Abstract
Vehicle stability is a widely studied topic today. It is crucial that we develop a better understanding of one of the main problems of vehicular accident rate problems throughout the world: the rollover accident. The main goal for researchers is to determine a way to predict vehicle behaviour under a variety of circumstances. Davies method is a mathematical tool that allows the static and kinematic analysis of any kind of mechanisms, as well as we can find in vehicle suspensions. This method uses the Graph theory that enables kinematic chain representation by means of a graph for later analysis. In this paper we present the vehicle stability kinematic analysis using Graph theory, Screw theory and the Davies method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Gillespie, T.D.: Fundamentals of vehicle dynamics. In: SAE International, 7th ed., ISBN1560911999 (1992)
Hac, A.: Rollover stability index including effects of suspension design. In: SAE International, SAE 2002 World Congress. Detroit, March 4-7 (2002)
Winkler, C.: Rollover of heavy commercial vehicles. In: UMTRI Research Review. The University of Michigan Transportation Research Institute, vol. 31, issue no. 4, pp. 1–20 (2000)
Lee, U.: A study on a method for predicting the vehicle controllability and stability using the screw axis theory. Ph.D. thesis. Hanyang University. Seoul, South Korea (2001)
Bidaud, P., Benamar, F. Poulain, T.: Kineto-static Analysis of an Articulated Six-wheel Rover. Climbing and Walking Robots, pp. 475–484. Springer Link (2006)
Erthal, J.: Modelo Cinestático para Análise de Rolagem em Veículos. Ph.D. These. Federal University of Santa Catarina. Florianópolis, Brazil (2010)
Mejia, L., Simas, H., Martins, D.: Force Capability Maximization of a 3RRR Symmetric Parallel Manipulator by Topology Optimization. 22nd International Congress of Mechanical Engineering (COBEM 2013), November 3–7, Ribeirão Preto, SP, Brazil (2013)
Davies, T. H.: The 1887 committee meets again. Subject: freedom and constraint. In: Ball 2000 Conference. Cambridge: Cambridge University Press, 56 (2000)
Tsai, L.-W.: Robot Analysis: the Mechanics of Serial and Parallel Manipulators. Wiley, New York. ISBN 0-471-32593-7 (1999)
Cazangi, H. R.: Aplicação do Método de Davies para Análise Cinemática e Estática de Mecanismos com Múltiplos Graus de Liberdade. Master’s thesis. Federal University of Santa Catarina. Florianópolis, Brazil (2008)
Davies, T.H.: Coupling, coupling networks and their graphs. Mech. Mach. Theory 30(7), 1001–1012 (1995)
Tsai, L.-W.: Mechanism Design: Enumeration of Kinematic Structures According to Function. London, CRC Press. ISBN 0849309018 (2001)
Davies, T.H.: Kirchhoff’s circulation law applied to multi-loop kinematic chains. Mech. Mach. Theory 16(3), 171–183 (1981)
Rill, G.: Road Vehicle Dynamics: Fundamentals and Modeling. CRC Press, ISBN 978-1-4398-3898-3 (2011)
Jazar, R.: Vehicle Dynamics: Theory and Application. 2nd edn. Springer, ISBN 978-1-4614-8544-5 (2014)
Pacejka, H.: Tire and Vehicle Dynamics. Published by Elsevier Ltd, 3rd ed. ISBN 9780080970165 (1995)
Heyman, J.: Basic Structural Theory. Cambridge: Cambridge University Press, 1st edn., ISBN-13 978-0-511-39692-2 (2008)
Acknowledgments
This research was supported by the Brazilian governmental agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendices
Appendix A. Wrench Parameters of the Mechanism
Constraints and forces | s i | \( s_{0i} \) | ||
---|---|---|---|---|
F x1 | 1 0 0 | 0 | 0 | 0 |
F y1 | 0 1 0 | 0 | 0 | 0 |
F z1 | 0 0 1 | 0 | 0 | 0 |
M y1 | 0 1 0 | 0 | 0 | 0 |
M z1 | 0 0 1 | 0 | 0 | 0 |
F z2 | 0 0 1 | 0 | t cos θ 1 | t sin θ 1 |
F z3 | 0 0 1 | −L | t cos θ 4 | t sin θ 4 |
F x4 | 1 0 0 | −L | 0 | 0 |
F y4 | 0 1 0 | −L | 0 | 0 |
F z4 | 0 0 1 | −L | 0 | 0 |
M y4 | 0 1 0 | −L | 0 | 0 |
M z4 | 0 0 1 | −L | 0 | 0 |
W | 0 0 −1 | −a 1 | t/2 | h |
m a y | 0 −1 0 | −a 1 | t/2 | h |
Appendix B. The Equations System from the Statics of the Mechanism
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Moreno, G.G., Barreto, R.L.P., Vieira, R.S., Nicolazzi, L., Martins, D. (2017). Three-Dimensional Analysis of Vehicle Stability Using Graph Theory. In: Zawiślak, S., Rysiński, J. (eds) Graph-Based Modelling in Engineering. Mechanisms and Machine Science, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-39020-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-39020-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-39018-5
Online ISBN: 978-3-319-39020-8
eBook Packages: EngineeringEngineering (R0)