Where – translation matrix with respect to a axis, and – rotational matrix with respect to a axis. H – homogeneous transformation matrix, which contains the position and rotation of the endpoint in global coordinates. ( is already included in because there is no difference where is located on this link)
With direct kinematics for an ordinary manipulator, everything is pretty simple. And what about the inverse? At a minimum, it’s worth to repeat that it is ambiguous. Let’s start with the two-links manipulator.
I will not copy Wikipedia, tell in my own words. Forward (direct) kinematics is when we know the positions of the motors in the joints and we want to find the position of the gripper (if we take the example of a manipulator).