## 1 Introduction  
Scientists have been trying to understand how the brain functions through brain stimulation, which includes both invasive and non-invasive stimulation techniques. Although invasive methods have advantages of high resolution and controllability of stimulation depth, they require brain surgery, which involves complications and potentially fatal risks. Non-invasive methods, in contrast, do not endanger the patient, as surgery is not necessary. Transcranial magnetic stimulation (TMS) is one of the most representative non-invasive stimulation methods [1]. The therapeutic application of TMS is widely used in neurology or psychiatry for the treatment of depression or schizophrenia. Thus, the number of studies on treating neuropsychiatric disease using TMS has increased rapidly. Unfortunately, there is a technical difficulty in implementing this non-invasive brain stimulation method. Since TMS is a neuromodulation technique using a coil that generates a magnetic field, it must be fixed in the direction and position above the subject's head [2]. Generally, manual positioning with a fixing arm is being used in clinical setups, but this procedure is complicated and time-consuming. Furthermore, patients should keep their head pose fixed during the treatment, which causes discomfort, because some treatments can take considerable time. For example, it takes more than 30 min for every session in the treatment of neuropsychiatric diseases [3]. For this reason, there have been studies on the development of a wearable positioning device to automatically position the brain stimulator [4]. It was designed for ultrasonic transducers that are far smaller in volume and lighter than TMS coils. Thus, we cannot apply it to TMS stimulation. In this study, a 6 degrees-of-freedom (DOF) serial manipulator was designed to enable the automatic positioning of TMS coils. The robot manipulator has an advantage in terms of accuracy and repeatability compared with manual positioning. Unlike typical 6-DOF serial manipulators, the developed manipulator has a spherical mechanism. By using a spherical joint in this manipulator, the shape of its workspace can also be made spherical. Therefore, not only is the moving of the manipulator highly dexterous and concise (as the workspace is only required to cover the human brain [5]), but also the manipulator can easily avoid gratuitous singular points. The spherical mechanism has been applied to the medical robot field because it can minimize robot movement and improve patient safety [6; 7]. In addition, a research study on robotic brain stimulation employed it to compensate for the unexpected movement of the subject [8]. We employed position-based visual servoing (PBVS) to compensate for the unexpected movement of the subject [9; 10; 11]. Although the robot can be moved to the desired position of the brain, a neuro-navigation system is required to determine the stimulus point while showing the brain [12; 13; 14; 15]. The system aligns the subject's medical image coordinates (e.g., computed tomography (CT), magnetic resonance imagining (MRI), functional MRI) with human coordinates, facilitating non-invasive brain stimulation, because the experimenter can simultaneously see the focus of the stimulator and the cortex of the brain. By selecting the desired stimulus point on the screen, one can easily determine the stimulation target. In this study, we developed an integrated system for non-invasive brain stimulation and conducted experiments to verify precise stimulation. First, a repeatability experiment was conducted to verify how consistently the developed system could locate the stimulator to a desired posture. A motion compensation experiment was executed to confirm the control to compensate for the small movements of the person that would occur during the brain stimulation experiment.