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In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-chain movable linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage. Spherical and ...
Link 1 (horizontal distance between ground joints): 4a Illustration of the limits. In kinematics, Chebyshev's linkage is a four-bar linkage that converts rotational motion to approximate linear motion. It was invented by the 19th-century mathematician Pafnuty Chebyshev, who studied theoretical problems in kinematic mechanisms.
A Chebyshev Translating Table Linkage, which combines together two cognate linkages: the Chebyshev Linkage and Chebyshev Lambda Linkage. In kinematics , the Chebyshev Lambda Linkage [ 1 ] is a four-bar linkage that converts rotational motion to approximate straight-line motion with approximate constant velocity. [ 2 ]
They can provide greater power transmission with more design flexibility than four-bar linkages. Jansen's linkage is an eight-bar leg mechanism that was invented by kinetic sculptor Theo Jansen. Klann linkage is a six-bar linkage that forms a leg mechanism; Toggle mechanisms are four-bar linkages that are dimensioned so that they can fold and lock.
An example of a simple open chain is a serial robot manipulator. These robotic systems are constructed from a series of links connected by six one degree-of-freedom revolute or prismatic joints, so the system has six degrees of freedom. An example of a simple closed chain is the RSSR spatial four-bar linkage.
These links are usually oriented 180 degrees of each other, so when pairing, these links can be fused. This creates a 4-bar linkage with two additional links, both of which are defined by the original four-bar linkage. The former ground link of the fusing 4-bar linkage becomes a rectilinear link that travels follows the same coupler curve.
The exception in this list is Watt's parallel motion, which combines Watt's linkage with another four-bar linkage – the pantograph – to amplify the existing approximate straight line movement. It is not possible to create perfectly straight line motion using a four-bar linkage, without using a prismatic joint. Watt's linkage (1784)
Burmester's approach to the synthesis of a four-bar linkage can be formulated mathematically by introducing coordinate transformations [T i] = [A i, d i], i = 1, ..., 5, where [A] is a 2×2 rotation matrix and d is a 2×1 translation vector, that define task positions of a moving frame M specified by the designer.