## 1 Introduction  
Several appendages of satellites were stowed inside the launch vehicle (LV) fairing during the launch phase and has to be deployed in orbit using various deployment mechanisms [1; 2; 3; 4]. If the deployment of appendages was not achieved successfully, this could have a critical impact on the mission of satellites. Therefore, deployment structures, such as satellite solar panels, SAR antennas, and antenna booms, should be verified through ground-based deployment tests and analyzed to determine whether they can be deployed in space orbit successfully. The deployment schemes that have been employed so far released the clamping units to allow the stowed appendages to dynamically deploy and self-latch. However, it needs to be fully understood and optimized considering severe dynamic effects at the latching of deployment, which could damage the structure. Conversely, a slow and highly damped deployment may end without achieving the fully deployed configuration. Thus, balancing between these effects is challenging as noticed by the development process of the MARSIS booms of 20 m length [5; 6] needing a large amount of testing and simulation. As many deployment mechanisms [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19], articulated spring (AS) hinges and tape spring (TS) hinges have been widely employed for solar panels and antennas in small satellites due to their simplicity and easy fabrication. Among those, AS hinges are a representative example of rigid hinges, composed of a torsional spring, a latch, and a stopper. The torsional spring stores strain energy during folding, and releases it for deployment operation. Its moment-rotation profile is very simple and almost linear elastic for entire rotation angles. The latch and stopper are used to maintain the deployment configuration and avoid the overshooting of deployment panels. Typically, AS hinges can realize high deployment stiffness; thus, they are suitable as deployment devices for satellites requiring high agility. However, at the moment of latching, its coupling parts come into contact with each other for stopping and latching. Therefore, high latching forces are generated, which require proper compensation. TS hinges are a representative example of flexible hinges. They consist of curved short strip tape springs and a hinge bracket, as shown in Figure 1, the moment-rotation relationship of TS is linearly elastic for small rotations but suddenly dropped at the critical rotation angle due to the snap-through buckling. After that, the torque is almost constant for large rotations for forward rotation (see Figure 2). However, when the backward rotation is applied, it does not go back to the original moment-rotation profile obtained from the forward rotation. Its path-dependent moment-rotation profile generates high structural damping; thus, the impact energy at the latching dissipates, which leads to much smaller impact loads. In addition, it is well known that TS hinges have sufficient self-driving forces and self-locking function, which is simple in shape and reduces mass and manufacturing cost. To model such complex mechanisms of TS hinges, several approaches have been proposed, such as analytical methods [4], experimental methods [5] and finite-element methods [12; 13; 14]. [PERSON] et al. used both an analytical approach and finite-element (FE) analysis to investigate the relationship between the geometric parameters and the moment-rotation behavior of TS hinges [12; 13]. [PERSON] carried out a nonlinear FE analysis of TS hinges using an artificial damping method in ABAQUS software [14]. [PERSON] et al. investigated the moment-rotation relationship when TS hinges were folded at some skew angle, also termed three-dimensional (3D) folding theoretically and experimentally [15; 16]. [PERSON] et al. employed a response surface method using the Box-Behnken method to describes the relationship between the geometric parameters of the TS hinges and the bending stiffness, deployment torque, and maximum folding stress [17].