Research Article
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Year 2023, Volume: 11 Issue: 2, 504 - 517, 01.06.2023

Mert Eren Ayğahoğlu Ziya Şaka

https://doi.org/10.36306/konjes.1249830

Abstract

References

  • [1] J. Yu, H. Luo, J. Hu, T. V. Nguyen, and Y. Lu, “Reconstruction of high-speed cam curve based on high-order differential interpolation and shape adjustment,” Appl Math Comput, vol. 356, pp. 272–281, Sep. 2019, doi: 10.1016/j.amc.2019.03.049.
  • [2] H. A. Rothbart, “Cam Design Handbook: Dynamics and Accuracy,” 2004, doi: 10.1036/0071433287.
  • [3] H. Martini, L. Montejano, and D. Oliveros, Bodies of Constant Width. Cham: Birkhäuser, 2019.
  • [4] S. Rabinowitz, “A Polynomial Curve of Constant Width,” MathPro Press, vol. 9, pp. 23–27, 1997.
  • [5] H. Lu, “Plane curve of constant width research,” 2001.
  • [6] T. Bayen and J.-B. Hiriart-Urruty, “Convex objects of constant width (in 2D) or thickness,” Annales des sciences mathématiques du Québec, pp. 17–42, 2017.
  • [7] H. L. Resnikoff, “On Curves and Surfaces of Constant Width,” Apr. 2015, [Online]. Available: http://arxiv.org/abs/1504.06733
  • [8] A. David Irving, “Curves of Constant Width & Centre Symmetry Sets,” 2006.
  • [9] C. Panraksa and L. C. Washington, “Real algebraic curves of constant width,” Period Math Hung, vol. 74, no. 2, pp. 235–244, Jun. 2017, doi: 10.1007/s10998-016-0149-9.
  • [10] L. Paciotti, “Curves of Constant Width and Their Shadows,” 2010.
  • [11] S. G. Dhande and Rajaram N., “Kinematic Analysis of Constant-Breadth Cam-Follower Mechanisms,” Journal of Mechanisms Transmissions and Automation in Design, no. 106, pp. 214–221, 1984, [Online]. Available: https://mechanicaldesign.asmedigitalcollection.asme.org
  • [12] Jinjiang Z., “Research on flat surface and constant width curve,” 2001.
  • [13] G. Figliolini and P. Rea, “Reuleaux Triangle and its Derived Mechanisms.”
  • [14] Yüzbaşı Ş. and Karaçayır M., “A Galerkin-like scheme to determine curves of constant breadth in Euclidean 3-space,” TWMS Journal of Applied and Engineering Mathematics, vol. 11, no. 3, pp. 646–658, 2021, [Online]. Available: https://orcid.org/0000-0001-6230-3638.
  • [15] H. Satoshi and T. Shun, “Development of a reduction mechanism integrated with a constant-breadth cam,” in Proceedings of JSPE Semestrial Meeting, 2017.
  • [16] L. Wang, W. Zhang, C. Wang, F. Meng, W. Du, and T. Wang, “Conceptual Design and Computational Modeling Analysis of a Single-Leg System of a Quadruped Bionic Horse Robot Driven by a Cam-Linkage Mechanism,” Appl Bionics Biomech, 2019, doi: 10.1155/2019/2161038.
  • [17] M. Asgari, E. A. Phillips, B. M. Dalton, J. L. Rudl, and D. L. Crouch, “Design and Preliminary Evaluation of a Wearable Passive Cam-Based Shoulder Exoskeleton,” JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME, vol. 144, no. 11, 2022, doi: 10.1115/1.4054639.
  • [18] E. E. Zayas-Figueras and I. Buj-Corral, “Comparative Study about Dimensional Accuracy and Surface Finish of Constant-Breadth Cams Manufactured by FFF and CNC Milling,” Micromachines (Basel), vol. 14, no. 2, Feb. 2023, doi: 10.3390/mi14020377.
  • [19] Artobolevsky I. I., Mechanisms in Modern Engineering Design, A Handbook for Engineers, Designers and Inventors, Volume IV: Cam and Friction Mechanisms Flexible-Link Mechanisms. Moscow: Mir Publishers, 1977.
  • [20] V. I. Smirnov, “CHAPTER I ORDINARY DIFFERENTIAL EQUATIONS,” in A COURSE OF Higher Mathematics , vol. 2, PERGAMON PRESS, 1964, pp. 32–36.
  • [21] K. J. Waldron, G. L. Kinzel, and A. S. K., Kinematics, Dynamics, and Design of Machinery. Chichester: John Wiley & Sons Ltd, 2016.
  • [22] E. Söylemez, Mechanisms. METU Publications, 1986.

KINEMATIC ANALYSIS OF CONSTANT BREADTH CAM DRIVEN LINKAGES

Year 2023, Volume: 11 Issue: 2, 504 - 517, 01.06.2023

Mert Eren Ayğahoğlu Ziya Şaka

https://doi.org/10.36306/konjes.1249830

Abstract

Several constant breadth curves are defined that can be used as cam profiles in constant breadth cam mechanisms that are closed cam mechanisms. There are two objectives for this study. One of them is to study the kinematic analysis of different type of constant breadth cam mechanisms. The other objective is to obtain a dwell period for constant breadth cam driven linkages that is impossible for a standard cam mechanism. A general kinematic analysis of a constant breadth cam mechanism with translating flat-faced follower was carried out with the principle of kinematic inversion. With the results, the kinematic analyses of the constant breadth cam driven inverted slider crank mechanism and four bar mechanism were examined in detail and a general method is given for all constant breadth cam profiles and cam driven linkages. It has been seen that a dwell period of 45° (with the fixed joint coordinates as x_n = 18 mm and y_n= 8.5 mm) and 40° (with the fixed joint coordinates as x_n = 18.5 mm and y_n= 8.5 mm) can be obtained in designed cam driven four bar and inverted slider crank mechanism respectively. After the displacement analysis, some velocity and acceleration analysis examples are given by taking the derivative of displacement. Similar kinematic analyses are possible for cam-driven mechanisms with more links. Also, it has been seen that changing the location of fixed joint of the cam profile can affect the displacement, velocity and acceleration graphics of the mechanism. With this, the dwell period can be changed too.

Keywords

Support Function Constant Breadth Curve Constant Breadth Cam Mechanism Cam Driven Mechanism Kinematic Analysis

References

  • [1] J. Yu, H. Luo, J. Hu, T. V. Nguyen, and Y. Lu, “Reconstruction of high-speed cam curve based on high-order differential interpolation and shape adjustment,” Appl Math Comput, vol. 356, pp. 272–281, Sep. 2019, doi: 10.1016/j.amc.2019.03.049.
  • [2] H. A. Rothbart, “Cam Design Handbook: Dynamics and Accuracy,” 2004, doi: 10.1036/0071433287.
  • [3] H. Martini, L. Montejano, and D. Oliveros, Bodies of Constant Width. Cham: Birkhäuser, 2019.
  • [4] S. Rabinowitz, “A Polynomial Curve of Constant Width,” MathPro Press, vol. 9, pp. 23–27, 1997.
  • [5] H. Lu, “Plane curve of constant width research,” 2001.
  • [6] T. Bayen and J.-B. Hiriart-Urruty, “Convex objects of constant width (in 2D) or thickness,” Annales des sciences mathématiques du Québec, pp. 17–42, 2017.
  • [7] H. L. Resnikoff, “On Curves and Surfaces of Constant Width,” Apr. 2015, [Online]. Available: http://arxiv.org/abs/1504.06733
  • [8] A. David Irving, “Curves of Constant Width & Centre Symmetry Sets,” 2006.
  • [9] C. Panraksa and L. C. Washington, “Real algebraic curves of constant width,” Period Math Hung, vol. 74, no. 2, pp. 235–244, Jun. 2017, doi: 10.1007/s10998-016-0149-9.
  • [10] L. Paciotti, “Curves of Constant Width and Their Shadows,” 2010.
  • [11] S. G. Dhande and Rajaram N., “Kinematic Analysis of Constant-Breadth Cam-Follower Mechanisms,” Journal of Mechanisms Transmissions and Automation in Design, no. 106, pp. 214–221, 1984, [Online]. Available: https://mechanicaldesign.asmedigitalcollection.asme.org
  • [12] Jinjiang Z., “Research on flat surface and constant width curve,” 2001.
  • [13] G. Figliolini and P. Rea, “Reuleaux Triangle and its Derived Mechanisms.”
  • [14] Yüzbaşı Ş. and Karaçayır M., “A Galerkin-like scheme to determine curves of constant breadth in Euclidean 3-space,” TWMS Journal of Applied and Engineering Mathematics, vol. 11, no. 3, pp. 646–658, 2021, [Online]. Available: https://orcid.org/0000-0001-6230-3638.
  • [15] H. Satoshi and T. Shun, “Development of a reduction mechanism integrated with a constant-breadth cam,” in Proceedings of JSPE Semestrial Meeting, 2017.
  • [16] L. Wang, W. Zhang, C. Wang, F. Meng, W. Du, and T. Wang, “Conceptual Design and Computational Modeling Analysis of a Single-Leg System of a Quadruped Bionic Horse Robot Driven by a Cam-Linkage Mechanism,” Appl Bionics Biomech, 2019, doi: 10.1155/2019/2161038.
  • [17] M. Asgari, E. A. Phillips, B. M. Dalton, J. L. Rudl, and D. L. Crouch, “Design and Preliminary Evaluation of a Wearable Passive Cam-Based Shoulder Exoskeleton,” JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME, vol. 144, no. 11, 2022, doi: 10.1115/1.4054639.
  • [18] E. E. Zayas-Figueras and I. Buj-Corral, “Comparative Study about Dimensional Accuracy and Surface Finish of Constant-Breadth Cams Manufactured by FFF and CNC Milling,” Micromachines (Basel), vol. 14, no. 2, Feb. 2023, doi: 10.3390/mi14020377.
  • [19] Artobolevsky I. I., Mechanisms in Modern Engineering Design, A Handbook for Engineers, Designers and Inventors, Volume IV: Cam and Friction Mechanisms Flexible-Link Mechanisms. Moscow: Mir Publishers, 1977.
  • [20] V. I. Smirnov, “CHAPTER I ORDINARY DIFFERENTIAL EQUATIONS,” in A COURSE OF Higher Mathematics , vol. 2, PERGAMON PRESS, 1964, pp. 32–36.
  • [21] K. J. Waldron, G. L. Kinzel, and A. S. K., Kinematics, Dynamics, and Design of Machinery. Chichester: John Wiley & Sons Ltd, 2016.
  • [22] E. Söylemez, Mechanisms. METU Publications, 1986.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Mert Eren Ayğahoğlu 0000-0001-7363-159X

Ziya Şaka 0000-0002-9269-7081

Publication Date June 1, 2023
Submission Date February 10, 2023
Acceptance Date April 1, 2023
Published in Issue Year 2023 Volume: 11 Issue: 2

Cite

IEEE M. E. Ayğahoğlu and Z. Şaka, “KINEMATIC ANALYSIS OF CONSTANT BREADTH CAM DRIVEN LINKAGES”, KONJES, vol. 11, no. 2, pp. 504–517, 2023, doi: 10.36306/konjes.1249830.
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