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This paper presents a monolithic shape memory alloy (SMA) microgripper, which was developed to assemble microscopic building blocks of width 60 μm into tissue engineering scaffolds. It consists of two small fingers for grasping, an actuator which changes its shape upon heating by Joule effect and a parallel elastic structure to provide a pullback force on cooling as well as to guide the finger movement. All the elements are laser-cut from the same Ni-Ti-Cu sheet but have different mechanical properties and are used for different functions. Using local laser annealing, a local shape memory effect is introduced on the actuator while leaving other areas in a cold-worked state, i.e. no shape memory effect occurs. The material has nonlinear mechanics and the actuator undergoes large deflections. A numerical method is introduced to compute the nonlinear dynamics of the coupled system formed by the actuator and pullback spring. The predicted deflection and force are in good agreement with the measured ones, and this model can be used to optimize the design.