2024/10/20 by Tomohiro Tachi, Tachi, Tomohiro · 1 citation
Mathematics · #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2410.15541
openalex publication_date 2024/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
[Connelly and Servatius, 1994] shows the difficulty of properly defining n-th order rigidity and flexiblity of a bar-and-joint framework for higher order (n >= 3) through the introduction of a cusp mechanism. The author proposes a "proper" definition of the order of rigidity by the order of elongation of the bars with respect to the arclength along the path in the configuration space. We show that the classic definition using formal n-th derivative of the length constraint is a sufficient condition for the n-th flexiblity in the proposed definition and also a necessary condition only for n = 1, 2.