## 1 Introduction
[64] applied a TLBO method with a constraint-handling technique, named a path-repairing technique, to address the constraints of both input crank rotation and Grashof's criterion, and some metaheuristic algorithms, including ABC, JADE, PBIL, ACOR, SCA, GWO, and TLBO, were applied to determine the optimum solutions of path-generating four-bar linkages. Three representative cases were investigated, and the optimum results revealed that TLBO outperformed the other methods. Based on the optimal trajectory tracking control theory of a shadow robot, [PERSON] et al. [65] proposed a contour-error-based proportional-derivative objective function for synthesizing path-generating four-bar mechanisms, and employed a global optimization method, known as the multi-start heuristic algorithm, to solve the optimal synthesis problem. [PERSON] et al. [66] presented a hybrid Lagrange interpolation differential evolution (HLIDE) algorithm to enhance the local exploitation capability of DE for optimal synthesis problems. Five cases of optimal four-bar path generating linkages were tested and compared to those of three evolutionary algorithms (PSO, TLBO, and DE), and the results demonstrated the significantly enhanced performance of HLIDE compared to those of the other algorithms. [PERSON] et al. [67] presented an adaptive DE, and incorporated a local search with the Lagrange interpolation argument algorithm (ADELI) to enhance the exploitation capability of DE. Thirty benchmark function sets in the CEC 2014 were tested to verify the feasibility and effectiveness of ADELI, and a synthesis problem of a path-generating four-bar linkage with prescribed timing was optimized. [PERSON] et al. [68] proposed a robust objective function formulation based on natural coordinates and the Hermitian conjugate operator, and implemented a modified TLBO algorithm for the optimal synthesis of a four-bar path generator. [PERSON] et al. [69] proposed a search procedure for the optimal solution of the dimensional synthesis of planar linkages by hybridizing a local search approach (generalized reduced gradient method) and DE. They compared three hybrid strategies and verified that the cluster-based hybridization in DE (DEC) is the best hybrid approach. [PERSON] et al. [70] proposed an improved harmony search (ImHS) algorithm to solve the dimensional synthesis problems of a four-bar path generator without prescribed timing. [PERSON] [71] proposed a population-based heuristic algorithm called a gravitational search algorithm (GSA) to determine multiple cognate- and defect-free optimal solutions for the path synthesis problems of planar four-bar and slider-crank mechanisms. [PERSON] et al. [72] presented an error feedback method (EFM) for linear constraint optimization problems. They optimized two path-generating four-bar linkages using DE, PSO, and TLBO methods, and the objective function with linear inequality constraints was optimized using the penalty function method and EFM. The experimental results revealed that EFM exhibited significantly enhanced stability and faster convergence than the traditional penalty function method. [PERSON] et al. [73] proposed a new constraint handling technique which deals with both input crank rotation and Grashof's criterion for the synthesis of path-generating four-bar linkages. In addition, they solved several optimization problems using a new adaptive TLBO with a diversity archive (ATLBO-DA) algorithm. [PERSON] et al. [74] proposed a new objective function, the geometrical similarity error function (GSEF), and applied an innovative adaptive algorithm (IAA) operator to form the GSEF-IAA methodology for the synthesis problem of a path-generating four-bar mechanism. [PERSON] et al. [75] applied a differential evolution variant (DE/best/1/bin) to solve the optimal dimensional synthesis of a four-bar path generation mechanism using a relative angle and the Cartesian space link parameterization (ODSRA + CP) method.