FREMONT, Calif. — It was just past sunrise on an early-spring morning at Netflix’s DVD operations here, where metallic arms whirred in a giant glass box and rolling carts holding millions of DVDs lined the walls. The company’s iconic red envelopes buzzed through an assembly line at the other end of the warehouse.

The machine sucked a returned Netflix mailer into the system then proceeded to slice open the envelope, identify and clean the disc inside, check that the DVD worked and reinsert it into the original sleeve. That disc was then returned to the storage carts or shipped out to another customer who had requested the title.

About 3,400 discs zip through the rental return machine each hour, five times as many as when teams of Netflix employees used to process the discs by hand. Called the Amazing Arm by engineers here, the machine symbolizes the way Netflix has managed to maintain a profitable physical DVD operation even as it transforms itself into a global streaming service.

Netflix now counts more than 65 million streaming members in more than 50 countries and plans to expand across the world in the next 18 months. But that breakneck growth comes at a cost: The company expects its streaming business to just break even globally through 2016 as it pours billions of dollars into content and an aggressive expansion.