Direct Kinematics- Link Coordinates
Questions:
How do we assign frames? At the Joints? At the Links?
Denavit-Hartenberg (D-H) Representation
• Associates frames with links
• Lk is the frame associated with link k,
• Lk= {xk, yk, zk} where xk, yk, zk are orthonormal vectors.
• Link(k) is “attached” to the axis xk
• Joint(k) connects link(k-1) to link(k)
• zk is the axis of motion at the frame Lk
• Joint(k) is “attached” to zk-1
COMP322/S2000/L8
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Kinematics Parameters
• Joint Angle (q ) - the rotational angle about z(k-1) to bring
x(k-1) to xk
– variable for revolute(rotational) joints
– constant for prismatic(translational) joints
• Joint Distance (d ) - the translational distance along z(k-1)
to bring x(k-1) to intersect with xk
– constant for revolute (rotational) joints
– variable for prismatic (translational) joints
Note: Refer class notes for details and diagrams
COMP322/S2000/L8
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Kinematics Parameters
• Link Twist Angle (a ) - the rotational angle about xk to
bring z(k-1) to zk
• Link Length (a ) - the translational distance along xk to
bring z(k-1) to intersect with zk
Both parameters are constants, they are the specifications of
the robot.
Note: Refer class notes for details and diagrams
COMP322/S2000/L8
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Link Coordinates
For an n-axis robot arm, the 4n kinematics parameter set if
the minimal set to specify the kinematics configuration of
the arm.
By the D-H representation convention, the numbering of
joints and links starts at the fixed base which is link 0
ending at the end-effector (the tool), link n.
The Frame at the tool:
zn, (roll) - the approach vector, usually align with z(n-1)
yn, (pitch) - the sliding vector, usually align with the openclose motion of the tool
xn, (yaw) - the normal vector, once zn and yn are determined,
xn is determined by the right-hand rule.
Note: Refer to class notes for diagrams and details
COMP322/S2000/L8
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D-H Representation (Algorithm)
An algorithm to derive the link coordinates and the
kinematics parameters of a robotic arm is given by the
reference text (Schilling, Page 54).
An example of the Alpha II robotic arm is used.
Note: Refer to class notes for diagrams and details
COMP322/S2000/L8
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