A flexible coupling includes a first flange and a second flange, wherein in a relaxed state the first flange and the second flange are each aligned along a longitudinal axis. A plurality of first coupling members extends from the first flange. Each first coupling member includes a first and second driving beam meeting at a first node to form a topologically triangular truss. A plurality of second coupling members extend from the second flange. Each second coupling member includes a first and second driven beam extending from the second flange and meeting at a second node to form a topologically triangular truss. The first node of each of the first coupling members is connected to the second node of a respective one of the second coupling members.