Proper execution of the muscle snatch is a contentious subject. The following is my preferred method to ensure it serves the purpose of training, reinforcing and strengthening proper snatch turnover mechanics.
Set your snatch starting position and push with the legs against the floor through the whole foot similarly to a squat, maintaining approximately the same back angle until the bar is above the knee. Continue aggressively pushing against the floor with the legs and extend the hips violently, keeping the bar as close to the body as possible and ensuring full contact with the hips.
Extend the entire body close to vertically rather than leaning the trunk farther back as you would in a snatch. Keep the legs tight and pushing into the floor as you pull the elbows up and out to maintain as much bar speed as possible, shrugging up and back as you do.
As the elbows reach approximately shoulder height, turn the bar over, squeezing the shoulder blades back to keep the bar as close as possible, and continuing to actively pull so the elbows remain at the same height rather than dropping.
Finish the turnover as you would a snatch, punching straight up into the bar over the back of the neck with the head pushed through the arms. Lock forcefully and stabilize before lowering.
Notes
It can be helpful to think of the movement as a snatch high-pull with an added turnover of the bar afterward. This will reinforce the idea of driving vertically and lifting the elbows high and out before the turnover.
Generally the muscle snatch should be done without straps, especially if needing to practice the release of the hook grip overhead. It is sometimes done with no hook grip by default.
Purpose
The muscle snatch is helpful at lighter weights to learn and reinforce the proper upper body mechanics of the turnover (third pull) of the snatch. At more challenging weights, the muscle snatch will help strengthen the turnover of the snatch and reinforce an aggressive, active motion.
Programming
The muscle snatch can be performed early in a training session as a
technique primer, or as a training exercise. It can also be performed at the end of a training session as accessory work. Use 3-5 reps per set generally, although the muscle snatch can also be done for heavy singles and doubles.
Variations
The muscle snatch can be performed with essentially any variation possible with a snatch—from any hang or block position, from a riser, or from the tall position (arms only). It can also be done without contacting the body (AKA snatch long pull) and without the hook grip.
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More Effective Muscle Snatches
Drills for a Better Muscle Snatch