New answers tagged kinematics
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As far as I understand your question that you want the Jacobian matrix for the 6 DOF joint.
Let me start with very basics of robotics. You are in the vary initial phase of robotics learning. You need to understand that each joint represent a single DOF either it would be revolute or prismatic joint.
As far as spherical joint is concern, it can be ...
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I'm unable to comment due to reps shortage, so, I'm adding it as an answer. This might answer your question.
In your new attempt, the transformation of axes from origin-1 (i.e. $x_1, y_1, z_1$) to origin-2 ($x_2, y_2, z_2$) is incorrect as $x_2 \not\perp z_1$ and $x_2 \not\cap z_1$, violating DH convention.
PS: It would be better if you could update your ...
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There are 2 main rules in assigning frames following DH convention: source: Robot Modeling and Control, Spong et. al
$x_i \perp z_{i-1}$
$x_i$ intersects $z_{i-1}$
In your attempts,
Your first attempt is incorrect as your $z_2$ axis is not in the direction of actuation of the prismatic joint.
I'm not clear on your second attempt as $x_1$ appears to be ...
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Rather than rotating the box, I would attach a calibration chessboard on the box to calculate the extrinsic. If you know the homography matrix between your camera and the board you can calculate the extrinsic(have a look at zhang camera calibration method).
Or using multiple cameras is one good way around. Place two cameras so that they can see each side of ...
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