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Hyper redundancy, high reliability, and high task repeatability are the main advantages of binary manipulators over conventional manipulators with continuous joints, especially when manipulators are operated under tough and complex work conditions. The precise and complex movement of a binary manipulator necessitates many modules. In this case, numerically efficient inverse kinematics algorithms for binary manipulators usually require impractically large memory size for the real-time calculation of the binary states of all joints. To overcome this limitation by developing a new inverse kinematics algorithm is the objective of this research. The key idea of the proposed method is to formulate the inverse kinematics problem of a binary manipulator as an optimization problem with real design variables, in which the real variables are forced to approach the permissible binary values corresponding to two discrete joint displacements. Using the proposed optimization method, the inverse kinematics of 3-D binary manipulators with many modules can be solved almost in real time (say, less than a second for up to 16 modules) without requiring a large memory size. Furthermore, some manipulation considerations, such as operation power minimization, can be easily incorporated into the proposed formulation. The effectiveness of the proposed method is verified through several numerical problems, including 3-D inverse kinematics problems.