Kinematic pair

A kinematic pair is a connection between two physical objects that imposes constraints on their relative movement. Franz Reuleaux introduced the kinematic pair as a new approach to the study of machines that provided an advance over the motion of elements consisting of simple machines.
Description.
Kinematics is the branch of classical mechanics which describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion. Kinematics as a field of study is often referred to as the "geometry of motion". For further detail, see Kinematics.
Hartenberg & Denavit presents the definition of a kinematic pair:
In the matter of connections between rigid bodies, Reuleaux recognized two kinds; he called them higher and lower pairs (of elements). With higher pairs, the two elements are in contact at a point or along a line, as in a ball bearing or disk cam and follower; the relative motions of coincident points are dissimilar. Lower pairs are those for which area contact may be visualized, as in pin connections, crossheads, ball-and socket joints and some others; the relative motion of coincident points of the elements, and hence of their links, are similar, and an exchange of elements from one link to the other does not alter the relative motion of the parts as it would with higher pairs.In kinematics, the two connected physical objects, forming a kinematic pair, are called `rigid bodies’. In studies of mechanisms, manipulators or robots, the two objects are typically called ‘links’.
Lower pair.
A lower pair is an ideal joint that constrains contact between a surface in the moving body to a corresponding in the fixed body. A lower pair is one in which there occurs a surface or area contact between two members, e.g. nut and screw, universal joint used to connect two propeller shafts.
Cases of lower joints:
Higher pairs.
Generally, a higher pair is a constraint that requires a curve or surface in the moving body to maintain contact with a curve or surface in the fixed body. For example, the contact between a cam and its follower is a higher pair called a "cam joint". Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints, as is a wheel rolling on a surface. It has a point or line contact.
Wrapping pair/ Higher pair.
A wrapping/higher pair is a constraint that comprises belts, chains, and such other devices. A belt-driven pulley is an example of this pair.
In this type of which is very similar to the higher pair (which is having point or line contact), but having multiple point contact...
Joint notation.
Context.
Mechanisms, manipulators or robots are typically composed of links connected together by joints.  Serial manipulators, like the SCARA robot, connect a moving platform to a base through a single chain of links and joints.  In robotics the moving platform is called the `end effector’.   Multiple serial chains connect the moving platform to the base of parallel manipulators, like the Gough-Stewart mechanism.  The individual serial chains of parallel manipulators are called `limbs’ or ‘legs’. Topology refers to the arrangement of links and joints forming a manipulator or robot.  Joint notation is a convenient way of defining the joint topology of mechanisms, manipulators or robots.
Abbreviations.
Joints are abbreviated as follows: prismatic "P," revolute "R", universal "U", cylindrical "C", spherical "S", parallelogram "Pa".  Actuated or active joints are identified by underscores, i.e., "P," "R", "U", "C", "S", "Pa".
Notation.
Joint notation specifies the type and order of the joints forming a mechanism. It identifies the sequences of joints, starting from the abbreviation of the first joint at the base to the last abbreviation at the moving platform.  For example, joint notation for the serial SCARA robot is "RRP" , indicating that it is composed of two active revolute joints "RR" followed by an active prismatic "P" joint.  Repeated joints may be summarized by their number; so that joint notation for the SCARA robot can also be written 2"RP" for example. Joint notation for the parallel Gough-Stewart mechanism is "6-UPS" or "6(UPS)" indicating that it is composed of six identical serial limbs, each one composed of a universal "U", active prismatic "P" and spherical "S" joint.  Parentheses "()" enclose the joints of individual serial limbs. 