scissor theories: biology, engineering, art

Abstract

Most beautiful things we encounter in life (Taylor expansions, Jean Genet’s "Un Captif Amoureux", a California burrito, etc.) do not consist of a lattice of scissor mechanisms carefully interconnected to enable global mechanical deformations. This dissertation studies three objects which do. More formally, this dissertation examines the geometry, mechanics, and dynamics of systems which share the common geometric motif of a two-bar linkage – what we will call a scissor mechanism. First, we discuss the tail of the T4 bacteriophage – the contractile injection system – and demonstrate a coarse grained analytical model which allows us to treat the geometry and energetics of its contraction process. Next, we turn to the morphology of woven materials, and indicate the surprising geometric complexity of this quotidian regime. Finally, we introduce a class of metamaterials assembled from lattices of scissor mechanisms and trace a mathematical analogy to origami and kirigami which in turn inspires their name: “hasamigami”.