Function Generation Synthesis of the Four-bar Linkage Based on Four and Five Precision Points using Newton-HCM
الموضوعات :
Seyyed Mojtaba Varedi-Koulaei
1
(Department of Mechanical and Mechatronics Engineering,
Shahrood University of Technology, Iran)
تاريخ الإرسال : 07 الأربعاء , ذو الحجة, 1443
تاريخ التأكيد : 08 الثلاثاء , ربيع الأول, 1444
تاريخ الإصدار : 07 الخميس , جمادى الأولى, 1444
الکلمات المفتاحية:
Newton’s method,
Precision points,
Function generation synthesis,
HCM,
Planar four-bar linkage,
ملخص المقالة :
The length values selection for a determined type of linkage to achieve the necessary task, dimensional synthesis, is classified into three classes based on the mechanism’s task: function generation, path generation, and motion generation. The case considered in this study, Function generation synthesis, aims to create a relation between the angular motions of the input and output links of the mechanism. For this problem, a semi-analytical method called the Newton-HCM is used for numerical solutions, which combines Newton’s method with the semi-analytical Homotopy Continuation Method (HCM). Function generation synthesis of a planar four-bar linkage for four and five precision points is the main challenge of the current study, which is highly nonlinear and complicated to solve. Numerical examples of the function generation problem for a four-bar linkage with four and five precision points are presented and authenticate the excellent performance of the proposed algorithm.
المصادر:
Kachapi, S. H., Ganji, D. D., Davodi, A. G., and Varedi, S. M., Periodic Solution for Strongly Nonlinear Vibration Systems by He's Variational Iteration Method, Mathematical Methods in the Applied Sciences, Vol. 32, No. 18, 2009, pp. 2339-2349, DOI: 1002/mma.1135.
Kosari, A., Jahanshahi, H., and Razavi, A. A., Design of Optimal PID, Fuzzy and New Fuzzy-PID Controller for CANSAT Carrier System Thrust Vector, ADMT Journal, Vol. 8, No. 2, 2015, pp. 1-9.
Varedi-Koulaei, S. M., Rezagholizadeh, H., Synthesis of the Four-Bar Linkage as Path Generation by Choosing the Shape of The Connecting Rod, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 234, No. 13, 2020, pp. 2643-2652, DOI: 1177/0954406220908616.
Chebyshev, P. L., Theorie Des Mecanismes Connaissent Comme Parallelogrames, Memoires Presenes à l’Academie Imperial Des Sciences De St.- Petersbourg Par Divers Savants, 1854, pp. 539-568.
Freudenstein, F., An Analytical Approach to The Design of Four-Link Mechanisms, Trans. ASME, Vol. 76, 1954, pp. 483–492, DOI: 1115/1.4014881.
Rao, A. C., Kinematic Design of Four-Bar Function Generators with Optimum Sensitivity, Mech Mach Theory, Vol. 10, 1975, pp. 531–535, DOI: 1016/0094-114X(75)90008-7.
Rao, A. C., Optimum Design of Four-Bar Function Generators with Minimum Variance Criterion, J Optim Theory Appl, Vol. 29, No. 1, 1979, pp. 147–153, DOI: 10.1007/BF00932641.
Sun, W., Optimum Design Method for Four-Bar Function Generators, J. Optim Theory Appl, Vol. 38, No. 2, 1982, pp. 287–293, DOI: 10.1007/BF00934089.
Chen, F. Y., Chan, V. L., Dimensional Synthesis of Mechanisms for Function Generator Using Marguardt’s compromise, J. Eng Ind, Vol. 96, 1974, pp. 131–137, DOI: 1115/1.3438287.
Guj, G., Dong, Z. Y., and Giacinto, M. D., Dimensional Synthesis of Four Bar Linkage for Function Generation with Velocity and Acceleration Constraints. Meccanica, Vol. 16, No. 4, 1981, pp. 210–219, DOI: 10.1007/BF02128323.
Söylemez, E., Freudenstein, F., Transmission Optimization of Spatial 4-Link Mechanisms, Mech Mach Theory, Vol. 17, No. 4, 1982, pp. 263–283, DOI: 1016/0094-114X(82)90050-7.
Gosselin, C., Angeles, J., Optimization of Planar and Spherical Function Generators as Minimum-Defect Linkages, Mech Mach Theory, Vol. 24, No. 4, 1989, pp. 293–307, DOI: 1016/0094-114X(89)90049-9.
Angeles, J., Alivizatos, A., and Akhras, R., An Unconstrained Nonlinear Least-Square Method of Optimization of RRRR Planar Path Generators, Mech Mach Theory, Vol. 23, No. 5, 1988, pp. 343–353, DOI: 1016/0094-114X(88)90048-1.
Akhras, R., Angeles, J., Unconstrained Nonlinear Least-Square Optimization of Planar Linkages for Rigid-Body Guidance, Mech Mach Theory, Vol. 25, No. 1, 1990, pp. 97–118, DOI: 1016/0094-114X(90)90110-6.
Shariati, M., Norouzi, M., Optimal Synthesis of Function Generator of Four-Bar Linkages Based on Distribution of Precision Points, Meccanica, Vol. 46, 2011, pp. 1007–1021, DOI: 10.1007/s11012-010-9357-1.
Daniali, H. M., Varedi, S. M., Dardel, M., and Fathi, A., A Novel Algorithm for Kinematic and Dynamic Optimal Synthesis of Planar Four-bar Mechanisms with Joint Clearance, Journal of Mechanical Science and Technology, Vol. 29, No. 5, 2015, pp. 2059-2065, DOI: 10.1007/s12206-015-0426-1.
Farajtabar, M., Daniali, H. M., and Varedi, S. M., Pick and Place Trajectory Planning of Planar 3-Rrr Parallel Manipulator in The Presence of Joint Clearance, Robotica, Vol. 35, No. 2, 2017, pp. 241-253. DOI: 10.1017/S0263574714002768.
Sardashti, A., Daniali, H. M., and Varedi, S. M., Optimal Free-Defect Synthesis of Four-Bar Linkage with Joint Clearance Using PSO Algorithm, Meccanica, Vol. 48, No. 7, 2013, pp. 1681-1693, DOI: 10.1007/s11012-013-9699-6.
Penunuri, F., Peon Escalante, R., Villanueva, C. and Pech Oy, D., Synthesis of Mechanism for Single- and Hybrid-Tasks Using Differential Evolution. Mech Mach Theory, Vol. 46, No. 10, 2011, pp. 1335-1349, DOI: 1016/j.mechmachtheory.2011.05.013.
Shpli, O. A., Genetic Algorithms in Synthesis of Path Generator Four-Bar Mechanism with Maximum Mechanical Advantage. ASM 2007, The 16th IASTED International Conference on Applied Simulation and Modelling; 2007 Aug 29-31, Palma de Mallorca, Spain, California: ACTA Press, pp. 154-161.
Fernández-Bustos, I., Aguirrebeitia, J., Avilés, R., and Angulo, C., Kinematical Synthesis of 1-Dof Mechanisms Using Finite Elements and Genetic Algorithm, Finite Elements in Analysis and Design, Vol. 41, No. 15, 2005, pp. 1441-1463, DOI: 1016/j.finel.2005.04.001.
Cabrera, J. A., Simon, A., and Prado, M., Optimal Synthesis of Mechanisms with Genetic Algorithms, Mech Mach Theory, 37, 2002, pp. 1165–1177, DOI: 1016/S0094-114X(02)00051-4.
Wampler, C. W., Solving the Kinematics of Planar Mechanisms, ASME Journal of Mechanical Design, Vol. 121, 1999, pp. 387-391, DOI: 1115/1.2829473.
Wampler, C.W., Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation, ASME J. Mechanical Design, Vol. 123, 2001, 3382–387, DOI: 10.1115/1.1372192.
Wampler, C. W., Sommese, A. J., Numerical Algebraic Geometry and Algebraic Kinematics, Acta Numerica, 2011, pp. 469–567, DOI: 1017/S0962492911000067.
Varedi, S. M., Daniali, H. M., and Ganji, D. D., Kinematics of an Offset 3-Upu Translational Parallel Manipulator by The Homotopy Continuation Method, Nonlinear Analysis: Real World Applications, Vol. 10, 2009, pp. 1767–1774, DOI: 1016/j.nonrwa.2008.02.014.
Tari, H., Su, H. J., and Li, T. Y., A Constrained Homotopy Technique for Excluding Unwanted Solutions from Polynomial Equations Arising in Kinematics Problems, Mech Mach Theory, Vol. 45, No. 6, 2010, pp. 898–910, DOI: 1016/j.mechmachtheory.2010.01.002.
Tari, H. Su, H. J., A Complex Solution Framework for The Kinetostatic Synthesis of a Compliant Four-Bar Mechanism, Mech Mach Theory, Vol. 46, No. 8, 2011, pp. 1137–1152, DOI: 1016/j.mechmachtheory.2011.03.003.
Shafiee-Ashtiani, M., Yousefi-Koma, A., Keshavarz, H., and Varedi-Koulaei, S. M., Real Time Direct Kinematics Solution of 3-RPS Parallel Robot Using a Semi-Analytical Homotopy Method, Modares Mechanical Engineering, Vol. 17, No. 6, 2017, pp. 303-310 (in Persian).
Varedi-Koulaei, S. M., Rahimi, M., Direct Kinematics Solution of 3-RCC Parallel Robot using a Semi-Analytical Homotopy Method, ADMT Journal, Vol. 12, No. 1, 2019, pp. 1-12.
