1. KINEMATIC CHAINS AND ROBOTS (III)

2. Many robots can be viewed as an open kinematic chains. This lecture continues the discussion on the analysis of kinematic analysis robots. After this lecture, the student should be able to: Solve problems of kinematic analysis using transformation matrices Kinematic Chains and Robots III

3. Link Assignment

4. Link (0): Base The base is chosen to act as link (0)

5. Link (1) The next link coupled to the base is link (1) Link (0): Base

6. The next link coupled to link (1) is link (2) Link (1) Link (2)

7. Link (3): Gripper The next link coupled to link (2) is link (3) Link (2)

8. Link (3): Gripper Link (0): Base Link (1) Summary of Link Assignment Link (2)

9. Joints Definition

10. Link (0): Base Link (1) Joint is between link (0) and link (1) Revolute joint

11. Link (2) Link (1) Revolute joint Joint is between link (1) and link (2)

12. Link (2) Revolute joint Joint is between link (2) and link (3) Link (3): Gripper

13. Link (0): Base Link (1) Summary of Links and Joints Assignment Revolute joint Link (2) Revolute joint

14. Frame-assignment

15. Define the base or reference frame {0} with origin at joint. Notice that Z 0 is pointing towards you and X 0, Y 0, & Z 0 form a right hand frame of reference. Note that this base frame is used to describe the global position of the end-effector (or gripper). X0X0 Y0Y0

16. Revolute joint The intersection between the common perpendicular of axes through and with is the origin of frame {1}. X 1 points along the common perpendicular from to. Z 1 is pointing towards you and defines the axis of rotation of joint. X 1, Y 1, & Z 1 form a right hand frame of reference. Y1Y1 X1X1

17. Y1Y1 X1X1 Remember that Z 1 is pointing towards you and defines the axis of rotation of joint, i.e.  1 is positive if link (1) rotates counter- clockwise 11

18. Revolute joint The intersection between the common perpendicular of axes through and with is the origin of frame {2}. X 2 points along the common perpendicular from to. Z 2 is pointing towards you and defines the axis of rotation of joint. X 2, Y 2, & Z 2 form a right hand frame of reference. Revolute joint Y2Y2 X2X2

19. X2X2 Y2Y2 Remember that Z 2 is pointing towards you and defines the axis of rotation of joint, i.e.  2 is positive if link (2) rotates counter- clockwise 22

20. Revolute joint Choose the origin of frame {3} on axis. Z 3 is pointing towards you and defines the axis of rotation of joint. We have selected X 3 to point along the length of link. X 3, Y 3, & Z 3 form a right hand frame of reference. X3X3 Y3Y3

21. Y3Y3 X3X3 Remember that Z 3 is pointing towards you and defines the axis of rotation of joint, i.e.  3 is positive if link (3) rotates counter- clockwise 33

22. Summary of Frame-assignment X0X0 Y0Y0 Y1Y1 X1,X1, Y2Y2 X2X2 X3X3 Y3Y3

23. X0X0 Y 0,X 1 X2X2 Y2Y2 Y1Y1 Y3Y3 X3X3 A1A1 A2A2 We shall let the above configuration to be called the home position for the robot. A 1 and A 2 are the lengths of links (1) & (2) respectively Tabulation of D-H parameters

24. X0X0 Y 0,X 1 Y1Y1  0 = (angle from Z 0 to Z 1 measured along X 0 ) = 0° a 0 = (distance from Z 0 to Z 1 measured along X 0 ) = 0 d 1 = (distance from X 0 to X 1 measured along Z 1 )= 0  1 = (angle from X 0 to X 1 measured along Z 1 )  1 = 90° (at home position) but  1 can change as the arm moves

25. X1X1 X2X2 Y2Y2 Y1Y1 A1A1  1 = (angle from Z 1 to Z 2 measured along X 1 ) = 0° a 1 = (distance from Z 1 to Z 2 measured along X 1 ) = A 1 d 2 = (distance from X 1 to X 2 measured along Z 2 ) = 0  2 = (angle from X 1 to X 2 measured along Z 2 )  2 = -90° (at home position) but  2 can change as the arm moves

26.  2 = (angle from Z 2 to Z 3 measured along X 2 ) = 0° a 2 = (distance from Z 2 to Z 3 measured along X 2 ) = A 2 d 3 = (distance from X 2 to X 3 measured along Z 3 ) = 0  3 = (angle from X 2 to X 3 measured along Z 3 )  3 = -90° (at home position) but  3 can change as the arm moves X2X2 Y2Y2 A2A2 Y3Y3 X3X3

27. Link i Twist  i Link length a i Link offset d i Joint angle  i i=000…… i=10A1A1 0  1 (  1 =90° at home position) i=20A2A2 0  2 (  2 =-90° at home position) i=3……0  3 (  3 =-90° at home position) Summary of D-H parameters

28. Summary Many robots can be viewed as an open kinematic chains. This lecture continues the discussion on the analysis of kinematic analysis robots. The following were covered: Kinematic analysis using transformation matrices