1. About The Robot:
FANUC Robotics is one of the biggest manufacturers in the field of robotics and automation systems and has over 160,000 industrial robots installed worldwide so we considered taking one of the FANUC robots to be our case of study.
We choose the FANUC S-900W because it is a popular robot in industry world wide, The S-900 series is engineered for precision, high speed/high payload operation, user friendly set and maximum reliability. This robot is a six-axis, modular construction, electric servo-driven designed for a variety of manufacturing and system processes.
This is a small robot footprint and reduced controller size conserves floor space. Its slim arm and wrist assemblies minimize interference with system peripherals and allow operation in confined spaces. The large wrist allows moments and inertias meet a variety of heavy handling challenges. The stationary outer arm simplifies hose and cable dress out, which prolongs service life. This particular servo drive provides highest uptime and productivity and its re bust mechanical design reduces down time, increases meantime between failure and minimizes spare part requirements. Also provides longer maintenance intervals equate to lower operating costs. Its high performance motion yields fast cycle times and high throughput.

2. FIGURE (1): The FANUC S-900W
Position Analysis of the Fanuc S-900W Robot
Figure 1 shows a 6-dof manipulator manufactured by Fanuc. The coordinate frames are also shown in the diagram. The last three joint axes intersect one another at a common point P, called wrist center, which is d4 distance away from point C. The kinematics problem of this manipulator can be partitioned into two sections, one associated with the first three moving links and the other with the last three moving links. This division is useful in solving inverse kinematics where the position of the wrist center becomes independent of the hand orientation.
FIGURE (1): The FANUC S-900W

3. The resulting overall transformation matrix is given by:

4. the overall transformation matrix are given by:

5. INVERSE KINEMATICS
Knowing that Theta1 and Theta 3 have a second solution with 90 degrees difference.

6. Dynamic analysis