The cylindrical snap-fit is a ubiquitous fastening method that is both simple to manufacture and assemble, and yet secure. It consists of a partial cylindrical shell that snaps' onto a cylindrical object. We build on previous work to describe the mechanics of the cylindrical snap-fit as a naturally curved thin elastic shell placed atop a rigid cylinder; we investigate the shell's behaviour when subject to a point force pushing it onto or pulling it off the cylinder. We classify the possible contact regimes according to whether the shell has a nonzero lifting capacity. We term situations with lifting capacity grip-fits’ and show that this includes both the snap-fit and a stick-fit' regime, which allows lifting despite not having the characteristic snap’. Regimes without lifting capacity are also characterized for completeness. We show that the different regimes may be characterized entirely by the shell/cylinder geometry and the coefficient of friction. We then consider different metrics for the lifting performance in the grip-fit regime. Our analysis reveals the trade-offs between assembly force, disassembly force, lifting force, and clamping force, providing design principles for secure lifting, easy detachment, and safe handling of fragile objects.

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