## 2 Materials and Methods
### Design of the Aerial Manipulator
#### 2.1.3 Design of Manipulator Links  
The links are designed through a topology optimization method. Topology optimization is a form of structural optimization in which the material distribution and geometry are used to minimize costs, such as its minimal weight, stress, and displacement, as well as to maximize stiffness [18]. It does so while ensuring that the design constraints, in the form of multiple static loads applied to the structure, are met, and the various methods are available and applied commercially [18].  
A simple profile of the link is then created, which outlines its length and width. A set of loads is applied to the joints of the link. These loads simulate the forces the links would experience in operation and constitute the design constraints in the optimization problem. The cost function to be minimized is the total weight of the links, subject to the  
Figure 3: Conceptual design of the aerial manipulator.  
constraints. Topology optimization is conducted using Autodesk Fusion 360 [19] under these conditions to generate the initial profile. This profile indicates the materials needed under the applied loads to perform the same function, while reducing the mass of the component. The optimized profile is then used as a reference to remove material from the original profile.  
A stress analysis simulation is then performed to ensure that the component will be able to sustain the applied loads. This is done by computing the internal normal and shear stresses, \(\sigma_{x}(x,y),\ \sigma_{y}(x,y),\ \tau(x,y)\), and ensuring that the von Mises stress does not exceed the material's allowable maximum stress, \(\sigma_{a}\)[20]. The stress is computed by discretizing the geometry and applying a finite element method on the mesh, which is done here using the commercial software Autodesk Fusion 360 [19]. Figure 4 shows the optimization process, the von Mises stress, and the resulting manipulator assembly.  
The cable system consists of cables passing through the hollowed-out links and pulleys at the joint. It facilitates the joint rotations and reduces the motor torque required to rotate the joints. The pulley of the arm operates with a mechanical advantage of 1.5 at a ratio of 3:2, with the actuator rotating 3 times to turn the link 2 times. This limits the motion of the arm to 120 degrees, as the servo motors rotate up to 180 degrees. The pulley of the forearm operates with a ratio of 7:6 with the actuator rotating 7 times to turn the link 6 times, giving a mechanical advantage of 1.16. This limits the motion of the forearm to 154 degrees when the servo motor turns 180 degrees. Idler pulleys are also attached to each joint for a continuous cable connection, as shown in Figure 4.  
Once the desired profile is created, all the links are then modelled in 3 dimensions (3D) using the same process with the necessary features, such as pulleys and slots, being added. After all the links are modelled, they are assembled in the following manipulator assembly along with the integrated electronics, as shown in Figure 5.  
Figure 4: (a) Link design process; (b) Aerial manipulator assembly.