1. Inverse Kinematics Problem: Input: the desired position and orientation of the tool Output: the set of joints parameters

2. Kinematics equations of this arm: The structure of the transformation: Algebraic Solution

3. We are interested in x, y, and (of the end-effector) By comparison of the two matrices above we obtain: And by further manipulations: and …… Algebraic Solution (cont.)

4. Example 1 100L1L1 2L2L2 0 300

5. Kinematic Equations of The Arm

6. Target By comparison we get:

7. Kinematic Equations - Solution

8. Example 2 100L1L1 200 3L2L2 00 4L3L3 00

9. Example 2 (cont.)