Serial and Parallel Manipulators

1
Serial and Parallel Manipulators
2
Serial and Parallel Manipulators
PUMA560
Hexapod
3
Links and Joints
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
ai-1
?i-1
7
Link Transformation
?i
8
Denavit-Hartenberg Parameters
Axis i
between Xi-1 to Xi
?i
Link i
di
distance along Zi
distance along Xi-1
between Zi-1 to Zi
9
Direct Kinematics
Direct Kinematics HERE!
10
DK Algorithm

• 1) Draw sketch
• 2) Number links. Base0, 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
• 1011) Write link transformation and concatenate

11
Inverse Kinematics
How do I put my hand here?
IK Choose these angles!
12
One of many problems There may be multiple
solutions
 Elbow down - Elbow up