Mechatronics 1

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Mechatronics 1

• Week 3 4

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Learning Outcomes

• By the end of week 3-4 session, students will
  understand kinematics of industrial robots.

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Course Outline

• Forward Kinematics
• Homogeneous Transformation Matrix.
• Denavit Hartenberg (D-H) parameters.
• D-H Transformation Matrix
• Interpretation and application of homogeneous
  tranformation matrix
• Inverse kinematics.

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Homogenous Transformation Matrix

• It provides information on position and
  orientation in a 4x4 matrix.

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Coordinate Frame Placement(Denavit Hartenberg
Concept)
ai length of link i di offset distance at
joint i
joint angle of link i twist angle of link i
Ref. Lee, Fu, Gonzalez, 1987
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Rotation Matrix with D-H Parameters
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Homogenous Transformation Matrix with D-H
Parameters
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Coordinate Frame Placement (1)
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Coordinate Frame Placement (2)
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Homogenous Transf Matrix
Physical Intepretation ?
Ref. Craig, 1987
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Kinematics Inverse Kinematics
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Inverse Kinematics

• Given a desired position (P) orientation (R) of
  the end-effector.
• Find the joint variables which can bring the
  robot to the desired posture.

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Inverse Kinematics

• More difficult
• Solution not unique
• Redundant robot
• Elbow-up/elbow-down configuration

A shorter path is generally desirable
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Solving The Problems

• Geometric approach
• Algebraic approach
• Numeric approach

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Upper Lower Configuration(Condition arises in
Inverse Kinematics problems)
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Kinematics(Mitsubishi RV-M1)
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Kinematics (RV-M1)
Limitation on Movement of Robot RV-M1 Total Span Min Max
Limitation on Movement of Robot RV-M1 Waist 300o -150o 150o
Limitation on Movement of Robot RV-M1 Shoulder 130o -100o 30o
Limitation on Movement of Robot RV-M1 Elbow 110o 0o 110o
i ai ai di ?i
1 0 -90º 0 ?1
2 a2 L2 0 0 ?2
3 a3 L3 0 0 ?3
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Work Space
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Direction of Joint Movements
Joint Direction () Direction ()
1 150o 150o
2 30o 100o
3 110o -