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Robotic Systems(3)
Dr Richard Crowder
School of Electronics and Computer Science
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Robot Kinematics
Requires a unified approach to identify the variables of arobots or manipulator's joints and links.
Robotics depends on the use of right handed Cartesian
frames of reference.
X
Y
Z
+ve rotation
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Link - 1
A link holds two joints apart.
The axes of the joints are always along the Z axis of theoriginating frame.
The link axis is always along the X axis of the originatingframe.
The normal displacementbetween the two frames is giventhe symbol, a.
The twist angle between the two joint frames is given thesymbol, .
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Link - 2
a
Joint 1
Joint 2
Note direction of
rotation
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Link - 3
Z1
Z2
X1
Y2
J1
J2
X2
Y2
a1
Joint displacement = a1
Twist angle = 1 = 270o or -90o
1
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Joint
Rotary or Prismatic identical kinematic geometry
The displacement between two links is along the Z-axis and is given
the symbol d, and is the variable in the prismatic joint.
The angle between the two links is , and is the variable in a revolutejoint.
Link 1
Link 2
Z1
Z2
X1
Y1
X2d1
1
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Geometric parameters
A manipulator consists of a collection of joints and links,organised intojoint-link pairs.
While the sequence through the manipulator chain is
arbitrary, the selection should minimised the number of variables,
and reflect the mechanical arrangement,
and the sense of rotation of a revolute joint.
The effect of reversing the sense changes a variable from to 360- .
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Example
Joint 5
S1
S2 S3
S4
Joint 1
Joint 4
Joint 2
Joint 3
Determine the 5 joint-link
Pairs for the manipulator
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Joint 1
1d
q
a
a
S1
S2 S3
S4
Joint 1
Joint 4Joint 2
Joint 3
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Joint 2 and Joint 3
2 3
d
q
a
a
S1
S2 S3
S4
Joint 1
Joint 4Joint 2
Joint 3
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Joint 4
Joint 4
Joint 5
4d
q
a
a
S1
S2 S3
S4
Joint 1
Joint 4Joint 2
Joint 3
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Joint 5
5d
q
a
a
S1
S2 S3
S4
Joint 1
Joint 4Joint 2
Joint 3
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Example
S1
S2 S3
S4
Joint 1
Joint 4
Joint 2 Joint 5
Joint 3
i 1 2 3 4 5
di S1 0 0 0 S4
qi 1 2 3 4 5
ai 0 S2 S3 0 0
ai 270 0 0 90 0
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Example 2
S1
Joint 3 S3
S4
Joint 1
Joint 5
Joint 2 Joint 6
Joint 4 Determine the 6 joint-link
Pairs for the manipulator
i 1 2 3 4 5 6
di S1 0 S2 0 0 S4
qi 1 2 0 4 5 5
ai 0 0 0 S3 0 0
ai 90 90 270 0 90 0
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Example 3
Joint 2
Joint 4
S4
Joint 1
Joint 3
Joint 6
Joint 5
Determine the 6 joint-link
Pairs for the manipulator
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Example 4
Joint 1
Joint 2
Joint 3
Tool
Interface