KINEMATIC CHAIN: Refers to an assembly of rigid bodies connected by joints that is the mathematical model for a mechanical system. As in the familiar use of the word chain, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator.
KINEMATIC PAIR:Refers to Mathematical models of the connections, or joints, between two links. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called lower pair and the surface contact joints critical to cams and gearing, called higher pair. These joints are generally modeled as holonomic constraints