# Research on the Performance of an Aircraft Landing
## 1 Introduction  
Landing gear retraction systems are safety devices that guarantee the retraction action and locking capability in the retracted state of landing gear after aircraft take off as well as the extension action and locking capability in the deployed state prior to landing [1]. According to a Federal Aviation Administration (FAA) investigation report [2] and Boeing's Statistical Summary of Commercial Jet Airplane Accidents [3], a considerable portion of landing gear failures are caused by failures of the retraction mechanism, in which lock mechanism failures are prevalent. The main failure modes include the locking failure, unlocking failure, and automatic unlocking of landing gear. Thus, the rational design of landing gear lock mechanisms and the analysis of locking performance are critical to the safe and reliable operation of the landing gear retraction system [4]. Earlier methods of designing landing gear lock mechanisms were often based on empirical modification and experimental verification. Such design patterns were procedurally cumbersome, causing high repetition rates and long cycles of design as well as high costs of development [5]. With the advancement of digital mockup technology [6], multidisciplinary co-simulation has become the mainstream method of lock mechanism design [7]. [PERSON] [8] proposed a multidisciplinary co-simulation-based method for analyzing a system with a hydromechatronically coupled landing gear lock mechanism. The method allowed preferential analysis of the fault mechanism and fastimplementation of fault diagnosis. [PERSON] [9] and [PERSON] [10] created co-simulation models of landing gear retraction dynamics with a hook lock and a linkage lock separately based on the Siemens Virtual.Lab Motion (Siemens, Berlin, Germany) and Siemens Imagine.Lab AMESim (Siemens, Berlin, Germany) and explored the effects of lock mechanism motion on the dynamic properties of the retraction system. After modeling the double-lock bar mechanism of a certain unmanned aerial vehicle (UAV) in Adams, [PERSON] [11] analyzed the intersection load and stress level of the lock bars. However, virtual prototypes and digital simulation technology also have severe limitations regarding the design of complex mechanisms, which are reflected in the following two aspects. One aspect involves handling changes in the stability characteristics of mechanical systems. The majority of today's landing gear lock mechanisms (regardless of whether they employ hook or linkage locks) [1] jump instantaneously from an unstable state to a stable locked state at the moment of locking. In such a state, the lock mechanism cannot be unlocked without the unlocking device. This is also the case for the unlocking process. Prior to the advent of bifurcation theory, it was impossible to explain the jump phenomenon of lock mechanisms by only simulative or experimental means. Accordingly, it was also difficult to analyze the conditions and influencing factors of the lock jump from the mechanism perspective, which greatly restricted the design level of lock mechanisms. In fact, the lock jump phenomenon can be well explained by bifurcation theory. The lock mechanism bifurcates in the critical unstable state to reach a stable locked state from an unstable unlocked state from an unstable unlocked state to reach a stable unlocked state from an unstable locked state [12]. The other aspect involves handling the system of complex nonlinear mechanisms. To analyze the instability characteristics of lock mechanisms, virtual simulation technology needs to employ a dynamic perturbation method for acquisition of the characteristics. If a parameter influence analysis is required, substantial iterative computations are needed, which are heavily burdensome. Therefore, virtual simulation technology can hardly offer fast, effective support for the selection of various key parameters in the early phase of mechanism design.