1. Serial and Parallel Manipulators

2. Serial and Parallel Manipulators
PUMA560
Hexapod

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

4. Joints. Joints connect parts of manipulators.
The most common joint types are:
revolute link (rotation around a fixed axis)
prismatic link (linear movement)
These joints provide the DOF for an effector.

5. Homogeneous Coordinates
Homogeneous coordinates: embed 3D vectors into 4D by adding a “1”
More generally, the transformation matrix T has the form:

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

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

8. Denavit-Hartenberg Parameters
Axis i
Axis i-1
ai-1
i-1
between Xi-1 to Xi i
Link i di
distance along Zi
distance along Xi-1
between Zi-1 to Zi

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

10. 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

11. IK: Choose these angles!
Inverse Kinematics
How do I put my
hand here?
IK: Choose these angles!

12. There may be multiple solutions
One of many problems:
There may be multiple solutions
 Elbow down - Elbow up