## 1 Introduction
In this regard, methods to control the stiffness of flexure elements that do not imply a radical change in their overall dimensions can be found in the literature [23; 24]. Some methods, such as static balancing [25; 26; 27; 28; 29; 30], antagonism principle [31; 32], and lever mechanism [33; 34; 35], consist of pre-deforming the flexure elements of compliant systems, reducing actuation effort, thus increasing range of motion. Flexure elements used in these methods are commonly coil springs. Others techniques are based on changing the effective length of elastic components in a compliant system to achieve variable stiffness [36; 37; 38; 39; 40]. Despite the success in modifying the stiffness via pre-deformation or change in effective length of flexures, the use of external systems or actuators is demanded, thus increasing complexity, size, and cost. Intentional contact between elements in compliant systems is another approach to modify their stiffness known as contact-aided.Besides, as contact surfaces are common parts of the compliant systems, this method avoids the use of external elements and actuators. Examples of contact-aided compliant systems can be found in the literature, addressing topics such as morphing [41; 42; 43], stress relief [44; 45; 46], improve load-bearing capacity [47], and energy absorption [48; 49]. In all cases, global strain capability of contact-aided compliant systems is increased. Furthermore, in [50; 51] variable stiffness compliant joints are achieved through changing the effective length during deformation by self-contact between the flexible parts and support points manufactured as part of the same system. Contact-aided compliant systems act as stiffness switches during deformation and are suitable only in applications where abrupt changes of stiffness are needed. Approaches to tailor the stiffness of compliant systems based on selectively removing material from flexure elements maintaining their overall dimensions appear as the possible solution to deal with inaccuracies and limitations of compliant systems. These approaches termed as Cellular Materials and Topology Optimization allow an accurate modification of the stiffness of flexure elements avoiding the use of external elements and actuators. Tailoring stiffness via Cellular Materials is based on using predefined periodic arrays combining material and void spaces to substitute the flexure elements of compliant systems [22]. The process to tailor the stiffness of a flexure element via Cellular Materials is graphically explained in Figure 2a. Topology Optimization has been widely used in the design and synthesis of compliant systems [53; 54], and even to obtain specific stiffness values [55]. However, the resulting compliant systems often have complex architectures and distributed compliance, thus leading to complicated analysis, manufacture, and further implementation. Therefore, recent efforts have been focused on applying Topology Optimization processes only in the flexible parts (flexures) of compliant systems allowing an acceptable characterization of the stiffness while maintaining original system macro-shape and thus manufacturability. Then, tailoring stiffness via Topology Optimization consists of removing material from flexure elements based on a goal function [56]. The process to tailor the stiffness of a flexure element via Topology Optimization is graphically explained in Figure 2b. Both techniques are intimately related, as shown in Figure 2, as to achieve the optimal configuration of the cellular structure, it is necessary to perform an optimization process commonly called size or shape optimization, and the result of a Topology Optimization process after a post-processing refinement is often a cellular structure. Optimization via cellular materials is often done intuitively and manually, while Topology optimization is automated via computational algorithms.