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 ...

Each step can be represented by its transformation matrix, $$\begin{bmatrix} \cos{\theta'_{i}} & -\sin{\theta'_{i}} & x'_{i}\\ \sin{\theta'_{i}} & \phantom{-}\cos{\theta'_{i}} & y'_{... View answer 0 votes I think it is likely that you are confusing two uses of the word “singular”: The singular values of a matrix as found via singular value decomposition. The singular configurations (or singularities) ... View answer 2 votes A robot manipulator that’s designed to mimic an operator in real-time can be called a “waldo” or "telemanipulator". The term "waldo" originates from Robert Heinlein, and was widespread enough at least ... View answer Accepted answer 2 votes Rigid link kinematics assumes that the robot is made of rigid structural elements connected by pivot or sliding joints, and describes the locations of points on the robot (or more generally, the ... View answer Accepted answer 1 votes Your axes and link vectors seem off. The axes z_{1} and z_{2} should be parallel, and your O^{0}_{2} and O^{0}_{3} don’t seem to be accounting for all the rotations that occur prior to the ... View answer 1 votes If I understand correctly, your end effector is at pose A, you want to move it to pose B, and you have Jacobian pseudo-inverse control set up so that you can specify a pose velocity v and get a ... View answer 0 votes For your second question: Moving in the xy plane, rotating around the z axis can be treated as instantaneously rotating around a "virtual center", located along the line perpendicular to the xy ... View answer Accepted answer 6 votes The pseudoinverse gives a “least squared error, minimum-norm” solution: Out of all \dot{q} vectors at your current q, the vector$$\dot{q}_{s} = J^{+}(q)\dot{p}_{\text{in}} satisfies two ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 $J^{b}_{i}$), ...