1. Inverse Kinematics CSIS 5838: Graphics and Animation for Gaming

2. Forward Kinematics What is end location/orientation of chain of bones given – Location/orientation of start of chain – Lengths of bones – Relative angles of bones © yaldex.com

3. Forward Kinematics Can compute as series of transformations – Rotate by ϴ 1 – Translate by L 1 – Rotate by ϴ 2 – Translate by L 2 –…–… © yaldex.com

4. Inverse Kinematics Given desired location/orientation of end of chain Given lengths of all joints (L 1, L 2, L 3, …) What angles (ϴ 1, ϴ 2, ϴ 3, …) would achieve that? © mathworks.com

5. Degrees of Freedom in 3 Dimensions

7. Forward Kinematics

8. Jacobian Matrix

9. Inverse Jacobian Matrix