# 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

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2.37

Simulation by Matlab

Exercise 2A 2B

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