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The Chebychev–Grübler–Kutzbach criterion determines the number of degrees of freedom of a kinematic chain, that is, a coupling of rigid bodies by means of mechanical constraints. [1] These devices are also called linkages .
This linkage clearly consists of eight bars when the ground frame is counted as a bar. The Chebychev–Grübler–Kutzbach criterion shows that an eight-bar linkage must have ten single degree-of-freedom joints, while the Peaucellier linkage appears to have only six hinged joints. This is resolved by noting that four of the hinged joints each ...
This is known as Kutzbach–Grübler's equation. There are two important special cases: (i) a simple open chain, and (ii) a simple closed chain. A simple open chain consists of n moving links connected end to end by j joints, with one end connected to a ground link. Thus, in this case N = j + 1 and the mobility of the chain is
Chebychev–Grübler–Kutzbach criterion for the mobility analysis of linkages; Roberts–Chebyshev theorem on the generation of cognate coupler-curves. Other
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The mathematical derivation for the threshold at which a complex network will lose its giant component is based on the Molloy–Reed criterion. [6] > The Molloy–Reed criterion is derived from the basic principle that in order for a giant component to exist, on average each node in the network must have at least two links.
John E. Kutzbach (June 14, 1937 (Reedsburg, Wisconsin) – January 29, 2021 (Madison, Wisconsin) [1] [2]) was an American climate scientist who pioneered the use of climate models to investigate the causes and effects of large changes of climate of the past.
Barkhausen's criterion is a necessary condition for oscillation but not a sufficient condition: some circuits satisfy the criterion but do not oscillate. [5] Similarly, the Nyquist stability criterion also indicates instability but is silent about oscillation. Apparently there is not a compact formulation of an oscillation criterion that is ...