Abstract
This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this approach, crucial features in the response surface, such as bifurcation points, can be identified. By numerically continuing these points in the appropriate parameter space, the resulting bifurcation diagram can be used to guide parameter selection and optimization. In this paper, we demonstrate the potential of this technique by considering an aircraft nose landing gear, with a novel locking strategy that uses a combined uplock/downlock mechanism. The landing gear is locked when in the retracted or deployed states. Transitions between these locked states and the unlocked state (where the landing gear is a mechanism) are shown to depend upon the positions of two fold point bifurcations. By performing a two-parameter continuation, the critical points are traced to identify operational boundaries. Following the variation of the fold points through parameter space, a minimum spring stiffness is identified that enables the landing gear to be locked in the retracted state. The bifurcation analysis also shows that the unlocking of a retracted landing gear should use an unlock force measure, rather than a position indicator, to de-couple the effects of the retraction and locking actuators. Overall, the study demonstrates that bifurcation analysis can enhance the understanding of the influence of design choices over a wide operating range where nonlinearity is significant.
Highlights
Mechanism design processes tend to focus on determining paths for key parts of the mechanism [1,2,3]
Owing to the capabilities of multibody dynamics software packages to simulate dynamic systems in general, engineers working in an industrial context where mechanism analysis is not commonplace, will tend to use these methods during the design process
Numerical continuation applied to the constraint equations was shown to provide an efficient means of finding equilibria, and how they depend on different parameters of interest
Summary
Mechanism design processes tend to focus on determining paths for key parts of the mechanism [1,2,3]. The field of kinematic mechanism analysis has seen the use of numerical continuation [26,27,28]; the key dynamical systems concept of considering how bifurcations populate the model parameter space appears to be distinct from all of these applications. The alternative landing gear system uses the same locking mechanism to uplock (as well as downlock) the NLG, through clever mechanism design This results in the need for only two actuators: a retraction actuator and an unlock actuator. A landing gear model consisting of a set of coupled kinematic and force equilibrium equations was presented in [31,32] In these papers, the effect of the location of the lock springs and retraction actuator placement, respectively, for a landing gear with a traditional locking mechanism was analysed with the tool of continuation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
