2014/04/05 by Anthony Nixon, Nixon, Anthony, Bernd Schulze +5
Engineering · #52C25 #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Modular Robots and Swarm Intelligence #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1404.1505
openalex publication_date 2014/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.