# Optimization of the Position and Stiffness of Passive Walking Assistance Devices
## 1 Introduction  
Walking is the method of locomotion used by humans to move from one location to another. Aging [1], overweight [2], disease [3], etc., can cause a reduction in mobility. Those with reductions in mobility require assistance to conduct daily life routines, and these reductions create barriers to socialization, among others. Walking assistance systems are one of the ways to regain mobility as they decrease the requirements for joint moments and power. Recently, there has been a tremendous amount of effort devoted to developing assistive systems to reduce the metabolic cost of walking [4; 5; 6; 7; 8; 9; 10; 11; 12], to facilitate the carrying of objects [13; 14], etc. There are active [4; 5; 6] and passive [7; 8; 9; 10; 11; 12] walking assistance systems that are classified depending on the requirements for external power. Whereas passive devices store and release energy using elastic elements, active devices use electric motors, hydraulic, pneumatics systems, etc., to generate forces and moments. Although active systems reduce the metabolic cost of walking more than passive systems, passive walkingassistance systems are advantageous due to being light and easy to use compared with active systems. Reducing the metabolic cost of walking is one of the important goals of walking assistance systems [15]. Previous studies showed that elderly people reduce their walking speed to reduce the metabolic cost of walking [16]. Instead of reducing walking speed, a walking assistance system can help to reduce the cost of walking while maintaining the walking speed. An active ankle exoskeleton reduced the metabolic cost of walking by 24% via the optimization of the assistive torque profile of the device [4]. [PERSON] et al. developed a passive ankle exoskeleton that reduced the metabolic cost of walking by 7.2% and showed that the passive walking assistance system could reduce the metabolic cost of walking [7]. The spring system around ankle joint stores and releases energy with a clutch system depending on the motion. In another study by [PERSON] and [PERSON] [10], the effect of walking speed on the optimal stiffness characteristics of an ankle joint assistance system was investigated. [PERSON] et al. showed that an elastic band that was placed around hip joint reduced the metabolic cost of walking by 4.2% [8]. [PERSON] et al. proposed an exotendon that reduced the load on hamstring muscles [11]. Many different designs and methods have been used to investigate walking assistance devices for various purposes, as shown in Table 1. Most of the previous studies have investigated the performance of walking assistance systems through experiments [4; 5; 7; 8; 10; 11; 17; 18; 19]. There are some limitations to and disadvantages of these experimental investigations. The locations that the walking assistance devices have been placed are mostly the same, and the stiffness of the structures were changed [7; 10; 11]. In addition, several procedures have been used to conduct experiments, and these experiments take a significant amount of time. Therefore, computational studies are promising, and the result of experimental studies can be used to validate the findings of simulations. Moreover, the placement of the various types of walking assistance systems have been limited to certain locations [4; 5; 7; 8; 10; 11; 17; 18; 19; 20]. The locations of walking assistance systems have been determined based on joint kinematics, joint kinetics, and experience. The number of design alternatives can be increased by using simulation-based investigation. [PERSON] et al. [20] conducted a simulation-based investigation for seven different locations. However, the location where the walking assistance systems are used can be determined through the optimization using simulation model. In the present study, an optimization-based method to determine the location of walking assistance system use was presented, and many design alternatives were considered during the optimization.