A kinematic chain is the assembly of several kinematic pair

Kinematic pair

A kinematic pair is a connection between two bodies 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 notion of elements consisting of simple machines.Hartenberg & Denavit...

s connecting rigid body

Rigid body

In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...

 segments. The complexity (in terms of calculating the forward

Forward kinematics

Forward kinematics is computation of the position and orientation of robot's end effector as a function of its joint angles. It is widely used in robotics, computer games, and animation. The reverse process is known as inverse kinematics....

 and inverse kinematics

Inverse kinematics

Inverse kinematics is a subdomain of kinematics, which is of particular interest in robotics and computer animation. In contrast to forward kinematics, which calculates the position of a body after a series of motions, inverse kinematics calculates the motions necessary to achieve a desired...

) of the chain is determined by the following factors:

• Its topology
  Topology
  Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
  
  : a serial chain, a parallel manipulator
  Parallel manipulator
  Parallel robots and parallel manipulators are articulated robots that use similar mechanisms for the movement of either the robot on its base, or one or more manipulator arms...
  
  , a tree
  Tree (graph theory)
  In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...
  
   structure, or a graph
  Graph theory
  In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
  
  .
• Its geometrical
  Euclidean geometry
  Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
  
   form: how are neighbouring joints
  Kinematic pair
  A kinematic pair is a connection between two bodies 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 notion of elements consisting of simple machines.Hartenberg & Denavit...
  
   spatially connected to each other?

Explanation:-

Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system.

The term kinematic pairs actually refers to kinematic constraints between rigid bodies. The kinematic pairs are divided into lower pairs and higher pairs, depending on how the two bodies are in contact:

Formula:
L=2P-4

Where, L=No. of links, P=No. of pairs.

See also

• Linkage
  Linkage (mechanical)
  A mechanical linkage is an assembly of bodies connected together to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for...
  
  
• Grashof condition
  Grashof Condition
  The Grashof Condition is used when analysing kinematic chains. The Grashof's law or condition states that "For a four-bar mechanism, the sum of the shortest and longest link lengths should not be greater than the sum of two remaining link lengths"....