Modeling large spatial deflections of flexible beams has been one of the most challenging problems in the research of compliant mechanism. This study presents an approach called chained power series model for modeling large spatial defections of flexible beams with uniform rectangular cross section. This approach is based on the power series model developed in our previous work for modeling spatial deflections of rectangular beams in the intermediate deflection range. The chained power series model splits a rectangular beam into several elements and models each element by the power series model, and then, the deflections of all elements are assembled to form the deflection of the beam through transformations using quaternions. The effectiveness of the approach is demonstrated by comparing with the nonlinear finite element model preformed in ansys and the chained 3D pseudo-rigid-body model. Several examples are demonstrated to show the capability of the chained power series model for solving the deflections of rectangular beams in compliant mechanisms.