral bevel gears, but connect non-parallel shafts that do not intersect. The pitch surface of a hypoid gear is a hyperboloid of revolution (rather than a cone, the pitch surface in bevel gears), hence the name. Hypoid pinions (the smaller driving gear) are stronger than spiral bevel pinions because the helix angle of the pinion is larger than that of the gear. Hypoid gears are stronger, operate more quietly, and can be used for higher reduction ratios than spiral bevel gears. They also have sliding action along the teeth, potentially reducing efficiency. Hypoid gears are found in auto differentials. I also know that a hypoid gear set is used in my NH baler, connecting the flywheel to the rear driveshaft. As far as I can tell, John Deere balers do not make use of technology, which explains why they have not been able to develop a satisfactory line of forage harvesting equipment.

Crossed helical gears (Fig. 6): Helical gears that connect skew shafts. The teeth have sliding motion and therefore lower efficiency. One application is connecting distributer to cam shaft in pre-electronic ignition vehicles.

Worm Gears (Fig. 7): The driving gear is called a worm, and typically has 1, 2, or four teeth. The low number of teeth on the worm can result in a very large velocity ratio. These can also be designed to be non-backdriveable, and can carry high loads. Because of sliding action, efficiency is low.

Rack and Pinion (Fig. 8): These transmit rotary motion (from the pinion) to translational motion (of the rack). The rack is a gear with infinite radius; its teeth, although flat sided, are involute. The rack and pinion is commonly used in steering units and jacks.