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The complete classification of hexapods - also known as Stewart Gough platforms - of mobility one is still open. To tackle this problem, we can associate to each hexapod of mobility one an algebraic curve, called the configuration curve. In this paper we establish an upper bound for the degree of this curve, assuming the hexapod is general enough. Moreover, we provide a construction of hexapods with curves of maximal degree, which is based on liaison, a technique used in the theory of algebraic curves.
40 pages, 6 figures
Computer Science - Symbolic Computation, FOS: Computer and information sciences, Kinematics of a rigid body, bond theory, Segre cubic primal, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], hexapod, Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, Computer Science - Robotics, Mathematics - Algebraic Geometry, Liaison theory, FOS: Mathematics, Stewart Gough platform, self motion, Kinematics of mechanisms and robots, Robotics (cs.RO), Algebraic Geometry (math.AG)
Computer Science - Symbolic Computation, FOS: Computer and information sciences, Kinematics of a rigid body, bond theory, Segre cubic primal, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], hexapod, Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, Computer Science - Robotics, Mathematics - Algebraic Geometry, Liaison theory, FOS: Mathematics, Stewart Gough platform, self motion, Kinematics of mechanisms and robots, Robotics (cs.RO), Algebraic Geometry (math.AG)
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