Abstract
This paper presents a novel method to select self-aligning mechanisms enumerated using Davies’ method and matroid theory. Davies’ method and screw theory are used to model mechanisms in terms of freedoms and constraints. Matroids are used to enumerate self-aligning mechanisms using the model created with Davies’ method as input. Matroid contraction is then applied in order to select a set of feasible self-aligning mechanisms. The herein proposed method is applied to a well known mechanism, the Quadrupteron. Using matroid contraction, design requirements are employed to select a set of feasible self-alingning mechanisms. A novel familiy of self-aligning mechanisms, called Quadriflex family, is finally proposed.
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References
Artmann, V.N., Barreto, R.L., Carboni, A.P., Simoni, R., Martins, D.: Type synthesis of self-aligning mechanisms applied to the leg rest section of an hospital bed. In: IFToMM World Congress on Mechanism and Machine Science, pp. 1413–1422. Springer (2019)
Artmann, V.N., Barreto, R.L., Martins, D., Simoni, R.: Analysis and elimination of redundant constraints in clamping devices. In: Proceedings of the 25th International Congress of Mechanical Engineering - COBEM, 20–25 October 2019, pp. 147–161. ABCM (2019)
Barreto, R.L., Martins, D., Simoni, R., Dai, J.S., et al.: Self-aligning analysis of the metamorphic palm of the KCL/TJU metamorphic hand. In: 2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR), pp. 1–8. IEEE (2018)
Blanding, D.L.: Exact Constraint: Machine Design Using Kinematic Principles. ASME, New York (1999)
Carboni, A.P., Simas, H., Martins, D.: Analysis of self-aligning mechanisms by means of matroid theory. In: International Symposium on Multibody Systems and Mechatronics, pp. 61–73. Springer (2017)
Davies, T.: Kirchhoff’s circulation law applied to multi-loop kinematic chains. Mech. Mach. Theory 16(3), 171–183 (1981)
Davies, T.: Couplings, coupling networks and their graphs. Mech. Mach. Theory 30(7), 991–1000 (1995)
Davies, T.: Dual coupling networks. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 220(8), 1237–1247 (2006)
Gosselin, C.M., Masouleh, M.T., Duchaine, V., Richard, P.L., Foucault, S., Kong, X.: Parallel mechanisms of the multipteron family: kinematic architectures and benchmarking. In: Proceedings of the 2007 IEEE International Conference on Robotics and Automation, pp. 555–560. IEEE (2007)
Kamm, L.: Designing Cost-Efficient Mechanisms: Minimum Constraint Design, Designing with Commercial Components, and Topics in Design Engineering. McGraw-Hill, New York (1990)
Kong, X., Gosselin, C.: Forward displacement analysis of a quadratic 4-DoF 3T1R parallel manipulator. Meccanica 46(1), 147–154 (2011)
Laus, L., Simas, H., Martins, D.: Efficiency of gear trains determined using graph and screw theories. Mech. Mach. Theory 52, 296–325 (2012)
Mejia, L., Simas, H., Martins, D.: Force capability in general 3 DoF planar mechanisms. Mech. Mach. Theory 91, 120–134 (2015)
Moreno, G., Nicolazzi, L.C., Vieira, R.D.S., Martins, D.: Stability of long combination vehicles. Int. J. Heavy Veh. Syst. 25(1), 113–131 (2018)
Oxley, J.G.: Matroid Theory, vol. 3. Oxford University Press, Oxford (2006)
Recski, A.: Matroid Theory and Its Applications in Electric Network Theory and in Statics, vol. 6. Springer, Heidelberg (2013)
Reshetov, L.: Self-aligning mechanism, \(2^{nd}\) revised edition edn. MIR, Moscow (1979). Translated from Russian by Leo M. Sachs
Richard, P.L., Gosselin, C.M., Kong, X.: Kinematic analysis and prototyping of a partially decoupled 4-DoF 3T1R parallel manipulator (2006)
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This work was funded by CAPES under project PGPTA \(n^o\) 59/2014 and CNPq.
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Barreto, R.L.P., Carboni, A.P., Simoni, R., Martins, D. (2021). Method for Selecting Self-aligning Mechanisms Enumerated by Matroid Contractions. In: Lenarčič, J., Siciliano, B. (eds) Advances in Robot Kinematics 2020. ARK 2020. Springer Proceedings in Advanced Robotics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-50975-0_24
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DOI: https://doi.org/10.1007/978-3-030-50975-0_24
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