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Using successive stages, or nesting compliant amplification mechanisms, soft actuators with performance suitable for robotic applications can be constructed with piezoelectric ceramic as the active material. This paper presents a mathematical framework that describes the interactions among the various amplification mechanisms in a hierarchical nested structure. A formal treatment of nested amplification mechanisms results in two theorems that describe the stiffness properties of the whole actuator in terms of the properties of each mechanism in the hierarchy. These theorems show that the stiffness properties of the actuator can be computed by considering only the outermost few layers in the nested configuration. By virtue of this hierarchical structure, the actuator also assumes a cellular structure; it functions by summing the effects of on-off inputs coupled by a flexible connective medium. This requires a paradigm shift when selecting control strategies. A multilayer strain amplification mechanism is designed to meet the required range of travel for a biologically inspired camera positioning mechanism, and a switching control method for the actuator's 16 on-off inputs is discussed.