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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
An important consideration in this design process is the degree of freedom of the system of links and joints, which is determined using the Chebychev–Grübler–Kutzbach criterion. Planar mechanisms
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.
Chebychev–Grübler–Kutzbach criterion for the mobility analysis of linkages; Roberts–Chebyshev theorem on the generation of cognate coupler-curves. Other
The general mobility of a mechanism is the difference between the unconstrained freedom of the links and the number of constraints imposed by the joints. It is described by the Chebychev–Grübler–Kutzbach criterion.
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.