Although involute gears are the most common type of gear used in mechanical engineering, such as in conventional gearboxes, cycloidal gears are also used in some cases.
A cycloid is constructed by rolling a circle on a base circle. A point on the rolling circle then describes the cycloid as a trajectory.
An epicycloid is created when the circle rolls on the outside of the base. If the circle is rolled on the inside of the base circle, it is called a hypocycloid.
In cycloidal gears, the tooth face is designed using the epicycloid and the tooth flank using the hypocycloid. To ensure that the teeth of two cycloidal gears mesh correctly, the outer rolling circle for the design of the tooth face of one gear is then used as the inner rolling circle for the design of the tooth flank of the opposite gear!
Conversely, the inner rolling circle for the design of the tooth flank of one gear corresponds to the outer rolling circle for the design of the tooth face of the opposite gear.
The inner circles have a specific ratio to their base circle, as the diameter ratio determines the shape of the tooth profile. A ratio of about one to three is often found, where this ratio refers to the inner rolling circle for the construction of the hypocycloid.
An important special case of a cycloidal gear is when the rolling circle used to construct the epicycloid is made larger and larger. In the extreme case, you end up with a circle of infinite diameter which is equivalent to a rolling straight line. The resulting epicycloid is called an involute and the gear is called an involute gear.
However, the cycloidal shape of a tooth shows less wear and friction than the involute shape. In addition, compared to involute gears, cycloidal gears allow the production of gears with a significantly lower number of teeth without undercuts.
The line of action shown, along which the contact point moves, consists of two circular paths whose diameters correspond to the diameters of the rolling circles.
The fact that cycloidal gearing also obeys the law of gearing and therefore results in a constant transmission ratio is due to the fact that the rolling circles for tooth design are applied equally to both gears.
The law of gearing states that for a constant transmission ratio, the direction of force on the meshing teeth must always pass through the pitch point.
00:00 What is a cycloid (hypocycloid, epicycloid)?
01:10 How are cycloidal gears constructed?
02:11 Geometry of cycloidal gears
03:17 Special case of the epicycloid: the involute
03:42 Advantages and disadvantages of cycloidal gears
04:57 Line of action & line of contact (meshing)
05:43 nLaw of gearing
07:03 Point gearing