# Multicriteria Optimization of Lower Limb Exoskeleton Mechanism
## 1 Introduction  
Exoskeleton robots have found broad applications for augmenting power and aiding in rehabilitation [1; 2; 3; 4; 5; 6; 7]. Power augmentation is important for tasks involving heavy load transportation with limited muscle strength, while robot-assisted technologies employing upper and lower limb exoskeletons are used for rehabilitating individuals who have experienced a loss of mobility in their joints and muscles. Studying human walking apparatus and motion diagrams representing the leg movement has been useful in various fields, including the development of human prosthetics, human mimicking robots, and advancements in research areas such as biomimetics, military combat, cinematography, toys, and terrestrial and extraterrestrial exploration [7; 8]. For a comprehensive overview of bipedal walking robots and exoskeletons, refer to [1; 2; 3; 4]. Various design and control architectures of exoskeletons were summarized in the relevant references [3; 5]. In recent years, various design schemes of lower limb exoskeletons aimed at achieving compact devices and meeting specific optimality criteria have been proposed [9; 10; 11]. Generally, the kinematic scheme of the leg exoskeleton is based on an open-loop kinematic chain with the motors mounted directly on the movable joints. Although these open kinematic chains offer greater flexibility and ease of design, their large number of degrees of freedom (DOF) contributes to increased costs and complexities in control. Using heavy servo-motors to meet significant torques generated in active joints leads to complicated and cumbersome design. The bulkiness and substantial weight of this kind of device are highlighted in [6; 12]. Numerous researchers have studied the walking apparatus, demonstrating that walking patterns are measurable, predictable, and repeatable. Ref. [13] presents a passiveexoskeleton with 17 DOF for load-carrying, which includes two 3 DOF ankle joints, two 2 DOF hip joints, two 1 DOF knee joints, a 1 DOF backpack, and redundant degrees of freedom at the thigh and the shank to improve the compatibility of human-machine locomotion. In [14], a mechanism has been designed for a walking robot, effectively minimizing the number of required motors, thereby contributing to reduced energy consumption. The dimensional synthesis is conducted analytically to formulate a parametric equation, and the resulting geometry of the leg mechanism is established. However, it should be noted that this mechanism is not suitable for exoskeletons due to its significant deviation in shape from that of the human leg. [PERSON] et al. [6; 12] introduced a 1 DOF mechanism for lower limb rehabilitation exoskeletons. In [12] proposed an integrated type and dimensional synthesis method for designing compact 1 DOF planar linkages with only revolute joints and applied the method on a leg exoskeleton that can generate human gait patterns simultaneously at hip and knee joints. Reducing the number of motors resulted in decreased energy consumption. Ref. [6] reports a close match to human gait and stable hip and knee joint outputs in their prototype due to its parallel structure. The drawback of [PERSON]'s mechanism is its use of an 8-bar-10-joint configuration; simplification would involve reducing the number of these linkages. Ref. [15] presents a leg exoskeleton consisting of a planar five-link closed linkage. The robotic system is intended for patients who have suffered strokes. The design is simple, wearable, light, and anthropomorphic in structure, and it operates with only one motor. The drawbacks mentioned in the paper include the limitation of providing mobility solely to the knee and hip joints, as well as the need for future design improvements, such as an adjustable length mechanism to accommodate patients with varying anthropometric data. In [10], the author introduced a new 1 DOF structure, allowing adjustments of mechanism links to accommodate varying human body types. However, the geometry of the novel design is bulkier.