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Plants are not exactly known to move much, but many species have the ability to orient or fold their leaves in order to optimize photosynthesis or ward off herbivores. Leaf actuation is executed by pulvini—joint-like motor organs that operate like hydraulically powered hinges. In the mimosa leaf, pulvini are incorporated at multiple locations in the compound leaf allowing it to rapidly and efficiently fold upon touch. To explore how the rapid movement is triggered, we applied calibrated mechanical loads and found that the magnitude of an angular motion perceived at the adaxial surface of the tertiary pulvini seems to be the key signal triggering plant response. To understand the mechanical principles underlying the execution of the rapid motion, we investigated pulvinus structure at tissue and cell scales and found that circumferential hoop reinforcements optimize the translation of hydraulic changes into motion. Specialized cell wall structures and epidermis morphologies direct tissue swelling into directed organ shape changes. These findings provide insight into the role of cell wall structure in plant motor strategies, underscore the hierarchical, emergent nature of biomechanical systems, and highlight design principles that can inform the development of biologically inspired soft actuators.