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In this article, we focus on a design problem of planar compliant mechanisms within the framework of isogeometric topology optimization. An integrated model is developed to identify the optimal deformation transferring path for precise motion output. The model comprises two coupled computational layers: the upper layer for geometry representation and the lower layer for sensitivity calculation. In the upper layer, the structural geometries are described explicitly by parameterized level-set surfaces, which is quite different from the implicit description way of topology optimization, giving great advantages to improve the identification accuracy of elaborate structures (e.g., flexible hinges), which are usually encountered in compliant mechanism systems. By moving, deforming, overlapping and merging these level-set surfaces, the generated shape can be projected onto the lower layer which is discretized using a NURBS patch, and NURBS-based isogeometric analysis is adopted to calculate the structural sensitivity which is then fed back to the upper layer for driving new iteration. The proposed method has the higher ability to search the optimal topology with complex kinematic behavior with respect to the conventional topology optimization methods in terms of computational effectiveness and numerical robustness. Design formulation of compliant mechanisms is constructed under the framework of the proposed method, in which the Jacobian and stiffness matrices of compliant mechanism are optimized simultaneously to achieve kinematic and stiffness requirement respectively. Three typical benchmark problems (e.g., displacement inverter, amplifier, and redirector) are tested to demonstrate these advantages.