Next: Iterative methods
The algebraic solution of equation (2) exists only for a restricted
class of cases. The joint angles could be expressed using the end
effector position. The number of nonlinear equations increases with
the DOFs ( DOFs mean equations). Each joint angle -
one by one - could be solved by the system of equations
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.