2. JOINTS CS 490.006/582.001 KINEMATIC LINKAGES PAGE 36 REVOLUTE JOINT (1 DOF) TRANSLATIONAL JOINT (1 DOF) CYLINDRICAL JOINT (2 DOF) SPHERICAL JOINT (3 DOF) PLANAR JOINT (3 DOF)

3. ARTICULATED HIERARCHY CS 490.006/582.001 KINEMATIC LINKAGES PAGE 37

4. TREE-BASED HIERARCHICAL MODEL CS 490.006/582.001 KINEMATIC LINKAGES PAGE 38

5. SKELETON HIERARCHY CS 490.006/582.001 KINEMATIC LINKAGES PAGE 39

6. KINEMATICS CS 490.006/582.001 KINEMATIC LINKAGES PAGE 40 FORWARD KINEMATICS THE MODELER ROTATES OR MOVES INDIVIDUAL JOINTS TO POSE AND ANIMATE THE JOINT CHAINS INVERSE KINEMATICS THE MODELER MOVES A HANDLE TO POSE THE ENTIRE JOINT CHAIN

7. FORWARD KINEMATICS CS 490.006/582.001 KINEMATIC LINKAGES PAGE 41

8. INVERSE KINEMATICS CS 490.006/582.001 KINEMATIC LINKAGES PAGE 42

9. CASE STUDY: TWO-LINK ARM CS 490.006/582.001 KINEMATIC LINKAGES PAGE 43 1111 2222 L1L1L1L1 L2L2L2L2 x y 3333 4444

10. USING THE JACOBIAN MATRIX CS 490.006/582.001 KINEMATIC LINKAGES PAGE 44 1111 2222 L1L1L1L1 L2L2L2L2 x y  Effector Position Effector Destination yyyy xxxx