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Theoretical and numerical analysis reveals multiple inverse kinematics solutions in a cuspidal robot, indicating complex movement capabilities.
We present a theoretical and numerical analysis of the kinematics for the Transpressor, a cuspidal 6R robot. It admits up to 16 inverse kinematics solutions which are described geometrically. For special target poses, we provide the solutions analytically and present a simple numerical solver for the general case. Moreover, an analytical estimate of the Jacobian determinant on a path between two solutions proves cuspidality for a class of robots similar to the transpressor.
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Feeß et al. (2026) studied this question.
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