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 spatial four-bar linkages also exist and are used in practice [1].

Coordinates of the 2nd link are demonstrated in the following illustrations.

Furthermore, variation of links lengths are provided in Fig. 3.

Finally, constraint Error is depicted in the figure below .

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