The joint angle is expressed using the previous angles. The last joint angle is expressed only by the end effector position and orientation.

The forward kinematics solution
for the end effector position in 2 DOF structure
could be expressed as follows:

Thus, by applying elementary trigonometry the inverse solution is:

As the DOFs for most of cases are higher, the state vector is not analytically expressible using such a trivial way. Therefore more sophisticated approaches are necessary.

Lukas Barinka 2002-03-21