We report that spin supercurrents can be induced in diffusive superconductor-ferromagnet-superconductor Josephson junctions without any magnetic misalignment or intrinsic spin-orbit coupling. Instead, the pathway to spin-triplet generation is provided via geometric curvature, and results in a long-range Josephson effect. In addition, the curvature is shown to induce a dynamically tunable $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition in the junction. We provide the analytic framework and discuss potential experimental and innovation implications.
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