An intermediate CrossFit athlete has his form in check for most of the exercises and is adept enough to perform most of the WODS (workouts of the day) with the prescribed weights, only occasionally scaling his reps or weight down. However, these athletes lack the comprehensive strength that allows them to compete with the elite CrossFit athletes. They definitely have more skills and power than a beginner, but still need coaching and development to progress.
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A few specific exercises help the intermediate CrossFitter develop the strength and skills necessary to earn the moniker, "advanced," and potentially even progress in the CrossFit games.
Whether you agree with the form or not, kipping pull-ups are a staple in CrossFit. They're performed like a standard pull-up with your hands grasping an elevated, fixed bar with an overhand grip. However, you hike your hips to help you get up and over the bar and complete more reps than you might with a straight body.
Take time outside of the WOD to hone your kipping pull-up skills and regularly check your progress.
Handstand push-ups aren't your grade-school exercise. You do these by getting into a handstand, usually against a wall, and pressing yourself up and down for as many reps as you can squeeze out.
The handstand push-up teaches you body awareness and great physical control, which only serves to benefit you in anything CrossFit throws your way.
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Hauling your body up a rope teaches you to control your body weight along a vertical midline, certainly no easy feat. Your upper body and your legs, as well as your core, all put in the effort. Playing with different foot wraps, such as corkscrewing the rope around your lower leg or pinching it between the feet, will train you how to understand your body and how it works as a unit.
Ring dips require you to hoist and hold yourself up on gymnastic rings as you bend your elbows to perform a dip. You'll train your core strength, along with your triceps. It also gives you more freedom than a bar dip, as you can alter the distance between your hand or the depth of your dip more readily with the hanging rings.
The squat clean requires good technique, which makes it ideal for a CrossFitter who has mastered the basics and wants cerebral as well as muscular development. The best way to describe the exercise is by calling it a combination of the power clean and the front squat. It builds lower-body strength and cultivates your full range of motion. Because of the nuances involved in learning this exercise, you're best off working with a CrossFit coach to hone your form.