A four-bar linkage, also called a four-bar, is the simplest movable closed chain 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.[1]
If the linkage has four hinged joints with axes angled to intersect in a single point, then the links move on concentric spheres and the assembly is called a spherical four-bar linkage. Bennett's linkage is a spatial four-bar linkage with hinged joints that have their axes angled in a particular way that makes the system movable.[2][3]
Links to animations of planar, spherical and spatial four-bar linkages are listed in the section External links.
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Planar four-bar linkages are important mechanisms found in machines. The kinematics and dynamics of planar four-bar linkages are important topics in mechanical engineering.
Planar four-bar linkages are constructed from four links connected in a loop by four one degree of freedom joints. A joint may be either a revolute, that is a hinged joint, denoted by R, or a prismatic, as sliding joint, denoted by P. The planar quadrilateral linkage is formed by four links and four revolute joints, denoted RRRR. The slider-crank linkage is constructed from four links connected by three revolute and one prismatic joint, or RRRP. The double slider is a PRRP linkage.
One link of the chain is usually fixed, and is called the ground link, fixed link, or the frame. The two links connected to the frame are called the grounded links and are generally the input and output links of the system. The last link is the floating link, which is also called a coupler or connecting rod because it connects an input to the output.
Planar four-bar linkages can be designed to guide a wide variety of movements.
Grashof's criterion for a planar quadrilateral linkage, which is a planar four-bar linkage constructed from four hinged joints, states: If the sum of the shortest and longest link of a planar quadrilateral linkage is less than or equal to the sum of the remaining two links, then the shortest link can rotate fully with respect to a neighboring link.
For a four-bar linkage, the Grashof Condition is satisfied if S+L ≤ P+Q where S is the shortest link, L is the longest, and P and Q are the other links. When the Grashof condition is satisfied, at least one link will be completely rotatable. The figure shows examples of the various cases for a planar quadrilateral linkage.[4]
