Patek Philippe Calatrava Self-winding watch in 18-k rose gold with diamonds, $38,440 at London Jewelers, 2046 Northern Blvd., Manhasset, LI. Photo by Jeffrey Westbrook; Prop Stylist: Miako Katoh.

The workings of a self-winding watch were inspired by a seesaw almost 100 years ago. Today’s designers of the EvoTec -- powered by an ultradense geared ring rotating on carbon rollers ...