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TL;DR (quoted from the article):

"When a flamingo shifts onto one leg, two things happen. First, the leg inclines so that the foot moves from being directly under the hip to being directly under the center of the body. Second, the center of mass moves to just in front of the flamingo’s (hidden) knee, so its body weight naturally pulls the hip and knee forward. These two changes, combined with gravity’s pull and the shape of the leg bones, keeps all the joints in place."




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