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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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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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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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