#### Summary of Robot Manipulator Arms

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We summarise the important points from this masterclass.

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We summarise the important points from this masterclass.

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We learn the concepts of a robot’s task space and its configuration space, and the relationship between the dimensions of these two spaces.

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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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We describe the velocity coupling terms of the robot as a matrix which represents how the torque on one joint depends on the velocity of other joints.

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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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If your knowledge of dynamics is a bit rusty then let’s quickly revise the basics of second-order systems and the Laplace operator. Not rusty? Then go straight to the next section.

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A characteristic of inverse kinematics is that there is often more than one solution, that is, more than one set of joint angles gives exactly the same end-effector pose.

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The simplest smooth trajectory is a polynomial with boundary conditions on position, velocity and acceleration.

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The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles. Note that in the MATLAB example at 8:24 note that recent versions of the Robotics Toolbox (9.11, 10.x) give a different result: >> rpy2r(0.1,0.2,0.3)ans = 0.9363 -0.2751 0.2184 0.2896 0.9564 -0.0370 -0.1987 0.0978 […]

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We revisit the fundamentals of geometry that you would have learned at school: Euclidean geometry, Cartesian or analytic geometry, coordinate frames, points and vectors.