Unlocking a nose landing gear in different flight conditions: folds, cusps and a swallowtail

This paper investigates the unlocking of a non-conventional nose landing gear mechanism that uses a single lock to fix the landing gear in both its downlocked and uplocked states (as opposed to having two separate locks as in most present nose landing gears in operation today). More specifically, we present a bifurcation analysis of a parameterized mathematical model for this mechanical system that features elastic constraints and takes into account internal and external forces. This formulation makes it possible to employ numerical continuation techniques to determine the robustness of the proposed unlocking strategy with respect to changing aircraft attitude. In this way, we identify as a function of several parameters the steady-state solutions of the system, as well as their bifurcations: fold bifurcations where two steady states coalesce, cusp points on curves of fold bifurcations, and a swallowtail bifurcation that generates two cusp points. Our results are presented as surfaces of steady states, joined by curves of fold bifurcations, over the plane of retraction actuator force and unlock actuator force, where we consider four scenarios of the aircraft: level flight; steep climb; steep descent; intermediate descent. A crucial cusp point is found to exist irrespective of aircraft attitude: it corresponds to the mechanism being at overcentre, which is a position that creates a mechanical singularity with respect to the effect of forces applied by the actuators. Furthermore, two cusps on a key fold locus are unfolded in a (codimension-three) swallowtail bifurcation as the aircraft attitude is changed: physical factors that create these bifurcations are presented. A practical outcome of this research is the realization that the design of this and other types of landing gear mechanism should be undertaken by considering the effects of forces over considerable ranges, with a special focus on the overcentre position, to ensure a smooth retraction occurs. More generally, continuation methods are shown to be a valuable tool for determining the overall geometric structure of steady states of mechanisms subject to (external) forces.