Crossed helical gears, precision mechanics worms and crossed helical gear with rack

Crossed helical gears are helical gears that are mounted on crossed axes. Usually the shaft angle is Σ = 90°. In contrast to the line contact shown in enveloping worms, crossed helical gears only contact at one point during generation. As a result, they can only transmit very small forces, and are primarily used for control purposes.

In precision engineering, a worm wheel is often manufactured in the same way as a helical gear. This makes it easier to produce and assemble than a globoid gear manufactured using a worm-shaped cutter. In this situation, you should calculate the geometry of the worm wheel in the same way as a crossed helical gear. This is because, if the profile shift total is not equal to zero, the gear's helix angle will not match the worm's lead angle. Both gears have the same hand of gear. If the worm wheel has right-hand teeth, the same applies to the crossed helical gear. The total of both helix angles at the operating pitch diameter/spiral is exactly the same as the shaft angle. However, due to the profile shifts, the total for the helix angles at the reference circle is not identical to the shaft angle.

In special cases, the shaft angle can also be smaller than the helix angle of gear 1. In this situation, gear 2 has the opposite hand of gear to gear 1.

Gear 2 can also have internal teeth.
The following data applies to the shaft angle:

*): Applies if gear 1 and gear 2 have the same hand of gear (either both right or both left). Otherwise, a negative value for β2 must be entered.

In this chapter

Underlying principles of calculation

Basic data

Rating (load)



Crossed helical gear with rack