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MECH572A Introduction To Robotics

Midterm Exam. Date

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MECH572A Introduction To Robotics

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    1. MECH572A Introduction To Robotics Lecture 5

    2. Midterm Exam Date & Time: 19:00 - 21:00 ,Oct 25, 2004 Open Book Chapters 2 & 3 of the text book Note: Regular lecture will take place 18:00 –18:45 on Oct 25

    3. Review New concepts Twist of rigid body Wrench (static analysis) Instantaneous Screw of rigid-body motion Define by direction + one point Similarity between Velocity and Force/Moment Analysis Screw-like force and moment property: Wrench axis

    4. Review Acceleration Analysis Fixed reference frame: Moving Reference frame Corilios term in the expression Basics in Rigid Body Dynamics Mass properties - Mass 1st & 2nd Moment; Parallel Axes Theorem; Principle Axes/Moments (Eigenvectors/values) Equation of Motion – Newton-Euler Equations

    5. Robotic Kinematics Overview Basic Concepts Robot Kinematics - Study robot motion without resorting to force and mass properties. Dealing with position, velocity and acceleration Kinematic Chain - A set of rigid bodies connected by kinematic pairs Kinematic Pairs Upper Pair - Line/point contact (gear, cam-follower) Lower Pair - Surface contact (revolute, prismatic)

    6. Robotic Kinematics Overview Basic Concepts (cont'd) Typical Lower Kinematic Pairs Revolute (R) - 1 Dof (Rotation) Prismatic (P) - 1 Dof (Translation) Cylindrical (C) - 2 Dof (Rotation + Translation) Helical (H) - 1 Dof (Coupled Rotation/Translation) Planar (E) - 2 Dof (Translation in 2 directions) Spherical (S) - 3 Dof (Rotation in 3 directions)

    7. Robotic Kinematics Overview Basic Concepts (cont'd) Two Basic Types of Kinematic Pairs - R & P All six lower pairs can be produced from Revolute (R) and Prismatic (P)

    8. Robot Kinematics Overview Robot Manipulators Kinematic Chains : Link + Joint Rigid bodies Kinematic Pairs Basic Topologies of Kinematic Chain

    9. Robot Kinematics Overview Basic Problems in Robotic Kinematics Direct Kinematics Inverse Kinematics

    10. Denavit-Hartenberg Notation Purpose To uniquely define architecture of robot manipulator (Kinematic chains) Assumptions Links : 0, 1, …, n - n+1 links Pairs: 1, 2, … , n - n pairs Frame Fi (Oi - Xi -Yi -Zi) is attached to (i-1)st frame (NOT ith frame)

    11. Denavite-Hartenberg Notation Definition of Axes Zi - Axes of the pair (Rotational/translational)

    12. Denavite-Hartenberg Notation Definition of Axes (cont'd) Xi - Common perpendicular to Zi+1 and Zi directed from Zi+1 to Zi (Follow right hand rule if intersect) Yi = Zi ? Xi

    13. DH Notation Joint Parameters & Joint Variables ai - Distance between Zi and Zi+1 bi - Z-coordinate of Zi and Xi+1 intersection point (absolute value = distance between Xi and Xi+1 ) ?i - Angle between Zi and Zi+1 along +Xi+1 (R.H.R) ?i - Angle between Xi and Xi+1 along +Zi (R.H.R) Joint Variables ?i - R joint bi - P joint

    14. DH Notation Summary

    15. DH Notation Summary – Prismatic joint

    16. DH Notation Example - PUMA

    17. DH Notation Example - PUMA

    18. DH Notation Example – PUMA DH Parameters of PUMA Robot

    19. DH Notation Example - Stanford Arm

    20. DH Notation Example - Stanford Arm

    21. DH Notation Example - Stanford Arm (cont'd) DH Parameters of Stanford Arm

    22. DH Notation Summary

    23. DH Notation Relative Orientation and Position Analysis Orientation

    24. DH Notation Relative Orientation and Position Analysis Orientation (cont'd) (Xi, Yi, Zi) (Xi', Yi', Zi') (Xi', Yi', Zi') (Xi+1, Yi+1, Zi+1)

    25. DH Notation Relative Orientation and Position Analysis Orientation (cont'd)

    26. DH Notation Relative Orientation and Position Analysis Position To find the position vector ai in Fi frame (position vector connecting Oi to Oi+1

    27. DH Notation Relative Orientation and Position Analysis Position Observation:

    28. DH Notation Relative Orientation and Position Analysis Summary Orientation Position

    29. Direct Kinematics 6-R Serial Manipulator Problem description: Known ?1 … ?n, find Q and p in the base frame

    30. Direct Kinematics 6-R Serial Manipulator 1. Orientation With DH Parameter defined, Q1, … Q6 can be calculated.

    31. Direct Kinematics 6-R Serial Manipulator 2. Position 3. Homogeneous form (position + orientation)

    32. Direct Kinematics Some useful properties of Qi

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