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This work provides incremental progress in robotics and algebraic geometry by solving a specific theoretical problem for hexapod classification.
The paper addresses the open problem of classifying hexapods (Stewart Gough platforms) with mobility one by establishing an upper bound for the degree of their associated algebraic configuration curves and constructing hexapods that achieve this maximal degree using liaison techniques.
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.