# Calibration of a 3-Component External Balance for MAVs Wind Tunnel Research
## 2 External Balance Prototype  
Figure 1 shows an overview of the external balance design, illustrating the three load cells (\(\text{LC}-1,\text{ LC}-2\), and \(\text{LC}-3\)) together with the different mechanisms employed for measuring lift force (L), aerodynamic drag force (D), and pitching moment (\(\text{M}_{\text{y}}\)). This prototype will consist of a metallic structure composed of several mechanisms, designed to isolate and measure the forces involved. These mechanisms form the core components of the mechanical balance, facilitating accurate force measurements. The instrumentation of the external balance uses three piezoresistive sensors, specifically, three bending load cells, fixed to various mechanisms, bearing, and bushing, enabling the measurement of lift, aerodynamic drag, and pitching moment. All components that constitute the 3-component external balance are a rectangular base, three mechanisms (1, 2, and 3), a balancing counterweight, three load cells (\(LC-1\), \(LC-2\), and \(LC-3\)), two load cell supports, load cell locking systems, ball bearings and bushings, component \"U\", a bearing assembly, and a rod. The joints of the different mechanisms are formed by a set of ball bearings with bushings, allowing the forces in the \(X\) (aerodynamic drag) and \(Z\) (lift) axes to be properly transmitted to the load cells independently. Thus, during operation of the system, due to the lift force of the MAV in the vertical direction, mechanism 1, to which the model is attached, moves in the \(Z\) direction and forces mechanism 3 to rotate around the fixed joint. Mechanism 3 creates a force that generates a state of bending loads on the load cell (\(LC-3\)) and thus the lift force is measured. In the case of the drag force on the MAV in the \(X\) direction, the force is transmitted from mechanism 1 through mechanism 2. Commercial load cells with a measurement range of 200 \(g\) (\(LC-1\) and \(LC-3\)) and 1000 \(g\) (\(LC-2\)) were used. Figure 2 shows the junction between the load cell for measuring lift (\(LC-2\)) and mechanism 3. The load cell is aligned in the same direction as mechanism 3 (in \(X\)-axis) and is interconnected through a combination of two ball bearings (bearing A) and bushings (A.1, A.2, and A.3). The component \"B\" is meticulously crafted to facilitate the integration between the bearing assembly and the load cell within mechanism 3. To ensure controlled movement, the opposing side of the load cell is intentionally immobilized, allowing only rotational motion at the junction with mechanism 3. Figure 1: Diagram of the forces generated in the external balance (**left**) and 3D balance design with the position of the mechanisms and load cells (**right**). Figure 2: 3D view (**left**) and manufactured assembly (**right**) for the lift measurement. Figure 3 illustrates the connection between the \(LC-2\) load cell, utilized for measuring aerodynamic drag force, and mechanism 2. The \(LC-2\) load cell is oriented perpendicularly to mechanism 2 and affixed to it via a set of 4 ball bearings (bearing C) and bushings (B.1). Similar to the previous case, one end of the load cell remains fixed to prevent undesirable movement (fixed to the support), allowing controlled motion within the bearing section. Figure 4 shows the assembly required to measure the pitching moment (\(M_{y}\)). The load cell (\(LC-3\)) is positioned horizontally, in the \(X\)-axis direction. The assembly involves a bearing assembly (bearing D) and bushings (C.1), enabling rotational movement on one side of the load cell while keeping the other side stationary to prevent unintended motion (fixed to the mechanism 1). Figure 5 shows the junction of the external balance with the wind tunnel model, including the components required for adjusting the position of the model. The component \"U\" enables the wind tunnel model to rotate along the \(Y\)-axis, while the bearing assembly allows adjusting the angle of attack (\(\alpha\)).