Consider a Manipulator with ‘x’ No. of DOF thereby, it has ‘x’ No. of joints. Each joint has a variable parameter (i.e. ‘θ’ for revolute joint and ‘d’ for prismatic joint) which is referred as joint parameter. For a particular set of these joint parameters of all joints, the End effector will be having a definite configuration (position and orientation). Using Forward Kinematics, we can find the End effector configuration given joint parameters in prior. As already known the main task of the Manipulator is to move from ‘point A’ to ‘point B’. Thereby we have end effector configuration and we need to find the joint parameters which is obtained through Inverse Kinematics.

Forward and Inverse Kinematics:
2 D Geometry
As you are already aware of, we can represent a point in 2D space as a 2D vector by:
X = (■(x@y))
Augmented vector: