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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We summarise the important points from this lecture.
A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.
We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.
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.
We consider a robot, which has two rotary joints and an arm.