Search of variants of assemblies of structural groups in planar linkages

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Authors:

I.M.Matsyuk, Cand. Sc. (Tech.), Assoc. Prof.,State Higher Educational Institution “National Mining University”, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

Т.I.Morozova,State Higher Educational Institution “National Mining University”, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

E.М.Shlyahov,State Higher Educational Institution “National Mining University”, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract:

Purpose. To determine the effect of the presence of prismatic kinematic pairs on possible versions of assemblies of the structural group of the third class in modern planar mechanisms.

Methodology. In the work an analytical study is carried out of possible assemblies of a four-link third class structural group, in which there are prismatic kinematic pairs in two links. The study was carried out using Mathcad mathematical packages.

Findings. Possible variants of the mutual arrangement of the links of a third class structural group at fixed positions of its external kinematic pairs are found. A polynomial of degree six is obtained and all its coefficients are defined. It means that the polynomial is of degree six both for the structural group with two prismatic pairs and for the group with revolute pairs.

It is shown that, for the variant of the group under consideration, the search for assemblies reduces itself to finding the real roots of a sixth-degree polynomial.

Dependences of the polynomial coefficients on the geometric parameters of the structural group are obtained. The finding of the roots of the polynomial is performed using the standard procedure of the Mathcad, which does not require specifying the initial approximations of unknowns.

Originality. It consists in determining the number of possible assemblies of a four-links third class structural group, in which two links have prismatic kinematic pairs. It has been determined for the studied structural group that maximum assembling number is four.

Practical value. The results of the research can be used in designing the mechanisms of new machines when choosing a specific variant of assembly of a third class structural group appropriate in the best way of set problem. The search for possible assemblies of third-class structural groups can be carried out numerically with the help of modern computer technologies, which makes it possible to determine both the number of possible solutions and the solutions themselves without specifying initial approximations.

References

1. Kolovsky, M.Z., Evgrafov, A.N., Semenov, Yu.A. and Slousch, A.V., 2000. Advanced Theory of Mechanisms and Machines. Springer. New York: Verlag Berlin Heidelberg.

2. Čavić, M., Zlokolica, M. and Kostić, M., 2005. Kinematic Evaluation of the High ClassKinematic Group Mechanisms. In: The 19th Conference of Mechanical Engineering Network of Thailand, 19‒21 October, Phuket, Thiland. [online] Available at: <http://www.me.psu.ac.th/ME_NETT/paper/DRC/DRC038.pdf> [Acce­ssed 30 March 2017].

3. Čavić, M., Kostić, M. and Zlokolica, M., 2007. Position Analysis of the High Class Kinematic Group Mechanisms. Proceedings of 12th World IFTOMM Congress, Besancon, (CD Rom) pp. 1‒6. [online] Available at: <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.477.234&rep=rep1&type=pdf> [Accessed 30 March 2017].

4. Čavić, M., Zlokolica, M. and Kostić, M., 2008. Application Of The High Class Kinematic Groups In Contemporary Machine Design. In: Proceeding of 8th International Conference on Advanced Manufacturing Operations, 18‒20 June 2008. Kranevo, Bulgaria. [online] Available at: <http://amo.dmt-product.com/amo-08/pdfamo08/66.pdf> [Accessed 30 March 2017].

5. Čavić, M., Kostić, M. and Zlokolica, M., 2010. Kinematic analysis and synthesis of complex mechanisms with high class kinematic group. Machine design, 2, pp. 187‒192. [online] Available at: <http://www.mdesign.ftn.uns.ac.rs/pdf/2010/187-192_for_web.pdf> [Acce­ssed 30 March 2017].

6. Matsyuk, I.N., and Shlyahov E.M., 2015. The research of plane link mechanisms of a complicated structure with vector algebra methods. Eastern-European Journal of Enterprise Technologies, 3 (7 (75)), pp. 34–38. doi: 10.15587/1729-4061.2015.44236.

7. Protsiv, V.V., 2013. Usage of tire-shoe brake on mine locomotive. Naukovyi Visnyk Natsionalnohо Hirnychoho Universytetu, 3, pp. 59–64.

8. Ziborov, K.A., Protsiv, V.V., Blokhin, S.Ye. and Fedoriachenko S.O., 2013. Applicability of computer simulation while designing mechanical systems of mining rolling stock. Naukovyi Visnyk Natsionalnohо Hirnychoho Universytetu, 6, pp. 55–59.

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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
Registration number КВ No.17742-6592PR dated April 27, 2011.

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