Disentanglement puzzles, aka disentanglements, are the brain teaser puzzles that usually require the removal / extrication of a ring or long oval piece (known as a shuttle). These puzzles will often employ chains or ropes for complexity and/or aestetics. These types of puzzles have a long, long history dating back at least hundreds of years.
In general, these puzzles, at first glance, will appear to be unsolvable without force. However, upon closer inspection there are "weaknesses" to be discovered in the design. There are design weaknesses of many kinds, but some of the more common can be described as "loose" joints, "suspicious" gaps, or "pull-overs". The more difficult disentanglement puzzles could require the exploitation of more than one of these weaknesses in concert to reach the solution. In fact, some of the more challenging disentanglement puzzles even use recursive procedures to arrive at the solution (like Patience Puzzle, a super classic, http://www.seriouspuzzles.com/patiencepuzzle.html)
ex. of the "Pull-Over" weakness
ex. of the "Loose" joint weakness
ex. of the "Suspicious" gap weakness
IMHO, the best disentanglement puzzles are the intersection of visual simplicity and obscurity of weakness. They may not be considered the most challenging puzzles. They look strong, sturdy, and simple. Their weakness is difficult to describe, uncommon, and hard to "see". Here are some of my favorites:
And of course, who can forget the Classic Horseshoe Puzzle...For sale at http://www.seriouspuzzles.com/luchorshoes.html
This puzzle still mesmerizes me. It uses a slip and twist motion only made possible by the links between the horseshoe. With the ring nearly in stand still while the horseshoes twist and slip between it, the horseshoes are suddenly side by side and the ring ready to slip off!
SPOILER Alert -- solution for Lucky Horseshoes here:
For a slow mo video, check this out.
Horse Shoe Puzzle Secret Explanation How To Solve It