Synthesizing a Planar Four Bar Linkage and Coupler Curve

Authors

DOI:

https://doi.org/10.26713/cma.v12i4.1622

Keywords:

Mechanism of four bar linkages, Homotopy continuation method, Coupler curve, Displacement matrix

Abstract

Synthesis of planar four bar mechanism is an important area in robotics and mechanical engineering.  The analysis of the lengths of the four-bar mechanism and the associated angle helps in determining the coupler curve. In this paper, we present the problem of synthesizing a planar four-bar linkages whose coupler curve passes through five precision points that points are chosen from quadratic polynomial function. Also, we analyze its solution and to find out suitable solution for a chosen coupler curve.

Downloads

Download data is not yet available.

References

D. A. Cox, J. Little and D. O’Shea, Ideals, Varieties, and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra, 4th edition, Springer (2015), URL: https://link.springer.com/book/10.1007/978-3-319-16721-3.

M. Gebreslasie and A. Bazezew, Synthesis, analysis and simulation of a four-bar mechanism using matlab programming, Journal of EAEA 18 (2001), 85 – 96, URL: https://www.ajol.info/index.php/zj/article/view/124097/113614.

X. Huang, G. He, Q. Liao, S. Wei and X. Tan, Solving a planar four-bar linkages design problem, in: Proceedings of the 2009 International Conference on Information and Automation, pp. 1586 – 1590 (2009), DOI: 10.1109/ICINFA.2009.5205170.

A. Jaiswal and H. P. Jawale, Synthesis and optimization of four bar mechanism with six design parameter, AIP Conference Proceedings 1943 (2018), 020014, DOI: 10.1063/1.5029590.

D. Manocha, Solving systems of polynomial equations, IEEE Computer Graphics and Applications 14(2) (1994), 46 – 55, DOI: 10.1109/38.267470.

H. Montazeri, F. Soleymani, S. Shateyi and S. S. Motsa, On a new method for computing the numerical solution of systems of nonlinear equations, Journal of Applied Mathematics 2012 (2012), Article ID 751975, DOI: 10.1155/2012/751975.

Y. J. Nahon, Method for solving polynomial equations, Journal of Applied & Computational Mathematics 7(3) (2018), 12 pages, DOI: 10.4172/2168-9679.1000409.

R. L. Norton and M. P. Higgins, Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines, 6th edition, McGraw-Hill Education (2020), URL: https://designofmachinery.com/books/design-of-machinery.

K. Russell and R. S. Sodhi, Kinematic synthesis of planar five-bar mechanisms for multi-phase motion generation, JSME International Journal Series C: Mechanical Systems, Machine Elements and Manufacturing 47(1) (2004), 345 – 349, DOI: 10.1299/jsmec.47.345.

B. P. Silalahi, R. Laila and I. S. Sitanggang, A combination method for solving nonlinear equations, IOP Conference Series: Materials Science and Engineering 166 (2017), 012011, DOI: 10.1088/1757-899X/166/1/012011.

S. Sleesongsom and S. Bureerat, Optimal synthesis of four-bar linkage path generation through evolutionary computation with a novel constraint handling technique, Computational Intelligence and Neuroscience 2018 (2018), Article ID 5462563, DOI: 10.1155/2018/5462563.

H.-J. Su and J. M. McCarthy, Synthesis of bistatble compliant four-bar mechanisms using polynomial homotopy, Journal of Mechanical Design 129(10) (2007), 1094 – 1098, DOI: 10.1115/1.2757192.

T. S. Todorov, Synthesis of four bar mechanisms as function generators by Frudenstein-Chebyshev, Journal of Robotics and Mechanical Engineering Research 1(1) (2015), DOI: 10.24218/jrmer.2015.01.

S. M. Varedi-Koulaei and H. Rezagholizadeh, Synthesis of the four-bar linkage as path generation by choosing the shape of the connecting rod, in: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234(13) (2020), 2643 – 2652, DOI: 10.1177/0954406220908616.

D. Wang and W. Wang, Kinematic Differential Geometry and Saddle Synthesis of Linkages, Wiley, Singapore (2015), URL: https://www.wiley.com/en-ie/Kinematic+Differential+Geometry+and+Saddle+Synthesis+of+Linkages-p-9781118255049.

T.-M. Wu, Non-linear solution of function generation of planar four-link mechanisms by homotopy continuation method, Journal of Applied Sciences 5 (2005), 724 – 728, DOI: 10.3923/jas.2005.724.728.

A. Zhauyt, K. Alipov, A. Sakenova, A. Zhankeldi, R. Abdirova and Z. Abilkaiyr, The synthesis of fourbar mechanism, Vibroengineering Procedia 10 (2016), 486 – 491, URL: https://www.jvejournals.com/article/17871.

Downloads

Published

13-12-2021
CITATION

How to Cite

James, V., & Sivakumar, B. (2021). Synthesizing a Planar Four Bar Linkage and Coupler Curve. Communications in Mathematics and Applications, 12(4), 1045–1050. https://doi.org/10.26713/cma.v12i4.1622

Issue

Section

Research Article