I have heard that locking the knee when stretching the legs is harmful for the joint. Is this true and are there any common movements where locking the knee should be avoided completely?
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Yes, this can be harmful in some individuals. If a dancer is hypermobile (meaning they have more mobility in their ligaments and joints) it can be a little dangerous for them to lock the knees back. Dancer's who have this excessive mobility in their legs may have a tendency to lock the knees back in normal standing, especially when standing on one leg or when in an arabesque or penché position. It is important that they are encouraged not to do this as it may lengthen the ligaments behind the joint and make the knee even more unstable.
However, girls who have very tight legs and tight joints and ligaments must focus on pulling up the leg in order to improve the alignment of the leg, so it really does depend on what kind of body you have.
There is a fine line between 'pulling up' and 'snapping back' the knees, and it is a difficult area to control for many individuals. Hypermobile individuals must focus on lengthening the leg, rather than overly contracting the quadricep to 'pull up' when straightening the leg, to prevent the knees from going too far back. Many dancers feel that they have to bend the knee, however this is not the case. You do not have to bend the knee, just make sure that it is not 120% straight! This is also very important when walking normally, not just in ballet.
There is a little pad called your 'infrapatella fat pad' that sits under the tendon at the front of your knee, below your knee cap. If you over extend your knees over a period of time, you can squash this fat pad and cause irritation, swelling and pain in the area. Sometimes taping in a cross across the back of the knee can improve awareness of when the knee is fully straightened and this can help reduce the compression of the fat pad to help it heal. Obviously, if the fat pad is swollen it will tend to get compressed more easily, and a continual cycle of pain and inflammation may develop.
I hope this helps!