With the bevel gears considered so far, the axes of the ring gear and pinion intersect at a certain point. In these cases, an offset of the axes (skew axes) cannot be realized.

However, if rotational motions are also to be transmitted between axes that do not intersect, the pinion of a bevel gear unit in particular must be designed differently when the axes are offset. In particular, one no longer gets a rolling motion but a screwing motion. The pinion then forms a conical screw gear, which is then called a hypoid gear (hypoid gearbox).

With hypoid gears, rotary motions between non-intersecting axes can be realized!

As can be seen from the animation below, the positive offset increases the spiral angle of the screw gear. A positive offset means that the axis of the screw gear is shifted in the direction of the curved flanks of the ring gear (here: downwards). In the case of a negative offset, however, the screw gear is shifted against the curved flanks of the ring gear (here: upwards). If the offset is positive, the diameter of the pinion increases; or decreases if the axis offset is negative.

As the axial offset increases, the tooth line of the pinion must twist more strongly because the curved teeth of the ring gear are then inclined more strongly against the axis of the pinion.

Due to the stronger spiral shape of the teeth in the case of a positive offset, it is also achieved that several teeth are simultaneously involved in meshing (higher overlap ratio). This not only allows higher torques to be transmitted than with normal bevel gears, but also significantly reduces noise emissions.

Hypoid gears have higher load capacities and lower noise emissions than conventional bevel gears!

Hypoid gears are therefore used, for example, in differentials in the automotive industry. The figure below shows one of a total of two differential gears of a truck for the rear-wheel drive. The driving hypoid pinion and the driven ring gear with spiral toothing can be seen. The shown gearbox has a mass of about 150 kg.

The hypoid gear can ultimately be regarded as a mixture between a bevel gear and a worm gear and accordingly combines features of both variants. In particular, the bevel-shaped base bodies used for bevel gears and the screwing motion in worm drives.

Note that the basic bodies of the hypoid gears are no longer pitch bodies in the true sense. This is because the power transmission no longer takes place rolling in any contact point of the flanks but purely screwing, i.e. the tooth flanks slide permanently onto each other. Because of this gliding process, which is typical for screwing motions, hypoid gears require special lubrication with so-called hypoid gear oils.

Hypoid gears must be specially lubricated due to the screwing power transmission!

For cylindrical gears, a basic distinction can be made between external gears and internal gears. In the case of external toothing, the teeth are directed outwards on the circumference. In the case of internal gears, the teeth are directed inwards. An internal gear wheel is sometimes simply called a ring gear (although a ring gear can also have an external toothing!).

While the direction of rotation changes when two externally toothed gears are used, the sense of rotation remains the same when pairing with a internal gear. In addition, the centre distance can be shortened by using a ring gear with internal toothing instead of external toothing (with maintaining  the transmission ratio). This makes a space-saving gear design possible. Under certain circumstances, internally toothed gears can also offer better protection against dirt due to the internal teeth, if the gear unit has been designed accordingly.

The counterpart of the tooth flank profile of an external gear corresponds in principle to the tooth flank profile of an internally toothed gear. Thus the tooth profile of an external toothing is always convex, i.e. they have an outwardly curved shape (external curvature). With internal toothing, however, the tooth profile is concave, i.e. they are arched inwards (internal curvature).

When two external gears are meshing, a relatively narrow contact surface results due to the purely convex pairing of the tooth flanks. This in turn leads to a high tooth load (also called Hertzian contact stress). Therefore, the wear of the gears and tooth flanks is very high.

If, however, an externally toothed gear is paired with an internally toothed gear, the result is a convex/concave-flank pairing. The contact surfaces “nestle” up against each other, so to speak. This results in a larger contact area, which in turn results in lower tooth load. This reduces the wear of the gears. Conversely, this means that higher torques can be transmitted with the same wear with internal toothing than with the pairing of two externally toothed gears.

Even though internal gears offer many advantages compared to external gears, internal toothing is limited to a few special cases due to the relatively complex and thus expensive production. Internal gearing is used, for example, in planetary gears (epicyclic gears).

Herringbone gears

In order to combine the advantage of helical gears (higher load capacity and lower noise emission) with the advantage of spur gears (no axial forces and lower wear), so-called herringbone gears are used in special cases.

Due to the reciprocal arrangement of the helixes, each side generates an opposing axial force, which cancel each other out. This prevents axial thrusts that would have to be absorbed by bearings.

Due to the relatively long tooth length (due to the inclination), high torques can be transmitted with herringbone gearings. However, the complex and thus expensive production of such gear types is limited to special applications. (e.g. for large transmissions). Furthermore, subsequent fine machining of the teeth (e.g. by grinding) is almost impossible due to the difficult accessibility.

Herringbone gears allow high torques to be transmitted without generating axial forces. The bearing wear is correspondingly low. The production of such a gearing is very complex and therefore expensive!

Due to the complicated manufacturing process, the double helical gearing described below is often used in practice instead of herringbone gearing.

Double helical gears

The same effect as with herringbone gears is in principle achieved by the mirror-image arrangement of two helical gears, whose respective tooth flanks then also taper in the shape of an arrow. Such gears are then referred to as double helical gears.

The respective helix halves are produced on a common shaft, whereby a groove must exist in the middle for the manufacturing tool to exit. The production of a double helical gear is cheaper than the production of a herringbone gear.

Double helical gears consists of the mirror-image production of two helical gearing, with a groove in the middle between the helix halves!

In practice, it is almost not possible to assemble two separate helical gears in order to obtain a “double helical gear” due to the very precise arrangement with the mating gear.

When it comes down to reduce noises and transmit high torques, helical gears are often used. With such helical gears, the teeth no longer run as a straight line in axial direction as with spur gears, but at a certain angle (depending on the application between 20° and 45°). Since the gear wheel has a cylindrical basic shape, the tooth profile describes a segment of a helix (analogous to the spiral thread of a screw).

One can only get a straight tooth line if you imagine the teeth as a winding off (helical toothed rack), just as the unwinding of a thread also produces a straight thread line. The angle between the unwinded tooth line and the original axis of rotation is called the helix angle \(\beta\).

With helical toothing, the force for a pair of mating gears does not suddenly apply over the entire tooth width but is point-shaped (point contact!). At the end of the meshing, the force transmission does not drop abruptly, but the tooth gradually slips out, so to speak. This special meshing reduces the noise level of the gearbox significantly.

Since the circumferential forces at the beginning and end of the meshing only concentrate on a very small tooth area, these initially cause very high tooth loads. For this reason, several teeth should always be engaged at the same time in helical gears in order to distribute the load accordingly over several teeth (higher overlap ratio). If this is taken into account, helical gears can transmit higher torques than spur gears with the same dimensions.

Helical gears have a lower noise level and can transmit higher torques than spur gears!

The higher noise level of spur gears compared to helical gears can be heard very clearly, for example, in automobiles when reversing. In contrast to the gears for forward speed, the gears for the reverse speed are straight-cut toothed for cost reasons. This leads to the typical and significantly louder transmission noises while reversing!

While the tooth loads in a spur gear act purely in the circumferential direction, axial forces are generated by the pitch of the helix in helical gears. The larger the helix angle \(\beta\), the greater the axial forces will be. This must be taken into account when bearing the gear shafts. The direction of axial force depends on the sense of rotation of the helical gear.

Helical gears cause axial forces which must be absorbed by bearings!

This disadvantage due to the generation of axial forces can be eliminated by means of herringbone gears or double helical gears, as described in more detail in the next section.

Helical gears also have a negative effect on bearing wear, since the axial forces that occur lead to greater bearing forces.

The bearing wear is greater with helical gears than with spur gears!

When mating two helical gears, care must be taken to ensure that the helix angles are identical (and the module of course). Furthermore, the helix directions must be directed in the opposite direction. Analogous to screw threads, one speaks of left-hand helical gear or a right-hand helical gear (see figure above). This designation results from the direction in which the flank rises when the axis of rotation of the gear wheel is vertically aligned.

A spur gear can ultimately be regarded as a special case of helical gear with a helix angle of 0°. Accordingly, the properties of helical gears merge smoothly into those of spur gears with a decreasing helix angle. However, it should be noted that a helix angle of less than 10° offers hardly any advantage compared to spur gears!

With the gears considered so far, the axes of rotation are always parallel when meshing. With a special variant of helical gearing, gears can also be manufactured in such a way that the axes run skew, i.e. they cross each other without intersecting. In such a case one speaks of so-called screw gears or crossed helical gears (hyperboloid gears). Usually the axes of paired screw gears run at an angle of 90° to each other, but in principle any other angle is also possible.

Screw gears or crossed helical gears allow the skew mating of the gear shafts!

While the helix angles must be identical (but with different hand of helix) when pairing helical gears, paired screw gears have different helix angles (but with identical hand of helix)! The transmission ratio depends on the ratio of these helix angles by the way.

As the name suggests, the screw gears no longer show a pure rolling movement during engagement, but a screw motion. Typical for screw motions is the permanent sliding of the flanks. Thus, there are no points on the reference bodies of crossed helical gears to which a pure rolling process can be assigned (i.e. the circumferential speeds of the gears are not identical at any point). The reference bodies of screw gears are no longer “pitch bodies” but so-called rotational hyperboloids! A hyperbolioid is obtained by rotating a skew straight line around an axis of rotation.

The constant sliding of the flanks usually requires special lubrication of the screw gears (hypoid gear oil), otherwise increased wear is to be expected. Due to the screw course of the teeth, the flanks no longer touch each another line-shaped, but the contact is punctiform (exception: worm gears). In addition, the screw tooth path causes strong lateral forces, which must be absorbed constructively by an appropriate bearing.

Therefore, screw gears are designed for moderate torques and speeds, e.g. for drives for machine tools. The use of screw gears also has a disadvantageous effect on transmission efficiency, which is lower due to the sliding processes on the flanks.

The advantage of crossed helical gears, in addition to the already mentioned oblique arrangement of the gear axes, is their low-noise operation. In addition, screw gears can be shifted axially within relatively wide limits without having too much negative influence on power transmission.

Screw gears enable low noise emission in the medium load and speed range!

When pairing screw gears, which are designed as “cylindrical” helical gears, one also speaks of hyperboloid gears. However, the reference shape of screw gear can also be “conical” (see article bevel gears). Such screw bevel gears are also referred to as hypoid gears.

A special case of a screw gear is the so-called worm gear. Compared to the general case of a screw gear, the worm gear offers a line-shaped contact of the flanks and thus allows the transmission of higher torques.

If the teeth of a toothed gearwheel run in a straight line, i.e. in the direction of the rotation axis, it is referred to as a spur gear or a straight-cut gear. Such a toothing can be produced very cost-efficiently by gear hobbing, gear planing or gear shaping.

With spur gears, up to three teeth mesh simultaneously with each other. However, at least one tooth must always engage the mating gear to ensure continuous power transmission. The more teeth are engaged at the same time, the lower the load for each tooth and the higher the power that can be transmitted.

Since with spur gears the entire width of a tooth engages at the beginning of meshing, the force transmission also suddenly starts and abruptly breaks off at the end of meshing. This leads to relatively high noise levels. Spur gears are therefore only suitable for low circumferential speeds.

Spur gears are the simplest and therefore most cost-effective type cylindrical gears! Spur gears do not allow the transmission of excessive torques and speeds.

Higher rotational speeds and torques can be achieved with the helical toothing described below.

While only rotary motions occur with conventional cylindrical gears, a rack can be used to generate a linear motion. In a rack, the teeth are no longer arranged on the circumference of a cylinder, but along a straight bar (toothed bar). The mating gear of a rack is always an cylindrical gear.

The rack can be considered as a unwinding of teeth from a cylindrical gear. In principle, the rack can also be regarded as a cylindrical gear with an infinitely large diameter. In this respect, the rack is only a limiting case of a cylindrical gear.

While the tooth profile for involute gears is convex with an external toothing (external curvature) and concave with an internal toothing (internal curvature), racks have straight tooth flanks (no curvature).

A rack corresponds in principle to a cylindrical gear with an infinitely large diameter. Racks for involute gears have straight tooth profiles.

A transmission which converts a rotary motion into a linear motion by means of a cylindrical gear (called pinion) and a rack is also called a rack gear. Such rack drives are used, for example, in machine tools for moving machine slides.

Introduction

In contrast to cylindrical gears, where the rotary axes are always arranged parallel to each other, the axes of gear shafts can be rotated by any angle by using bevel gears. A shaft angle of 90° is often found. A gearbox with non-parallel axes is often referred to as an angular gear.

In bevel gearboxes, the axes of the bevel gears are usually perpendicular to each other!

The figure below shows an example of a hand drill. While the first gear stage is a spur gear, the second gear stage is a bevel gear which also serves to rotate the axis of rotation by 90°. The speed of the crank shaft is increased with gear stage in order to obtain a high rotational speed of the drill bit.

Due to its ring-shaped appearance, the larger of the bevel gears is also referred to as the ring gear. The ring gear itself is driven by a smaller bevel gear, which is then also called a pinion.

Pitch cones

With bevel gears, the shape of the gears forms a truncated cone (called pitch cone), whereby the teeth are arranged on the lateral surface. The imaginary pitch cones of two paired bevel gears roll onto each other without sliding. The peripheral speeds at the respective points of contact of the mating surface of the two pitch cones are thus identical.

The axes of the bevel gears intersect at one point, whereby the intersecting angle is usually 90°. This intersection corresponds to the point at which the tips of the imaginary pitch cones intersect when they are no longer regarded as truncated cones but as pointed cones.

Types of toothing

As with cylindrical gears, bevel gears can also have different tooth lines. The most important toothings are described in more detail in the following sections.

Straight cut tooth line

If the teeth run in a straight line, i.e. in the radial direction to the rotational axis of the gearwheel, this is referred to as straight cut bevel gear.

Such a straight cut toothing has the disadvantage already explained in the article cylindrical gears that the sudden onset of the complete face width causes high noise levels. However, this can be counteracted with spiral tooth lines described in more detail below.

Spiral tooth line

If the tooth flank line no longer runs radially outwards but with a certain twist (similar to helical toothing on cylindrical gears), then an spiral tooth line is obtained (spiral bevel gears). The spiral shape can also be involute, cycloidal or circular.

Compared to straight cut bevel gears, spiral bevel gears offer more favourable meshing conditions, higher transmissible torques and lower noise levels as well as higher installation tolerances. For this reason, spiral bevel gears are preferably used in mechanical engineering.

Planar (crown) gear

A special case of a bevel gear occurs when the pitch angle (cone angle) of the ring gear is chosen to be larger and larger and in extreme cases is 90°. The “height” of the pitch cone becomes smaller and smaller and, in the extreme case of 90°, has become a flat plane. Such a bevel gear is referred to as planar (crown) gear. The mating gear to the planar gear is a conventional bevel gear, without which a pure rolling process on the pitch plane of the planar gear would not be possible, as the circumferential speed on the rotating pitch plane decreases inwards.

Thus an shaft angle of 90° cannot be achieved with a planar gear, since the pinion would then have to be a cylindrical spur gear. However, the pitch cylinder of a spur gear has a constant circumferential speed and cannot therefore adapt to the different circumferential speeds of the planar gear! This would require an adjustment of the tooth profile on the ring gear in the radial direction – see the next section on crown gears.

The planar crown gear for bevel gears can be considered in analogy to the rack for cylindrical gears. In both cases, the originally “curved” pitch body has become a plane. In the same way as the rack profile is used as a reference for the design of cylindrical gears (see article on “Gear cutting“), the planar crown gear is used as the reference gear for bevel gears.

Crown gear

A special case of an angular gear occurs when a conventional spur gear is used as a pinion, which in principle rolls on a rack that is bent into a ring. The teeth arranged in the plane resemble the teeth of a crown in their appearance. This is why one speaks of a so-called crown gear. The tooth line of a crown gear can be either straight cut or spiral.

The animation above shows a straight cut crown gear driven by a conventional spur gear. In contrast to the bevel gear with a conical shape, the crown gear allows axial displacement of its mating gear! In addition, no axial forces occur as with conical bevel gears.

Since the circumferential speed of the crown gear increases towards the outside, but the spur gear has a constant circumferential speed, the tooth profile of the crown gear must be adapted in radial direction for a sliding-free rolling process of the pitch bodies (large pressure angle at the outside and small pressure angle inside).

The crown gear is not a bevel gear in the actual sense, since the pitch bodies are not cones anymore! In contrast to the planar crown gear, a shaft angle of 90° can be achieved with a regular crown gear. In general, the shaft angle can range be between 0° and 180°.

Operating principle

A special design of the gear wheel is the so-called worm. In this case, the tooth winds around the worm shaft like the thread of a screw. The mating gear to the worm is the worm gear. Such a gearbox, consisting of worm and worm wheel, is generally referred to as a worm drive.

The worm can be regarded as a special case of a helical gear. Imagine there was only one tooth on a helical gear. Now increase the helix angle (lead angle) so much that the tooth winds around the gear several times. The result would then be a “single-toothed” worm.

One could now imagine that instead of one tooth, two or more teeth would be wound around the cylindrical gear at the same time. This would then correspond to a “double-toothed” worm (two thread worm) or a “multi-toothed” worm (multi thread worm).

The “number of teeth” of a worm is referred to as the number of starts. Correspondingly, one speaks of a single start worm, double start worm or multi-start worm. In general, mainly single start worms are produced, but in special cases the number of starts can also be up to four.

Worms are basically spirally wound “teeth” that screw into the worm gear and drive it!

Transmission ratio

Since the number of starts is of a worm ultimately the equivalent to the number of teeth of a toothed wheels, the number of teeth to be used to determine the transmission ratio \(i\) corresponds to the number of starts of the worm:

\begin{align}
\label{uebersetzungsverhaeltnis}
&\boxed{ i = \frac{z_{\text{worm gear}}} {z_{\text{worm}}} } ~~~ \text{} z_{\text{worm}} = 1 … 4 ~~~\text{depending on the number of starts}\\[5px]
\end{align}

That the number of starts of a worm corresponds to the number of teeth of a cog wheel can also be seen clearly from the animation below of a single start worm drive. With one rotation of the worm the worm thread pushes straight on by one position. The worm gear is thus moved on by one tooth. Compared to a toothed wheel, in this case the worm actually behaves as if it had only one tooth around its circumference.

On the other hand, with one revolution of a two start worm, two worm threads would each move one tooth further. In total, two teeth of the worm wheel would have moved on. The two start worm would then behave like a two-toothed gear.

The animation below shows the comparison between a double start worm and the single start worm. Note that the worm gear driven by the double start worm rotates twice as fast as the worm gear of the single start worm (lower transmission ratio).

Due to the generally very low number of starts of the worm (usually one!) and the comparatively large number of teeth of the worm gear, the transmission ratio of worm drives is correspondingly very high. With worm drives, very high transmission ratios of more than 100 can be achieved in a space-saving manner!

Since several sections of the worm thread are generally engaged simultaneously while meshing with the worm gear, the load capacity of such worm drives is very high, i.e. very high power can be transmitted.  In addition, worm drives are very quiet due to the continuous sliding of the flanks between worm and worm gear and the required lubrication or cooling (more on this in the following section).

Worm drives are very space-saving and are suitable for transmitting high power at high transmission ratios!

Power transmission

In worm drives, power is transmitted almost exclusively through sliding between the flanks of the worm and the worm gear, i.e. the flanks slide onto each another as a screw. Worms are ultimately a special case of screw gears. In contrast to screw gears, which generate a point-shaped flank contact, worms have a linear flank contact. This results in the advantage of transmitting higher power at higher transmission ratios.

Due to the sliding processes and the associated friction on the flanks, the efficiency of worm drives is generally lower than wirh  spur gear drives or bevel gear drives. Due to the heat generated by friction, worm drives must be cooled at high power transmissions in addition to lubrication.

Worm types

Depending on the shape of the worm, worm drives can be classified differently.

Cylindrical worms

If the external shape of the worm has a cylindrical design, the worm is called a cylindrical worm. If the worm gear maps this cylindrical profile in the cross-section of the circumference, the gear wheel is called globoid worm gear. Due to the relatively simple production of a cylindrical worm, this variant is preferably used (cylindrical worm drive).

Cylindrical worms are relatively easy to produce and are preferred for cost reasons!

Globoid worms (enveloping worms)

In a modified variant, the external shape of the worm describes an arc which partly envelopes the globoid worm gear. One then speaks of a globoid worm or an enveloping worm (globoid worm drive).

Compared to a cylindrical worm, with a globoid worm it is achieved by wrapping the worm wheel that more sections of the worm thread are involved in meshing. Globoid worms can thus transfer higher powers than cylindrical worms.

The production of a globoid worm is relatively complicated compared to a cylindrical worm and therefore expensive. Such globoid worms are therefore less used.

With globoid worms (enveloping worms) higher powers can be transmitted; however, they are relatively expensive due to the complex production!

In special cases, the globoid worm can even be paired with a simple helical gear. However, this requires a special adaptation of the worm to the helical gear, which makes production correspondingly expensive. However, the advantage is the lower design effort, since the radial positioning of the worm when mating with a simple helical gear allows a greater tolerance than is the case with a globoid worm gear.

Self-locking

Transmissions are called self-locking if torque transmission can only take place in one direction. The gear unit can only be set in motion by the input shaft. However, the gear unit cannot be set in motion by the output shaft. Input and output are thus fixed.

Worm drives are often self-locking due to their special operating principle. This self-locking is due to the screw motion of the worm thread at low lead angles. Thus the worm can drive the worm wheel by its helical flank motion, but vice versa no motion can usually be produced. The contact force of the worm gear flanks against the thread flanks of the worm is so large and the lead angle just to small that the resulting frictional force prevents a rotational motion. For this reason, self-locking worm drives are always driven by the worm.

Self-locking worm drives can only be set in motion by the worm!

Note that the thread of a single start worm generally has a smaller lead angle than multi-start worms. Single start worms twist more and are therefore more often self-locking than multi start thread worms. Conversely, this means that self-locking can be prevented (if desired) with multi-thread worms.

Types of self-locking

Self-locking worm drives are used, for example, in lifting platforms. The self locking mechanism prevents the platform from moving down again on its own when the motor is switched off (statically self-locking). An additional holding brake can be dispensed with if the self-locking mechanism is large enough and cannot be released by any vibrations. If such a release should be the case, then often a “rattling” of the worm drive is to be noted.

Depending on the application, it must also be ensured that the gear unit stops automatically on its own if the motor is switched off when lowering the lifting platform (dynamically self-locking or self-braking).

As this example shows, a distinction must therefore be made between two types of self-locking:

• self-locking(statically self-locking)
  “self-locking from the resting state” (static friction is not overcome)
• self-braking (dynamically self-locking)
  “self-braking rom the operating state” (sliding friction acts as a brake)

A gearbox is considered statically self-locking if it has come to a halt and cannot be set in motion by the worm wheel under a vibration-free state!

However, vibrations or shocks can eliminate this static self-locking mechanism and cause the gear unit to start up under output-side load.

A gearbox is considered self-braking (dynamically self-locking) if the disengaged gear comes to a halt after a short time when a load on the output is present (e.g. lowering a lifting platform).

Self-locking and efficiency

Self-locking is always associated with friction, without which there would otherwise be no self-locking. Self-locking gears therefore always have a lower efficiency than comparable non-self-locking gears. Usually the efficiency of self-locking worm drives is less than 50 %. Above 50 %, worm drives are often non-self-locking.

If self-locking is not required, the focus is usually on the highest possible efficiency. Efficiencies of well over 90 % are also possible for worm drives, but without self-locking in principle. However, if for economical reasons a high efficiency is required with “self-locking”, then the gearbox must be equipped with a holding brake.

As already explained, the individual threads of a multi-start worm have a larger pitch angle and thus a lower tendency to self-locking, since the friction forces are lower due to the reduced “wedge effect”. This increases the efficiency!

Multi-start worms have higher efficiencies and a lower tendency to self-locking!

Over travel

Self-locking can become problematic when large masses are moved with the worm wheel. If the worm drive is then suddenly switched off, the worm wheel is still trying to move due to the inertia of the driven mass. However, since the worm does not allow a rotational motion due to self-locking, enormous flank loads can occur and fracture the worm.

In such cases, the worm cannot be stopped abruptly, but must rotate a little bit further after switching off the gear drive (called over travel). Special lubricants can help the worm to over travel. It may also be necessary to implement special over traveling devices that bring the transmission slowly to a standstill.

If large masses are moved with worm drives, it must be ensured that the gear does not come to a standstill immediately after switching off!

The figure below shows a selection of different gear types as they are used in mechanical engineering. A rough classification can be made as follows:

• Cylindrical gears
  • external toothed gears
  • internal toothed gears
  • toothed racks
  • screw gears (hyperboloid gears)
• Bevel gears
  • “normal” bevel gears
  • screw bevel gears (hypoid gears)
• Worm and worm gears
  • cylindrical worm and cylindrical worm gear
  • globoid worm and globoid worm gear

The most common type of gears used in mechanical engineering are cylindrical gears; they can be produced very economically. In this type, the teeth are arranged on the circumference of a cylindrical disc (called pitch cylinder).

Cylindrical gears can only mesh with each other with their respective circumferences. For this reason, the rotary axes of the different gear shafts are always parallel to each other.

With cylindrical gears, the teeth are arranged on the circumference of a (pitch) cylinder! The gear axes always run parallel to each other.