Degree of running
The degree of movement F used in transmission technology (also degree of mobility or degree of freedom of the transmission ) determines the number of mutually independent movements that must be initiated in a given coupling mechanism so that it is inevitable.
" Inevitability is the property that every position of any link is clearly assigned the position of the other links".
For a simple kinematic chain with one driven link, F = 1, for two independently driven links, F = 2, and so on. A running degree of zero characterizes a rigid chain.
When determining the degree of running with the help of the Grüblers equation , the respective mobility of all joints occurring in the transmission is used as their respective degree of mobility or degree of freedom . In static systems , the degree of freedom of each of the connections between the components is used to examine whether the system (e.g. a supporting structure ) as a whole is in an unrestrained immobility, whether it is statically determined .
Gruger equation
The general form of Grübler's equation is:
it stands
- Q: Degree of running
- T: type of gear (T = 6 for three-dimensional, T = 3 for spherical or plane gear)
- n: number of transmission links (including the frame )
- g: number of joints
- b i : mobility of a single joint i (b i = 1, 2, ...).
Spatial transmission
T = 6
Flat and spherical gear
T = 3
It stands
- c: number of joints with mobility b i = 1
- d: Number of joints with mobility b i = 2 (e.g. rolling and sliding at the contact points of spur gear flanks or combined thrust-pivot bearing).
Compulsory condition
The inevitability of a gear to F = 1 is checked with the so-called Grübler's forced running condition - a corresponding change in the Grübler's equation (with F = 1). For planar gears, which only have joints with b i = 1 (d = 0 and c = g), the condition is:
Values of the degree of running (gear technology)
-
: The transmission is operational.
- : The gearbox with one drive is inevitable.
- : The gearbox is inevitable if it has more than one drive. F = 2: two drives; F = 3: three drives; ...
- : The gearbox cannot run, is rigid. The exception is the so-called locked gear .
Values of the degree of freedom ( structural engineering )
The symbol for the run degree F .
The symbol for the degree of freedom is f .
For comparison with the above values for F and their respective meanings, the following are the values for f and their respective meanings.
- . There is a statically undetermined or indeterminate system. The structure (construction) is not stable.
- . There is a statically determined system. The structure is stable.
- . There is a statically overdetermined system. There are competing links that hinder the free distribution of forces.
Individual evidence
- ^ Johannes Volmer : Getriebetechnik - Koppelgetriebe , Verlag Technik, Berlin, 1979, p. 29/30
- ↑ a b c Denis Jung: Formula collection gear theory , page 5 ( PDF; 907 KB ( Memento from December 14, 2009 on WebCite ))
- ↑ Manfred Husty, Adolf Karger, Hans Sachs, Waldemar Steinhilper: kinematics and robotics . Springer-Verlag, Berlin Heidelberg 1997, ISBN 978-3-642-63822-0 , p. 281 .
- ^ Siegfried Hildebrand : Feinmechanische Bauelemente , Hanser 1968, page 628