Robot design is a major component in robotics, as it allows building robots capable of performing properly in given tasks. However, designing a robot with multiple types of parameters and constraints and defining an optimization function analytically for the robot design problem may be intractable or even impossible. Therefore black-box optimization approaches are generally preferred. In this work we propose GlobDesOpt, a simple-to-use open-source optimization framework for robot design based on global optimization methods. The framework allows selecting various design parameters and optimizing for both single and dual-arm robots. The functionalities of the framework are shown here to optimally design a dual-arm surgical robot, comparing the different two optimization strategies.