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To expand on my comment, the last line of your DH table gives the transform between END_EFFECTOR-1 and END_EFFECTOR frames, right? I'm saying instead of <θ2, 0, 0, 0> to have <180+θ2, 180, 0, 0>. There's no movement between your end effector and the object you're attaching to the end effector, so there's no point in keeping the end effector frame....


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The main problem is the continuity of the representation. This paper explains it.


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Every three-dimensional parameterization of rotations has singularity. So even if you would implement the kinematics directly you would still run into trouble for some rotations when using Euler angles (or any other three-dimensional parameterization). Quaternions, or more accurately unit quaternions, do not have such singularities. Though, do not have a ...


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