Research Article
BibTex RIS Cite

Üç Döner Mafsallı Düzlemsel Manipülatörün (3RM) Parametrik Pozisyon Denklemlerini Kullanarak Bir Dört Çubuk Mekanizmasının Parametrik Pozisyon Denklemlerinin Elde Edilmesi

Year 2021, Volume: 9 Issue: 1, 8 - 16, 02.03.2021
https://doi.org/10.36306/konjes.715768

Abstract

Bir dört çubuk mekanizmasında, kol uzvu sabit bir açısal hız ile dönerken, diğer iki uzuv sürekli değişen açısal hızlara sahiptir. Bir 3RM mekanizması, dört çubuk mekanizmasına dönüştürülmek istenirse, biyel uzvunun her iki ucundaki döner aktuatörlerin değişken açısal hızlarının doğru olarak belirlenmesini gerekir. 3RM’nin kartezyen koordinatlarını veren genel parametrik denklem seti serbestlik derecesi sınırlanarak dört çubuk mekanizması için kullanılabilecek şekilde düzenlenebilir. Bu durumda kol uzvu sabit bir açısal hız ile dönerken, biyel uzvunun her iki ucundaki aktuatörlerin açısal hızları belirlenmelidir. Aktüatörlerin açısal hızları, geometrik parametreleri kol-sarkaç çalışmasına göre seçilen bir dört çubuk mekanizması için WorkingModel2D (WM2D) "dinamik hareket simülasyon yazılımı" kullanılarak elde edilmiştir. Açısal hız verileri kullanılarak, biyel uzvuna bağlı döner aktuatörlerin açısal hızlarını ifade eden polinomlardaki bilinmeyen katsayılar Mathematica yazılımı kullanılarak bulunmuştur. WM2D’den elde edilen yörünge ve açısal hız verileri, yörünge ve açısal hız denklemlerinin sonuçları karşılaştırılmış ve elde edilen sonuçların kabul edilebilir seviyelerde olduğu bulunmuştur.

Thanks

Sağlıklı günler dilerim...

References

  • Acharyya, S. K., Mandal, M., 2009, “Performance of EAs for four-bar linkage synthesi”, Mechanism and Machine Theory 44, 1784–1794.
  • Alfaro, M. E., Bolnick, D. I., Wainwright, P. C., 2004, “Evolutionary Dynamics of Complex Biomechanical Systems: An Example Using the Four-Bar Mechanism”, Evolution, Vol. 58, No. 3, pp. 495-503.
  • Cruz, M., A., et al., 2015, “Modeling, Simulation and Construction of a Furuta Pendulum Test-Bed”, International Conference on Electronics, Communications and Computers (CONIELECOMP), 25-27 Feb. 2015, DOI: 10.1109/CONIELECOMP.2015.7086928.
  • Çatalkaya, M., AKAY, O. E., 2018, “Obtaining Human Step Trajectory Curves Using 2R Manipulator”, Journal of Engineering Sciences, ISSN: 1309-1751, Vol. 21, No. 3, 267-271.
  • Dong, H., Du, Z., Chirikjian, G. S., 2013, “Workspace Density and Inverse Kinematics for Planar Serial Revolute Manipulators”, Mechanism and Machine Theory Volume 70, 508-522.
  • Fujie, H., Kimura, K., Yamakawa, S., “Static and Dynamic Properties of a 6-DOF Robotic System for Knee Joint Biomechanics Study”, Asme 2013 Summer Bioengineering Conference Paper No. SBC2013- 14849, pp. V01BT23A012; 2 pages DOI:10.1115/SBC2013-14849.
  • Hirose, M., Ogawa K., 2007, “Honda humanoid robots development”, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Science, 365, 11-19.
  • Krovi, V., Ananthasuresh, G. K., Kumar, V., 2002, “Kinematic and kinetostatic synthesis of planar coupled serial chain mechanisms”, Journal of Mechanical Design, 124, 301-312.
  • Leardini, A., Moschella, D., “Dynamic Simulation of the Natural and Replaced Human Ankle Joint”, Medical and Biological Engineering and Computing, Volume 40, pages193–199(2002).
  • Nie, X., Krovi, V., 2005, “Fourier Methods for Kinematic Synthesis of coupled serial chain”, Journal of Mechanical Design, 127, 232-241.
  • Pennock, G. R., Yang, A. T., 1983, “Dynamic Analysis of a Multi-Rigid-Body Open-Chain System,”J. Mech., Trans., and Automation 105(1), 28-34, (7pages)doi:10.1115/1.
  • Roy, L., Sen, A., Chetia, R. P., Borah, M. J., 2008, “Analysis and Synthesis of Fourbar Mechanism”, International Journal of Theoretical and Applied Mechanics ISSN 0973-6085 Volume 3 Number 2, pp. 171–186.
  • Shala, A., Bruqi, M., , August 2017, “Kinetostatic Analysis of six-bar Mechanism Using Vector Loops and The Verification of Results Using Working Model”, International Journal of Mechanical Engineering and Technology (IJMET), Volume 8, Issue 8, pp. 1109–1117.
  • Shieh, W. B., 1996, Design and Optimization of Planar Leg Mechanisms Featuring Symmetrical Foot-Point Paths, Doctor of Philosophy, Department of Mechanical Engineering, University of Maryland, Maryland.
  • Tang, Y., Chang, Z., Dong, X., Yafei Hu, Zhenjiang Yu, 2013, “Nonlinear Dynamics and Analysis of a Four- Bar Linkage with Clearance”, Frontiers of Mechanical Engineering, 8(2): 160–168, DOI 10.1007/s11465-013-0258-6.
  • Vukobratovic, M., Kircanski, M., 1986, “Kinematics and Trajectory Synthesis of Manipulation Robots”, Springer-Verlag, ISBN-13: 978-3642821974.
  • Wampler, C. W., Morgan, A. P., Sommese, A. J., 1992, “Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkage”, Journal of Mechanical Design, Vol. 114, pp. 153-159, doi:10.1115/1.2916909.

OBTAINING THE PARAMETRIC POSITION EQUATIONS OF A FOUR-BAR MECHANISM USING THE PARAMETRIC POSITION EQUATIONS OF THE PLANAR MANIPULATOR WITH 3 REVOLUTE JOINTS (3RM)

Year 2021, Volume: 9 Issue: 1, 8 - 16, 02.03.2021
https://doi.org/10.36306/konjes.715768

Abstract

In a four-bar mechanism, the crank link rotates at a constant angular velocity, while the other two links have constantly changing angular velocities. If it is desired to convert a 3RM into a four-bar mechanism, the variable angular velocities of the rotary actuators at both ends of the coupler link should be accurate. The general parametric set of equations that give the cartesian coordinates of 3RM can be arranged so that they can be used for the four-bar mechanism by limiting the degree of freedom. In this case, the angular velocities of the actuators on both ends of the coupler link should be determined while the crank link rotates at a constant angular speed. Angular velocities of actuators have been obtained using the WorkingModel2D (WM2D) "dynamic motion-simulation software" for a four-bar mechanism, whose geometric parameters have been selected as the crank-rocker. Using the angular velocity data, unknown coefficients in polynomials expressing the angular velocities of the rotary actuators connected to the coupler link have been found using Mathematica software. The trajectory and angular velocity data have been obtained from WM2D, the results of trajectory and angular velocity equations have been compared and the results have been at acceptable levels.

References

  • Acharyya, S. K., Mandal, M., 2009, “Performance of EAs for four-bar linkage synthesi”, Mechanism and Machine Theory 44, 1784–1794.
  • Alfaro, M. E., Bolnick, D. I., Wainwright, P. C., 2004, “Evolutionary Dynamics of Complex Biomechanical Systems: An Example Using the Four-Bar Mechanism”, Evolution, Vol. 58, No. 3, pp. 495-503.
  • Cruz, M., A., et al., 2015, “Modeling, Simulation and Construction of a Furuta Pendulum Test-Bed”, International Conference on Electronics, Communications and Computers (CONIELECOMP), 25-27 Feb. 2015, DOI: 10.1109/CONIELECOMP.2015.7086928.
  • Çatalkaya, M., AKAY, O. E., 2018, “Obtaining Human Step Trajectory Curves Using 2R Manipulator”, Journal of Engineering Sciences, ISSN: 1309-1751, Vol. 21, No. 3, 267-271.
  • Dong, H., Du, Z., Chirikjian, G. S., 2013, “Workspace Density and Inverse Kinematics for Planar Serial Revolute Manipulators”, Mechanism and Machine Theory Volume 70, 508-522.
  • Fujie, H., Kimura, K., Yamakawa, S., “Static and Dynamic Properties of a 6-DOF Robotic System for Knee Joint Biomechanics Study”, Asme 2013 Summer Bioengineering Conference Paper No. SBC2013- 14849, pp. V01BT23A012; 2 pages DOI:10.1115/SBC2013-14849.
  • Hirose, M., Ogawa K., 2007, “Honda humanoid robots development”, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Science, 365, 11-19.
  • Krovi, V., Ananthasuresh, G. K., Kumar, V., 2002, “Kinematic and kinetostatic synthesis of planar coupled serial chain mechanisms”, Journal of Mechanical Design, 124, 301-312.
  • Leardini, A., Moschella, D., “Dynamic Simulation of the Natural and Replaced Human Ankle Joint”, Medical and Biological Engineering and Computing, Volume 40, pages193–199(2002).
  • Nie, X., Krovi, V., 2005, “Fourier Methods for Kinematic Synthesis of coupled serial chain”, Journal of Mechanical Design, 127, 232-241.
  • Pennock, G. R., Yang, A. T., 1983, “Dynamic Analysis of a Multi-Rigid-Body Open-Chain System,”J. Mech., Trans., and Automation 105(1), 28-34, (7pages)doi:10.1115/1.
  • Roy, L., Sen, A., Chetia, R. P., Borah, M. J., 2008, “Analysis and Synthesis of Fourbar Mechanism”, International Journal of Theoretical and Applied Mechanics ISSN 0973-6085 Volume 3 Number 2, pp. 171–186.
  • Shala, A., Bruqi, M., , August 2017, “Kinetostatic Analysis of six-bar Mechanism Using Vector Loops and The Verification of Results Using Working Model”, International Journal of Mechanical Engineering and Technology (IJMET), Volume 8, Issue 8, pp. 1109–1117.
  • Shieh, W. B., 1996, Design and Optimization of Planar Leg Mechanisms Featuring Symmetrical Foot-Point Paths, Doctor of Philosophy, Department of Mechanical Engineering, University of Maryland, Maryland.
  • Tang, Y., Chang, Z., Dong, X., Yafei Hu, Zhenjiang Yu, 2013, “Nonlinear Dynamics and Analysis of a Four- Bar Linkage with Clearance”, Frontiers of Mechanical Engineering, 8(2): 160–168, DOI 10.1007/s11465-013-0258-6.
  • Vukobratovic, M., Kircanski, M., 1986, “Kinematics and Trajectory Synthesis of Manipulation Robots”, Springer-Verlag, ISBN-13: 978-3642821974.
  • Wampler, C. W., Morgan, A. P., Sommese, A. J., 1992, “Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkage”, Journal of Mechanical Design, Vol. 114, pp. 153-159, doi:10.1115/1.2916909.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Orhan Erdal Akay

Publication Date March 2, 2021
Submission Date April 7, 2020
Acceptance Date September 11, 2020
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

IEEE O. E. Akay, “OBTAINING THE PARAMETRIC POSITION EQUATIONS OF A FOUR-BAR MECHANISM USING THE PARAMETRIC POSITION EQUATIONS OF THE PLANAR MANIPULATOR WITH 3 REVOLUTE JOINTS (3RM)”, KONJES, vol. 9, no. 1, pp. 8–16, 2021, doi: 10.36306/konjes.715768.