# Bi-Stability in Flexure Beams: Introducing a Setup for Experimental Characterization
## 1 Introduction  
Bi-stable mechanisms can stay in two positions without a power input or locking systems. These mechanisms can achieve large displacements with lower energy requirements and are versatile alternatives for various types of applications. Bi-stable mechanisms have been used in microdevices (MEMs) [1; 2; 3], aerospatiale applications [4], biomedical devices [5], robotic systems [6], and to add functionalities to autonomous vehicles [7; 8]. The emerging area of soft robotics also harnesses bi-stable mechanisms due to their ability to move faster, amplify force outputs, overcome low actuation energy, and generate extreme compliance through their hyperplastic components [9]. Previous literature has introduced bi-stable elements that enable locomotion in soft robots [8; 10; 11]. Another use is in mechanical metamaterials with purposes such as deployable objects [12; 13], shape-reconfigurable materials [14], or auxeticity (negative stiffness) [15; 16; 17]. When bi-stability is employed in compliant mechanisms, they gain advantages such as a decrease in the number of parts, reduced friction, a simplified manufacturing process, and a reduction of backlash, friction, and wear [18]. The deflected elements store and releasestrain energy to stay in two or more configurations, allowing the integration of motion and energy storage into a single component [19]. Compared with traditional rigid-body mechanisms that continuously consume energy, bi-stable compliant mechanisms only employ power during switching. Regardless of their benefits and wide range of applications, bi-stable mechanisms are more difficult to design and analyze than traditional mechanisms, as they present high nonlinearity induced by the post-buckling behavior of their flexible beams [20; 21]. Furthermore, they must maintain a low stress concentration to avoid fracture [22]. Researchers have proposed various approaches for investigating bi-stable mechanisms using analytical modeling, finite element analysis, and experiments. Some analytical approaches are pseudo-rigid body modeling (PRBM), which lacks accuracy at the end slope of the beam [23], and the elliptic integral solution (EIS) [24; 25; 26], which is more efficient but limited to simple geometries due to its high complexity. In contrast, non-linear finite element simulation is commonly used as a design evaluation method due to its practicality. However, the results do not strictly coincide with the experimental ones [11] because this type of solver assumes that the model does not have the imperfections found in real life [21]. As it is challenging to establish a method to determine the nonlinearities caused by the buckling behavior of the bi-stable mechanism, many authors opt to validate their analysis experimentally, specifically the force-distance relationships. To do so, the specimen must be placed in the measuring device through a setup and fixtures that adhere to the defined boundary conditions. As the bi-stable mechanism studied in this publication is based on the basic fixed-fixed beam topology [22], only setups for variations of this arrangement are considered in this section. For instance, to evaluate the force-displacement characteristic of the perching aerial vehicle presented by [PERSON] et al. [7], the gripper is fixed to the test plate and a hook is attached to the gauge. Both are joined with a string that pulls the specimen to measure tension [7]. Similarly, [PERSON] et al. similarly attach the specimens of a multi-material, bi-stable structure to the testing machine with two customized 3D printed grippers [12]. These setups are restricted to the specific design and geometric characteristics of the samples. Other setups use glue to secure the bottom and top of the structures to the compression plate and base of the machine. This option is limited to specimens that require small forces to snap, either because of their small scale or because they are made of a material with low tensile strength [15; 27].