Chebychev–Grübler–Kutzbach criterion

The brooder 's equations were set up in 1917 and 1918 almost simultaneously and independently both by Martin Fear God brooder ( 1851-1935 ) and Maurice d' Ocagne. They are used in the art to describe the motion of gears. The mobility of the joints connecting the transmission parts are considered. A distinction is whether these movements take place in the plane ( planar transmission ), on a spherical surface (spherical gear ) or anywhere in space (spatial transmission ).

The equations

Generally

Spatial transmission

T = 6

Planar and spherical gear

T = 3

This is

Q: degree of freedom T: Type of transmission ( T = 6 for spatial, T = 3 for spherical or planar transmission ) n: number of transmission elements g: Number of joints bi: mobility of a single joint i ( bi = 1, 2, ...) c: Number of joints with mobility bi = 1 d: Number of joints with mobility bi = 2 (for example, rolling, and slipping at the contact points of Stirnradflanken )

The unit is called degree of freedom F value of the transmission must be F ≥ 1, so that the gear can move. If F = 1, the transmission is referred to as a positively. It corresponds to the usual use that one member moved ( driven ) and will follow the other links to the positively. At F = 2, the transmission requires two drives (one each on a respective element), it is defined to move.

The Zwangläufigkeit of a transmission is the so-called brooder 's forced overflow condition - a corresponding change of the brooder 's equations - checked. For flat gear that only have joints with bi = 1, the following relationship must hold:

This relationship results from the specified level for transmission brooder 's equation by substituting F = 1, c = g and d = to 0.