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6R Linkages with Hidden Singularities

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Advances in Robot Kinematics 2022 (ARK 2022)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 24))

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Mechanisms may possess kinematic singularities that are smooth points of the configuration space (c-space). At such points, a mechanism becomes shaky as its instantaneous mobility changes, but in contrast to c-space singularities, like bifurcations or cusps, these kinematic singularities are not reflected in the c-space. They are therefore called hidden singularities. Very few publications have addressed the analysis of hidden singularities. Recent research, employing methods from algebraic geometry, shows that they are often due to embedded points of the c-space variety but may also be due to singularities of the c-space variety where real and complex components intersect. Facilitating future research on the origin of hidden singularities necessitates a comprehensive list of mechanisms exhibiting this phenomenon. To this end, a constructive approach for the synthesis of 1-DOF 6R linkages with hidden singularities of prescribed rank is proposed in this paper. Various examples are shown that have hidden singularities of rank 3 or 4. Also, an example is shown that has a singularity which is a bifurcation as well as an embedded point.

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This research was funded by the Austrian Science Fund (FWF) [I 4452-N].

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Correspondence to Andreas Müller .

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Li, Z., Müller, A. (2022). 6R Linkages with Hidden Singularities. In: Altuzarra, O., Kecskeméthy, A. (eds) Advances in Robot Kinematics 2022. ARK 2022. Springer Proceedings in Advanced Robotics, vol 24. Springer, Cham.

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