joggle
To shake something with small, quick, repeated movements.
To joggle means to shake or move something with quick, repeated little bumps or jerks. When you joggle a table while writing, your pencil bounces slightly across the page. When you joggle a puzzle piece to make it fit, you wiggle it back and forth with small movements until it slides into place.
The word captures that specific kind of motion: not one big shake, but many small, rapid ones. A loose bolt might joggle in its hole. A painter might joggle their brush to create a textured effect. If you're carrying a tray of cups and someone bumps into you, the cups joggle and clink together (hopefully without spilling).
Joggle sounds like what it means: that light, rattling, repetitive motion. It's gentler than shake but more active than wobble. A joggle can also be a small bump or jerk, like the joggle you feel when a bus hits a pothole. When woodworkers create special notched joints that lock together, they sometimes call these joggle joints because the pieces must be joggled carefully into position. Next time something needs just a little wiggling to settle into place, you're joggling it.