The link diagram presented in the previous chapter suffices for our presentation. The Figure 1.1 represents the arm and forearm as links joined at the elbow. We will consider the two dimensional motion represented by Figure 1.1.
The movement of the robotic arm is represented by the coordinates
of the joints in the X-Y plane.
These coordinates are determined by he angle, 
,
that the arm makes with the body, by the angle, 
, that the
forearm makes with the arm, and by the lengths of the links.
As before the angle 
will be measured in degrees counterclockwise
from the positive Y axis.
The angle 
will be measured in degrees clockwise from the arm to
the forearm.
The equations that describe the X-Y position of the robotic elbow joint
as functions of the shoulder angle 
, are:
and
The equations that describe the X-Y position of the wrist joint
as a function of the angle of the robotic elbow joint 
, are:
and
In summary:
The Equations 1.2 and 1.1, result in a system of two coupled non-linear equations in two variable. This is but one example of a type of problem occurring frequently in computational science and engineering. How to obtain the solutions of a system of n simultaneous nonlinear equations in n unknowns? These problems are generally much more difficult than for a single equation and one unknown. An obvious strategy is to generalize Newton's method.
