A ketchup cap inspired engineers to build a motor-free shape-shifting robot

Kevin Liu showcases a geometry-powered robot that moves without motors or controls, PC: Aaron NathansAt Princeton Engineering, a team led by Glaucio Paulino has answered a question few people ever think to ask: what makes a ketchup bottle cap snap open and stay open rather than flopping shut? The hinge on a typical flip-top ketchup cap attaches a thin, flexible shell to a thicker, rigid base along a curved edge, creating 2 distinct stable positions separated by an energy barrier that the cap must overcome to switch between them. That simple piece of everyday plastic engineering helped reveal something much bigger: how curved, folded shells can hold multiple stable shapes without conventional locking mechanisms. Working from that insight, the team developed mathematical rules for predicting