Design and analysis of polycentric prosthetic knee with enhanced kinematics and stability

This paper describes a continuation of earlier work using the finite element method to conduct an engineering failure analysis of an existing polycentric prosthetic knee. The primary purpose of this work is to enhance the quality of the existing knee which has been reported with multiple cases of failure during its clinical practice in India. A modified design of the polycentric knee has been proposed based on the findings of failure analysis. Simulation-based comparative analysis of polycentric knees has been performed as per the ISO 10328:2016 standard in terms of stress distribution, total contour deformation, safety factor, and fatigue life. The upper extension lever is subjected to static and cyclic loads of 4130 and 1230 N, whereas the lower plate has a translational constraint. The modified polycentric knee prosthesis outperforms static and fatigue strength tests. The standard of the existing knee prosthesis has significantly improved as a result of design variations and integration of high-strength and lightweight aluminium 7075-T6 alloy. The modified polycentric knee prosthesis has a predicted maximum deformation of less than 0.7 mm and a minimum safety factor between 1.7 and 2 compared to 2.66 mm and 1.0 for the existing knee prosthesis. Based on the fatigue simulation results, it is predicted that the modified polycentric knee will have a lifespan of at least ten years indicating a safe design. It has improved alignment stability and kinematics, with a significant weight reduction of 33 g, and a high cost–benefit ratio to reach the maximum amputee population in low-income countries like India.


Introduction
According to statistics reported by WHO, there are around 40 million amputees in developing countries. The Census 2011 estimates around 26.8 million persons with disabilities in India, which is 2.22% of the entire population [1]. A comprehensive prosthetic rehabilitation program results in full independence and desirable functional ambulation [2]. Even though amputation is one of the primary causes of disability in India, only about 5% of the amputee population has access to some sort of prosthetic technology. Further, the need and expectations of Indian amputees for prosthetic devices are not properly fulfilled in most cases which ultimately leads to dissatisfaction among this population. The majority of amputees complain about the durability and reliability of products and materials used in the manufacture of prostheses. There are extremely rare indigenously developed products or genuine inventions in the field of prosthetic knees in India and most of the above products are being imported from the global market. Most amputees in developing countries can't bear the huge cost of knee prostheses due to poor economic conditions. The motivation for the present investigation lies in the design and development of a functionally efficient indigenous knee prosthesis that should possess enhanced stability and durability, at the same time, should be cost-effective to reach the maximum number of individuals with transfemoral amputation.
Phanphet et al. [3] have determined the appropriate dimensions for the optimal design to enhance existing knee prostheses. Following the requirements of the ISO 10328 structural test, the test result validated the finite element model under ultimate loading. In a separate study, Diaz et al. [4] used FEA to design a knee mechanism capable of supporting up to 100 kg of subject body weight by combining aluminium 6063, stainless steel 304, and bronze. They demonstrated that knee prostheses that are cost-effective, functional, and have dependable safety characteristics can be obtained. Lapapong et al. [5] described the virtual structural strength tests of a 4-bar knee to validate the ISO 10328:2006 standard. The simulation and validation findings have demonstrated that FEM is a valid and reliable tool for accurately calculating structural stress. Afzal et al. [6] utilized Solid-Works® for model construction, FEA for structural analysis, and Simulink® for functional verification. They concluded that by using these methods, a simple, reliable, anthropometric, and cost-effective component may be produced. Both Sugiyanto et al. [7] and Kadhim et al. [8] have utilized the same methods with success. Amador et al. [9] used FEA to propose that the design of a polycentric knee should involve an increase in the diameter of the axis and adjustments to all links to achieve stable kinematic function. The objective of Furse et al. [10] was to construct a realistic FEA model to redesign the existing knee component. They recommended that the knee prosthetic component may be injection-molded with Delrin to minimize the thickness of the main body. Due to the implementation of numerous geometric modifications and strength mechanisms, the stress in crucial locations has been reduced by two to six times the original design. Valentino et al. [11] described the three steps required to construct a 4-bar polycentric knee with a mechanical actuator. They utilized AutoCAD to design the knees with materials including stainless steel 304 and aluminium 6061, and ANSYS for analysis. The outcomes have developed a real polycentric knee with the ability to change the center of rotation and excellent clinical outcomes.
Earlier literature has reported more concentration on new prosthetic knee designs and their simulation studies [3][4][5][6][7][8][9][10][11]. However, few have examined prosthetic knee strength according to ISO standard [3,5]. Several 4-bar polycentric knee prostheses have been manufactured utilizing kinematic approaches [6,12], but few studies have investigated their structural designs using finite element analysis (FEA) [3][4][5][6]9] and its optimization methods [13]. Investigators have shown interest in the impact of static loading on stress distribution, total deformation, and safety factor of knee prostheses. Few researchers have examined the material fatigue characteristics by applying cyclic loads to knee prostheses to estimate their life. Prosthetic knee failure analysis based on clinical observations utilizing ISO standard is understudied [13,14].
In our review, the modular prostheses using polycentric 4-bar knees, developed, and utilized in National Institutes in India often require repair or replacement after 1-2 years of usage (Fig. 1). Contour failure and complete breakage of front joint bars are shown in Fig. 1a, b respectively. The fracture of the knee joint unit lower can be seen in Fig. 1c. Coronal and sagittal mal-alignment of the knee unit is depicted in Fig. 1d and e respectively. Figure 1.6f shows the complete detachment of the knee unit with failure of the back joint bar assembly. Breakage of the adapter of the knee joint unit lower can be observed in Fig. 1g. Failure of the knee joint unit upper with deformation of front joint bars is shown in Fig. 1h. Such clinical findings may suggest fatigue failure of polycentric knee structural components due to cyclic stress, which occurs at substantially lower stress than typical static mechanical load. Furthermore, neither the ISO standard test nor a performance study has been performed on this polycentric knee for its compliance.
This work discusses a continuation of earlier work performed by the same authors Mohanty et al. [15] on engineering failure analysis of existing knee prostheses. It has been observed that the existing knee is mildly strong enough to pass the static strength test and the fatigue life fails below ISO 10328:2016 norm. The accuracy of the model has been validated. The mean absolute error between FE simulation and experiment is 10 percent indicating high reliability and validation results. The development of maximum deformation of 2.66 mm on front and back joint bars, mainly at connections, and a safety factor of 1 are deemed critical from a design standpoint. Based on the poor fatigue life results of some common failure components, the existing polycentric knee is predicted to last 1-1.5 years. This expected result is in agreement with the reported clinical cases of failure in prosthetic knee joints which need repair in a few cases or a complete replacement in major cases. This failure analysis has characterized the mechanical and fatigue properties of different knee components for improving the quality of existing knee prostheses.
In continuation to our previous work, the novelty of this investigation has been to enhance the currently used polycentric knee through material and design changes to enhance the quality of life for those with transfemoral amputation. This work will establish a good standard of the prosthetic knee joint in terms of function, cosmesis, and cost-effectiveness to reach maximum amputee populations in developing countries like India.

Methods
This section reports the simulation of static and cyclic structural tests on polycentric knee prostheses by FEA [16]. A modification in the existing design of polycentric knee 1 3 prostheses through the incorporation of suitable materials with higher mechanical strength and altering the design of polycentric knee components has been suggested in this modified approach. The results of the modified polycentric knee prosthesis are compared with the existing knee in terms of structural stability, weight, and cost-benefit analyses.

Overview of modified polycentric knee prosthesis
The principal components in the existing and modified prosthetic knee assembly are the same with some alterations in the geometry. Thus the modified polycentric knee prosthesis consists of a knee joint unit upper, knee joint unit lower, hyperextension stopper, front joint bars, back joint bar assembly, roller pin (bush) upper and lower, alignment coupling unit, and a knee cap as presented in Fig. 2. The total weight of the polycentric knee joint is found to be 499 g compared to 532 g for the existing one.

Materials used and properties
Materials used for knee components are aluminium alloy (AA7075-T6), stainless steel (SS304), and high-damping rubber whose mechanical properties are presented in Table 1. AA7075-T6 has been chosen as the base material for the modified polycentric knee prosthesis as it is lighter in weight and possesses significantly improved mechanical properties. In addition to its high strength, it possesses good toughness, fatigue, and corrosion resistance and is most regularly utilized for severely stressed applications [17]. T6 heat treatment is used to improve mechanical characteristics by integrating thermal treatment and artificial aging [18,19]. Furthermore, AA7075 is used in lower-limb prosthetics with lightweight components [20].

Generation of prosthetic knee model
The dimensional information is used to create a 2D technical drawing. The design criteria involve giving strength to weaker components in critical areas and reducing base materials at high strength robust areas to achieve the light weight of the product. The 3D CAD model is created in CATIA V5. The components of the 4-bar knee are designed and assembled independently. The major design changes incorporated in the modified polycentric knee are based on simulation-based failure analysis reports and reported cases of damage from clinical observations as summarized in Table 2. Different transparent perspective views of the

Kinematics and design analysis
The kinematic evaluation of a 4-bar polycentric knee is based on Grashof's law double rocker with length bar condition ( a + b > c + d ) as shown in Fig. 4a, where a, b are the longest and shortest link respectively, and c, d are the other links. The optimal dimensions of the polycentric knee mechanism are based on the data of the trajectory of the instantaneous center of rotation (ICOR) calculated from the kinematic analysis of the four-bar polycentric knee. This verifies the stability to set the ICOR behind the load line (x = 12 mm) as shown in Fig. 4b.
In this scenario, the initial elevation of the ICOR is situated at less height from the center and the downward course of the instant center remains relatively elevated and within the zone of stability for the first few degrees of knee flexion. The instant center is approximately 100 mm above and 12 mm behind the vertical reference line (load line). The kinematic analysis of the modified polycentric knee has been performed in CATIA V5 as shown in Fig. 5. The digital mockup result has revealed smooth motion in the joint assembly without any interference. It is presumed to work well in real-time with true physical functions.

The finite element analysis
The 3D CAD model of the modified polycentric knee prosthesis is imported into ANSYS Workbench R19.2 for simulation. The mesh independence test, grid refinements, and mesh quality are ensured as defined in our earlier study [15]. The h-method has been followed for numerical convergence. The FE model has been discretized into 875639 nodes and 602951 elements satisfying the convergence criteria. The elements are 3D tetrahedral and mesh refinement has been performed at appropriate parts as shown in Fig. 6.
The procedure performed for conducting the ISO 10328:2016 structural standard test for static and fatigue performance in the case of an existing prosthetic knee as discussed in our earlier study [21] is similar to the modified polycentric knee prosthesis. The magnitude and direction of the applied force change depending on the test conditions   [5]. The S-N curve is an input property for fatigue analysis in ANSYS. The low cycle fatigue behavior of the assigned materials from the experimental data of the manufacturer has been used in terms of S-N curves for analysis. The S-N curves of various materials assigned to different components of the polycentric knee are presented in Fig. 7. These two column values for cycles and alternating stress are added in the material library in the engineering data of ANSYS Workbench. The cycle is defined and the load conditions and constraints are provided as mentioned in the static analysis.

Results
The present investigation relies on static and cyclic structural simulations of a modified 4-bar knee prosthesis. The results so obtained are compared with that of the existing polycentric knee prosthesis. Soderberg's theory for fatigue analysis has been used as the design criterion which is related to the yield stress. The ISO standard [3,22] recommends the following design criteria for a knee prosthesis subjected to 1230 N of cyclic and 4130 N of static loads.
1. The deflection must not exceed 2.5 mm and the component stress must be below its yield strength.

Simulation results of static test
The static strength simulation findings of the modified knee prosthesis are shown in Figs. 8 and 9. It shows prosthetic knee stress under loading conditions I and II. Stresses in front and back joint bars are 85-107 and 42-64 MPa respectively for load condition I ( Fig. 8a and b) and 81-101 and 40-60 MPa for load condition II ( Fig. 9a and b). The maximum von-Mises stress value of 300 MPa is observed at the front link bush for load conditions I (Fig. 8c) and 284 MPa for load conditions II (Fig. 9c). Comparing these results to corresponding material properties, the maximum stresses are sufficiently below the yield strength of AA7075-T6 aluminium alloy (503 MPa) utilized for the front and back joint bars and bush. These results suggest that the modified knee prosthesis will successfully pass the ISO 10328:2016 static strength test. The static strength test results for the modified knee are shown in terms of total deformation in Figs. 10 and 11. Maximum deformation is observed at the load application point which is 1.44 and 1.36 mm for loads I and II respectively as shown in Figs. 10a and 11a. The alignment coupling unit of the knee prosthesis experiences the most deformation at 0.7 mm, suggesting the least amount of displacement. The probe points are marked at different parts of the modified polycentric knee prosthesis ranging from 0.27 to 0.68 mm  as depicted in Figs. 10b, c and 11b, c. A deformation of less than 2.5 mm during static testing suggests that this modified prosthetic knee has the sufficient strain-bearing ability

Simulation results of cyclic test
The distribution of von-Mises stress, maximum deflection, number of cycles before failure, and safety factor of the modified polycentric prosthetic knee are investigated in this fatigue analysis. The results of von-Mises stress distribution during cyclic strength simulation are shown in Figs. 12 and 13. For both loading conditions, the von-Mises stress developed at the front and back joint bars is 18 to 23 MPa as shown in Figs. 12a, b and 13a, b. The maximum stresses of 91 and 71 MPa are developed in the knee joint unit lower for load conditions I and II respectively as depicted in Figs. 12c and 13c. Therefore, it can be predicted that the modified polycentric prosthetic knee prosthesis employed in this research can withstand The cyclic strength test results for the modified knee prosthesis are shown in terms of total deformation in Fig. 14. A maximum deformation has been observed at the point of load application which is 0.38 mm as shown in Fig. 14a. The alignment coupling unit of the knee prosthesis experiences the maximum deformation of 0.18 mm as depicted in Fig. 14b and c, suggesting the least amount of displacement. A deformation of less than 2.5 mm during fatigue testing suggests that this modified prosthetic knee has the sufficient strain-bearing ability to meet the structural norms, as recommended by the ISO 10328:2016 standard.  The maximum stress of 91 MPa is obtained from the simulation at the knee joint unit lower for load conditions I, which is below the fatigue strength of 150 MPa for AA7075-T6. So a minimum design safety factor of 1.7 is computed from the above stress values. This is also in good agreement with the simulation results. The safety factor for modified polycentric knee prosthesis including the critical areas is depicted in Fig. 15. An earlier report has suggested that any engineering design with a fatigue safety factor above 1.25 is considered safe [23]. It is observed that the von-Mises stress developed in regions other than critical areas of the knee prosthesis shows a stress magnitude below 23.21 MPa. This signifies that the modified knee has sufficient mechanical strength to endure cyclic loads.
The results of cyclic strength simulations for commonly failing components are summarized in Table 3. It is observed that the maximum developed stress is sufficiently below the fatigue strength of AA7075 T6 and the deformation produced is extremely minimal. There is a significant increase in fatigue life (no. of cycles) of most of the knee components. These values indicate that the modified polycentric knee prosthesis qualifies for the requirements of ISO 10328:2016 standard.

Comparison of simulation results between existing and modified knee
The modified polycentric mechanical knee prosthesis surpasses static and fatigue tests. The design variation and adoption of stronger materials have substantially improved the strength of knee prostheses. The    Table 4.
To estimate the fatigue life (number of cycles), the stress distribution data is utilized in the MSC fatigue module to plot the S-N curve as depicted in Fig. 7. A visual representation of the fatigue life of knee components under cyclic load circumstances in isometric views is presented in Fig. 16. The prosthetic fatigue life is indicated by the color legend bar. As illustrated in Fig. 16, the Allen screws made up of stainless steel are found to have an average fatigue life 10 × 10 6 . On the other hand, it is observed that the average fatigue life of the overall prosthetic knee is 240 × 10 6 .

Results for alignment stability and kinematics
The parameters such as link lengths, pivot locations, and the ICOR (centrode) path are used to design and characterize the relative geometric performance of the knees based on the requirements. In the current design, the ICOR is approximately 100 mm above and 12 mm behind the load line, compared to 80 mm and 8 mm in the existing knee design during full extension. Therefore, the trajectory of the ICOR does not begin in a position that is extremely elevated and/or posterior in full extension. This location permits the ICOR to move smoothly forward and downward with increasing knee flexion angles while remaining elevated within the stability zone for up to 15 degrees of knee flexion. Using the adjustable coupling between the socket and knee, the knee's  design permits a small extension of the socket in increments of approximately one degree. This provides an option of locating the ICOR in full extension within the desired stable region of the stability while preserving an acceptable cosmetic appearance at 90 degrees of flexion. The kinematic and swing performances of the polycentric 4-bar knees have been found to depend on their centrode. The located ICOR which is comparatively superior to the anatomical knee center during swing enables better knee extension and foot clearance. In addition, the provision of anterior translation of the socket through the alignment coupling unit can increase the toe and heel clearances. The predicted flexion of 150 degrees through simulation allows squatting and kneeling activities, especially suitable to Indian conditions.

Discussion
This research discusses a simulation approach to improve the standard of polycentric knee subjected to static and cyclic loading following the recommendation of ISO 10328:2016. The proposed modified design of the polycentric knee has been compared with the existing one in terms of stress distribution, total contour deformation, safety factor, and fatigue life. To reduce the mass of the modified polycentric knee prosthesis, the geometry of the linkages has been modified and intervening in regions where the various components are subjected to less stress. Results indicate that the modified polycentric mechanical prosthetic knee model outperforms static and fatigue strength tests. The quality of existing knee prostheses has greatly improved due to design alterations and the introduction of new materials with superior mechanical strength. The modified knee prosthesis made from highstrength and lightweight AA7075 T6 alloy has a predicted maximum deformation of less than 1 mm and a minimum safety factor between 1.7 and 2, indicating the design is safe. Based on the remarkable fatigue life findings of knee components, it is anticipated that the newly developed polycentric knee will have a lifespan of at least ten years. According to the presented data, it is apparent that this modified polycentric knee has sufficient stability to withstand the static load, has outstanding life prediction for its components, and has the potential to outlast the margin of cycles required by the ISO 10328:2016 standard. The final CAD version of the modified polycentric knee is depicted in Fig. 17.
The simulation-based static and cyclic strength analyses for knee prostheses have been the subject of investigation in current research. The investigators have followed ISO 10328 standard and the loading and boundary conditions have been followed similar to the current study. Kadhim et al. [8] aimed to improve the passive prosthesis using SolidWorks and FEA. The upper knee surface made of AISI 4130 steel was loaded with 1200 N of static load. The maximum von-Mises stress and deformation were measured to be 40.88 MPa and 0.034 mm, respectively with a safety factor of 12.31. Lu and Chen [24] evaluated stress distribution and deformation according to ISO 10328 using ANSYS. They employed polyethylene terephthalate (PET) material in a finite element model for topology optimization. The optimized design achieved 1.65 mm of deformation and 72 MPa von-Mises stress, which is less than the yield strength of PET. Chauhan and Bhaduri [12] applied FEM to a polycentric knee to examine the ISO 10328 static test. A static load of 4500 N was uniformly applied to the knee prosthesis made of aluminium 6063-T6. The researchers found average absolute percentage errors of 23% and 16% for load conditions I and II, respectively. Lapapong et al. [5] presented virtual knee strength tests. In the static test, loading conditions I and II indicate 27 and 15% mean absolute percentage errors respectively. Phanphet et al. [3] aimed to improve the standard of

Comparison and validation with the previous study
The work of Rosas et al. [25] has been considered for validation. This study seeks to computationally investigate the mechanical fatigue of polycentric knee prostheses using the ISO 10328 standard involving fluctuating loads for both load conditions. SolidWorks, which requires a static analysis with the maximum load from each condition and S-N curves of each material, was employed for the investigation. The knee prosthesis was constructed using five links made of aluminium alloy (AA7075 T6) and four axes made of stainless steel (SS304). The findings of this study show that the prosthetic knee has good fatigue life for over 3 million cycles. For steel components, the life was infinite, there was no damage, and the factor of safety was either 3.45 or 2.97, depending on the condition. Under condition I, the minimum life for aluminium parts was 73,262,632 cycles, the maximum damage was 4.095%, and the minimum factor of safety was 1.533. Under condition II, the minimum life for aluminium parts was 223,973,424 cycles, the damage was 1.322 percent, and the minimum factor of safety was 1.779. The polycentric knee was expected to last for a minimum of 5 years and 8 months time period. These validation findings support the FE model reliability with a 7.75% error. The same comparison is presented in Table 5.

Weight comparison analysis
The weight comparative analysis between the existing and modified polycentric knee prosthesis is presented in Table 6.
Some components such as the knee joint unit upper and lower, and back joint bar assembly are reduced in weight whereas the alignment coupling unit and hyperextension stopper are increased in weight. Moreover, components like front joint bars, knee cap, washers, screws, bolts, and accessory components are the same in weight. It is found that the overall saving in weight by adopting a modified design is 33 g.

Cost comparison analysis
This study develops a framework for constructing possibly low-cost, fully passive polycentric knee prosthesis suitable for transfemoral amputees' daily life activities in poor nations. Acute economic restraints, combined with socioeconomic factors, indicate an urgent need for a low-cost solution capable of delivering high levels of functional performance. Prosthetic knee joints cost several thousand dollars to produce and distribute in the United States and Europe. A popular active transfemoral prosthesis that works exceptionally well can cost more than $50,000 [26]. Even passive knee joints in wealthy nations are too costly to suit the needs of amputees in developing countries [27]. It is important to mention that, most of the polycentric mechanical knee prostheses in India are imported from the global market and the cost ranges from INR 6000 to 50,000. Table 7 presents a comparison of the cost of polycentric mechanical prosthetic knees from Indian manufacturers or suppliers. To determine the price of a potential product that can produce sufficient functional requirements, a full cost reduction analysis has been performed. AA7075 has been selected for this work as it is comparatively lower in cost, and has high strength and corrosion resistance. The suggested cost of the knee has been decreased by taking a more austere approach to design, such as using AA7075 alloy instead of contemporary composites or non-ferrous alloys to fulfill structural design goals without raising the cost of the system. The cost of fabricating the mechanical structure, including the cost of materials, is expected to be around 4,900 INR and the details are presented in Table 8. Though it is not so easy to understand the various aspects that influence the pricing of a product, still the following criteria have been taken into account while calculating the cost of the prosthetic knee model.    The preliminary prototype mentioned in this work is mostly made of AA7075 alloy which is relatively expensive but the overall cost of the proposed modified knee prosthesis is substantially reduced compared to the cost of imported or Indian-made prosthetic knee models as presented in Table 8. The cost of existing prosthetic knees used in National institutes and mass-manufactured by ALIMCO is 2678 INR compared to 4900 INR for the modified model. The increased cost of modified knee prostheses can be neglected because of the excellent mechanical properties and fatigue life of the product. Moreover, the predicted cost is within the budget of amputees from economically disadvantaged backgrounds, and the prosthesis can be provided free of charge to such amputees under the ADIP Scheme of the Government of India [28], which has a cost restriction of 15,000 INR for the entire prosthesis. Though the initial cost of the modified polycentric knee is increased by 83 percent, the same can be substantially reduced by the following means: 1. Replacing the components with the use of less expensive polymers [29] or other variants of aluminium alloy 2. Planning for commercialization that considers local manufacturing resources, design-for-manufacturing analysis, and design-for-assembly analysis 3. Utilizing the optimized criteria for "Designing for Machinability" 4. Simplifying the design further and using easier-tomachine material that can fulfill the design requirements

Technical advantages
1. Simple mechanical components with innovative shapes and ease of manufacturing 2. Light-weighted polycentric knee prosthesis kept under 500 g only 3. Qualifies ISO 10328:2016 standard including ultimate static load and prediction of fatigue life 4. Low profile design to suit subjects with long transfemoral or knee disarticulation 5. Optimized location of the instantaneous center of rotation to encourage voluntary control of knee stability and better swing clearance 6. Made of high strength and lightweight AA7075 T6 alloy 7. Provision of fine-tuning of linear and angular alignment to optimize functions specific to subjects' requirements 8. Provides knee flexion of 150 degrees for encouraging squatting activities 9. Suitable in Indian conditions including socioeconomic and environmental requirements 10. Cost-effective to reach the maximum amputee population in low-income countries like India People with transfemoral amputations are estimated to walk on an average of 3553 steps per day [30]. The modified polycentric knee is predicted to last at least 10 years, based on the outstanding fatigue life findings of knee components. However, this study has a few shortcomings. The fatigue testing with a knee prosthesis is limited in this study because a specific load can only be administered two times, during heel strike and the toe-off phase of gait, and not applied during the entire walking cycle. Additionally, ISO 10328:2016 conformity on the structural strength of knee components may be too high for the Indian population. Future works may focus on the experimental fatigue and clinical gait analysis using the modified polycentric knee prosthesis; the adoption of a comprehensive commercialization strategy for mass production to reduce the unit cost of the knee joint; and the study of a dynamic model based on bipedal locomotion theory to obtain a more realistic load condition.

Conclusion
The modified polycentric mechanical prosthetic knee model outperforms static and fatigue strength tests. The quality of existing knee prostheses has greatly improved due to design alterations and the incorporation of new materials with superior mechanical strength. The modified knee prosthesis made from high-strength and lightweight AA7075 T6 alloy has a predicted maximum deformation of less than 1 mm and a minimum safety factor between 1.7 and 2, indicating the design is safe. Based on the remarkable fatigue life findings of knee components, it is anticipated that the newly developed polycentric knee will have a lifespan of at least ten years. This work has resulted in the development of a light-weighted polycentric knee prosthesis weighing 499 g compared to the existing prosthetic knee which is 532 g. The cost of fabricating the mechanical structure, including the cost of materials, is expected to be around 4,900 INR which is within the budget of amputees from economically disadvantaged backgrounds. Moreover, the prosthesis can be provided free of charge to such amputees under the ADIP scheme of the Government of India.
Author contributions All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by RKM, RCM and SKS. The first draft of the manuscript was written by RKM and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
Data availability All the data are available from the corresponding author by request.