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. Grashof condition The Grashof condition for a four-bar linkage 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. In other words, the condition is satisfied if S + L ≤ P + Q, where S is the shortest link, L is the longest, and P and