New answers tagged inverse-kinematics
3
A fixed (not dependent on any changing parameter) coordinate system transformation can be defined between the TCP and the "end of the robot" coordinate system. Depending on how you formulate CS transformations this can be a 4x4 transformation matrix or a double quaternion or any other form of expressing coordinate system transformations.
Two possibilities ...
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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 ...
2
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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