# Optimization of Design Parameters Using SQP for an Agricultural Pipe Extraction Device
## 2 Materials and Methods
### Constraints  
If there is a contradiction in the range of parameters according to the objective function during optimization using the optimal design method, an error may occur. In this case, the initial height from the ground to the operating position of the extraction device is designed unrealistically. That is, if the constraints of the objective function are not considered during optimization, the height from the ground to the operating position of the extraction device may increase or decrease more than necessary because of the lengths of Link1 and Link2 and the angles \(\alpha\) and \(\beta\). Considering the action of actually stepping on the extraction device by lifting one's leg, if the operating distance range between the footest and the road surface is significantly reduced or increased, the extraction device operation is difficult. Consequently, work efficiency is lowered. In addition, owing to excessive motion, fatigue of the lower extremity muscles and pain in the knee joint may occur. In order to solve this problem, constraints were set using an ergonomic approach. The main design objective applied to ergonomics is to design objects, equipment, machinery, etc., for efficient use by humans. Its importance is emerging in all fields where interaction with humans occurs ([PERSON] and [PERSON], 2016) [11]. In this study, the values required for the constraints were defined based on the Korean body size data of Size Korea and the EMG (Electromyography) measurement values according to the knee joint. Considering the average age of farmers engaged in agriculture in Korea (KOSIS, Daejeon, Republic of Korea, 2022) [12], anthropometric data from  
Figure 4: Analysis of the forces of Link2. 40-to-69-year-old individuals were used. The EMG values measured by [PERSON] et al. (2015) [PERSON] et al. (2015) were used to assess changes in the lower extremity muscle activation and fatigue according to the knee joint angle. According to the 8 th Korean anthropometric survey (Size Korea, 2020) ([PERSON], 2020), the height of the anterior superior iliac spine (ASIS) was 914 mm, and the height of the tibialae was 447 mm among the body sizes of men aged 40-69 years. For women, they were 837 mm and 409 mm, respectively. Table 1 and Figure 5 show the definitions and measurement tools for the heights of the anterior superior iliac spine (ASIS) and tibialae. The height of the footrest was designed based on the body size of an elderly woman, and there are several reasons for selecting the body size standard. If it is based on the body size of a male, the height of the footrest can be designed higher. In this design, the angle of the knee that needs to be lifted increases to more than 60\({}^{\circ}\) when used by an elderly woman with relatively small body size. As a result, muscle fatigue greatly increases, causing the user to feel uncomfortable during the operation, which may eventually lead to injury. On the other hand, if the device is designed based on the body size of an elderly woman, most people can use the device without difficulty. In addition, rural society is rapidly aging. It is appropriate to design mechanical systems to meet these trends. Therefore, for more universal use, it was designed based on the body size of an elderly woman. ([PERSON] et al., 2020) [PERSON] et al. (2015). EMG values measured by [PERSON] et al. (2015) [PERSON] et al. (2015) were used to determine the activity and fatigue of the lower body muscles according to the angle of the initial knee joint when the extraction device was operated. Electromyography was used to record the change in the current generated by the muscle movement by attaching electrodes to the skin surface. This method is mainly used to analyze muscle activity and muscle fatigue in many studies. According to [PERSON] et al. (2015) [PERSON] et al. (2015), muscle activity according to the knee joint angle is highest when the knee joint angle is 60\({}^{\circ}\), among 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\).