Modeling and Simulation Process via Incremental Methods of a Production-Aimed Upper Limb Prosthesis

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This research shows a methodology for designing low-cost prosthesis manufacturing.

Abstract

This research presents a numerical analysis used for designing an upper limb prosthesis with seven degrees of freedom (DOF). The process was undertaken to carry out the manufacture. The detailed methodology exposes a static structural analysis with the materials for manufacturing a prototype, the components responsible for the movement of the prosthesis subject to maximum loads during simplified routines were optimized. The results show the classification of the pieces manufactured by an additive method and those made by material removal.

1. Introduction

According to the National Institute of Geographic Statistics and Informatics (INEGI), in the most recent census (2020), 4.9% of the population in Mexico suffers from a disability [1]. Therefore, one of the treatments for an amputee patient is the implementation of a prosthesis. The objective is to restore the functionality and cosmetic appearance of a human hand. Upper limb prostheses represent an ambitious goal, considering around 87 possible mechanical combinations for their restoration [2]. In the existing literature [3], two groups of prostheses are reported: the passive ones that are destined for a specific use or a cosmetic function [4,5] and the functional ones: of corporeal energy, extracorporeal, and hybrid [6]. In [7], a synthesis of a spherical manipulator for people with an amputation below the shoulder is presented. The optimization of three critical aspects for the performance of the prosthesis is analyzed: the workspace, the prototype dexterity, and the actuators’ torque responsible for movement. Continuity of the research is found in [8], where the design of a prosthetic device with 7 degrees of freedom (DOF) is distributed as follows: 3 DOF in the shoulder, 1 DOF at the elbow, and 3 DOF at the wrist. the low-cost prototype used 3D printing techniques to manufacture it.

Many prostheses used to restore normal functions of missing body parts exist. It is essential to design and assemble them per the patient’s specifications. Three-dimensional printing technology provides a platform to manufacture any complex-shaped polymeric parts economically based on a mechanism to deliver motion and action of upper limbs and hands for children [9]. Additionally, it provides exciting new opportunities for upper-limb prosthetics, and validation is required before the many potential benefits can be realized in clinical practice. Thus far, there is limited evidence of using 3D printing for upper-limb prostheses [10]. The finite element method obtained mechanical analysis of a practical and low-cost prosthetic hand. During the study, particular emphasis was placed on the design process, including functional and technical requirements, correct material selection, and numerical techniques to reproduce the intended DOF [11]. The prosthetic hand was assembled on a 3D printer using clear resin. This prosthetic hand provided the amputee with cosmetic, appearance, and control sensitivity that did not attract much attention in society and positively affected the person [12]. Additive manufacturing for prosthetic sockets using clinical settings reduces costs [13]. The 3D model orthoses are commonly used to complement therapy and for various purposes, not only for the upper limb but also for almost all body parts [14]. Three-dimensional printing is a low-cost method of producing sockets using clinical expertise to create well-fitting prosthetics [15]. An extensive range of prostheses has been 3D printed, of which the majority are upper limb prostheses, the majority designed for children [16]. Three-dimensional printing and rapid prototyping can contribute significantly to the manufacturing process of assistive technologies, mainly prostheses, by streamlining development processes and reducing product costs. In addition, 3D printing has contributed to the execution of tailor-made and user-tailored parts, which is much faster and more accurate than the conventional manual prosthetic process [17]. An affordable and functional upper-limb prosthesis for transradial amputees was tested and validated. Additionally, its modular, intrinsic, and versatile design allows for its adaptation to the user’s needs, such as providing alternate ways of gathering the user intent [18]. Analyses of print times and material costs indicate that injection modeling is advantageous to 3D printing due to lower prices and faster manufacturing times [19]. A functional prototype of a cosmetic prosthesis was obtained. The dual extrusion process caused certain defects, which will be prevented in future manufacturing iterations of this type of product using slightly different manufacturing parameters [20]. The manufacturing processes used to assemble orthoses and prostheses have been analyzed in this field of the subject’s morphology and accuracy of the final device, leading to a better rehabilitation process. Future development lines in this field will be based on the design of new structures and materials to improve comfort, which will grant the success of the new prosthetic aids [21]

However, 3D printing, or additive manufacturing techniques use brittle materials such as ABS, which implies a lack of reliability on the material’s performance when subjected to mechanical work. This research aims to manufacture a prosthesis for patients’ disjointed shoulders by optimizing the mechanisms responsible for the shoulder and elbow movement and replacing the ABS for a ductile material such as aluminum 7075-O to ensure reliability and in pieces for a testbed. This work presents a static structural analysis of the proposed design. The model considers an average force of 5 N in the palm, representing the load that the prototype can sustain.

2. Backgrounds and Manufacture Requirements

Static structural analysis was performed using the ANSYS Workbench^® computer program to examine the behavior of the proposed upper limb prosthesis design. Similarly, the weight was estimated, in five different materials, including the original, and through its density the lightest material and their machinability were determined.

The prosthesis model proposed by the authors is shown in Figure 1. It was manufactured in ABS [22]. The design of the arm prosthesis with 7 DOF distributes its movements as follows: 3 DOF in the shoulder, 1 DOF in the elbow, and 3 DOF in the wrist. As a result, the functional design of an upper limb prosthesis was conceived. The model’s weight is 0.96 kg considering the arm, forearm, and wrist, while the shoulder mechanism and the motors are 0.96 kg. Therefore, the total weight is 1.92 kg, unlike an actual upper limb as it is lighter [22].

The SolidWorks^® software was used to determine the physical properties of the model. The property of most significant interest was the volume since each material has its own density. With this data obtained, an estimate of the model’s mass was made. Concerning materials, it should be emphasized that researchers seek to satisfy the most significant number of demands of the prosthetic industry by selecting stronger, lighter, and more durable materials [23]. In

Table 1. Materials to manufacture.

Material	ρ	ν	E	$	Machinability	Density (kg/m3)	Mass (kg)
Aluminum 7075-O	2800	0.36	72	19	Perfect	2810	1.686
Stainless Steel SAE 304	8000	0.29	193	12.5	Regular	8000	4.8
Titanium Ti-6Al-4V	4430	0.34	114	118	Bad	4430	2.658
Steel AISI 1040-Normalized	7850	0.29	200	4.20	Good	7850	4.71
Original ABS	1060	0.33	2.30	5.18	N/A	1060	0.630

four materials are shown, compared with the original, using their properties of interest such as the density (ρ, kg/m³), the coefficient of Poisson (ν), and the modulus of elasticity (E, GPa) together with specific solicitation parameters to be evaluated such as the cost of mass production and the machinability of the material [24]. In addition, the ABS model’s properties were considered for comparison with the original model.

Each material density exposed in Table 1 and the volume of the prototype obtained in SolidWorks^® were required to estimate the mass of each material’s assembly. Although the prosthesis mass was reported around 1.92 kg, the actuators’ weight and components are neglected. Therefore, the starting mass is 0.630 kg for ABS.

An adaptive mesh of 83,405 elements and nodes 137,630 was proposed. The parties made the model verify the contact areas established manually (Figure 2).

Once the discretized model was obtained, the movement restrictions were established (Figure 3).

A load of 5 N was applied to the palm component “X”, whereas the model was in a completely rigid position of 180°. Therefore, it was considered the most critical arm position (Figure 4) to obtain the reaction forces on each of the joints of the links that set the mechanism.

Naturally, area containing the ball handler’s shoulder is expected to be the most critical. Therefore, the theory used was the maximum shear stress (TRESCA) because this criterion of static resistance is applied to ductile materials. After all, it has a greater inclination for safety. Since the selected material was aluminum 7075-O, Figure 5, Figure 6 and Figure 7 show the maximum displacement, shear stress, and strain.

Table 2. Conditions for finite element model in ANSYS^® Workbench^®.

Variable	Description
Type of analysis	Isotropic linear static
Model view	3D
Degrees of freedom	Ux, Uy and Uz
Iteration algorithm	Newton–Raphson
Mesh type	Mesh with adaptive size function
Element type	Solid-186/187
Nodes	137,630
Contacts	28,329
Solid elements	55,076
Total elements	83,405

summarizes the finite element model applied in the simulation.

Table 3. Numerical results of 7 DOF prosthesis with different materials.

Material	Total Displacement (mm)	Maximum Shear Stress (MPa)	Total Deformation
Aluminum; 7075-O	1.0207	32.772	0.00042631
Stainless Steel; SAE 304	0.37987	32.299	0.0001781
Titanium; Ti-6Al-4V	0.64199	32.94	0.00026773
Stainless; AISI 1040- Standardized	0.36631	32.329	0.0001721
ABS	31.814	N/A	0.014786

shows the results obtained. It is important to mention that the value of interest is the maximum deformation since it considers the modulus of elasticity, which is a different property in each material. It was observed that the displacements varied in each case due to the different densities exhibited by each material. However, the maximum shear stress was similar since the same load was always applied to the same area.

3. Topological Optimization

According to the FEA results, it was visible that the pieces that make up the shoulder area exhibited more significant stress than the other pieces. This is obvious if it is taken into consideration that the designed shoulder must have the capacity to support the rest of the prosthetic structure. The topological optimization of the mechanisms located at the transhumeral area of the prosthesis was carried out with ANSYS Workbench^®. In addition, the same program was used to corroborate the stress of the parts without optimization and optimization. The following flow chart shows how it was done (Figure 8).

3.1. Six-Bar Mechanism

The transhumeral area is presented according to the Schwartz classification (Figure 9a) applied to the model (Figure 9b), where the mechanism is located in the proposed design. Inside, it can see the mechanism with the parts to be optimized (Figure 9c). This mechanism is responsible for the hand’s flexion and extension movements.

In order to obtain the reaction forces in each link of the six-bar mechanism (Figure 10a), it was considered that the arm was in a critical position (Figure 10b), to be analyzed while holding a weight (w) of 5N in the palm.

SolidWorks Motion^® was used to obtain the reaction forces. As an essential point, this tool avoids redundancies, which can excessively restrict the movement of a component within an assembly, causing inaccuracies in the movement study [25]. The results for each binding site of interest are shown in

Table 4. Reaction forces of the six-bar mechanism.

Point of Interest	Results (N)
	Fx = 199
	Fy = 1
	Size = 199
	Fx = 1
	Fy = 199
	Size = 199
	Fx = 56
	Fy = 122
	Size = 134.2
	Fx = 32
	Fy = 55
	Size = 64
	Fx = 133
	Fy = 17
	Size = 134

.

With the obtained values and applying the methodology of Figure 8, contemplating data and the material used in their manufacture, shown in

Table 5. Mechanical properties of the 7075-O.

Property	Value
Poisson’s coefficient	0.36
Modulus of elasticity	72,000 MPa
Maximum strain	572 MPa
Density	2800 kg/m3
Yielding strain	503 MPa

, optimization of the components was carried out.

For the discretizing, a mesh based on curvature and proximity was used for each piece, and cylindrical fasteners with their respective loads were obtained previously. The results of each piece optimized and unoptimized are shown in

Table 6. Results of the six-bar mechanism.

Original Piece	Post-Processing	Optimized Piece
σVM = 10.70 MPa		σVM = 351.48 MPa
σVM = 37.41 MPa		σVM = 232.55 MPa
σVM = 7.68 MPa		σVM = 110.64 MPa
σVM = 9.50 MPa		σVM = 247.66 MPa
σVM = 4.79 MPa		σVM = 89.13 MPa

.

A safety factor of two was considered in each piece as it is the value commonly used in aluminum prostheses [26]. This does not mean that all parts will have this safety factor. It is only considered a parameter when optimizing since the restriction value to be used will be a von Mises global stress of 252 MPa to guarantee that this piece does not fail; however, anything below yield stress guarantees that the part will function.

3.2. Spheric Mechanism

In the transhumeral area of the prosthesis (Figure 11a), a spherical manipulator is located, which replicates the three movements of the human humerus, which are as follows (Figure 11b): flexion–extension, external–internal rotation, and abduction–adduction, so that the shoulder comprises three degrees of freedom.

The reaction forces were calculated using SolidWorks^® Motion. The spheric mechanism is composed of six links that interact, by known theoretical considerations of two points of interest subject to each pair, external and internal (Figure 12b). The results are shown in

Table 7. Reaction forces of the ball gripping mechanism.

Point of Interest	Results (N)
	External
	Fx = 1, Fy = −1
	Fz = 4
	Size = 4
	Internal
	Fx = 1, Fy = −1
	Fz = 4
	Size = 4
	External
	Fx = 1, Fy = −19
	Fz = −26
	Size = 32
	Internal
	Fx = 1, Fy = −19
	Fz = −26
	Size = 32
	External
	Fx = 9, Fy = 27
	Fz = 17
	Size = 33
	Internal
	Fx = 9, Fy = 27
	Fz = 17
	Size = 33

.

The topological optimization was performed, and

Table 8. Results of the spherical manipulator mechanism.

Original Piece	Post-Processing	Optimized Piece
External green σVM = 0.85 MPa		σVM = 308.55 MPa
Internal green σVM = 1.63 MPa		σVM = 68.09 MPa
External blue σVM = 11.543 MPa		σVM = 165.66 MPa
Internal blue σVM = 19.04 MPa		σVM = 94.48 MPa
External red σVM = 8.56 MPa		σVM = 137.45 MPa
Internal red σVM = 9.50 MPa		σVM = 69.91 MPa

shows the results obtained.

4. Manufacture Process

For the correct machining process of the optimized components, it is necessary to understand the different parameters (Figure 13) that impact manufacturing by removing material such as the material of the cutting instrument. For example, according to ISO 513, Classification and application of hard cutting materials for metal removal with defined cutting edges—Designation of the main groups and groups of application [27], the hardness of the material to be machined, the wear of the tooling edge, the way it is going to be machined, the cutting and clamping types, and the use of refrigerants.

4.1. Progress Sheet

According to the standard ISO 9000, the activities helped the resources to transform inputs into results. By determining what a process sheet is, the tasks or steps to be followed in carrying out the manufacturing to be carried out are reflected [28]. A process sheet manufacturing must have five significant points [29].

The first is the plane of the product showing the workpiece. The second refers to the data area of sheet processes, and the third is the description area that shows the operations to be carried out. These can be roughing, facing, or turning to mention a few examples. Fourth, there is a space for operating conditions such as cutting and feed speed with their respective operating times. Finally, the last paragraph has the area of the tools to be used for machining parts. Regarding these points, it is essential to emphasize that the order in which they are displayed is indistinct and that they are simply the most common in the process sheets; however, there is no regulation for the preparation of a process sheet, which means that they are varied in terms of the information presented.

4.2. FeatureCAM^® and Ultimaker Cura^®

To elaborate the parts to be manufactured, the FeatureCAM^® computer program was used, which automates the workflow from design to obtaining the numerical control code for milling and turning applications [16]. The fused deposition modeling technique is used for the parts manufactured in plastic through the Ultimaker Cura^® computer program that allows generating the G code for the 3D printing machine [30]. The following flow chart (Figure 14) summarizes the part selection process manufactured in aluminum and made using 3D printing.

4.3. Manufacturing with Feature CAM^®

To illustrate how the selected parts were manufactured with the feature CAM^®, the development of a prosthesis part is shown (Figure 15). The part is a link modeled in Solid Works^® and must be exported in Parasolid format.

Not all the pieces can be manufactured in aluminum because they perform critical mechanical work. Some perform a cosmetic function and machining them would generate extra weight for the prosthesis. Next, the type of initial shape of the block to be used is configured; in this case, the piece will be obtained from a rectangular prism with arbitrary measurements. The material type is aluminum and is indicated to the program if the part requires a fourth axis. The criterion for deciding if the part requires the fourth axis is established through the “Z” axis if the part requires a rotation to perform a machining operation that cannot be achieved through the machining tool’s input. The surface of the block of material is cut perpendicularly. Therefore, a fourth axis is implemented that allows the piece’s rotation. The shaft can be compared to “X”, “Y”, or “Z”.

With machining-based or pattern recognition, Knowledge-Based Machining (KBM) can be used to machine a workpiece from the model Parasolid. By way of illustration, each operation of the machining process is explained (Figure 16).

In operation, the Boss1 profile figure used the imported Parasolid to generate a closed loop to permit removal of the extra material. After the circular hole, the geometry Parasolid operation generated hole1 and likewise used the same strategy for poket1 and poket2. These two operations can be seen with a difference in the box poket1 with a less straight profile over the poket2. This is because, at times, the KBM is not able to detect the excellent operation machining, which implies the manual created by the user to generate a close profile as highlighted in yellow in the manual profile operation that is generated when using the imported sun visor as a reference, to guarantee a better profile similar to the original poket2 model. Finally, the hole2 hole is recognized, and the final piece is obtained

4.4. Manufacture with Ultimaker Cura^®

To illustrate how a piece is configured for manufacture by FDM with Ultimaker Cura^®, a piece of the cosmetic type of prosthesis is shown in Figure 17, the part is the frame modeling arm SolidWorks^®, which must be exported in stereolithography format (S.T.L., Standard Triangle Language).

After importing the STL format model, we proceeded to configure the parameters of

Table 9. Configuration Ultimaker Cura^® for manufacturing FDM material ABS.

Parameter	Description	Value
Quality	Sets the layer height that affects the resolution of the final piece.	0.1 mm
Shell	Sets the wall thickness, the number of walls generated, the thickness of the first and last layers.	Wall thickness = 0.8 mm Number of walls = 2 The thickness of the first/last layer = 0.8 mm
Infill	Sets the density of the part and the type of structural pattern.	Density = 40% Pattern= Triangular
Material	The temperature at which the material melts, the heat bed temperature, and the option to activate material shrinkage are given.	PLA = 200 °C Bed = 60 °C Retraction=Active
Print speed	Sets the speed of the stepping motor when inducing the material into the extruder tip.	60 mm/s
Cooling	Activates the printer ventilator and the percentage speed at which the print cooling fans rotate.	Ventilator = active Speed= 100%
Support	It activates the support material that can be placed on the entire model where it is required or only on the parts that are in contact with the surface and the protruding angle of the support.	Support = active Position = All Angle = 50°
Build plate adhesion	Provides three options for the material adhesion of the surface.	Type = Brim

in Ultimaker Cura^®.

5. Discussion

According to the finite element calculation results shown in Figure 5, Figure 6 and Figure 7, it is evident that the pieces that contemplate the shoulder area exhibit more significant stress concerning the rest of the pieces. This makes sense if it is considered that the prosthetic shoulder should support the whole structure of the prosthesis through the spherical manipulator that would emulate the articular loads that the human shoulder area receives. Therefore, topological optimization was performed to increase the performance of the transhumeral prosthesis mechanism from the elbow to the shoulder. In addition, ANSYS Workbench^® program was used to corroborate the non-optimized and optimized pieces’ stress, as shown in Table 6 and Table 8. Topological optimization seeks to obtain the maximum or minimum stiffness, that is, to minimize or maximize the deformation energy with a volume restriction. In other words, it is the reduction of the final weight of the structural, mechanical element, preserving its stiffness and functionality. This formulation finds the relative density distribution of material within a domain on a grid of finite elements called design isotropic solid microstructures whose dimensionless values must be between zero and one, where zero indicates that material is removed, and one indicates that material is required. For example, in the central column of Table 6 and Table 8, the topological optimization performed on the links located in different parts of the prosthetic device shows a reduction of material, which reduces machining process hours. Many 3D printing techniques are used to develop mechanical parts that reduce the cost during the manufacturing stage in the global industry. These techniques have been used to develop various aesthetic prostheses, active and passive (high geometric precision and accurate finish) [31], used in the human body, which improves the user’s quality of life from the psychological aspects to restarting the activities of daily living. In comparison with other research, this paper discussed a methodology that allows the fabrication of a total upper limb prosthesis through process sheets and the mixture of standard machining techniques on parts susceptible to failure and parts with passive and static functions. Various techniques used to fabricate integrated solutions involving roughing materials and 3D printing in the fabrication of functional prostheses to ensure the device’s durability were reported.

6. Conclusions

In this research, the manufacture of an upper limb prosthesis was analyzed. When evaluating the study model, initially manufactured in ABS, it can be understood that the parts of the shoulder and elbow mechanisms are not reliable for performing cyclical tasks due to the low mechanical resistance exhibited in the parts when performing mechanical work. This detail represents limitations when performing a test, so employing a material such as 7075-O in spherical parallel robot links ensures improved reliability and high dimensional accuracy compared to using a subtractive method such as CNC machining. The prototype was made with ABS, and the cost was around USD 1500 of 3D materials. The machine used to print the entire 7-DOF prosthesis was a Dimension SST 1200. The cost was reduced by around 67% with this research. Therefore, the prototype cost was estimated to be around USD 300 using PLA for the 3D printed parts and USD 200 for the spherical robot links used in the wrist and shoulder manufactured with aluminum. The topological optimization allows improved use of the mechanisms. Knowing the manufacturing processes and elaborating the process sheets allows generating a possible machining model report and a movement analysis allowed to identify the forces in the mechanisms to carry out a static structural study. Applying the FEM in a static structural study helps to identify loads’ effects on mechanisms and validate their optimization. The forces were obtained using SolidWorks^® Motion 2018 with the critical position for each mechanism. The optimization was carried out with ANSYS Workbench^® 19.1, the same program used for the static structural analyses. The results show a better use of the optimized parts.