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This paper presents the self-calibration of a novel biologically inspired 7 DOF cable-driven robotic arm. Similar to the human arm, the proposed robotic arm consists of three sequentially connected modules, i.e., a 3 DOF shoulder module, a 1 DOF elbow module, and a 3 DOF wrist module. Due to factors like manufacturing defects, assembly misalignments, compliance, and wear of connecting mechanisms, errors in the geometric model parameters always exist. Hence, the identification of such errors is critical for path planning and motion control tasks. Self-calibration models of the various modules in the robotic arm are formulated based on the differential change in the cable end-point distances. Due to the linear nature of these self-calibration models, an iterative least-squares algorithm is employed to identify the errors in the geometric model parameters. The calibration does not require any external pose measurement devices, because it utilizes the cable length data obtained from the redundant actuation scheme of the cable-driven arm. Computer simulations and experimental studies were carried out on both the 3 DOF and 1 DOF modules, to verify the robustness and effectiveness of the proposed self-calibration algorithm. From the experimental studies, errors in the geometric model parameters were precisely recovered after a minimum number of pose measurements.