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. Planar four-bar linkage 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 joint – also known as a pin joint or hinged joint – denoted by R, or a prismatic joint – also known as a sliding pair – denoted by P. A link that are fixed in place relative to the viewer is called a ground link. A link connecting to the ground by a revolute joint that can perform a complete revolution is called a crank link. A link connecting to the ground by a revolute joint that cannot perform a complete revolution is called a rocker link. A link connecting to a ground line by a prismatic joint is called a slider. Sliders are sometimes considered to be cranks that have a hinged pivot at an infinitely long distance away perpendicular to the travel of the slider. A link connecting to two other links is called a floating link or coupler. A coupler connecting a crank and a slider in a single slider crank mechanism is often called a connecting rod, however, it has also been used to refer to any type of coupler. There are three basic types of planar four-bar linkage, depending on the use of revolute or prismatic joints: Four revolute joints:It is denoted as RRRR, constructed from four links connected by four revolute joints. The planar quadrilateral linkage refers to all arrangements in this type.Examples of 4R linkages include: Double-crank linkage Crank-rocker (Treadle) linkage (used in pumpjacks) Double-rocker linkage (used in Ackermann steering) Parallelogram (Parallel Motion) and Antiparallelogram (Contraparallelogram, Inverse Parallelogram, Butterfly, Bow-tie) linkages Deltoid (Galloway) and Trapezium (Arglin) linkages Three revolute joints:It is denoted as RRRP, PRRR, RPRR, or RRPR, constructed from four links connected by three revolute joints and one prismatic joint. The slider-crank linkage (RRRP) is one type of arrangement such that one link is a crank, which is then connected to a slider by a connecting rod. The