In an unstructured environment, the arm can perform complicated tasks with rapidity, flexibility, and robustness. It is difficult to configure multiple artificial muscles similar to an arm in the compact space of a robotic arm. When muscle tension is transferred, mechanisms like tendon-sheath/tendon-pulley may be installed in a compact space to develop musculoskeletal robots that are closer to the arm. However, handling variable frictional nonlinearity and elastic cable deformation is necessary for transmission stability. In this study, the modular artificial muscle system (MAMS), including motor cable artificial muscle and tendon sheath–pulley system (TSPS), that can be installed remotely and transmit muscle tension in narrow paths, is designed. The feed-forward multi-layer neural network (FF-MNN) approach is utilized to discuss the relationship between the measurable input tension of TSPS and the unmeasurable output tension and cable elongation. Subsequently, the lightweight musculoskeletal arm (LM-Arm) is built to verify the validity of MAMS. Through trials, the experiments of MAMS after friction compensating and the LM-Arm’s end-point 3D trajectory tracking are investigated. The results show that average errors of the active and passive muscles tension are 3.87 N and 3.51 N, respectively, under conditions of larger load and higher contraction velocity. The average muscle length error of trajectory tracking is 0.00078 m (0.72%). The suggested MAMS may successfully build a musculoskeletal robot that has similar flexibility and morphology to the arm. It can also be utilized to power various pieces of machinery, such as rescue robot, invasive surgical robots, dexterous hands, and wearable exoskeletons.