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In this paper, we present a segmentation theory for designing a multi-axis actuator array. This array uses artificial muscle actuators, i.e. shape memory alloys, to control multiple axes in a coordinated manner. The multi-axis actuator array uses segmented binary control (SBC), which is a method of controlling artificial muscle actuators in a digital manner. In SBC, actuators are segmented and each segment is controlled independently, instead of controlling the strain of the actuator as a whole. The advantage of using SBC is that it allows us to avoid the nonlinear properties of the actuator and to use a simple control for each segment. However, one problem of using SBC is the increased number of segments. The segmentation theory provides a basis for using coupled segments, or segments to be shared within the actuator array, along with independent segments, to control the multiple axes with reduced number of segments. A segmentation design procedure is developed based on the theory and the method is applied to an actuator array for driving a five-fingered robot hand capable of taking variety of postures.