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1

No difference at all although φ∈[−π,π) is much more reasonable and intuitive. It is just a matter of system definition.


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Your computations of the transformation matrices are incorrect. DH transformation matrices are computed as a multiplication of four matrices: rotate about z by $\theta$, translate along z by $d$, translate along x by $a$, and rotate about x by $\alpha$. More simply: you are missing the $\theta$ terms in the rightmost columns of your transformation ...


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Since that arm is redundant, there are an infinite number of solutions for the inverse kinematics. Fortunately, Dr. Williams at Ohio U has developed the forward and inverse kinematics for this arm here. He describes the complete forward kinematics, and the inverse kinematics two ways: once for the case where $\theta_3$ is fixed at zero degrees, and again ...


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I think you may have a mistake in python code. That is: slerp_d = slerp * np.log(qf * q0.inverse()), I think the correct one is: slerp_d = slerp * np.log(q0.inverse()*qf).


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If $T^{ee}_{root}$ is the homogeneous transformation that relates coordinates expressed in the end-effector frame into coordinates expressed in the root frame, then it holds that $T^{root}_{ee} = \left( T^{ee}_{root} \right)^{-1}$. Interestingly, the computation of the matrix inverse is straightforward and can be done by applying the rules reported in https:/...


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So I guess you want to know the DOF of the moving platform. First of all keep in mind that for a parallel mechanism with a fixed base and one moving platform the maximum degrees of freedom for the moving platform are 6, e.g. 3 rotational and 3 translational DOF. In this case it is kind of hard to see intuitively what DOF the moving platform could reach. So I ...


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You can set the angular velocity to whatever you want, that's the control input and depends on the algorithm. You have to set it to be something proportional to the difference in the desired angle (from the intercept trajectory) and the actual angle as measured. You then update the desired angle and velocity and re-calculate. Try this: https://robotics....


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can we have the same TCP position and orientation for multiple configuraiton angles of the robot Sure! The number of DOF of a manipulator tells us if it's possible or not to reach a pose (position + orientation) in the operational space at hand (usually 6-dimensional). Examples If we work in a 6D operational space, then we are required to have at least a 6-...


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I can see several issues with your design. The motor control is just one. Gearing. For 1-3 bounces per second, that's 60-180 RPM. Your motor probably goes something like 1750 RPM. As jsotola commented, you'll need to add a gearbox, or else replace the motor with one that has an integrated gearbox ("gear motor"). You won't be able to reliably ...


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