#### Build your own 3D coordinate frame

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This is an exercise in which you can build a 3D coordinate frame by printing, cutting, folding and stapling.

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This is an exercise in which you can build a 3D coordinate frame by printing, cutting, folding and stapling.

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We revisit the fundamentals of 3D geometry that you would have learned at school: coordinate frames, points and vectors.

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We discuss the structure of a right-handed 3D coordinate frame and the spatial relationship between its axes which is encoded in the right-hand rule.

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An image is a two dimensional projection of a three dimensional world. The big problem with this projection is that big distant objects appear the same size as small close objects. For people, and robots, it’s important to distinguish these different situations. Let’s look at how humans and robots can determine the scale of objects […]

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We consider the most general type of serial-link robot manipulator which has six joints and can position and orient its end-effector in 3D space.

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We consider a robot with four joints that moves its end-effector in 3D space.

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We learn how to create smoothly varying orientation in 3D by interpolating Euler angles and Quaternions. In the MATLAB example starting at 5:44 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.

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The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. For Toolbox version 10 (2017) please use UnitQuaternion instead.

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The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.

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The orientation of a body in 3D can also be described by two vectors, often called the approach and orientation vectors.