# Optimization of a Truss Structure Used to Design of the Manipulator Arm from a Set of Components
## 1 Introduction
The components can be easily made from sheet metal or using additive manufacturing technologies. Composite materials may also be suitable for the production of components, e.g., composites with printed fibers [32; 33; 34]. The main goal of the article is to design the manipulator arm by optimizing the truss structure using a component system. The system of components is intended for piece production of manipulators (their arms) within research projects or student projects. One of the main conditions is the repeatable use of components to assemble arms of different sizes or even shapes. Nowadays, 3D technology (e.g., Machine Fortus 450 mc [35] and Solid Isotropic Material with Penalty (SIMP) method [36; 37] for topology optimization of the part) is often used. However, the resulting components cannot simply be reused with other manipulators due to different loads and dimensions. With regard to the use of manipulators, three basic criteria were chosen:  
* The stress states in the structure (permanent deformations must not occur during operational experiments);
* The weight of the structure (weight minimization);
* The displacement at the selected location for defined loads (static loadings is considered as basic). The use of a component system is shown in [13], but structural analysis with respect to the criteria described above would be very complicated due to the large number of contacts between components. In [38], beam elements (space frame) with a few types of cross-sections (solid circular, hollow circular, solid rectangular, thin-walled hollow rectangular, double symmetric I profile) were used in the optimization. In the paper, the fixed shape of the structure is used, and the individual parts are fixed to each other (by welding). A similar approach is also used in [39]. A beam element type could also be used to simulate the behavior of a structure created from a set of components (based on Merkur(r)). A truss structure was chosen to optimize because it is easier to solve. The solution to the problem can be divided into several steps:  
* Low number of shapes and lengths of components (two lengths and two different cross-sections were chosen for testing);
- Components made of different materials (with a view to the future use of 3D printing);
* Corrections resulting from the behavior of the selected component system and the truss structure used for optimization;
* Optimal selection of components for the construction simplified to an optimization of the truss structure (discrete variables);
* Comparison of results with the solution of the same task optimized and produced by an alternative method currently used. The topology of the truss structure is predetermined, and we do not deal with its design here. The article also does not deal with the joining of components since it is assumed that it is satisfactory in terms of strength. These steps would require a larger number of components and their more detailed analysis, and we assume that they will be one of the following steps in optimizing structures based on a component system. The rest of the article is organized as follows. Section 2 describes an optimization method. The optimization goal is to minimize the weight of the system subject to constraints. Components are represented by a discrete vector that contains a cross-section area and material parameters (yield stress, Young's modulus and density). In addition, the components for optimization are limited by other conditions, such as their material and dimensions. A genetic algorithm was used for the optimization, which is tested on a simple task taken from literature. The method application, i.e., the procedure for designing the manipulator arm from components, is presented in Section 3.