Explore new geometrical insights and techniques related to protein folding, robot kinematics, and auxetic behavior in crystalline or cellular materials in this 58-minute Fellows' Presentation from the Radcliffe Institute for Advanced Study. Join Ciprian S. Borcea and Ileana Streinu as they delve into various analogies and structural characteristics, covering topics such as bar-and-joint polygonal chains, closed robot arms, the Peaucellier Linkage, and the Hoberman Sphere. Learn about one degree-of-freedom mechanisms, rigidity analysis using KINARI-Web, and the intricacies of periodic motion and auxetic behavior. Gain insights into the application of these concepts in real-world scenarios, from space exploration with the Canadarm to predicting ligand binding effects in proteins. Discover the fascinating world of structural motion and its implications across multiple scientific disciplines.