501190 2013
POI38510.1177/0309364613501190Prosthetics and Orthotics InternationalKumar
INTERNATIONAL SOCIETY FOR PROSTHETICS AND ORTHOTICS
Original Research Report
Parametric optimization and design validation based on finite element analysis of hybrid socket adapter for transfemoral prosthetic knee
Prosthetics and Orthotics International 2014, Vol. 38(5) 363–368 © The International Society for Prosthetics and Orthotics 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0309364613501190 poi.sagepub.com
Neelesh Kumar
Abstract Background: Finite element analysis has been universally employed for the stress and strain analysis in lower extremity prosthetics. The socket adapter was the principal subject of interest due to its importance in deciding the knee motion range. Objectives: This article focused on the static and dynamic stress analysis of the designed hybrid adapter developed by the authors. A standard mechanical design validation approach using von Mises was followed. Four materials were considered for the analysis, namely, carbon fiber, oil-filled nylon, Al-6061, and mild steel. Study design: The paper analyses the static and dynamic stress on designed hybrid adapter which incorporates features of conventional male and female socket adapters. The finite element analysis was carried out for possible different angles of knee flexion simulating static and dynamic gait situation. Methods: Research was carried out on available design of socket adapter. Mechanical design of hybrid adapter was conceptualized and a CAD model was generated using Inventor modelling software. Static and dynamic stress analysis was carried out on different materials for optimization. Results: The finite element analysis was carried out on the software Autodesk Inventor Professional Ver. 2011. The peak value of von Mises stress occurred in the neck region of the adapter and in the lower face region at rod eye–adapter junction in static and dynamic analyses, respectively. Conclusions: Oil-filled nylon was found to be the best material among the four with respect to strength, weight, and cost. Clinical relevance Research investigations on newer materials for development of improved prosthesis will immensely benefit the amputees. The study analyze the static and dynamic stress on the knee joint adapter to provide better material used for hybrid design of adapter. Keywords Finite element analysis, socket adapter, stress analysis, parametric optimization, limb prostheses, amputees Date received: 27 November 2012; accepted: 19 July 2013
Background Above-knee prosthetics attempt to replace knee function in transfemoral (TF) amputees. In recent years, there have been significant advancements in this field. New materials such as glass fiber–reinforced plastic (GFRP) and oil-filled nylon have allowed artificial limbs to become stronger and lighter, minimizing the amount of energy required to operate the limb. In addition to new materials, the use of electronics is also becoming popular.1,2 The development of lower limb prosthetics through the years has led to better joint mechanisms and structures.3 A TF amputation affects the balance and strength of the muscles around the affected hip joint.4 As a result, proper prosthetic alignment has been
emphasized to enhance residual limb comfort and improve walking capabilities in persons with this kind of amputation.5–10 It has been found through observations in the field of lower limb prosthetic rehabilitation that many TF prostheses show signs of wear on some components of the knee CSIR-CSIO, Chandigarh, India Corresponding author: Neelesh Kumar, Biomedical Instrumentation Unit, CSIR-CSIO, Sector 30-C, Chandigarh-160030, India. Email: [email protected]
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unit.11 The usual way to attach a prosthetic limb to the body is with a socket. Discomfort and other problems resulting due to the socket fit are common and have been shown to adversely affect the quality of life and mobility.12 The adapter should help to provide a better natural gait pattern and a reduction in energy expenditure in walking.13 Consequently, a good and efficient design of socket adapter becomes very crucial because the adapter provides a coupling between the socket and prosthetic knee, so its properties such as strength, length,14,15 weight,16 and stress– strain 17,18 limits become important design parameters.19 This article deals with validation of design of a new kind of socket adapter developed by the authors for a TF prosthetic device, which would be henceforth referred to as hybrid adapter. The finite element analysis (FEA) of the adapter has been carried out on the software Autodesk Inventor Professional Ver. 2011. As the complexity of the structure increases, the difficulty in obtaining an acceptable understanding of the real loading also increases.20 FEA involves a complex system of points called nodes, which make a grid called a mesh. This mesh is programmed to contain the material and structural properties that define how the structure will react to certain loading conditions. Nodes are assigned a certain density throughout the material depending on the anticipated stress levels of a particular area. Regions that receive large amount of stress usually have a higher node density than those that experience little or no stress. Points of interest may consist of fillets, corners, complex detail, and high stress areas. FEA allows the users to validate component design by testing the part’s or assembly’s performance under forces and torques. The tools available as per classical mechanics are not suitable for irregular structure and contouring such as in the case of prosthetic knees. The powerful finite element method (FEM) is able to evaluate stresses in designs of intricate shape, variable loading, and material behavior.21 FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system. Similarly, the desired level of accuracy required and associated computational time requirements can be managed simultaneously to address most engineering applications. FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured. FEMs are extensively used in the field of biomedical engineering, especially biomechanics for computing stress and strain in complex systems. This article discusses the stress and strain distribution in the hybrid adapter (in isolation as well as when it is in the assembly) taking into account the loading character, the effect of material properties, and adapter geometry with the aim of contributing to the improvement of adapter design. Although there are many articles based on the finite element modeling of socket–limb interaction, only a few are there which discuss this method for the analysis of lower limb prosthetic components, especially the socket adapter.22 The socket adapter should allow for maximum range for knee flexion angle during the swing phase (flexion and
extension).23 FEA also helped to identify the regions of an artificial prosthetic, which contribute to faster fatigue.24 Thus, this article focused on parametric optimization based on material selection, weight, strength during static and dynamic gait, and cost. This analysis gives an insight for design of an efficient adapter with the help of an FEM to investigate stresses in load-bearing components, which could help to improve the functioning and comfort level of TF prosthetic users.
Methods This work involved the static and dynamic stress analysis of a TF prosthesis adapter. The need of a hybrid adapter was felt because the knee flexion angle range of up to 60° could be achieved with the male pyramid adapter. So to increase the knee flexion angle, a new design of a socket adapter was conceptualized incorporating the features of a male pyramid as well as those of the female pyramid adapter. Its threedimensional (3D) model was developed on Autodesk Inventor Professional Ver. 2011, which is shown in Figure 1.
Geometries Figure 2 shows the full mechanical assembly model of the prosthetic knee. The mechanical assembly consists of a GFRP outer cover, hybrid adapter, pneumatic cylinder of aluminum, a helical compression spring made of spring steel, nylon bushes, and bolt–nut sub-assembly. The computer-aided design (CAD) model was designed on the basis of manual measurements. The assembly was simulated in the Inventor Dynamic Simulation environment to see its actual working and to generate loads to export and use in stress analysis.
Material properties The FEA of hybrid adapter has been carried out on four types of materials: (1) mild steel, (2) carbon fiber, (3) Al-6061, and (4) oil-filled nylon. The mechanical properties of all the above materials were taken to be linearly elastic, isotropic, and homogeneous. Linear material properties imply that the stress is directly proportional to the strain in the material, meaning no permanent yielding of the material. Linear behavior results when the slope of the material stress–strain curve in the elastic region (measured as Young’s modulus of elasticity) is constant. Isotropic behavior implies that the material properties are not dependent on the direction. The values of Young’s modulus, Poisson’s ratio, yield strength, and ultimate tensile strength were taken from standard datasheets. A load of 600 N has been considered throughout for the stress analysis. Table 1 summarizes the material properties of the components (other than hybrid adapter) used. The total deformation is assumed to be small in comparison to the part thickness. For example, if studying the deflection of a beam, the calculated displacement must be less than the minimum cross section of the beam. The
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Kumar
Figure 1. (a) 3D model of the hybrid adapter and (b) fabricated oil-filled nylon hybrid adapter. 3D: three-dimensional.
Figure 2. 3D model of the mechanical assembly. 3D: three-dimensional.
temperature is assumed not to affect the material properties so the results computed are temperature independent.
Numerical analysis The finite element static and dynamic loading stress analysis was carried out on Autodesk Inventor Professional Ver.
2011. In the first phase of our analysis, the static stress analysis of the hybrid adapter (in isolation) was performed for all the four materials. In the second phase, the dynamic stress analysis of the full mechanical assembly was carried out by segregating the gait cycle in five stages taking the angle between the loading vector and the hybrid adapter as the standard parameter.
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Table 1. Material properties of components used in TF prosthesis. Component
Material
Young’s modulus (GPa)
Poisson’s ratio
Yield strength (MPa)
Outer cover Cylinder and rod eye Spring Bolt Nut Bush
GFRP Aluminum Spring steel Stainless steel Mild steel Nylon-6/6
13 68.9 180 193 220 2.93
0.34 0.33 0.3 0.31 0.27 0.35
148 275 413 250 207 82.75
TF: transfemoral; GFRP: glass fiber–reinforced plastic.
Static stress analysis. This was performed in three different orientations of hybrid adapter with respect to horizontal, that is, 0°, 45°, and 90°, for each of the four materials. Since FEA uses small elements to solve complex problems, a larger number of smaller elements can sometimes yield more accurate results. This is where convergence comes into play. Convergence in Inventor Stress Analysis is actually a series of settings that can be used to automatically make mesh elements smaller, and it helps to determine whether results are accurate. The basic concept is that the mesh will be automatically made of smaller elements and solved until the results of the refined mesh fall within a percentage of the previous mesh. The number of FE elements and nodes assigned was approximately 5226 and 8374, respectively. The number of refinement cycles for convergence was kept as five. The von Mises stress was the key parameter throughout the analysis. Dynamic stress analysis. In this analysis, the force was resolved into two components with respect to the angle between the force vector and the adapter while specifying the load on the adapter. The angles considered were 124°, 149°, 157°, 161°, and 164° for a gait cycle. The number of FE elements and nodes assigned was approximately 75,763 and 145,432, respectively. The fixed boundary was given to the outer cover of the assembly and the adapter was loaded with the two mutually perpendicular resolved forces as well as the spring force in the axial direction of the pneumatic cylinder acting on the lower surface of the adapter. The spring force was calculated by using the equation F = kx, where k is the spring constant in Newton/millimeter and x is the compression in the spring in millimeter. The value of the spring constant was calculated by using equation (1): Gd 4 k= 8D3 n
Figure 3. Von Mises stress distribution of hybrid adapter (carbon fiber).
Figure 4. Section view of the adapter for oil-filled nylon.
Results and discussion (1)
where G is the modulus of rigidity of spring material, d the wire diameter, D the mean coil diameter, and n the number of active coils which is the number of coils subjected to flexure. The number of refinement cycles for convergence was again kept as five.
This article discusses the design evaluation of hybrid adapter in various gait cycle angles. The FEM analysis is carried out to generate a stress profile of the adapter at various sections. The stress analysis is carried out in static and dynamic gait positions. Four material properties are evaluated for maximum and minimum stress. This evaluation gives the optimum material for the design of such hybrid adapters.
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Kumar Table 2. Peak von Mises stress during static gait (in megapascal). Material
Weight (g)
Maximum stress (0°)
Maximum stress (45°)
Maximum stress (90°)
Carbon fiber Oil-filled nylon Al-6061 Mild steel
46 32.6 77.8 225.74
12.09 11.39 11.5 11.79
50.6 46.29 47.17 49.66
35.98 33.1 32.89 33.43
Table 3. Peak von Mises stress for the full assembly (in megapascal). Peak von Mises stress (in megapascal) at different flexion angle (in degrees) Material Carbon fiber Oil-filled nylon Al-6061 Mild steel
124° 49.2 24.5 34.37 30.39
149° 58.45 34.3 44.53 37.53
Figure 5. Section view of the peak von Mises stress distribution in the full assembly.
Static stress analysis The aim of this analysis was to find a material best suited for the hybrid adapter minimizing the weight of the adapter keeping the maximum von Mises stress in mind as well as to achieve desired strength and knee flexion. It was evident from the analysis that the peak von Mises stress occurs at the neck of the adapter. Carbon fiber material experienced the maximum stress (Figure 3) and oil-filled nylon experienced the minimum stress (Figure 4) in all the three orientations. With respect to the weight parameter, machinability, and cost, oil-filled nylon was found to be the optimum material. Table 2 summarizes the peak von Mises stress for all the four materials.
Dynamic stress analysis This analysis was meant for checking the performance of the adapter under loading conditions when undergoing standard gait cycle. This analysis also revealed that the oilfilled nylon material gives the minimum value for the peak
157° 60.03 35.21 46.89 38.78
161° 61.67 35.51 47.06 39.33
165° 61.89 35.66 47.75 39.98
von Mises stress for all the five standard gait cycle angles. The peak von Mises stress was observed in the lower face of the adapter at the rod eye–adapter junction as shown in Figure 5. Table 3 summarizes the data obtained for peak von Mises stress for all the four materials with respect to the five angles. Similar types of stress analysis using FEM as an evaluation tool were carried by many researchers. In the presented case, a different approach is taken first to design the hybrid adapter and evaluate the design on the basis of static and dynamic stress. The material properties were also evaluated for deciding the optimum material for fabrication of such adapters. More strength to the claims can be provided if dynamic stress analysis is carried out for whole gait cycle. We can have improved results of stress calculation and material optimization. The detailed cost analysis for each material is required to have affordable hybrid adapter.
Conclusion The analysis presented in this article reflects the importance, capabilities, and use of FEM in parametric optimization and design evolution of an efficient hybrid socket adapter required for indigenously developed TF knee. The approach followed was a standard mechanical design validation process in which a 3D design is developed on CAD software; dynamic simulation is performed to assess its working, and finally, it is subjected to stress analysis to check its performance under variable loading conditions. Through this manner, design optimization is done with respect to weight, strength, material properties, and feasibility. A socket adapter was developed integrating the features of a male pyramid adapter and a female pyramid adapter. The FE analysis was carried out for four materials, namely, carbon fiber, oil-filled nylon, Al-6061,
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and mild steel, which are readily available in the market, and it was found that oil-filled nylon material gives the minimum value for peak von Mises stress, whereas carbon fiber gives the maximum corresponding value. The peak von Mises occurs in the neck region of the adapter in case of static stress analysis. In dynamic stress analysis, the peak is observed in the region constituting the lower face of the adapter where it is in contact with the rod eye. Oil-filled nylon was eventually found to be the best material among the four with respect to strength, weight, and machinability. The presented FEM model was thus found suitable for a parametric analysis of developed socket adapter. Funding The author thanks the Council of Scientific and Industrial Research for funding the project under grant no. BSH SIP0022.10.
Declaration of conflicting interest None declared.
References 1. Omasta M, Paloušek D, Návrat T, et al. Finite element analysis for the evaluation of the structural behavior, of a prosthesis for trans-tibial amputees. Med Eng Phys 2012; 34(1): 38–45. 2. Jia X, Zhang M and Lee WC. Load transfer mechanics between trans-tibial prosthetic socket and residual limb— dynamic effects. J Biomech 2004; 37(9): 1371–1377. 3. Zlatnik D, Steiner B and Schweitzer G. Finite-state control of a trans-femoral (TF) prosthesis. IEEE T Cntr Syst T 2002; 10(3): 408–420. 4. Fite K, Mitchell J, Sup F, et al. Design and control of an electrically powered knee prosthesis. In: IEEE 10th international conference on rehabilitation robotics, Noordwijk, 13–15 June 2007, pp. 902–905. New York: IEEE. 5. Pinzur MS, Cox W, Kaiser J, et al. The effect of prosthetic alignment on relative limb loading in persons with transtibial amputation: a preliminary report. J Rehabil Res Dev 1995; 32(4): 373–378. 6. Geil MD and Lay A. Plantar foot pressure responses to changes during dynamic trans-tibial prosthetic alignment in a clinical setting. Prosthet Orthot Int 2004; 28(2): 105–114. 7. Seelen HAM, Anemaat S, Janssen HMH, et al. Effects of prosthesis alignment on pressure distribution at the stump/ socket interface in transtibial amputees during unsupported stance and gait. Clin Rehabil 2003; 17(7): 787–796. 8. Jia X, Li X and Zhang M. The influence of dynamic transtibial prosthetic alignment on standing plantar foot pressure. Conf Proc IEEE Eng Med Biol Soc 2005; 7: 6916–6918. 9. Kang P, Kim J and Roh J. Pressure distribution in stump/ socket interface in response to socket flexion angle changes in trans-tibial prostheses with silicone liner. Phys Ther Korea 2006; 13(4): 71–78.
10. Chow DHK, Holmes AD, Lee CK, et al. The effect of prosthesis alignment on the symmetry of gait in subjects with unilateral transtibial amputation. Prosthet Orthot Int 2006; 30(2): 114–128. 11. Magnissalis EA, Stephan E, Spence WD, et al. Prosthetic loading during kneeling of persons with transfemoral amputation. J Rehabil Res Dev 1999; 36(3): 164–172. 12. Hagberg K, Branemark R, Gunterberg B, et al. Osseointegrated trans-femoral amputation prostheses: prospective results of general and condition-specific quality of life in 18 patients at 2-year follow-up. Prosthet Orthot Int 2008; 32(1): 29–41. 13. Van der Linden ML, Solomonidis SE and Spence WD. Stump-socket interface pressure as an aid to socket design in prostheses for trans-femoral amputees—a preliminary study. Proc IMechE, Part H: J Engineering in Medicine 1997; 211(2): 167–180. 14. Lee RY and Turner-Smith A. The influence of the length of lower-limb prosthesis on spinal kinematics. Arch Phys Med Rehabil 2003; 84: 1357–1362. 15. Friberg O. Biomechanical significance of the correct length of lower-limb prostheses—a clinical and radiological study. Prosthet Orthot Int 1984; 8(3): 124–129. 16. Bateni H and Olney JS. Effect of the weight of prosthetic components on the gait of transtibial amputees. J Prosthet Orthot 2004; 16(4): 113–120. 17. Silverthorn MB and Childress DS. Parametric analysis using the finite element method to investigate prosthetic interface stresses for persons with trans-tibial amputation. J Rehabil Res Dev 1996; 33(3): 227–238. 18. Quesada P and Skinner HB. Analysis of a below-knee patellar tendon-bearing prosthesis—a finite-element study. J Rehabil Res Dev 1991; 28(3): 1–12. 19. Simpson G, Fisher C and Wright DK. Modeling the interactions between a prosthetic socket, polyurethane liners and the residual limb in transtibial amputees using nonlinear finite element analysis. Biomed Sci Instrum 2001; 37: 343–347. 20. Sewell P, Noroozi S, Vinney J, et al. Improvements in the accuracy of an Inverse Problem Engine’s output for the prediction of below-knee prosthetic socket interfacial loads. Eng Appl Artif Intel 2010; 23(6): 1000–1011. 21. Zhang M, Mak AF and Roberts VC. Finite element modelling of a residual lower-limb in a prosthetic socket: a survey of the development in the first decade. Med Eng Phys 1998; 20(5): 360–373. 22. Lee WCC, Zhang M, Boone D, et al. Finite element analysis to determine the effect of monolimb flexibility on structural strength and interaction between residual limb and prosthetic socket. J Rehabil Res Dev 2004; 41(6A): 775–786. 23. Kalanovic VD, Popovic D and Skaug NT. Feedback error learning neural network for trans-femoral prosthesis. IEEE Trans Rehabil Eng 2000; 8(1): 71–80. 24. Chen NZ, Lee WCC and Zhang M. A numerical approach to evaluate the fatigue life of monolimb. Med Eng Phys 2006; 28(3): 290–296.
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POI38510.1177/0309364613501190Prosthetics and Orthotics InternationalKumar
INTERNATIONAL SOCIETY FOR PROSTHETICS AND ORTHOTICS
Original Research Report
Parametric optimization and design validation based on finite element analysis of hybrid socket adapter for transfemoral prosthetic knee
Prosthetics and Orthotics International 2014, Vol. 38(5) 363–368 © The International Society for Prosthetics and Orthotics 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0309364613501190 poi.sagepub.com
Neelesh Kumar
Abstract Background: Finite element analysis has been universally employed for the stress and strain analysis in lower extremity prosthetics. The socket adapter was the principal subject of interest due to its importance in deciding the knee motion range. Objectives: This article focused on the static and dynamic stress analysis of the designed hybrid adapter developed by the authors. A standard mechanical design validation approach using von Mises was followed. Four materials were considered for the analysis, namely, carbon fiber, oil-filled nylon, Al-6061, and mild steel. Study design: The paper analyses the static and dynamic stress on designed hybrid adapter which incorporates features of conventional male and female socket adapters. The finite element analysis was carried out for possible different angles of knee flexion simulating static and dynamic gait situation. Methods: Research was carried out on available design of socket adapter. Mechanical design of hybrid adapter was conceptualized and a CAD model was generated using Inventor modelling software. Static and dynamic stress analysis was carried out on different materials for optimization. Results: The finite element analysis was carried out on the software Autodesk Inventor Professional Ver. 2011. The peak value of von Mises stress occurred in the neck region of the adapter and in the lower face region at rod eye–adapter junction in static and dynamic analyses, respectively. Conclusions: Oil-filled nylon was found to be the best material among the four with respect to strength, weight, and cost. Clinical relevance Research investigations on newer materials for development of improved prosthesis will immensely benefit the amputees. The study analyze the static and dynamic stress on the knee joint adapter to provide better material used for hybrid design of adapter. Keywords Finite element analysis, socket adapter, stress analysis, parametric optimization, limb prostheses, amputees Date received: 27 November 2012; accepted: 19 July 2013
Background Above-knee prosthetics attempt to replace knee function in transfemoral (TF) amputees. In recent years, there have been significant advancements in this field. New materials such as glass fiber–reinforced plastic (GFRP) and oil-filled nylon have allowed artificial limbs to become stronger and lighter, minimizing the amount of energy required to operate the limb. In addition to new materials, the use of electronics is also becoming popular.1,2 The development of lower limb prosthetics through the years has led to better joint mechanisms and structures.3 A TF amputation affects the balance and strength of the muscles around the affected hip joint.4 As a result, proper prosthetic alignment has been
emphasized to enhance residual limb comfort and improve walking capabilities in persons with this kind of amputation.5–10 It has been found through observations in the field of lower limb prosthetic rehabilitation that many TF prostheses show signs of wear on some components of the knee CSIR-CSIO, Chandigarh, India Corresponding author: Neelesh Kumar, Biomedical Instrumentation Unit, CSIR-CSIO, Sector 30-C, Chandigarh-160030, India. Email: [email protected]
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unit.11 The usual way to attach a prosthetic limb to the body is with a socket. Discomfort and other problems resulting due to the socket fit are common and have been shown to adversely affect the quality of life and mobility.12 The adapter should help to provide a better natural gait pattern and a reduction in energy expenditure in walking.13 Consequently, a good and efficient design of socket adapter becomes very crucial because the adapter provides a coupling between the socket and prosthetic knee, so its properties such as strength, length,14,15 weight,16 and stress– strain 17,18 limits become important design parameters.19 This article deals with validation of design of a new kind of socket adapter developed by the authors for a TF prosthetic device, which would be henceforth referred to as hybrid adapter. The finite element analysis (FEA) of the adapter has been carried out on the software Autodesk Inventor Professional Ver. 2011. As the complexity of the structure increases, the difficulty in obtaining an acceptable understanding of the real loading also increases.20 FEA involves a complex system of points called nodes, which make a grid called a mesh. This mesh is programmed to contain the material and structural properties that define how the structure will react to certain loading conditions. Nodes are assigned a certain density throughout the material depending on the anticipated stress levels of a particular area. Regions that receive large amount of stress usually have a higher node density than those that experience little or no stress. Points of interest may consist of fillets, corners, complex detail, and high stress areas. FEA allows the users to validate component design by testing the part’s or assembly’s performance under forces and torques. The tools available as per classical mechanics are not suitable for irregular structure and contouring such as in the case of prosthetic knees. The powerful finite element method (FEM) is able to evaluate stresses in designs of intricate shape, variable loading, and material behavior.21 FEM software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system. Similarly, the desired level of accuracy required and associated computational time requirements can be managed simultaneously to address most engineering applications. FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured. FEMs are extensively used in the field of biomedical engineering, especially biomechanics for computing stress and strain in complex systems. This article discusses the stress and strain distribution in the hybrid adapter (in isolation as well as when it is in the assembly) taking into account the loading character, the effect of material properties, and adapter geometry with the aim of contributing to the improvement of adapter design. Although there are many articles based on the finite element modeling of socket–limb interaction, only a few are there which discuss this method for the analysis of lower limb prosthetic components, especially the socket adapter.22 The socket adapter should allow for maximum range for knee flexion angle during the swing phase (flexion and
extension).23 FEA also helped to identify the regions of an artificial prosthetic, which contribute to faster fatigue.24 Thus, this article focused on parametric optimization based on material selection, weight, strength during static and dynamic gait, and cost. This analysis gives an insight for design of an efficient adapter with the help of an FEM to investigate stresses in load-bearing components, which could help to improve the functioning and comfort level of TF prosthetic users.
Methods This work involved the static and dynamic stress analysis of a TF prosthesis adapter. The need of a hybrid adapter was felt because the knee flexion angle range of up to 60° could be achieved with the male pyramid adapter. So to increase the knee flexion angle, a new design of a socket adapter was conceptualized incorporating the features of a male pyramid as well as those of the female pyramid adapter. Its threedimensional (3D) model was developed on Autodesk Inventor Professional Ver. 2011, which is shown in Figure 1.
Geometries Figure 2 shows the full mechanical assembly model of the prosthetic knee. The mechanical assembly consists of a GFRP outer cover, hybrid adapter, pneumatic cylinder of aluminum, a helical compression spring made of spring steel, nylon bushes, and bolt–nut sub-assembly. The computer-aided design (CAD) model was designed on the basis of manual measurements. The assembly was simulated in the Inventor Dynamic Simulation environment to see its actual working and to generate loads to export and use in stress analysis.
Material properties The FEA of hybrid adapter has been carried out on four types of materials: (1) mild steel, (2) carbon fiber, (3) Al-6061, and (4) oil-filled nylon. The mechanical properties of all the above materials were taken to be linearly elastic, isotropic, and homogeneous. Linear material properties imply that the stress is directly proportional to the strain in the material, meaning no permanent yielding of the material. Linear behavior results when the slope of the material stress–strain curve in the elastic region (measured as Young’s modulus of elasticity) is constant. Isotropic behavior implies that the material properties are not dependent on the direction. The values of Young’s modulus, Poisson’s ratio, yield strength, and ultimate tensile strength were taken from standard datasheets. A load of 600 N has been considered throughout for the stress analysis. Table 1 summarizes the material properties of the components (other than hybrid adapter) used. The total deformation is assumed to be small in comparison to the part thickness. For example, if studying the deflection of a beam, the calculated displacement must be less than the minimum cross section of the beam. The
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Figure 1. (a) 3D model of the hybrid adapter and (b) fabricated oil-filled nylon hybrid adapter. 3D: three-dimensional.
Figure 2. 3D model of the mechanical assembly. 3D: three-dimensional.
temperature is assumed not to affect the material properties so the results computed are temperature independent.
Numerical analysis The finite element static and dynamic loading stress analysis was carried out on Autodesk Inventor Professional Ver.
2011. In the first phase of our analysis, the static stress analysis of the hybrid adapter (in isolation) was performed for all the four materials. In the second phase, the dynamic stress analysis of the full mechanical assembly was carried out by segregating the gait cycle in five stages taking the angle between the loading vector and the hybrid adapter as the standard parameter.
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Table 1. Material properties of components used in TF prosthesis. Component
Material
Young’s modulus (GPa)
Poisson’s ratio
Yield strength (MPa)
Outer cover Cylinder and rod eye Spring Bolt Nut Bush
GFRP Aluminum Spring steel Stainless steel Mild steel Nylon-6/6
13 68.9 180 193 220 2.93
0.34 0.33 0.3 0.31 0.27 0.35
148 275 413 250 207 82.75
TF: transfemoral; GFRP: glass fiber–reinforced plastic.
Static stress analysis. This was performed in three different orientations of hybrid adapter with respect to horizontal, that is, 0°, 45°, and 90°, for each of the four materials. Since FEA uses small elements to solve complex problems, a larger number of smaller elements can sometimes yield more accurate results. This is where convergence comes into play. Convergence in Inventor Stress Analysis is actually a series of settings that can be used to automatically make mesh elements smaller, and it helps to determine whether results are accurate. The basic concept is that the mesh will be automatically made of smaller elements and solved until the results of the refined mesh fall within a percentage of the previous mesh. The number of FE elements and nodes assigned was approximately 5226 and 8374, respectively. The number of refinement cycles for convergence was kept as five. The von Mises stress was the key parameter throughout the analysis. Dynamic stress analysis. In this analysis, the force was resolved into two components with respect to the angle between the force vector and the adapter while specifying the load on the adapter. The angles considered were 124°, 149°, 157°, 161°, and 164° for a gait cycle. The number of FE elements and nodes assigned was approximately 75,763 and 145,432, respectively. The fixed boundary was given to the outer cover of the assembly and the adapter was loaded with the two mutually perpendicular resolved forces as well as the spring force in the axial direction of the pneumatic cylinder acting on the lower surface of the adapter. The spring force was calculated by using the equation F = kx, where k is the spring constant in Newton/millimeter and x is the compression in the spring in millimeter. The value of the spring constant was calculated by using equation (1): Gd 4 k= 8D3 n
Figure 3. Von Mises stress distribution of hybrid adapter (carbon fiber).
Figure 4. Section view of the adapter for oil-filled nylon.
Results and discussion (1)
where G is the modulus of rigidity of spring material, d the wire diameter, D the mean coil diameter, and n the number of active coils which is the number of coils subjected to flexure. The number of refinement cycles for convergence was again kept as five.
This article discusses the design evaluation of hybrid adapter in various gait cycle angles. The FEM analysis is carried out to generate a stress profile of the adapter at various sections. The stress analysis is carried out in static and dynamic gait positions. Four material properties are evaluated for maximum and minimum stress. This evaluation gives the optimum material for the design of such hybrid adapters.
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Kumar Table 2. Peak von Mises stress during static gait (in megapascal). Material
Weight (g)
Maximum stress (0°)
Maximum stress (45°)
Maximum stress (90°)
Carbon fiber Oil-filled nylon Al-6061 Mild steel
46 32.6 77.8 225.74
12.09 11.39 11.5 11.79
50.6 46.29 47.17 49.66
35.98 33.1 32.89 33.43
Table 3. Peak von Mises stress for the full assembly (in megapascal). Peak von Mises stress (in megapascal) at different flexion angle (in degrees) Material Carbon fiber Oil-filled nylon Al-6061 Mild steel
124° 49.2 24.5 34.37 30.39
149° 58.45 34.3 44.53 37.53
Figure 5. Section view of the peak von Mises stress distribution in the full assembly.
Static stress analysis The aim of this analysis was to find a material best suited for the hybrid adapter minimizing the weight of the adapter keeping the maximum von Mises stress in mind as well as to achieve desired strength and knee flexion. It was evident from the analysis that the peak von Mises stress occurs at the neck of the adapter. Carbon fiber material experienced the maximum stress (Figure 3) and oil-filled nylon experienced the minimum stress (Figure 4) in all the three orientations. With respect to the weight parameter, machinability, and cost, oil-filled nylon was found to be the optimum material. Table 2 summarizes the peak von Mises stress for all the four materials.
Dynamic stress analysis This analysis was meant for checking the performance of the adapter under loading conditions when undergoing standard gait cycle. This analysis also revealed that the oilfilled nylon material gives the minimum value for the peak
157° 60.03 35.21 46.89 38.78
161° 61.67 35.51 47.06 39.33
165° 61.89 35.66 47.75 39.98
von Mises stress for all the five standard gait cycle angles. The peak von Mises stress was observed in the lower face of the adapter at the rod eye–adapter junction as shown in Figure 5. Table 3 summarizes the data obtained for peak von Mises stress for all the four materials with respect to the five angles. Similar types of stress analysis using FEM as an evaluation tool were carried by many researchers. In the presented case, a different approach is taken first to design the hybrid adapter and evaluate the design on the basis of static and dynamic stress. The material properties were also evaluated for deciding the optimum material for fabrication of such adapters. More strength to the claims can be provided if dynamic stress analysis is carried out for whole gait cycle. We can have improved results of stress calculation and material optimization. The detailed cost analysis for each material is required to have affordable hybrid adapter.
Conclusion The analysis presented in this article reflects the importance, capabilities, and use of FEM in parametric optimization and design evolution of an efficient hybrid socket adapter required for indigenously developed TF knee. The approach followed was a standard mechanical design validation process in which a 3D design is developed on CAD software; dynamic simulation is performed to assess its working, and finally, it is subjected to stress analysis to check its performance under variable loading conditions. Through this manner, design optimization is done with respect to weight, strength, material properties, and feasibility. A socket adapter was developed integrating the features of a male pyramid adapter and a female pyramid adapter. The FE analysis was carried out for four materials, namely, carbon fiber, oil-filled nylon, Al-6061,
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and mild steel, which are readily available in the market, and it was found that oil-filled nylon material gives the minimum value for peak von Mises stress, whereas carbon fiber gives the maximum corresponding value. The peak von Mises occurs in the neck region of the adapter in case of static stress analysis. In dynamic stress analysis, the peak is observed in the region constituting the lower face of the adapter where it is in contact with the rod eye. Oil-filled nylon was eventually found to be the best material among the four with respect to strength, weight, and machinability. The presented FEM model was thus found suitable for a parametric analysis of developed socket adapter. Funding The author thanks the Council of Scientific and Industrial Research for funding the project under grant no. BSH SIP0022.10.
Declaration of conflicting interest None declared.
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