One of principles of strength building is keeping tension across the longest range of movement that the exercise can be done safely. Although, not absolutely required - you can build strength with half reps, quarters reps, even isometric holds - partial reps are not the fastest most efficient way to build strength. Full reps while maintaining tension throughout the full range of motion is the fastest way to build strength. Unfortunately, some exercises, especially the squat, get significantly easier at the top of the motion and a whole lot harder at the bottom. If you use a low enough weight to deep squat, then you aren't keeping good tension at the top. If you half squat, then you aren't exercising the full range of the muscle. Both will work, but neither is the optimal way to build muscle.
Chains help solve this problem, because as you raise the bar higher, more links come off the ground adding weight to the bar, thus increasing the tension at the top.
Knee wraps and sleeves also help with this problem. When used correctly, knee wraps load like a spring at the bottom of the squat, thus providing assistance at the hardest part of the lift. This allows the use of heavier weights so proper tension is maintained at the top of the squat.
A lot of people claim wraps help protect the ligaments, and they do, but not because they hold the ligaments together, but because the reduce the load at the bottom of the squat, making it easier on the knees. The same applies to chains. Knee sleeves also perform this function, just to a lesser degree.
The bench press also suffers from the same dilemma, and so chains add benefit to bench press training as well. The legendary strength coach Louie Simmons is a huge proponent of chains. He's not one of the greatest strength coaches ever for no reason.
An added benefit of chains is that they add instability. If you are unstable in your lift, this will cause the chain to sway, thus amplifying the effect of your instability. This instant feedback will help you develop better technique for a smoother, more stable lift. In fact, it's good practice to occasionally use the chains without them touching the ground. In this configuration, they won't add additional weight as you raise the bar, but they will help you develop a much smoother lift.
How much weight do you need? Everyone is different, but I've found that a
pair of chains that weigh 40-50 pounds (18-23 kilos) works well for most
people. You can of course have several sets of different weights and combine
them as needed.
A good feature to have are bar collars for the chains. This allows you to
easily attach/remove them to your bar. It's generally cheaper to buy a set of
chains that include them, but they can be purchased separately.
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