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Robotics 2018, 7(2), 27;

Hexapods with Plane-Symmetric Self-Motions

Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10/104, 1040 Vienna, Austria
Received: 30 April 2018 / Revised: 5 June 2018 / Accepted: 5 June 2018 / Published: 8 June 2018
(This article belongs to the Special Issue Kinematics and Robot Design)
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A hexapod is a parallel manipulator where the platform is linked with the base by six legs, which are anchored via spherical joints. In general, such a mechanical device is rigid for fixed leg lengths, but, under particular conditions, it can perform a so-called self-motion. In this paper, we determine all hexapods possessing self-motions of a special type. The motions under consideration are so-called plane-symmetric ones, which are the straight forward spatial counterpart of planar/spherical symmetric rollings. The full classification of hexapods with plane-symmetric self-motions is achieved by formulating the problem in terms of algebraic geometry by means of Study parameters. It turns out that besides the planar/spherical symmetric rollings with circular paths and two trivial cases (butterfly self-motion and two-dimensional spherical self-motion), only one further solution exists, which is the so-called Duporcq hexapod. This manipulator, which is studied in detail in the last part of the paper, may be of interest for the design of deployable structures due to its kinematotropic behavior and total flat branching singularities. View Full-Text
Keywords: hexapod; self-motion; spatial symmetric rolling; plane-symmetric motion; Duporcq manipulator hexapod; self-motion; spatial symmetric rolling; plane-symmetric motion; Duporcq manipulator

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Nawratil, G. Hexapods with Plane-Symmetric Self-Motions. Robotics 2018, 7, 27.

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