Abstract
A general algorithm to trace the first and second order centrodes of slider-crank mechanisms is proposed by using the instantaneous geometric and kinematic invariants. Bresse’s circles can be also traced in order to validate the instantaneous positions of the velocity and acceleration poles. In particular, the second order centrodes give kinematic properties of the coupler motion and, thus, they are computed and traced for a constant angular velocity of the driving crank. Significant examples are included in the paper to validate the proposed algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Di Benedetto, A., Pennestrì, E.: Introduction to the Kinematics of Mechanisms, vol. 1, 2, 3, Casa Editrice Ambrosiana, Milan (1991). (in Italian)
Krause, M.: Analysis der ebenen Bewegung, Vereinigung Wissenschaftlicher Verleger, Berlin (1920)
Figliolini, G., Rea, P., Conte, M.: Mechanical design of a novel biped climbing and walking robot. In: Parenti-Castelli, V., Schielen, W. (eds.) ROMANSY 18 - Robot, Design, Dynamics and Control, pp. 199–206. Springer, Vienna (2010).https://doi.org/10.1007/978-3-7091-0277-0_23
Figliolini, G., Lanni, C., Kaur, R.: Kinematic synthesis of spherical four-bar linkages for five-poses rigid body guidance. In: Uhl, T. (ed.) Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science. MMS. Advances in Mechanism and Machine Science, vol. 73, pp. 639–648. Springer, Cham (2019).https://doi.org/10.1007/978-3-030-20131-9_64
Figliolini, G., Lanni, C.: Jerk and jounce relevance for the kinematic performance of long-dwell mechanisms. In: Uhl, T. (ed.) Proceedings of the 15th IFToMM World Congress on Mechanism and Machine Science, MMS, vol. 73, pp. 219–228, Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20131-9_22
Figliolini, G., Lanni, C.: Geometric loci for the kinematic analysis of planar mechanisms via the instantaneous geometric invariants. In: Gasparetto, A., Ceccarelli, M. (eds.) MEDER 2018. MMS, vol. 66, pp. 184–192. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-00365-4_22
Figliolini, G., Lanni, C., Tomassi, L.: Kinematic analysis of slider – crank mechanisms via the Bresse and Jerk’s circles. In: Carcaterra, A., Paolone, A., Graziani, G. (eds.) AIMETA 2019. LNME, pp. 278–284. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-41057-5_23
Figliolini, G., Lanni, C., Angeles, J.: Kinematic analysis of the planar motion of vehicles when traveling along tractrix curves. ASME. J. Mech. Robot. 12(5), 054502 (2020)
Pennestrì, E., Belfiore, N.P.: On the numerical computation of generalized Burmester points. Meccanica 30(2), 147–153 (1995)
Figliolini, G., Angeles, J.: Synthesis of the pitch cones of N-lobed elliptical bevel gears. ASME J. Mech. Des. 133(3), 031002–031011 (2011)
Figliolini, G., Rea, P., Angeles, J.: The synthesis of the axodes of RCCC linkages. ASME J. Mech. Robot. 8(2), 021011 (2015)
Figliolini, G., Angeles, J.: The spherical equivalent of Bresse’s circles: The case of crossed double-crank linkages. ASME J. Mech. Robot. 9(1), 011014 (2017)
Bottema, O.: On instantaneous invariants. In: Proceedings of the International Conference for Teachers of Mechanism, pp. pp. 159–164. Yale University, New Haven, CT (1961)
Veldkamp, G.R.: Curvature Theory in Plane Kinematics. T.H. Delft, Groningen (1963)
Kamphuis, H.J.: Application of spherical instantaneous kinematics to the spherical slider-crank mechanism. J. Mech. 4(1), 43–56 (1969)
Roth, B., Yang, A.T.: Application of instantaneous invariants to the analysis and synthesis of mechanisms. ASME J. Eng. Industr. 99(1), 97–103 (1977)
Bottema, O., Roth, B.: Theoretical Kinematics. Dover, New York, NY (1990)
Yang, A.T., Pennock, G.R., Hsia, L.M.: Instantaneous invariants and curvature analysis of a planar four-link mechanism. ASME J. Mech. Des. 116(4), 1173–1176 (1994)
Roth, B.: On the advantages of instantaneous invariants and geometric kinematics. Mech. Mach. Theor. 89, 5–13 (2015)
Inalcik, A., Ersoy, S., Stachel, H.: On instantaneous invariants of hyperbolic planes. Math. Mech. Solids 22(5), 1047–1057 (2017)
McDonald, E.W.: Determination of the reducible cases of the fixed centrode of three-bar motion. Am. Math. Mon. 33(2), 90–93 (1926)
Carter, W.J.: Second Acceleration in four-bar mechanisms as related to rotopole motion. J Appl. Mech. Brief Notes 25, 293–294 (1958)
Schiller, R.W.: Method for determining the instantaneous center of acceleration. J. Appl. Mech. 32(1), 217–218 (1965)
Hwang, W.-M., Fan, Y.-S.: Coordination of two crank angles and two acceleration poles for a slider crank mechanism using parametric equations. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 222(3), 483–491 (2008)
Sun, H., Liu, T.: Analysis of instantaneous center of zero acceleration of rigid body. Mod. Appl. Sci. 3(4), 191–195 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Lanni, C., Figliolini, G., Tomassi, L. (2022). First and Second Order Centrodes of Slider-Crank Mechanisms by Using Instantaneous Invariants. In: Altuzarra, O., Kecskeméthy, A. (eds) Advances in Robot Kinematics 2022. ARK 2022. Springer Proceedings in Advanced Robotics, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-031-08140-8_33
Download citation
DOI: https://doi.org/10.1007/978-3-031-08140-8_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-08139-2
Online ISBN: 978-3-031-08140-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)