Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 10 Sayı: 2, 401 - 408, 31.05.2023
https://doi.org/10.31202/ecjse.1239481

Öz

Kaynakça

  • [1]. L. Burmester, Textbook of kinematics, Leipzig, published by Arthur Felix, 1888, (in German).
  • [2]. A. P. Kotelnikov, “Burmester points, their properties and construction,” Mathematical Handbook “Mathematical Society”, vol. 24, no. 3-4, pp. 205-348, 1927, (in Russan).
  • [3]. R. Mueller, Introduction to theoretical kinematics, Berlin, Springer, 1932, (in German).
  • [4]. J. Hirschorn, Kinematics and Dynamics of Plane Mechanisms, McGraw - Hill, New York, 1972.
  • [5]. C. Rodenberg, “Determination of the circling-points curves by four plane positions,” Mathematics and Physics, vol. 36, pp. 267-277, 1891, (in German).
  • [6]. R. Beyer, Kinematic synthesis of mechanisms, Berlin, Springer-Verlag, 1953, (in German).
  • [7]. Ya. L. Geronimus, Geometric apparatus of the theory of synthesis of plane linkages, Moscow, Fizmatgiz, 1962, (in Russan).
  • [8]. W. Lichtenheldt, K. Luck, Synthesis of mechanisms, 5th edited and expanded edition, Akademie-Verlag, Berlin 1979, (in German).
  • [9]. E. A. Dijksman and J. M. Herve, “Instantaneous four-bar kinematics based on the Carter-Hall circle,” Proceedings of the first international applied mechanical systems design conference: with tutorial workshops; June 11-14, 1989, Nashville, Tennesee, Technological University, vol. 1, pp. P1.1-P1.12.
  • [10]. J. J. Uicker, G. R. Pennock and J. E. Shigley, Theory of Machines and Mechanisms, 5th ed., Oxford University Press, New York, 2017.
  • [11]. G. R. Veldkamp, “Some Remarks on Higher Curvature Theory,” American Society of Mechanical Engineers (ASME), Journal of Engineering for Industry, February, 1967, vol. 87B, pp. 84-86.
  • [12]. B. Roth and A. T. Yang, “The Application of the Instantaneous Invariants to the Analysis and Synthesis of Mechanisms,” American Society of Mechanical Engineers (ASME), Journal of Engineering for Industry, vol. 99B, no. 1, pp. 97-103, 1977.
  • [13]. J. Haschek, “For the Isogonal kinematics of the circling-point curve,” Mechanism and Machine Theory, vol. 21, pp. 167-172, 1986, (in German).
  • [14]. J. Angeles, A. Alivizatos and A. Akhras, “An Unconstrained Nonlinear Least-Square Method of Optimization of RRRR Planar Path Generator,” Mechanisms and Machine Theory, vol. 23, no. 5, pp. 343-353, 1988.
  • [15]. V. Galabov, Synthesis of mechanisms in robotics, Technical University - Sofia, 1992, (in Bulgarian).
  • [16]. V. Galabov, “Structural-metric synthesis of linkages,” DSc-technical sciences dissertation, Technical University - Sofia, 1998, (in Bulgarian).
  • [17]. R. G. Mitchiner and H. H. Mobie, “The synthesis of 4-bar linkage coupler curves using derivatives of the radius of curvature-I. Straight path procedure”, Mechanism and Machine Theory, vol. 12, pp. 133-146, 1977.
  • [18]. K. Eren and S. Ersoy, “Revisiting Burmester theory with complex forms of Bottema’s instantaneous invariants,” Complex Variables and Elliptic Equations, vol. 62, no. 4, pp. 431-437, 2017.
  • [19]. K. Eren and S. Ersoy, “Cardan Positions in the Lorentzian Plane,” Honam Mathematical Journal, vol. 40, no. 1, pp. 187-198, 2018.
  • [20]. K. Eren and S. Ersoy, “Burmester theory in Cayley–Klein planes with affine base,” Journal of Geometry, vol. 109, no. 3, art. 45, pp. 12, 2018.
  • [21]. K. Eren and S. Ersoy, “A Comparison of Original and Inverse Motion in Minkowski Plane,” Applications and Applied Mathematics: An International Journal, vol. 40, Special Issue no. 5, pp. 56-67, 2019.
  • [22]. W. J. Carter, “Kinematic Analysis and Synthesis Using Colleneation-Axis Equation,” Transactions of the American Society of Mechanical Engineers (Trans. ASME), vol. 79, no. 6, pp. 1305-1312, 1957, (with discussion by A. S. Hall, Jr.).
  • [23]. K. Lakshminarayana, “On the Carter-Hall Circle and its Application,” Journal of Mechanisms, vol. 6, pp. 517-532, 1971.
  • [24]. V. Galabov and I. Andonov, “Determining the area of the initial position of the initial unit in the synthesis of cam, belt and lever mechanisms. Part I - Mechanisms with rotation of the inlet and rocker at the outlet,” Mechanics of Machines, vol. 105, pp. 69-75, 2014.
  • [25]. F. Freudenstein, “On the Maximum and Minimum Velocities and Accelerations in Four-Link Mechanisms,” Transactions of the American Society of Mechanical Engineers (Trans. ASME), vol. 78, no. 4, pp. 779-787, 1956.

Synthesis of Four-Bar Linkages by Four Infinitely Close Relative Positions and Pressure Angle

Yıl 2023, Cilt: 10 Sayı: 2, 401 - 408, 31.05.2023
https://doi.org/10.31202/ecjse.1239481

Öz

A computer-applicable linear mathematical model has been developed to determine Burmester’s curves for infinitely close relative positions (cubic of stationary curvature), which indirectly uses Carter-Hall’s circle. By varying a free parameter and using elements of kinematic and analytical geometry, an incomparably simpler solution is achieved than that obtained by the third-degree equations of the Burmester's curves for stationary curvature. The mathematical model for the synthesis of four-bar linkages includes and a condition for the pressure angle, whereupon is uniquely defined the kinematic diagram of the mechanism. Of the pressure angle, the reactions of the forces in the kinematic pairs and the force sizing of the mechanism depend. The model would facilitate the engineers in the synthesis of four-bar linkages by generating a function approximating a given function in the vicinity of a given position, where the two functions have four infinitely close common points (3rd-order approximation). An example of the synthesis of a four-bar linkage illustrates the application of the model, which is linear - it includes only equations of straight lines written in Cartesian coordinates, which is why it is convenient for computer calculations.

Kaynakça

  • [1]. L. Burmester, Textbook of kinematics, Leipzig, published by Arthur Felix, 1888, (in German).
  • [2]. A. P. Kotelnikov, “Burmester points, their properties and construction,” Mathematical Handbook “Mathematical Society”, vol. 24, no. 3-4, pp. 205-348, 1927, (in Russan).
  • [3]. R. Mueller, Introduction to theoretical kinematics, Berlin, Springer, 1932, (in German).
  • [4]. J. Hirschorn, Kinematics and Dynamics of Plane Mechanisms, McGraw - Hill, New York, 1972.
  • [5]. C. Rodenberg, “Determination of the circling-points curves by four plane positions,” Mathematics and Physics, vol. 36, pp. 267-277, 1891, (in German).
  • [6]. R. Beyer, Kinematic synthesis of mechanisms, Berlin, Springer-Verlag, 1953, (in German).
  • [7]. Ya. L. Geronimus, Geometric apparatus of the theory of synthesis of plane linkages, Moscow, Fizmatgiz, 1962, (in Russan).
  • [8]. W. Lichtenheldt, K. Luck, Synthesis of mechanisms, 5th edited and expanded edition, Akademie-Verlag, Berlin 1979, (in German).
  • [9]. E. A. Dijksman and J. M. Herve, “Instantaneous four-bar kinematics based on the Carter-Hall circle,” Proceedings of the first international applied mechanical systems design conference: with tutorial workshops; June 11-14, 1989, Nashville, Tennesee, Technological University, vol. 1, pp. P1.1-P1.12.
  • [10]. J. J. Uicker, G. R. Pennock and J. E. Shigley, Theory of Machines and Mechanisms, 5th ed., Oxford University Press, New York, 2017.
  • [11]. G. R. Veldkamp, “Some Remarks on Higher Curvature Theory,” American Society of Mechanical Engineers (ASME), Journal of Engineering for Industry, February, 1967, vol. 87B, pp. 84-86.
  • [12]. B. Roth and A. T. Yang, “The Application of the Instantaneous Invariants to the Analysis and Synthesis of Mechanisms,” American Society of Mechanical Engineers (ASME), Journal of Engineering for Industry, vol. 99B, no. 1, pp. 97-103, 1977.
  • [13]. J. Haschek, “For the Isogonal kinematics of the circling-point curve,” Mechanism and Machine Theory, vol. 21, pp. 167-172, 1986, (in German).
  • [14]. J. Angeles, A. Alivizatos and A. Akhras, “An Unconstrained Nonlinear Least-Square Method of Optimization of RRRR Planar Path Generator,” Mechanisms and Machine Theory, vol. 23, no. 5, pp. 343-353, 1988.
  • [15]. V. Galabov, Synthesis of mechanisms in robotics, Technical University - Sofia, 1992, (in Bulgarian).
  • [16]. V. Galabov, “Structural-metric synthesis of linkages,” DSc-technical sciences dissertation, Technical University - Sofia, 1998, (in Bulgarian).
  • [17]. R. G. Mitchiner and H. H. Mobie, “The synthesis of 4-bar linkage coupler curves using derivatives of the radius of curvature-I. Straight path procedure”, Mechanism and Machine Theory, vol. 12, pp. 133-146, 1977.
  • [18]. K. Eren and S. Ersoy, “Revisiting Burmester theory with complex forms of Bottema’s instantaneous invariants,” Complex Variables and Elliptic Equations, vol. 62, no. 4, pp. 431-437, 2017.
  • [19]. K. Eren and S. Ersoy, “Cardan Positions in the Lorentzian Plane,” Honam Mathematical Journal, vol. 40, no. 1, pp. 187-198, 2018.
  • [20]. K. Eren and S. Ersoy, “Burmester theory in Cayley–Klein planes with affine base,” Journal of Geometry, vol. 109, no. 3, art. 45, pp. 12, 2018.
  • [21]. K. Eren and S. Ersoy, “A Comparison of Original and Inverse Motion in Minkowski Plane,” Applications and Applied Mathematics: An International Journal, vol. 40, Special Issue no. 5, pp. 56-67, 2019.
  • [22]. W. J. Carter, “Kinematic Analysis and Synthesis Using Colleneation-Axis Equation,” Transactions of the American Society of Mechanical Engineers (Trans. ASME), vol. 79, no. 6, pp. 1305-1312, 1957, (with discussion by A. S. Hall, Jr.).
  • [23]. K. Lakshminarayana, “On the Carter-Hall Circle and its Application,” Journal of Mechanisms, vol. 6, pp. 517-532, 1971.
  • [24]. V. Galabov and I. Andonov, “Determining the area of the initial position of the initial unit in the synthesis of cam, belt and lever mechanisms. Part I - Mechanisms with rotation of the inlet and rocker at the outlet,” Mechanics of Machines, vol. 105, pp. 69-75, 2014.
  • [25]. F. Freudenstein, “On the Maximum and Minimum Velocities and Accelerations in Four-Link Mechanisms,” Transactions of the American Society of Mechanical Engineers (Trans. ASME), vol. 78, no. 4, pp. 779-787, 1956.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Vitan Galabov 0000-0002-8514-4542

Roumen Roussev 0000-0002-8514-4542

Blagoyka Paleva-kadiyska 0000-0002-8514-4542

Yayımlanma Tarihi 31 Mayıs 2023
Gönderilme Tarihi 19 Ocak 2023
Kabul Tarihi 9 Mayıs 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 10 Sayı: 2

Kaynak Göster

IEEE V. Galabov, R. Roussev, ve B. Paleva-kadiyska, “Synthesis of Four-Bar Linkages by Four Infinitely Close Relative Positions and Pressure Angle”, ECJSE, c. 10, sy. 2, ss. 401–408, 2023, doi: 10.31202/ecjse.1239481.