RLH
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Inertial frame VS Body-fixed frame momentum correction factor
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1 votes

The cross-product correction factor shows up any time we take the time derivative of a vector described in a moving frame. When I teach this topic in my classes, I generally introduce it when talking ...

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Compute path in absolute frame from sequence of measurements
1 votes

Each step can be represented by its transformation matrix, $$ \begin{bmatrix} \cos{\theta'_{i}} & -\sin{\theta'_{i}} & x'_{i}\\ \sin{\theta'_{i}} & \phantom{-}\cos{\theta'_{i}} & y'_{...

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Design optimization method using indices
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I think it is likely that you are confusing two uses of the word “singular”: The singular values of a matrix as found via singular value decomposition. The singular configurations (or singularities) ...

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Name of imitating motion technique in Robotics
2 votes

A robot manipulator that’s designed to mimic an operator in real-time can be called a “waldo” or "telemanipulator". The term "waldo" originates from Robert Heinlein, and was widespread enough at least ...

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Difference between constant curvature kinematics and rigid link kinematics
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2 votes

Rigid link kinematics assumes that the robot is made of rigid structural elements connected by pivot or sliding joints, and describes the locations of points on the robot (or more generally, the ...

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Jacobian to determine the linear velocity of each node (DOF 3 RRR robot arm)
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1 votes

Your axes and link vectors seem off. The axes $z_{1}$ and $z_{2}$ should be parallel, and your $O^{0}_{2}$ and $O^{0}_{3}$ don’t seem to be accounting for all the rotations that occur prior to the ...

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Controlling the pose of a manipulator using inverse kinematics
1 votes

If I understand correctly, your end effector is at pose A, you want to move it to pose B, and you have Jacobian pseudo-inverse control set up so that you can specify a pose velocity $v$ and get a ...

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Understanding Twists as 3D Velocities
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For your second question: Moving in the xy plane, rotating around the z axis can be treated as instantaneously rotating around a "virtual center", located along the line perpendicular to the xy ...

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Why with the pseudo-inverse it is possible to invert the Jacobian matrix even in a singular configuration?
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6 votes

The pseudoinverse gives a “least squared error, minimum-norm” solution: Out of all $\dot{q}$ vectors at your current $q$, the vector $$\dot{q}_{s} = J^{+}(q)\dot{p}_{\text{in}}$$ satisfies two ...

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Screw Axes in the Base Frame
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1 votes

If I'm understanding you correctly, you're attempting to put the position of the joint in for the translational velocity component of the screw axis. What you actually want to put in there is the ...

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How to understand the angular velocity of link i+1?
3 votes

What bewilders me most is I don't think every point on Link 2 share the same angular velocity with respect to joint 1, because the axis of rotation is not joint 1. Then how come $^1\omega_2$ be ...

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How to compute the orientation error between two 3D coordinate frames?
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5 votes

The rotation error between two frames can be viewed in two ways: The orientation of one frame as seen from the other, calculated by multiplying the inverse of the observing frame by the observed ...

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Why applied joint torque will affect another joint?
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3 votes

When you apply torque to the first joint, it makes the first link rotate. This means that the far end of the first link translates. Because the second joint pins the near end of the second link to the ...

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Velocity description in Screw Motion Theory
3 votes

The body velocity $V_{b}$ is the velocity of the frame with respect to the world, as seen from the frame's perspective. Its rotational component $\omega_{b}$ contains the rotation rates around the ...

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How do I get the matrix for the mass?
2 votes

If you have the Jacobians from joint velocities to link body velocities (you can calculate these by taking each link $i$ as if it were the end effector and calculating its body Jacobian $J^{b}_{i}$), ...

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relationship between geometric twist jacobian and wrench
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2 votes

I'd suggest thinking about the problem this way: When you construct a Jacobian for an arm, it will typically map your joint velocities to to one of three representations of the end effector velocity: ...

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Robotic manipulator Jacobian by product of exponentials
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4 votes

The Jacobian in that equation is from the joint velocity to the "spatial velocity" of the end effector. The spatial velocity of an object is a somewhat unintuitive concept: it is the velocity of a ...

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