Abaza, Khaldoun

Chigarev, Anatoli V.

Minchenia, Vladimir T.

Zimmermann, Klaus

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  50. Internationales  Wissenschaftliches Kolloquium   September, 19-23, 2005   Maschinenbau  von Makro bis Nano / Mechanical Engineering  from Macro to Nano   Proceedings    Fakultät für Maschinenbau / Faculty of Mechanical Engineering     Startseite / Index:  http://www.db-thueringen.de/servlets/DocumentServlet?id=15745 Impressum  Herausgeber: Der Rektor der Technischen Universität llmenau  Univ.-Prof. Dr. rer. nat. habil. Peter Scharff  Redaktion: Referat Marketing und Studentische Angelegenheiten  Andrea Schneider   Fakultät für Maschinenbau  Univ.-Prof. Dr.-Ing. habil. Peter Kurtz, Univ.-Prof. Dipl.-Ing. Dr. med. (habil.) Hartmut Witte, Univ.-Prof. Dr.-Ing. habil. Gerhard Linß,  Dr.-Ing. Beate Schlütter, Dipl.-Biol. Danja Voges,  Dipl.-Ing. Jörg Mämpel, Dipl.-Ing. Susanne Töpfer,  Dipl.-Ing. Silke Stauche  Redaktionsschluss: 31. August 2005 (CD-Rom-Ausgabe)  Technische Realisierung:  Institut für Medientechnik an der TU Ilmenau (CD-Rom-Ausgabe) Dipl.-Ing. Christian Weigel Dipl.-Ing. Helge Drumm Dipl.-Ing. Marco Albrecht  Technische Realisierung: Universitätsbibliothek Ilmenau (Online-Ausgabe)   Postfach 10 05 65  98684 Ilmenau  Verlag:   Verlag ISLE, Betriebsstätte des ISLE e.V.  Werner-von-Siemens-Str. 16  98693 llmenau   © Technische Universität llmenau (Thür.) 2005   Diese Publikationen und alle in ihr enthaltenen Beiträge und Abbildungen sind urheberrechtlich geschützt.   ISBN (Druckausgabe): 3-932633-98-9  (978-3-932633-98-0) ISBN (CD-Rom-Ausgabe): 3-932633-99-7 (978-3-932633-99-7)  Startseite / Index: http://www.db-thueringen.de/servlets/DocumentServlet?id=15745 50. Internationales Wissenschaftliches Kolloquium Technische Universität Ilmenau 19.-23. September 2005  V.T. Minchenia/A.V.Chigarev/K.Abaza/K.Zimmermann   The Dynamics of the Microrobot with Three Fulcrums  on the Planar Surface   ABSTRACT   Microrobots achiveved wide distribution in many fields of technics. There is well known area of application of the microrobot for the transportation of the instruments and devices within the channels of small diameter. Piezo drive is one of the most efficient. The design of microrobot is developed by us, which implies three fulcrums. Moreower, one of the legs is formed by the "tail" of the robot. The theoretical basis of the structure is considered in the work presented.  THE FORMALISM      The structure is considered that has three fulcrums on the planar surface, which moves by excitation of high frequency (ultrasonic) oscillations in the fulcrums. In contrast to the existing designs of microrobots with four, six fulcrums the robot considered in this work has tree fulcrums. Moreover the third fulcrum is formed by the “tail” of the robot. Thus the basing of the whole structure on the planar surfaces can be maintained more effectively. The robot’s “legs” motion during operation can be represented as the complex ultrasonic oscillations. The motion control is implemented on the base of frequency modulation of the waves in the fulcrums providing high flexibility of the control. Fig. 1 shows the scheme of the microrobot.                                                                Fig.1 Here, the absolute coordinate system X1OxX2 and the mobile system X1OX2 related to point O presented. Let the angle φ be the course angle of the robot. C – mass centre of the robot. The next relations are equitable: А1А2=2l, OA1=OA2=l1. The velocity of the movement of the point Aα, α = 1,2 can be written as: ( ) 1)(0)( elVV iαα ω+=       (1) where )(αω i – axial angular velocities of points A1, A2. Equation (1) corresponds to the case when points A1, A2 rotate in plane //  1e , which provides maximal velocity of the forward movement. On the base of the laws of impulse and moment of impulse variation mechanics the equations of the body dynamics can be written as follows: ( )∑=+−=21)2()1(0iii FFdtPd     (2) [ ] ∑∑ −−=ααααα,)(,)()(0iiiii MFRdtКd     (3) Let's consider points A1 and A2 are leading ones in this case and point O is passive fulcrum. However, in more common case it is possible to activate three fulcrums or excite them in pairs (elements in touch with the plane). The common equations of the microrobot dynamics can be evaluated from Eq. (1)-(3). After several conversions the system of nonlinear dynamic equations is obtained, which describes the microrobot motion under the influence of ultrasonic oscillations.  CONCLUSIONS  The formalism considered in the work allows us to solve practical problems of the microrobot design with given technical characteristics and to evaluate the laws of the motion control.   References: [1] Pohl D.W., Dynamic piezoelectric translation devices, Rev. Sci. Instr.., vol. 58 (1), pp54-57, Jan. 1987. [2] Minchenia V.T., Ibragimov V.A., Kiselev M.G. Mathematical modeling of the operation of vibro-impact acoustical system with substructure element. Minsk: Technoprint, 2003. ISBN 985-464-355.   Authors: Doc. Dr.-Ing. Vladimir Minchenia,  Prof., Dr.-Ing. habil Anatoli Chigarev  Belorussische Nationale Technische Universitat. Minsk, Prosp. F. Skariny 65, Minsk. 220027 Belarus,  tel. +375(17)239-91-01 E-mail:vlad_minch@mail.ru  Dipl.-Ing. Klaudoun Abaza Uni. prof. Dr.-Ing. habil. Klaus Zimmermann Technical University Ilmenau Department of Mechanical engineering    PF 100565 D-98684   Ilmenau      E-mail: klaus.zimmermann@tu-ilmenau.de 

The dynamics of the microrobot with three fulcrums on the planar surface

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The dynamics of the microrobot with three fulcrums on the planar surface

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