Joint Velocities and Manipulator Mechanism Design

1
Joint Velocities and Manipulator Mechanism
Design

• Contents of lecture
• Resume
• Joint Velocity
• Jacobian
• Singularities
• Selection of Manipulators

2
Direct Kinematics
Direct Kinematics HERE!
3
Denavit-Hartenberg Parameters
Axis i
ai
di
Link i
?i
4
Affixing frames to links
1) Identify the joint axes and draw lines along
them. For step 2 through 5 below consider two of
these neighboring lines 2) Identify the common
perpendicular between them, or point of
intersection. At the point of intersection, or at
the point where the common perpendicular meets
the ith axis, assign the link frame origin.
3) Assign Zi pointing along the direction of
axis i. 4) Assign Xi pointing along the common
perpendicular, or if the axes intersect, assign
Xi to be normal to the plane containing the two
axes. 5) Assign Yi to complete a right-hand
coordinate system. 6) Assign 0 to match 1
when the joint variable is zero. For N choose
an origin location and XN direction freely, but
generally so as to cause as many link parameters
as possible to become zero.
5
Denavit Hartenberg Parameters
ai the distance from Zi to Zi1 measured along
Xi ?i the angle between Zi to Zi1 measured
about Xi di the distance from Xi-1 to Xi
measured along Zi ?i the angle between Xi-1 to
Xi measured about Zi
6
Link transformation
7
Link parameters
8
Inverse Kinematics
How do I put my hand here?
IK Choose these angles!
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Velocity Propagation
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Velocity Propagation (cont.)

• Rotational velocities may be added as vectors

Where
Also
With respect to the linear velocity
11
An Example
V3
L2
L1
12
Task Dependent requirements

• Workspace
• Must reach a number of fixtures and workpieces
• Air around fixtures and workpieces in order to
  avoid collisions
• Consider the shape and singularities
• Load capacity
• Speed
• Repeatability and accuracy

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Degrees of Freedom (DOF)

• General positioning and orienting requires 6
  degrees of freedom (DOF).
• Tasks with with symmetric tool requires only 5
  DOF (welding, grinding, polishing etc.)

• Positioning parts on planar surface (pick and
  place) requires only 4 DOF (X,Y,Z and ?).

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Degrees of Freedom (DOF)

• Application of external tilt/roll manipulators
  may be required due to process requirements
  (welding)

• Externally applied DOFs counts in the system.
  I.e. symmetric tool and 2 External DOFs leaves
  only a requirement for 3 DOFs in the robot.
• Symmetric parts may reduce the number of required
  DOFs.

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Kinematic configuration

• Number of joints equals number of DOFs for serial
  kinematic linkages.
• Positioning structure and orienting
  structure/wrist.
• Classification according to first 3 joints
  (positioning structure)

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Kinematic configuration
Articulated (RRR)

• Two shoulder joints (vertical horizontal
  elevation) and an elbow joint parallel to the
  elevation joint.
• Provides the least intrusion of the manipulator
  structure into the workspace.

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Kinematic configuration
Cartesian (TTT)

• Stiff structures allow construction of large
  robots, often referred to as gantry robots.
• Does not produce kinematic singularities for
  first 3 axes.
• All feeders, fixtures and other equipment must be
  placed inside the robot

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Kinematic configuration
Scara (RRT)

• Three revolute parallel joints allowing it to
  move and orient in plane.
• First three joints dont support weight of
  manipulator/tool/workpiece.
• Usually very fast robots.
• Well suited to pick and place.

21
Kinematic configuration
Spherical (RRT)

• Much like articulated robot, except that joint 3
  is prismatic.
• More suitable than articulated robot for some
  applications (entering narrow holes).

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Kinematic configuration
Cylindrical

• Much like spherical robots, except that joint 2
  is prismatic.
• More suitable to some applications than
  articulated and spherical robots.

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Kinematic configuration
Closed structures

• Increased stiffness
• Reduced allowable range of motion

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Bukning
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Skitse af bukkecelle I
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Skitse af bukkecelle II
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Opgave

• Find the Jacobian of the manipulator with three
  degrees of freedom from Exercise 3 of chapter 3.
  Write it in terms of a frame 4 located at the
  tip of the hand with the same orientation as
  frame 3.