Mobile icosapods
Copyright policy )Mobile icosapods
Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical joints. It is possible to prove that the maximal number of legs of a mobile pod, when finite, is 20. In 1904, Borel designed a technique to construct examples of such 20-pods, but could not constrain the legs to have base and platform points with real coordinates. We show that Borel's construction yields all mobile 20-pods, and that it is possible to construct examples with all real coordinates.
22 pages, 4 figures
- TU Wien Austria
- London South Bank University United Kingdom
- Austrian Academy of Sciences Austria
- University of Trieste Italy
- Johann Radon Institute for Computational and Applied Mathematics Austria
FOS: Computer and information sciences, line-symmetric motion, spectrahedra, Computer Science - Robotics, Mathematics - Algebraic Geometry, Differential geometric aspects in kinematics, 14L35, 70B15, 14P10, FOS: Mathematics, Semialgebraic sets and related spaces, Kinematics of mechanisms and robots, Classical groups (algebro-geometric aspects), icosapods, body-bar framework, Robotics (cs.RO), Algebraic Geometry (math.AG)
FOS: Computer and information sciences, line-symmetric motion, spectrahedra, Computer Science - Robotics, Mathematics - Algebraic Geometry, Differential geometric aspects in kinematics, 14L35, 70B15, 14P10, FOS: Mathematics, Semialgebraic sets and related spaces, Kinematics of mechanisms and robots, Classical groups (algebro-geometric aspects), icosapods, body-bar framework, Robotics (cs.RO), Algebraic Geometry (math.AG)
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