A friend gave me this pair of clamps. They were made by Brown & Sharpe, perhaps 1950s or so, and have the part number 754-A-5/8. I believe the 5/8 in the part number indicates 5/8 inch jaw depth.

The bars here are of 5/16 square section and the threads are 6-32. Brown & Sharpe still offers such clamps (see Amazon) but nothing as small as these. McMaster-Carr has some similar clamps with jaw depth as small as 3/4 inch. Also known as “parallel clamps” or “parallel bar clamps”.