# A New Methodology for Type Synthesis of Planar Linkages for Exoskeletons up to Five Angular Outputs
## 1 Introduction  
In recent years, the use of mechanical systems for medical applications has increased. Rehabilitation processes are applied to eliminate deficiencies such as joint range of motion (ROM), muscle weakness and coordination in the upper or lower limb. Therefore, many robotic systems have recently been proposed. An exoskeleton or rehabilitation robot is a powered wearable mechanism that can track the user's movements. Type synthesis is the process of generating all independent alternatives of exoskeleton linkage structures regardless of their dimensions. That is helpful to select a suitable candidate for a predetermined motion. The structure of a mechanism is defined by the number of links, number of joints, and their type. Several methods have been introduced for structural synthesis of mechanisms since the 1960s [1; 2; 3; 4; 5]. Type synthesis has been investigated by [PERSON] et al. [6] to develop a systematic procedure suitable for computer implementation. Graph theory and Assur group were applied to generate a group of kinematic structures with specified features. Graph theory is involved to enumerate all linkages with a given number of links and DOFs, and eliminating isomorphic linkages [7; 8]. Starting from the simplest Baranov trusses, all types of kinematic chains can be derived by adding Assur group which is simpler to build up linkages with additional loops [9; 10; 11; 12]. Dimensional synthesis is applied as a second stage to detect optimal linkage parameters. That can be achieved by graphical,analytical, or optimization-based methods [13; 14]. Design parameters of rehabilitation robots include degree of freedom, weight and inertia, range of motion, torque and velocity requirements for joints, actuation type, and kinematic considerations. Mechanism synthesis is a proper tool to obtain a rehabilitation robot with a desired movement of the limbs with a minimum number of degrees of freedom. That will simplify the control of the exoskeleton system and provide reliability, light weight, and lower cost. Lightweight exoskeletons were obtained by replacing rigid links of exoskeleton with lightweight cuffs which are fixed to moving limb segments of human upper or lower limbs. Cable-driven systems were used to control exoskeleton movements [15; 16]. It is verified that n+l wires are necessary and sufficient to realize the motion with n DOFs. Besides that, both pull and push movements were achieved. However, the limitation of a cable-driven system is that each cable can only pull but not push. [PERSON] et al. [17] used a cable-driven system to calculate the workspace of a serial limited DOF robot. Mechanical systems, such as four-bar linkage, are used to reduce the number of DOFs and actuators consequently [18; 19; 20]. However, the design of the exoskeleton depends on actuators that are used for manipulation. Electric, pneumatic, and hydraulic actuators are frequently used [19]. Mechanical linkage systems have some advantages as they provide high stability and large forces transmission. Therefore, one DOF linkages with revolute joints are preferable for rehabilitation applications due to their parallel nature, accuracy, compactness, portability, and ease of manufacturing. Mechanical linkage exoskeletons were applied for finger rehabilitation processes with one DOF with fewer motors [21; 22; 23]. Low-price exoskeletons and planar twelve-bar linkage mechanisms were presented to reproduce an accurate finger movement. Both planar and spatial exoskeletons with one DOF have been widely used for hand rehabilitation process systems [24; 25; 26; 27; 23]. Some prototypes and their mechanical design, actuation, and power transmission methods were introduced. Lower limb exoskeletons can be used for providing strength during walking, to carry heavy loads, or aiding the disabled people for walking. Different types of exoskeletons and orthotic devices have been developed to assist lower limb motion [28; 29; 30]. Design, kinematic analysis, and simulation of low-cost leg and knee exoskeletons were presented.