RICHMOND—The recession and overseas competition have carved away at Bay Area machine shops, but Paragon Machine Works, like some other local outfits, has found its footing by cultivating customers in the region's emerging businesses.

The shop, which makes metal parts for everything from bicycles to bulldozers, has seen a shift in its customer base that mirrors changes in the Bay Area economy. While Paragon is fielding fewer orders from makers of industrial equipment and wine-making gear, sales of high-end bike parts have grown....