#### Velocity of 6-Joint Robot Arm – Rotation

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We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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An alternative for smooth motion between poses is Cartesian interpolated motion which leads to straight line motion in 3D space.

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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 learn the mathematical relationship between angular velocity of a body and the time derivative of the rotation matrix describing the orientation of that body.

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A more efficient trajectory has a trapezoidal velocity profile.

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We introduce spatial operators by a simple example of taking the average value of all pixels in a box surrounding each input pixel. The result is a blurring or smoothing of the input image.

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As we did for the simple planar robots we can invert the Jacobian and perform resolved-rate motion control.

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Robots today are ubiquitous in manufacturing but they can do much, much more.

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Frequently we want a trajectory that moves smoothly through a series of points without stopping.

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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.