Puzzle Classification by Jerry Slocum

Jerry Slocum, the famous puzzle collector and author of many puzzle books classifies mechanical puzzles the following way.

1. Put-Together Puzzles - Putting the object together is the puzzle
  1.1 2-Dimensional assembly puzzles (Tangrams, jigsaw, pentominoes, etc.)
  1.2 3-Dimensional assembly puzzles (Soma, box packing, pentacubes, etc.)
  1.3 Miscellaneous put-together puzzles (Instant Insanity, magic squares, puzzle rings, etc.)
  1.4 Matchstick puzzles
2. Take-Apart Puzzles - Taking the object apart or open is the puzzle
  2.1 Trick or secret opening puzzles (Japanese trick boxes, puzzle boxes, etc.)
  2.2 Secret compartment puzzles (Finding & opening the secret compartment, Kamei, etc.)
  2.3 Trick locks & keys (Open the trick lock with hidden keyhole, etc.)
  2.4 Trick matchboxes (Open the trick matchbox/matchsafe, etc.)
  2.5 Trick knives (Open or close blade of the trick knife, etc.)
3. Interlocking Solid Puzzles - Disassembly & assembly to solve the puzzle
  3.1 Figural (Animals, people, objects, vehicles, etc.)
  3.2 Geometric objects (Cube, sphere, etc.)
  3.3 3-Dimensional jigsaw puzzles (Egg, furniture, sphere, block, animal, etc.)
  3.4 Burr puzzles (6 piece burr, Altekruse, etc.)
  3.5 Keychain (People, animals, vehicles, made of plastic with keychain, etc.)
  3.6 Miscellaneous interlocking solid puzzles
4. Disentanglement Puzzles - Disentangle & re-entangle to solve the puzzle
  4.1 Cast iron & sheet metal puzzles (Cast iron ABC, 3 snakes, Bootlegger & his flask, etc.)
  4.2 Wire puzzles (Chinese rings, 3 horseshoes, folding cross, etc.)
  4.3 String puzzles (Bar & 2 rings, buttonhole, Cherry cheat made of leather, etc.)
  4.4 Miscellaneous disentanglement puzzles
5. Sequential Movement Puzzles - Moving parts of the puzzle to a goal is the puzzle
  5.1 Solitaire puzzles (Remove pegs, counters, marbles, etc.)
  5.2 Counter puzzles (rearange pegs, counters by jumping, etc.)
  5.3 Sliding Piece Puzzles (2D & 3D, Dad's puzzle, 15-puzzle, etc. with empty spaces)
  5.4 Rotating cube-type puzzles (Rubic's cube, Pyramix, etc. with no empty spaces)
  5.5 Maze & route puzzles (16/1 maze, Oskar's Cube, Pike's Peak, etc.)
  5.6 Misc. Sequential Movement Puzzles (Tower of Hanoi, etc.)
  5.7 Mazes and Labyrinths for People
6. Dexterity Puzzles - Manual dexterity is primary to solve the puzzle
  6.1 Throw & catch (Cup & Ball, Bilboquet, etc.)
  6.2 Rolling Ball puzzles (R. Journet, Glass top dexterity, etc.)
  6.3 Maze dexterity puzzles (Flat, cube, cylinder dexterity maze with 1 or more balls, etc.)
  6.4 Miscellaneous dexterity puzzles
7. Puzzle Vessels - puzzle jugs & mugs, Cadogan teapots, Chinese wine pots etc.
8. Vanish Puzzles - Loyd's Get Off the Earth, Vanishing Leprechauns, etc.
9. Folding Puzzles - Flexagons, etc.
10. Impossible Objects - Arrow through Coke bottle, Harry Eng bottles, etc.
11. Other Mechanical Puzzles

Source: Directory of Puzzle Collectors by Jerry Slocum. 4th Edition May 2000.