An exercise is 'open chain' when it involves a phase where the foot is free and not in contact with any surface.

Open chain exercise known as full arc extensions.
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FORUM DISCUSSIONS
Closed vs Open Chain exercises for the knee - Are you doing the no-no opens?
Closed to open chain exercises and VMO strenghtening.
CLINICAL PUBLICATIONS
The Effect of Open and Closed Kinetic Chain Exercises on Dynamic Balance Ability of Normal Healthy Adults. Kwon YJ, Park SJ, Jefferson J and Kim K. J Phys Ther Sci. 2013 Jun; 25(6): 671–674.