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 is 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 inverted slider-crank is another type of arrangement such that there are two cranks with a slider acting as the coupler.Examples of 3R1P linkages include: Single-slider crank mechanism (used in internal combustion engines) Whitworth Quick Return mechanism (used in early types of shapers) Crank and slotted lever Quick Return mechanism (used in shapers) Fixed piston mechanism (used in hand pumps) Two revolute joints and two prismatic joints:It is denoted as PRRP, and is constructed by connected two sliders with a coupler link. The doubler slider refers to all arrangements in this type.Examples of 2R2P linkages include: Trammel of Archimedes (Elliptical trammel) Scotch yoke (slotted link) mechanism (used in valve actuators) Oldham's coupling
Planar four-bar linkages can be designed to guide a wide variety of movements, and are often the base mechanisms found in many machines. Because of this, the kinematics and dynamics of planar four-bar linkages are also important topics in mechanical engineering.
Planar quadrilateral linkage
Planar quadrilateral linkage, RRRR or 4R linkages have four rotating joints. 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, sometimes called the input link and output link. The last link is the floating link, which is also called a coupler or connecting rod because it connects an input to the output.
Assuming the frame is horizontal there are four possibilities for the input and output links: A crank: can rotate a full 360 degrees A rocker: can rotate through a limited range of angles which does not include 0° or 180° A 0-rocker: can rotate through a limited range of angles which includes 0° but not 180° A π-rocker: can rotate through a limited range of angles which includes 180° but not 0° Some authors do not distinguish between the types of rocker.