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We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot...
Fixed-angle polygonal chains in three dimensions serve as an interesting model of protein backbones. Here we consider such chains produced inside a "machine" modeled crudely as a cone, and examine the constraints this model places on the producible chains. We call this notion producible, and prove as our main result that a chain whose maximum turn angle is α is producible in a cone of half-angle...
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