Members of the animal kingdom produce motion by muscle contraction. Biological muscle can be viewed as a unidirectional actuator. To achieve bidirectional motion, each muscle has a corresponding antagonist muscle whose contraction produces motion in the opposite direction. This gives biological systems the unique ability to modulate the stiffness of a joint, which is important when interacting with the environment. Certain bio-inspired robotic systems incorporate antagonistic pairs in an attempt to produce similar desirable properties. The cellular actuator employs nested compliant mechanisms to produce human-scale motion from piezoelectric stack actuators, which on their own have a small displacement. The expression for the stiffness of the actuator composed of these mechanisms takes the form of a continued fraction, which results from the nested structure. In this way, the stiffness can be easily approximated to a desired degree of accuracy by considering only the outermost mechanisms.

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