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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 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
Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.
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.
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.
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.
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.
In kinematics, a five-bar linkage is a mechanism with two degrees of freedom that is constructed from five links that are connected together in a closed chain.All links are connected to each other by five joints in series forming a loop.