robotics ch2

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    .

    Understand a need for representing positions and orientations

    of parts, tools, and the mechanism itself.

    Know and be able to use the special descriptions: positions,orientations, and frames.

    from frame to frame.

    Be able to use the operators: translations, rotations, andrans orma ons.

    Intelligent Robotics Lab.

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    Chapter 2 covers the mathematics used to describe positions

    and orientations in 3-space. This is extremely importantmater a : y e n t on, mec an ca man pu at on concerns tsewith moving objects (parts, tools, the robot itself) around inspace. We need ways to describe these actions in a way that is

    easily understood and is as intuitive as possible. Descriptions

    Positions orientations and frames.

    Mappings

    Changing descriptions from frame to frame.

    Translations, rotations, and transformations.

    Transformation arithmetic

    Intelligent Robotics Lab.

    Euler angles

    Computational considerations

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    , ,

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    Rotation Matrix : {B} relative to {A}

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    Descri tion of frame A relative to B : B A T

    R R=

    Inverse of a rotation matrix

    1A B B TR R R

    = =

    Description of a Frame

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    -.

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    General Frames

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    12Operators: Translations, Rotations, and

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    ~ . . ,

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    Inverse Problem

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    Z-Y-Z Euler angles

    -

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    Exercise 2.1

    2.3 2.5

    2.18

    .

    2.37

    Simulation by Matlab

    Exercise 2A 2B

    Intelligent Robotics Lab.