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.

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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

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    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

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