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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 version of the kinematic diagram has proven effective in enumerating kinematic structures in the process of machine design. [2] 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.
Kempe's design procedure has inspired research at the intersection of geometry and computer science. [7] [8] In the late 1800s F. Reuleaux, A. B. W. Kennedy, and L. Burmester formalized the analysis and synthesis of linkage systems using descriptive geometry, and P. L. Chebyshev introduced analytical techniques for the study and invention of ...
This version of the kinematic diagram has proven effective in enumerating kinematic structures in the process of machine design. [1] 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.
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.
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In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and, working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. [8] In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.