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End effector End effector - the last coordinate system of figure Located in joint N. But usually, we want to specify it in base coordinates. 1

# End effector

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rasul

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• #### base coordinate frame

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End effector. End effector - the last coordinate system of figure Located in joint N . But usually, we want to specify it in base coordinates . 1. End effector. A transformation from the link N to the base : . 2. End effector. We can also express it as - PowerPoint PPT Presentation

### Text of End effector

End effector•End effector - the last coordinate system of

figure•Located in joint N.•But usually, we want to specify it in base

coordinates.

1

End effectorA transformation from the link N to the

base :

2

End effector•We can also express it as •three rotations (around each of the

coordinate axes)• followed by a translation

•How can we establish a relation with the other expression ?

3

End effector•The origin of a coordinate frame

relative to some base coordinate frame is specified by the translation :

4

End effector•Any 3D orientation relative to some base coordinate frame can be specified by :three rotations, one around each of the coordinate axes.

We do them in this order : around x, y, z. 5

End effector

6

End effector•Orientation•The roll, pitch and yaw

transformation is then expressed :

7

End effector•Finally, the transformation from a coordinate

frame to the base frame is expressed :

8

End effector

We obtain directly the translation vector :

9

End effector

We can obtain the yaw angle :Because :

arctan is π-periodic. Let’s use our function arctan2 to get the right angle.

10

End effectorKnowing the yaw angle, we can obtain the pitch angle :

Because :

Again, let’s use our function arctan2 :

11

End effector

We can obtain the roll angle :

Because :

Again, let’s use our function arctan2 :

12

21

11

sin cos sinarctan arctan arctancos cos cos

mm

2 21 11( , )arctan m m

End effectorLet’s define the state vector

13

End effectorAs previously shown,

The state vector is composed of elements of this matrix. It’s also a function of joint parameters :

14

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