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2019 | OriginalPaper | Chapter

Torsional Stability of a U-Joint Based Parallel Wrist Mechanism Featuring Infinite Torsion

Authors : Guanglei Wu, Stéphane Caro

Published in: ROMANSY 22 – Robot Design, Dynamics and Control

Publisher: Springer International Publishing

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Abstract

In this paper, the dynamic stability problem of a parallel wrist mechanism is studied by means of monodromy matrix method. This manipulator adopts a universal joint as the ball-socket mechanism to support the mobile platform and to transmit the motion/torque between the input shaft and the end-effector. The linearized equations of motion of the mechanical system are established to analyze its stability according to the Floquet theory. The unstable regions are presented graphically in various parametric charts.

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Literature
1.
go back to reference Asada, H., Granito, J.: Kinematic and static characterization of wrist joints and their optimal design. In: IEEE International Conference on Robotics and Automation, pp. 244–250 (1985) Asada, H., Granito, J.: Kinematic and static characterization of wrist joints and their optimal design. In: IEEE International Conference on Robotics and Automation, pp. 244–250 (1985)
2.
go back to reference Asokanthan, S.F., Hwang, M.C.: Torsional instabilities in a system incorporating a Hooke’s joint. J. Vib. Acoust. 118(3), 368–374 (1996)CrossRef Asokanthan, S.F., Hwang, M.C.: Torsional instabilities in a system incorporating a Hooke’s joint. J. Vib. Acoust. 118(3), 368–374 (1996)CrossRef
3.
go back to reference Bulut, G., Parlar, Z.: Dynamic stability of a shaft system connected through a Hooke’s joint. Mech. Mach. Theory 46(11), 1689–1695 (2011)CrossRef Bulut, G., Parlar, Z.: Dynamic stability of a shaft system connected through a Hooke’s joint. Mech. Mach. Theory 46(11), 1689–1695 (2011)CrossRef
4.
go back to reference Chang, S.I.: Torsional instabilities and non-linear oscillation of a system incorporating a Hooke’s joint. J. Sound Vib. 229(4), 993–1002 (2000)CrossRef Chang, S.I.: Torsional instabilities and non-linear oscillation of a system incorporating a Hooke’s joint. J. Sound Vib. 229(4), 993–1002 (2000)CrossRef
5.
go back to reference Chicone, C.: Ordinary Differential Equations with Applications. Springer, New York (2006)MATH Chicone, C.: Ordinary Differential Equations with Applications. Springer, New York (2006)MATH
6.
go back to reference Desmidt, H.A., Wang, K.W., Smith, E.C.: Coupled torsion-lateral stability of a shaft-disk system driven through a universal joint. ASME J. Appl. Mech. 69(3), 261–273 (2002)CrossRef Desmidt, H.A., Wang, K.W., Smith, E.C.: Coupled torsion-lateral stability of a shaft-disk system driven through a universal joint. ASME J. Appl. Mech. 69(3), 261–273 (2002)CrossRef
7.
go back to reference Éidinov, M.S., Nyrko, V.A., Éidinov, R.M., Gashukov, V.S.: Torsional vibrations of a system with Hooke’s joint. Sov. Appl. Mech. 12(3), 291–298 (1976)CrossRef Éidinov, M.S., Nyrko, V.A., Éidinov, R.M., Gashukov, V.S.: Torsional vibrations of a system with Hooke’s joint. Sov. Appl. Mech. 12(3), 291–298 (1976)CrossRef
8.
go back to reference Floquet, G.: Sur les équations différentielles linéaires à coefficients périodiques. Annales de l’École Normale Supérieure 12, 47–88 (1883)MathSciNetCrossRef Floquet, G.: Sur les équations différentielles linéaires à coefficients périodiques. Annales de l’École Normale Supérieure 12, 47–88 (1883)MathSciNetCrossRef
9.
go back to reference Gosselin, C.M., Hamel, J.F.: The Agile Eye: a high-performance three-degree-of-freedom camera-orienting device. In: IEEE International Conference on Robotics and Automation, pp. 781–786 (1994) Gosselin, C.M., Hamel, J.F.: The Agile Eye: a high-performance three-degree-of-freedom camera-orienting device. In: IEEE International Conference on Robotics and Automation, pp. 781–786 (1994)
10.
go back to reference H. Ota, M.K., Sugita., H.: Lateral vibrations of a rotating shaft driven by a universal joint: 1st report, generation of even multiple vibrations by secondary moment. Bull. JSME 27(231), 2002–2007 (1984)CrossRef H. Ota, M.K., Sugita., H.: Lateral vibrations of a rotating shaft driven by a universal joint: 1st report, generation of even multiple vibrations by secondary moment. Bull. JSME 27(231), 2002–2007 (1984)CrossRef
11.
go back to reference Kotera, T.: Instability of torsional vibrations of a system with a cardan joint, vol. 26, pp. 19–30. Memoirs of the Faculty of Engineering Kobe University (1980) Kotera, T.: Instability of torsional vibrations of a system with a cardan joint, vol. 26, pp. 19–30. Memoirs of the Faculty of Engineering Kobe University (1980)
12.
go back to reference Li, T., Payandeh, S.: Design of spherical parallel mechanisms for application to laparoscopic surgery. Robotica 20(2), 133–138 (2002)CrossRef Li, T., Payandeh, S.: Design of spherical parallel mechanisms for application to laparoscopic surgery. Robotica 20(2), 133–138 (2002)CrossRef
13.
go back to reference Porter, B.: A theoretical analysis of the torsional oscillation of a system incorporating a Hooke’s joint. ARCHIVE J. Mech. Eng. Sci. 3(4), 324–329 (1961)CrossRef Porter, B.: A theoretical analysis of the torsional oscillation of a system incorporating a Hooke’s joint. ARCHIVE J. Mech. Eng. Sci. 3(4), 324–329 (1961)CrossRef
14.
go back to reference Porter, B., Gregory, R.W.: Non-linear torsional oscillation of a system incorporating a Hooke’s joint. ARCHIVE J. Mech. Eng. Sci. 5(2), 191–209 (1963)CrossRef Porter, B., Gregory, R.W.: Non-linear torsional oscillation of a system incorporating a Hooke’s joint. ARCHIVE J. Mech. Eng. Sci. 5(2), 191–209 (1963)CrossRef
15.
go back to reference Saigo, M., Okada, Y., Ono, K.: Self-excited vibration caused by internal friction in universal joints and its stabilizing method. J. Vib. Acoust. 119(2), 221–229 (1997)CrossRef Saigo, M., Okada, Y., Ono, K.: Self-excited vibration caused by internal friction in universal joints and its stabilizing method. J. Vib. Acoust. 119(2), 221–229 (1997)CrossRef
16.
go back to reference Szymkiewicz, R.: Numerical Solution of Ordinary Differential Equations. Academic Press, New York (1971) Szymkiewicz, R.: Numerical Solution of Ordinary Differential Equations. Academic Press, New York (1971)
17.
go back to reference Wu, G., Bai, S., Kepler, J.: Mobile platform center shift in spherical parallel manipulators with flexible limbs. Mech. Mach. Theory 75, 12–26 (2014)CrossRef Wu, G., Bai, S., Kepler, J.: Mobile platform center shift in spherical parallel manipulators with flexible limbs. Mech. Mach. Theory 75, 12–26 (2014)CrossRef
18.
go back to reference Wu, G., Caro, S., Bai, S., Kepler, J.: Dynamic modeling and design optimization of a 3- DOF spherical parallel manipulator. Robot. Auto. Syst. 62, 1377–1386 (2014)CrossRef Wu, G., Caro, S., Bai, S., Kepler, J.: Dynamic modeling and design optimization of a 3- DOF spherical parallel manipulator. Robot. Auto. Syst. 62, 1377–1386 (2014)CrossRef
19.
go back to reference Wu, G., Caro, S., Wang, J.: Design and transmission analysis of an asymmetrical spherical parallel manipulator. Mech. Mach. Theory 94, 119–131 (2015)CrossRef Wu, G., Caro, S., Wang, J.: Design and transmission analysis of an asymmetrical spherical parallel manipulator. Mech. Mach. Theory 94, 119–131 (2015)CrossRef
20.
go back to reference Zeman, V.: Dynamik der drehsysteme mit kardagelenken. Mech. Mach. Theory 13, 107–118 (1978)CrossRef Zeman, V.: Dynamik der drehsysteme mit kardagelenken. Mech. Mach. Theory 13, 107–118 (1978)CrossRef
Metadata
Title
Torsional Stability of a U-Joint Based Parallel Wrist Mechanism Featuring Infinite Torsion
Authors
Guanglei Wu
Stéphane Caro
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-78963-7_20