#### Right-Handed 3D Coordinate Frame

lesson

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.

lesson

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.

lesson

We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.

lesson

We can also derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different 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.

lesson

We can describe the relationship between a 3D world point and a 2D image plane point, both expressed in homogeneous coordinates, using a linear transformation – a 3×4 matrix. Then we can extend this to account for an image plane which is a regular grid of discrete pixels.

lesson

We introduce the idea of attaching a coordinate frame to an object. We can describe points on the object by constant vectors with respect to the object’s coordinate frame, and then relate those to the points described with respect to a world coordinate frame. We introduce a simple algebraic notation to describe this. Try your […]

lesson

We summarise the important points from this lecture.

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We consider the simplest possible robot, which has one rotary joint and an arm.

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We learn how to describe the orientation of an object by a 2×2 rotation matrix which has some special properties. Try your hand at some online MATLAB problems. You’ll need to watch all the 2D “Spatial Maths” lessons to complete the problem set.

lesson

We learn a method for succinctly describing the structure of a serial-link manipulator in terms of its Denavit-Hartenberg parameters, a widely used notation in robotics.