Quadcopters have become a mass consumer product thanks to their ability to transport and deliver different loads, from online book orders to first aid kits, although their primary market comes from the hobbies and entertainment enthusiasts. In academia, quadrotor helicopters are also a great platform for teaching flight mechanics, control principles and even mechatronic systems design. One way to get a deeper understanding of the operating principles of this system is by building your own quadcopter, so you have more freedom to choose all the components of the system. This method provides hands on experience on the effect that each design parameter has on the performance of the system. Some of the design parameters of greater influence on the flight behavior of the aircraft are the blades size and the arms length. Another approach to modify the performance of a quadcopter is by changing the control strategy that enables stable flight. One of the most common control strategies used for flight stabilization of a quadrotor helicopter is the optimal control technique. The optimal control system design problem focuses on finding the values of the gains for state feedback control by optimizing a cost function that balances control effort versus performance. This idea is useful for stabilization of plants that already exist. However, the philosophy of mechatronic system design suggests that one must consider the control system design and the mechanical design right from the beginning of the project, during the modeling and simulation stages, so that the final design features actuators of reasonable size while the performance of the system meets a set of desired specifications, among other outcomes. To assist in the design of a homemade quadcopter, this work proposes, as a case study of mechatronics system design, to simultaneously optimize the parameters of the optimal controller and one parameter of the mechanical design of the quadcopter, namely the length of the arms. The results obtained provide guidelines on how to optimally design a mechatronic system, which in this case not only is a multiphysics system but also requires a control system to operate. The quadrotor designed by means of this methodology is expected to have better maneuverability as compared to a quadrotor whose control system design is decoupled from the mechanical design. The results also help to reduce the number of iterations during the mechatronic system design process, which many times is cumbersome due to the inherent multiphysics nature of mechatronic systems. A future step of this work will include more design parameters in the optimization problem such as the diameter of the blades, or the ratio of own weight of the aircraft to payload.