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Your muscles have a force-velocity curve. MVIC stands for "maximum voluntary isometric contraction", in other words, how much weight you can hold in place (isometric). The faster you move (concentric), the less force your muscles can generate. In the other direction (eccentric), you can control a heavier weight or resistance than you could hold in place.
Video by Flow High Performance: The Force-Velocity Relationship - Meaning and Implications
How about energy ? When you lift a weight, your muscles have to work to increase the potential energy of the weight. There is a significant metabolic cost for the concentric movement. When you lower a weight, potential energy is returned to you. Except for a minimal amount of tendon elasticity, this energy is lost - your muscles actually some energy to control the negative movement.
Research shows that both concentric and eccentric movements are useful for muscle hypertrophy. Eccentric-only training can be very effective given the high loads possible, but is not practical in a normal gym or home environment.
When training with a barbell or dumbbells, there is virtually no friction.
The friction of machines varies widely depending on the design and how well they are maintained (almost none for Hammer Strength machines with ball bearings, more for selectorized equipment with linear bearings).
Resistance bands by themselves are almost ideal springs with little internal friction.
A conventional foot plate changes things. As you pull on the band, the band will slide and rub against the foot plate. On the concentric part of the movement, where you are weaker, you have to pull harder to overcome this friction. When you let the band contract, it will rub in the opposite direction. The friction will reduce the load for the eccentric movement, where you are stronger. You have to use a narrower band with less resistance to manage the band resistance plus friction on the concentric, and get little eccentric training effect as band resistance minus friction is much less than what your muscles can do.
You could don rubber gloves and regularly apply silicone oil to your bands, or look for a better foot plate.
The Band Box uses rollers with ball bearings to minimize friction. The resistance for the concentric and eccentric portions of the rep will be almost the same. I cannot point to specific research, but given the way muscles work, I am very confident that the training effect will be better with less friction.
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