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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 .
Velocity Time physics graph We can take Δ r {\displaystyle \Delta r} by adding the top area and the bottom area. The bottom area is a rectangle, and the area of a rectangle is the A ⋅ B {\displaystyle A\cdot B} where A {\displaystyle A} is the width and B {\displaystyle B} is the height.
The JPL mobile robot ATHLETE is a platform with six serial chain legs ending in wheels. The arms, fingers, and head of the JSC Robonaut are modeled as kinematic chains. The movement of the Boulton & Watt steam engine is studied as a system of rigid bodies connected by joints forming a kinematic chain.
Dimensioned drawing of a slider-crank (left) and its kinematic diagram (right).. In mechanical engineering, a kinematic diagram or kinematic scheme (also called a joint map or skeleton diagram) illustrates the connectivity of links and joints of a mechanism or machine rather than the dimensions or shape of the parts.
Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility.In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges.
In graph theory, Mac Lane's planarity criterion is a characterisation of planar graphs in terms of their cycle spaces, named after Saunders Mac Lane who published it in 1937. It states that a finite undirected graph is planar if and only if the cycle space of the graph (taken modulo 2) has a cycle basis in which each edge of the graph ...
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
In graph theory, it is known as the circuit rank, cyclomatic number, or nullity of the graph. Combining this formula for the rank with the fact that the cycle space is a vector space over the two-element field shows that the total number of elements in the cycle space is exactly 2 m − n + c {\displaystyle 2^{m-n+c}} .