# Dimensional Synthesis for Multi-Linkage Robots Based on a Niched Pareto Genetic Algorithm
## 1 Introduction  
A multi-linkage robot is a linkage mechanism composed of multiple movable joints connecting rigid rods in series [1; 2]. It has the advantages of large range of working space, high flexibility, simple mechanical structure, good obstacle avoidance performance, and better avoidance of singularity of mechanism. They are widely used in medical surgery, underwater detection, construction, and many other engineering fields. The fact shows that dimensional synthesis for multi-linkage robots has been paid much attention by scholars. [PERSON] proposed a global condition index (GCI) that combines the working space and the Jacobian condition number to design the structure size of multi-linkage robots [3]. Based on the optimization goal of the subjective minimum robot criterion, [PERSON] optimized the robot size with the Lagrange multiplier method [4]. [PERSON] et al. used the means of a multi-objective optimization to carry out dimensional synthesis of a spherical parallel manipulator, the method of multi-objective evolutionary algorithm based on decomposition (MOEA/D) was proposed, objective functions were the dexterity, the variability of the dexterity, the maximum required torque, and the stiffness. The optimization of robots' workspace was performed using non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective particle swarm optimization algorithm (OMOPSO), MOEA/D separately, the results showed better performance of MOEA/D algorithm [5]. [PERSON] et al. obtained the best linkage by means of hybridizing a local search (LS) approach and an evolutionary algorithm (EA). Hybrid optimization strategy was selected by cluster and elite analyses, for the design of planar linkages, the best options were highlighted [6]. In [7], attitude maneuverability was used to optimize the links. The maneuverability as objective function designed robot parameters in [8]. In [9], the workspace distance, stiffness performance, and velocity fluctuation were taken as the standards, the link lengths were designed and optimized for service robots. In [10], link length optimization of 3R linkage robot was done based on the range that the end-effector reached. In [11], the method, which took the distribution area of workspace density function maximum value as the standard, was proposed for dimension design. In the literature [3; 4; 5; 6; 7; 8; 9; 10; 11], one or more algorithms and theories are used to design the size of multi-linkage robots with a single target or several targets as the optimized objective function. The reliability and superiority of the method are verified by means of software and simulation. However, whether the new method can achieve better results in the practical application has not been further studied, and its application value remains to be verified. In [12], a'magic hand' robot was developed on the basis of study regarding dimension synthesis, manipulators can complete the surgery basic operation and can replace an attending doctor. In [13], the structure size was solved by least squares in the view of energy consumption analysis, effectiveness was verified by means of KUKA robot. In [14], the size of collaborative space volume was quantified by the number of space cloud points, mechanical dimensional of the robot arm was were optimized aimed as maximum of collaborative space volume. In [15], the leg structure parameters of quadruped robot were analyzed based on the dynamic dimensional synthesis. In [16], the robot dimensional parameters, which combined with the signal-to-noise ratio (SNR) theory and Taguchi technology, were determined by taking the maximum SNR as the optimization object. In [17], the design of parameters was divided into three levels, it was verified that shortened the design cycle and difficulty and improved the design efficiency for industrial robots. In [18], bionics theory was cited to design the parameters of the crawling robot, which had high reliability, low cost, and good flexibility.