2020/12/09 by Hans‐Christian Graf von Bothmer, Hans-Christian Graf von Bothmer, Matteo Gallet +4
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Polynomial and algebraic computation #Robotic Mechanisms and Dynamics #cs.RO #cs.SC #math.AG
paper · pdf · doi:10.48550/arxiv.2012.05120
41 pages
arxiv created 2020/12/09 · arxiv updated 2020/12/10
The understanding of mobile hexapods, i.e., parallel manipulators with six legs, is one of the driving questions in theoretical kinematics. We aim at contributing to this understanding by employing techniques from algebraic geometry. The set of configurations of a mobile hexapod with one degree of freedom has the structure of a projective curve, which hence has a degree and an embedding dimension. Our main result is a classification of configuration curves of hexapods that satisfy some restrictions on their embedding dimension.