Modular design and simulation analysis of truss robot based on spatial bars structure

For industrial applications, truss robots can perform mutipleoperations, such as transporting objects and handling tools independently, but face the challenges of inconvenient disassembly and non-recyclability. Therefore, a truss robot load-bearing module based on a spatial bar structure is designed, which consists of truss bars and connectors. Ansys Workbench is used for the static analysis of the truss robot beam. The results show that the maximum stress of the truss robot beam is 32.46 MPa and the maximum deformation is 1.1 mm under the load of 12,000 N. The maximum stress of the beam is significantly small than the yield limit of the material and the deformation is small, which meets the requirements of structural strength and load stability of the truss robot. Based on the mode analysis of the truss robot, the inherent vibration and frequency of the truss robot are extracted, providing a reference basis for the stability control of the truss robot. The modular truss robot has mutiple advantages, including the large span, high load capacity and assembly flexibility.


Introduction
Truss type industrial robot, a significant component of automated intelligent manufacturing production lines, plays a crucial role in connecting the whole production chain, which can not only prominently improve production efficiency, but also reduce time costs and labor, deciding a predominant trend in intelligent manufacturing industry in the future [1][2].Highlighted by large workspace, high loadbearing capacity, and competence of large products transportation, truss robots are widely applied in intelligent warehousing, assembly and transportation of large products [3][4].The rationality of the truss robot structure is of great significance in the operational efficiency and product quality of the whole production chain.An integrated structure is the common design for the beams and columns of traditional truss robots [5][6], which is unavailable to be disassembled once installed, causing the truss robots oriented to fixed situations unilaterally with weak flexibility.Modular robot is of diversified competences, including high assembly flexibility, strong fault tolerance, and strong environmental adaptability [7][8][9][10][11].Therefore, designing the modular truss robot that can be reused and applicable for various occasions is of great application prospect.
There are numerous research literatures on the structure design of truss robots at home and aboard, with the main content as follows.Hou et al. designed a truss robot for welding and conducted dynamics analysis [12].Stoppler et al. analyzed the structure of gantry machine tools and designed their load-bearing structure with lightweight design [13].Yu Peng et al. designed an octahedron variable geometry truss robot, and proposed an analytical method of working spatial analysis for the truss robot [14].Zhu Fukang et al. conducted finite element analysis on the mechanical properties of the truss robot and optimized its structure and mass [15].Combining the typical working conditions of human interaction with truss robots, Wang Biao explored the dynamic response and deflection changes of the crossbeam, analyzed the effects of load and speed on the working performance of the truss robot by Matlab, and optimized the structure of the beam [16].Applying Solidworks Simulation, Ya Xiaodan conducted statics analysis and mode analysis on the truss robot, and improved the strength and stiffness of the truss robot [17].It's worth noting that the integrated design takes a high percentage in the current load-bearing structures of truss robots, and there is still improvement space for modular research on truss robot structures.
The paper designs the modular structure of the truss robot based on space bar, of which the columns, beams, and vertical beams of the truss robot are composed of modular units.Modular truss robots are of the characteristics of convenient installation, lightweight, and recyclability.In contrast, traditional mechanical analysis methods for robots shall establish a complex mathematical model and require a large amount of computation.Finite element analysis, an effective method for structure design and analysis [18][19], applies computer simulation of stress and strain parameters as well as mode information of truss robots.Taking the gantry truss robot as an instance, the ANSYS Workbench finite element analysis software adopted to numerically simulate the crossbeam of the truss robot, and the maximum stress and deformation of the crossbeam under typical working conditions were analyzed.Finally, the truss robot is conducted with mode analysis, which is of reference meaning for the stable operation and precise control of the truss robot.

Modular design of truss robot
The module unit of the truss robot that the paper studied is consisted of space bars.Taking the gantry truss robot as an instance, the load-bearing structure of the truss robot mainly includes columns, beams, and vertical beams, as shown in Figure 1, with motion space 10 mm * 18 mm * 9 mm.The single module of the truss robot is consisted of five components, including a vertical bar, chord bar, middle diagonal web bar, side diagonal web bar, and joint, with the structure details in Figure 2(a).It is worth noting that, the larger diameter of the vertical bar, as the main load-bearing component, is capable of improving the tensile, compressive, and flexural strength of the module unit.Chord bar and diagonal web bar is applicable to support the cube structure of modules, and improve the torsional and flexural strength of module units.Joints are the connection points between space bars and modules, which plays a significant role in modular truss robots.There are 9 connection planes and a spatially symmetric structure with the joint designed in the paper, as shown in Figure 2(b).The four types of bars are hollow rigid pipes with threaded holes at both ends, and the joints and bars are fixed with nuts.The internal size of the joint is greater than 140mm, and the specification of the fixing screw is M30 * 120mm.Therefore, screws can be threaded out from the inside of the joint to fix the bar to the joint.The size parameters of the four types of bars are shown in Table 1.The bar will be connected to the joint by fixing at both ends.If the space bar is simplified into a two-force bar, the most load of the truss robot will be converted into the tensile or compressive stress of the bar, which allows the truss robot to bear larger loads.Compared with I-beam or rectangular steel, the space bar structure not only significantly reduces the weight of the truss robot beam, but also is beneficial for increasing the span of the beam.In addition, the truss robot is high in modular degree, and can be assembled into two-degrees-of-freedom hanging arm truss robots or three-degrees-offreedom gantry truss robots according to requirements.

Statics analysis of cross beam
Under the effects of the fixed load, the truss robot structure will be influential on its natural frequency, especially the beam structure (the main load-bearing component) of the truss robot.Therefore, it is necessary to conduct the statics analysis on the beam of the truss robot before the mode analysis, with the formula as follows:   K x F (1) where, K is the stiffness matrix; x is the displacement vector; F is the force vector.
The crossbeam of the truss robot can be deemed as a simple supported beam model, as shown in Figure 3.When the load position centers in the beam, the beam will bear the maximum force.Influenced by the complexity of the stress situation of space bar structures, conventional mechanical analysis methods can generate a significant amount of workload, resulting in lower computational efficiency.Therefore, Ansys Workbench, the finite element analysis software, will be applied to simulate and analyze the entire beam when analyzing the force acting on the truss module structure.The slider and slide rail of the truss robot can be temporarily ignored when analyzing the statics analysis of the beam, and the motor, reducer, and gripper can be deemed as the load of the beam.Importing the simplified model of the crossbeam into Ansys Workbench, the diagram is shown in Figure 4(a).The robotic arm and load of the truss robot are applied as vertical loads in the middle of the crossbeam, with the diagram shown in F in Figure 4(a).As the main load-bearing component of truss robots, the beam requires high reliability in the calculation results.Therefore, the free tetrahedral mesh and mesh refinement methods are adopted to improve the quality of mesh division and thus improve computational accuracy.Finally, the grid division of the truss robot crossbeam is consisted of 564,577 nodes and 125,703 elements, with a slope of 0.28, representing a good grid division quality.The finite element model of the crossbeam is shown in Figure 4(b).
Through applying external loads to the components to calculate the displacement, stress, and strain of the whole system, structure statics analysis is capable of verifying whether the structure meets the stiffness and strength requirements under the effects of static loads, aiming at ensuring its deformation degree maintains within an allowable range of errors, and no occurrence of damage or fracture.The static load that applied in the simulation is 12,000 N.
The deformation and stress clouds of the crossbeam are shown in Figure 5.The simulation results show that the maximum deformation and maximum stress of the crossbeam occur at the position with applied load, with a maximum deformation of 1.1mm and a maximum stress of 32.46MPa.However, the yield stress of Q235 material is 220MPa, which is far less than the allowable stress.Therefore, the beam can bear a total weight of more than 1,200kg for both the robotic arm and the load.

Mode simulation analysis of the truss robot
Through analyzing the mode of the truss robot, the paper obtains natural frequencies and vibration modes, which is beneficial for obtaining the frequency range and structural deformation trend that are easily affected by the entire truss system, and avoiding resonance phenomena in its weak links.
The undamped mode analysis equation of the structure is as follows [20]:

K M
(2) Taking the stiffness matrix obtained from Equation (1) into Equation ( 2), the mode analysis equation with pre-stress can be obtained as follows: is the pre-stress matrix;  I is the vibration frequency; M is the mass matrix;  i is the mode.The truss robot is a complex assembly unit, and is usually composed of hundreds of components.If directly meshing the overall structure and analyzing the finite element, it probably affects its computational efficiency seriously, and even lead to non-convergence of the calculation.Based on the small structural characteristics of drive components, such as sliders, sliding rails, and motors, and the limited impact on mode analysis, those drive components can be ignored when conducting mode analysis on truss robots.Taking the simplified model of the truss robot into the Mode module in Ansys Workbench, the result is shown in Figure 6.The entire structure is made of Q235 structural steel, and fixed constraints can be added between the columns and the ground as boundary conditions.In accordance with the structural characteristics of the model, a compatible free tetrahedron can be selected as the grid partitioning unit, generating a total of 4,536,460 nodes and 1,011,538 units.The average inclination value is 0.42, indicating a sound grid partitioning quality.The finite element model of the truss robot is shown in Figure 7.To maximally ensure the reliability of the truss robot during operation, the paper simulates and analyzes the first ten natural frequencies and vibration modes of the truss robot.Considering the fact that the nature frequency of truss robots is determined by their structural characteristics and is independent from their motion state, the paper only analyzes their mode shapes for a typical working condition.The first 10 mode shapes of the truss robot are shown in Figure 8, and the corresponding natural frequencies are shown in Table 2.The simulation results of the mode vibration mode show that the vibration mode in Stage 1 exhibits a slight deviation of the truss robot column.However, the beam is affected slightly, and the end of the truss robot gripper is almost free from the influence.The vibration modes in Stages 2, 3, 4, and 5 will cause significant oscillation of the truss robot column around the Y or Z axis, which will cause the end of the truss robot gripper to translate in the YOZ plane and affect the position accuracy of the gripper end.The modes in Stages 6, 7, and 10 exhibit torsion and bending deformation of the crossbeam, with the deformation of the crossbeam having the greatest influence on the end effector of the truss robot, resulting in these three stages modes being the most necessary to avoid.The mode of vibration in Stages 8 and 9 are mainly manifested as bending deformation of the vertical beam, which can also cause translation in the YOZ plane of the gripper end.As shown in Table 2, there are small differences between the first ten natural frequencies of truss robots, which proves that the natural frequencies of truss robots are related to their structural characteristics.The first 10 stages' nature frequencies are relatively close and all are less than 14 Hz.The frequency of the drive motor generally ranges from 0 to 50 Hz.If the rotation speed of the driving motors of each motion axis of the truss robot is adjusted to 900~3000 r/min, the excitation frequency of the motor is between 15~50 Hz.Therefore, the excitation frequency of the driving motor can be far away from the natural frequency of the truss robot structure, thereby avoiding resonance of the truss robot and ensuring stable control of the end effector.

Conclusions
The article designs a truss robot module composed of space bars, of which each module consists of four types of bars and joints.The size of the module is 1*1*2 m.The module can be assembled into a two-degree-of-freedom wall-mounted truss robot or a three-degree-of-freedom gantry truss robot.The truss robot composed of modules is featured for large span, heavy load, and disassembly.Taking the gantry truss robot as an instance, the finite element simulation software is applied to conduct statics analysis and mode analysis of the truss robot.The truss robot beam is simplified as a simply supported beam model, and Ansys Workbench is used to conduct statics analysis on the beam.The simulation results indicate that the maximum stress and maximum deformation of the crossbeam occur at the load position.When the load is 12,000 N, the maximum deformation of the crossbeam is 1.1mm, and the maximum stress is 32.46 MPa, which is significantly lower than the allowable stress of the material of 220 MPa.Therefore, the strength and stiffness of the truss robot beam meet the usage requirements.
The mode analysis of the truss robot shows that the influence of the Stage 1 vibration mode on the robot is relatively limited.The Stages 2-5 vibration mode are characterized by the swing of the column, which will cause the end of the robot gripper to translate.The Stages 6, 7, and 10 vibration modes exhibit torsion and bending deformation of the crossbeam, which is of great significance on the end of the robot gripper.
The Stage 8 and 9 modes exhibit bending deformation of the vertical beam, which also causes displacement at the end of the robot gripper.The first 10 stages' modes frequencies are all less than 14 Hz.Therefore, reasonable control of the speed of the drive motor of the truss robot is capable of effectively avoiding resonance of the truss robot.The mode analysis will provide a reference basis for the stability control of truss robots.

Figure 3 .
Figure 3.The simple supported beam model of the truss robot beam.

Figure 4 .
Figure 4. Crossbeam model and finite element model of truss robot.

Figure 5 .
Figure 5. Deformation and stress cloud diagrams of the crossbeam under the load of 12,000 N.

Figure 6 .
Figure 6.Simplified 3D model of truss robot.Figure 7. Finite element model of truss robot.

Figure 7 .
Figure 6.Simplified 3D model of truss robot.Figure 7. Finite element model of truss robot.

Figure 8 .
Figure 8. Cloud map of the first 10 stages of mode shapes of the truss robot.

Table 1 .
Dimensional parameters of bar components.

Table 2 .
First 10 stages nature frequencies of truss robot.