1. Mechatronics 1
Week 3 & 4

2. Learning Outcomes
By the end of week 3-4 session, students will understand kinematics of industrial robots.

3. Course Outline
Forward Kinematics
Homogeneous Transformation Matrix.
Denavit Hartenberg (D-H) parameters.
D-H Transformation Matrix
Interpretation and application of homogeneous tranformation matrix
Inverse kinematics.

4. Homogenous Transformation Matrix
It provides information on position and orientation in a 4x4 matrix.

5. Coordinate Frame Placement (Denavit Hartenberg Concept)
ai : length of link i
di : offset distance at joint i
: joint angle of link i
: twist angle of link i
Ref. Lee, Fu, Gonzalez, 1987

6. Rotation Matrix with D-H Parameters

7. Homogenous Transformation Matrix with D-H Parameters

8. Coordinate Frame Placement (1)

9. Coordinate Frame Placement (2)

10. Homogenous Transf Matrix
Physical Intepretation ?
Ref. Craig, 1987

11. Kinematics & Inverse Kinematics
Direct Kinematics
Inverse Kinematics
Joint Coordinates
Position & Orientation of End Effector
Link Parameters

12. Inverse Kinematics
Given a desired position (P) & orientation (R) of the end-effector.
Find the joint variables which can bring the robot to the desired posture.

13. A shorter path is generally desirable
Inverse Kinematics
More difficult
Solution not unique
Redundant robot
Elbow-up/elbow-down configuration
A shorter path is generally desirable

14. Solving The Problems
Geometric approach
Algebraic approach
Numeric approach

15. Upper & Lower Configuration (Condition arises in Inverse Kinematics problems)

16. Kinematics (Mitsubishi RV-M1)

17. Limitation on Movement of Robot RV-M1
Kinematics (RV-M1)
Limitation on Movement of Robot RV-M1
Total Span
Min
Max
Waist
300o
-150o
150o
Shoulder
130o
-100o
30o
Elbow
110o 0o i ai αi di θi 1
-90º θ1 2
a2 = L2 θ2 3
a3 = L3 θ3

18. Work Space

19. Direction of Joint Movements1
150o 2
30o
100o 3
110o -