#### Analyzing a robot arm that moves in 3D

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We consider a robot with four joints that moves 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 revisit the fundamentals of 3D geometry that you would have learned at school: coordinate frames, points and vectors.

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Let’s recap the important points from the topics we have covered about homogeneous coordinates, image formation, camera modeling and planar homographies.

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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.

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Let’s recap the basics of homogeneous coordinates to represent points on a plane.

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Our population is getting older. Let’s look at how this ageing varies across countries, the problems it will create and how robots might help.

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The Jacobian matrix provides powerful diagnostics about how well the robot’s configuration is suited to the task. Wrist singularities can be easily detected and the concept of a velocity ellipse is extended to a 3-dimensional velocity ellipsoid.

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We revisit the important points from this masterclass.

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We start by looking at a number of different types of robot arm with particular focus on serial-link robot manipulators.

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Much of what we know about robots comes from fiction. Let’s look at fictional robots and the underlying reality.