While many player-generated games (in particular Escape Rooms) include puzzle elements, mechanical puzzles consist of "mechanically" interlinked pieces (see Jaap's Puzzle Page for many examples). There are several forms of mechanical puzzles but only a few have been implemented in Rec Room so far.
Construction puzzles consist of pieces that have to be moved into certain positions. Some examples are:
Combination puzzles (also known as sequential move puzzles) limit the ways in which the pieces may be moved:
Sliding puzzles are a special kind of combination puzzles:
Many Maze Games could be considered mechanical puzzles.