# Optimization of the Position and Stiffness of Passive Walking Assistance Devices
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Study** & **Type of** & **Type of** & **Joint** & **Purpose** \\ \hline [PERSON] et al. [4] & Active-tethered & Exp. & Ankle & Reducing the cost of walking \\ [PERSON] et al. [5] & Active & Exp. & Ankle & Reducing the cost of walking \\ [PERSON] et al. [17] & Active soft & Exp. & Ankle & Rehabilitation \\  & robotics & Exp. and & Hip & Rehabilitation \\ [PERSON] et al. [18] & Active soft & Exp. & Ankle & Reducing the cost of walking \\ [PERSON] et al. [7] &rosive elastic spring & Exp. & Ankle & Reducing the cost of walking \\ [PERSON] and [PERSON] [10] & Passive elastic & Exp. & Ankle & Reducing the cost of walking \\ [PERSON] et al. [8] & Passive elastic band & Exp. & Hip & Reducing the cost of walking \\ [PERSON] et al. [11] & Sexotendon & Exp. & Hip and knee & Reducing the cost of walking \\ [PERSON] et al. [19] & Passive elastic springs & Exp. & Ankle and knee & Reducing the cost of walking \\ [PERSON] et al. [20] & Passive elastic & Exp. & Seven different & Reducing the cost of walking \\ [PERSON] et al. [20] & Passive elastic & Comp. & locations & Reducing the cost of walking \\ This study & Passive elastic springs, but can be extended & Comp. & Location was found by optimization & Reducing the cost of walking, but \\  & be extended & & optimization & it can be extended. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The comparison of previous studies based on the type of assistance, the type of study (experimental (Exp.) or computational (Comp. )), the joint assisted, and the purpose. The purposes of walking assistance systems are mostly to reduce the energetic cost of walking [4; 5; 7; 8; 10; 11; 19; 20]. The purpose of assistive systems can be extended to rehabilitation, falling prevention, etc., by using different objective functions in the simulation model. Thus, the aim of the proposed method was to find the location and stiffness of walking assistance system to create a framework for future studies. In the present study, a two-dimensional multibody dynamic model of human walking with a walking assistance system was created. The walking assistance system was considered as a tension spring, and the two ends of the spring were found by minimizing the total positive joint power. Although previous studies developed walking assistance systems around the ankle, knee, and hip joints to reduce the metabolic cost of walking, the locations of the walking assistance system placement were empirically chosen. The present study proposes a way to determine the location of the walking assistance system based on the optimization. After determining the location of the walking assistance system placement, the optimal stiffness values at different walking speeds were found. Additionally, an optimal stiffness value that considers all walking speeds were also obtained. The contributions of the walking assistance system with a speed-specific stiffness and a general stiffness for all speeds were compared in terms of the reduction in the total positive joint power, joint moments, stiffness characteristics, etc.