To address the optimization challenges posed by higher-order nonlinear equations in the function generation of four-bar linkage (FBL), this paper presents a novel approach for the function-generation synthesis of planar FBL. Specifically, the auxiliary angle formula from trigonometric identity transformation is employed to derive an explicit analytical expression for the input-output angular relationship in FBL, simplifying the complexity of the derivation process in kinematic modeling. Additionally, a new form of constructing an error objective function based on the input-output dials is proposed, and the mapping model between the prescribed function and the input-output (I/O) function of the function generation is established. Furthermore, a hybrid hierarchical optimization algorithm is proposed to combine the gradient descent interior point method with a meta-heuristic algorithm for FBL parameter optimization. A simulated logarithmic function generator was produced, and the generated results were analyzed. It was found that the maximum error between the values produced by the generator and the true values of the logarithmic function is 0.0015, which is within the acceptable range.
ChoiHParkYJSeoK, et al. A multifunctional ankle exoskeleton for mobility enhancement of gait-impaired individuals and seniors. IEEE Robot Autom Lett2018; 3(1): 411–418.
2.
SinghRChaudharyHSinghAK.Defect-free optimal synthesis of crank-rocker linkage using nature-inspired optimization algorithms. Mech Mach Theory2017; 116: 105–122.
3.
GuoYYinSRenY, et al. A multilevel calibration technique for an industrial robot with parallelogram mechanism. Precis Eng2015; 40: 261–272.
4.
YangYLWeiYDLouJQ, et al. A new piezo-driven microgripper based on the double-rocker mechanism. Smart Mater Struct2015; 24(7): 075031.
5.
SleesongsomSBureeratS.Optimal synthesis of four-bar linkage path generation through evolutionary computation with a novel constraint handling technique. Comput Intell Neurosci2018; 2018: 5462563.
6.
PhukaokaewWSleesongsomSPanagantN, et al. Synthesis of four-bar linkage motion generation using optimization algorithms. Adv Comput Des2019; 4(3): 197–210.
7.
EbrahimiSPayvandyP.Efficient constrained synthesis of path generating four-bar mechanisms based on the heuristic optimization algorithms. Mech Mach Theory2015; 85: 189–204.
8.
SardashtiADanialiHMVaredi-KoulaeiSM.Geometrical similarity error function-innovative adaptive algorithm methodology in path generation synthesis of the four-bar mechanism using metaheuristic algorithms. Proc IMechE, Part C: J Mechanical Engineering Science2022; 236(3): 1550–1570.
9.
KangYHLinJWYouWC.Comparative study on the synthesis of Path-generating Four-Bar linkages using metaheuristic optimization algorithms. Appl Sci2022; 12(15): 7368.
10.
SinghRChaudharyHSinghAK.A new hybrid teaching–learning particle swarm optimization algorithm for synthesis of linkages to generate path. Sādhanā2017; 42(11): 1851–1870.
11.
WaghmareGGRaoRVKulkarniPC.Path synthesis of a four-bar linkage using a teaching-learning-based optimization algorithm. Int J Comput Methods Eng Sci Mech2023; 24(1): 40–51.
12.
ZarkandiS.A novel optimization-based method to find multiple solutions for path synthesis of planar four-bar and slider-crank mechanisms. Proc IMechE, Part C: J Mechanical Engineering Science2021; 235(21): 5385–5405.
13.
BureeratSSleesongsomS.Constraint handling technique for four-bar linkage path generation using self-adaptive teaching–learning-based optimization with a diversity archive. Eng Optim2021; 53(3): 513–530.
14.
EqraNAbiriAHVatankhahR.Optimal synthesis of a four-bar linkage for path generation using adaptive PSO. J Braz Soc Mech Sci Eng2018; 40(9): 469.
15.
KhorshidiMSoheilypourMPeyroM, et al. Optimal design of four-bar mechanisms using a hybrid multi-objective GA with adaptive local search. Mech Mach Theory2011; 46(10): 1453–1465.
16.
QaiyumAMohammadA.A novel approach for optimal synthesis of path generator four-bar planar mechanism using improved harmony search algorithm. Aust J Mech Eng2024; 22(1): 95–108.
17.
HernándezAMuñoyerroAUrízarM, et al. Comprehensive approach for the dimensional synthesis of a four-bar linkage based on path assessment and reformulating the error function. Mech Mach Theory2021; 156: 104126.
18.
SleesongsomSBureeratS.Four-bar linkage path generation through self-adaptive population size teaching-learning based optimization. Knowl Based Syst2017; 135: 180–191.
19.
AbuJabalNBaziyadMFarehR, et al. A comprehensive study of recent path-planning techniques in dynamic environments for autonomous robots. Sensors2024; 24(24): 8089.
20.
SunJWangPLiuW, et al. Non-integer-period motion generation of a planar four-bar mechanism using wavelet series. Mech Mach Theory2018; 121: 28–41.
21.
RussellKShenJ.Planar four-bar motion and path generation with order and branching conditions. J Adv Mech Des Syst Manuf2011; 5(4): 264–273.
22.
LiuXDingJWangC.Design framework for motion generation of planar four-bar linkage considering clearance joints and dynamics performance. Machines2022; 10(2): 136.
23.
BarqueroGEscaleraSPalmeroC. BeLFusion: latent diffusion for behavior-driven human motion prediction. In: Proceedings of the IEEE international conference on computer vision, 2023.
24.
SimionescuPA.A restatement of the optimum synthesis of function generators with planar four-bar and slider-crank mechanisms examples. Int J Mech Robot Syst2016; 3(1): 60.
25.
LiXWeiSLiaoQ, et al. A novel analytical method for four-bar path generation synthesis based on Fourier series. Mech Mach Theory2020; 144: 103671.
26.
QianYZhongHTanCA, et al. Fourier-based function generation of four-bar linkages with an improved sampling points adjustment and Sylvester’s dialytic elimination method. J Mech Des2025; 147(1): 013303.
27.
JiménezJMÁlvarezGCardenalJ, et al. A simple and general method for kinematic synthesis of spatial mechanisms. Mech Mach Theory1997; 32(3): 323–341.
28.
TutsoyOBarkanaDE.Model free adaptive control of the under-actuated robot manipulator with the chaotic dynamics. ISA Trans2021; 118: 106–115.
29.
TutsoyOAsadiDAhmadiK, et al. Minimum distance and minimum time optimal path planning with bioinspired machine learning algorithms for faulty unmanned air vehicles. IEEE Trans Intell Transp Syst2024; 25(8): 9069–9077.
