1. Direct Kinematics
Where is my hand?
Direct Kinematics:
HERE!

2. Serial and Parallel Manipulators

3. Serial and Parallel Manipulators
PUMA560
Hexapod

4. Links and Joints
Joints:
Links
2 DOF’s
End Effector
Robot Basis

5. Link Length and Twist
Axis i
Axis i-1
ai-1
i-1

6. Denavit-Hartenberg Parameters
Axis i
Axis i-1
ai-1
i-1 i
Link i di

7. Link Transformation
Axis i-1
Axis i di i
ai-1
i-1

8. Example: PUMA560

9. DK Algorithm 1) Draw sketch 2) Number links. Base=0, Last link = n
3) Identify and number robot joints
4) Draw axis Zi for joint i
5) Determine joint length ai-1 between Zi-1 and Zi
6) Draw axis Xi-1
7) Determine joint twist i-1 measured around Xi-1
8) Determine the joint offset di
9) Determine joint angle i around Zi
10+11) Write link transformation and concatenate