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.
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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.
For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.
We revisit the important points from this masterclass.
We summarise the important points from this masterclass.
We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.
We extend what we have learnt to a 3-link planar robot where we can also consider the rotational velocity of the end-effector.
For a real 6-link robot our previous approach to computing the Jacobian becomes unwieldy so we will instead compute a numerical approximation to the forward kinematic function.
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.
The relationship between world coordinates, image coordinates and camera spatial velocity is elegantly summed up by a single matrix equation that involves what we call the image Jacobian.