Next Article in Journal
Accuracy of Intraoral Scanners Versus Polyvinyl Siloxane Impression in Partially Edentulous Implant Rehabilitations: An In Vitro Comparison
Previous Article in Journal
Comparative Evaluation of Screw Loosening in Zirconia Restorations with Different Abutment Designs
Previous Article in Special Issue
Enhancing Quality of Life After Partial Brachial Plexus Injury Combining Targeted Sensory Reinnervation and AI-Controlled User-Centered Prosthesis: A Case Study
 
 
Article
Peer-Review Record

Personalized External Knee Prosthesis Design Using Instantaneous Center of Rotation for Improved Gait Emulation

Prosthesis 2025, 7(6), 163; https://doi.org/10.3390/prosthesis7060163
by Cristina Ayala *, Fernando Valencia *, Brizeida Gámez, Hugo Salazar and David Ojeda
Reviewer 2: Anonymous
Prosthesis 2025, 7(6), 163; https://doi.org/10.3390/prosthesis7060163
Submission received: 23 July 2025 / Revised: 28 October 2025 / Accepted: 30 October 2025 / Published: 9 December 2025

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article presents technologically sound and well-organised research on the design, simulation, and verification of a transfemoral prosthesis mechanism that follows the path of the instantaneous centre of rotation (ICR). The designed mechanism—consisting of a four-bar linkage with a gear train upgrade—is developed using both MATLAB and CAD and implemented physically via 3D printing. The third model (Model 3) produces an optimal approximation to the natural knee ICR path with a Fréchet distance of only 5.33 mm and performs adequately under gait testing.

The prosthetic device is customised to an individual's biomechanical data to a high level of anatomical and kinematic accuracy—an advancement in a field in which applications are of general design.

The authors correctly acknowledge an understandable limitation of the study: that design and validation are done in relation to the data of one patient's gait. While this constraint does not prevent the publication of the work in my opinion, I would suggest that discussion of this issue be extended to highlight its significance in future deployment across various patient groups.

The addition of a gear train to the final design adds a welcome level of mechanical complexity. The presentation would be reinforced with the addition of a detailed explanation of the justification for the chosen transmission ratio and why it improves performance in terms of either gait biomechanics or structural control. A concise justification for this design choice would enhance the work's engineering transparency.

Unfortunately, the manuscript just needs a revision for several minor issues. A word editor can rectify the typos and grammatical anomalies. There is a reference to "Model 5" at line 244, instead of just three models involved in the work. There are two duplicates in the references list that require verification.

Finally, the paper contributes significantly to patient-specific design for prosthetic knee mechanisms: the revisions suggested focus on improving clarity, completeness, and contextual framing to make the paper a strong candidate for publication.

Comments on the Quality of English Language

See the report to the Authors

Author Response

Comments 1: This article presents technologically sound and well-organised research on the design, simulation, and verification of a transfemoral prosthesis mechanism that follows the path of the instantaneous centre of rotation (ICR). The designed mechanism—consisting of a four-bar linkage with a gear train upgrade—is developed using both MATLAB and CAD and implemented physically via 3D printing. The third model (Model 3) produces an optimal approximation to the natural knee ICR path with a Fréchet distance of only 5.33 mm and performs adequately under gait testing.

 

The prosthetic device is customised to an individual's biomechanical data to a high level of anatomical and kinematic accuracy—an advancement in a field in which applications are of general design.

 

The authors correctly acknowledge an understandable limitation of the study: that design and validation are done in relation to the data of one patient's gait. While this constraint does not prevent the publication of the work in my opinion, I would suggest that discussion of this issue be extended to highlight its significance in future deployment across various patient groups.

Response 1: Thank you for pointing this out. We agree with this comment. We have extended the discussion section with the following paragraphs.

The importance of continuing the development of personalized external knee prostheses based on the Instantaneous Center of Rotation (ICR) is reinforced by current trends in modular and adaptive design [26]. Recent studies, such as [27], present this modular concept evaluated through kinematic and structural analysis, demonstrating its potential for integration with external components such as the ankle and foot [28]. This approach offers significant advantages, including adaptability, ease of maintenance, and the ability to configure the prosthesis according to the specific needs of each patient.

In combination with polycentric mechanisms based on the ICR, such as those developed in the present study, the possibility arises of hybrid devices that combine the naturalness of gait with modular and scalable configurations; [28]; Shrestha, 2025; [29]. Nevertheless, the results obtained represent only an initial approach, limited by the fact that validation was carried out with a single subject. In this regard, it is essential to expand the sample to more diverse groups [30] to determine whether the defined trajectory remains valid in the presence of anthropometric variations and different age ranges.

The absence of studies defining a representative trajectory of the knee joint highlights a knowledge gap that this work begins to address [31]; [32], but which still requires consolidation through the construction of large comparative databases. Achieving this would open the possibility of developing semi-personalized prosthetic mechanisms applicable to groups of patients, thereby promoting technology transfer.

The main limitation of this study lies in the fact that validation was performed with a single test subject, which restricts the ability to generalize the results to a broader population [28], [33]. Therefore, future research should include a larger number of participants, incorporating patients of different age groups, activity levels, and anthropometric characteristics, to evaluate the adaptability of the mechanism more comprehensively. It will also be necessary to implement gait cycle analyses under real conditions, such as walking, stair climbing, or moving on slopes, to ensure the applicability of the results [34], [35].

 

Comments 2: The addition of a gear train to the final design adds a welcome level of mechanical complexity. The presentation would be reinforced with the addition of a detailed explanation of the justification for the chosen transmission ratio and why it improves performance in terms of either gait biomechanics or structural control. A concise justification for this design choice would enhance the work's engineering transparency.

 

Response 2: We agree with your comment and have improved the manuscript by adding the following:

In Section 2.1.3.3 the following was added: This model represents an improved version that maintains both the link dimensions and the angles between them, differing by the incorporation of gears with a transmission ratio of Rt = 0.93 and an improved aesthetic design. In addition, the Rt guarantees an approximation between the relationship that the angle of the leg axis should have and the ICR.

The transmission ratio was established through numerical experiments using SolidWorks and MATLAB to adjust the ICR trajectory of the mechanism to that of a healthy knee. Incorporating the gear train enabled a more accurate alignment. The Fréchet distance, with a value of 5.33 mm at Rt = 0.93, indicated the best match achieved after multiple iterations. From a biomechanical perspective, this solution improves gait stability.

A simple gear train is implemented, with one gear per shaft, configured so that the direction of rotation corresponds to the flexion movement of the leg. Additionally, an idler gear is included, which does not affect the transmission ratio Rt. The gear specifications are detailed in Table 5 and Figure 7. Furthermore, interference in the gears and contact ratio was verified, complying with AGMA requirements

Then, in Section 3.1 the following was added: From a biomechanical perspective, the knee joint flexion angles were analyzed during the gait cycle. The results showed that the mechanism adjusted with Rt = 0.933 more accurately reproduced the flexion and extension peaks characteristic of the walking phases, closely approximating the kinematics of a healthy knee in both the stance and swing stages, as shown in Figure 12. This adjustment promotes a more natural movement, reduces undesirable residual displacements, and may improve load distribution on the stump, thereby decreasing the risk of high-pressure points and misalignment-related injuries.

In terms of structural control, achieving a movement closer to the physiological pattern reduces external compensatory forces, thereby increasing dynamic stability and user comfort. Therefore, selecting a transmission ratio of Rt = 0.933 constitutes a viable geometric adjustment that directly links the mechanical design with the functional and biomechanical performance of gait.

And also, at the end of Section 3.2 the following was added: The functional tests allowed quantification of basic gait parameters. The subject achieved a step length of 0.65 m, a cadence of 80 steps/min, and an average velocity of 0.86 m/s over a 52 m walk on a completely flat surface. These values are comparable to those reported in the literature for healthy adults, although with a slightly lower cadence, which may be associated with the adaptation process to prosthesis use, as shown in Table 7.

Table 7. Spatiotemporal metric by height and gender (males), patient with a height of 1.60 m

Metric

Result

Unit

Reference value*

Step length

0.65

m

0.72

Cadence

80

steps/min

110.06

Walking speed

0.86

m/s

1.32

* Normative Database of Spatiotemporal Gait Metrics Across Age Groups: An Observational Case–Control Study [25].

Model 3 is mechanically feasible with the transmission ratio obtained (Rt = 0.933), implemented through a gear train with manufacturable dimensions, thereby avoiding costly or difficult-to-produce configurations. The incorporated spring facilitates return during the swing phase, increasing both reliability and user-perceived comfort during gait testing.

The results show that Model 3 adequately emulates the angular pattern of a healthy knee and ensures a stable, biomechanically consistent movement in replicating human gait under a transfemoral amputation condition.

Comments 3:

Unfortunately, the manuscript just needs a revision for several minor issues. A word editor can rectify the typos and grammatical anomalies. There is a reference to "Model 5" at line 244, instead of just three models involved in the work. There are two duplicates in the references list that require verification.

Response 3: Agree. I/We have, accordingly, done/revised/changed/modified…..to emphasize this point.

Corrected in line 244 and also in the figure description.

The reference to Andriacchi TP was indeed duplicated, and one instance has been removed.”

 

Comments 4:

 

Finally, the paper contributes significantly to patient-specific design for prosthetic knee mechanisms: the revisions suggested focus on improving clarity, completeness, and contextual framing to make the paper a strong candidate for publication.

Response 4:

We appreciate your timely comments. The contextual framework has been strengthened, and additional references have been added and updated.”

 

4. Response to Comments on the Quality of English Language

Point 1:

Response 1:    Regarding the English language, all mistranslated terms have been corrected, a grammar checker was applied, and the manuscript was carefully proofread to ensure linguistic accuracy.

 

Note: In the paper, the main changes are highlighted in blue

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

This manuscript presents an innovative prosthetic knee joint design using personalized ICR-based modeling and 3D prototyping. The approach is original and relevant, with strong engineering merit. However, the validation is limited (single subject, largely qualitative testing), and methodological rigor and presentation require significant improvement. With revisions to address these points, the study could make a valuable contribution to the field.

 

Strengths

  • The manuscript addresses a highly relevant problem in prosthetics: improving gait emulation through individualized knee joint design.

  • The use of the Instantaneous Center of Rotation (ICR) as a design parameter is innovative and biomechanically sound.

  • The iterative design process using CAD, MATLAB simulations, and 3D printing demonstrates a modern and pragmatic methodology.

  • Functional testing with prototypes (Models 1 and 3) provides important translational validation, bridging engineering design and clinical application.

  • The reduction of Fréchet distance error (5.33 mm) and the demonstration of more natural gait patterns are convincing results.

  • The manuscript is generally well-structured, with clear descriptions of the design process, and has potential clinical impact.

Weaknesses

  1. Study scope and validation: The entire study is based on data from a single test subject, which severely limits generalizability. More participants are necessary to claim clinical applicability.

  2. Methodological rigor: The “trial-and-error” design approach is described but lacks detail on systematic optimization criteria beyond Fréchet distance. It remains unclear whether other performance metrics (energy cost, durability, comfort) were quantitatively assessed.

  3. Functional testing: Validation is limited to qualitative observations of gait with prototypes. No quantitative gait analysis (e.g., spatiotemporal parameters, EMG, metabolic cost) was performed, reducing the strength of the conclusions.

  4. Comparative context: The Discussion compares the new design to “standard prostheses,” but no direct head-to-head comparisons were made. This weakens claims of superiority.

  5. Language and clarity: The manuscript contains grammatical errors and awkward phrasing (e.g., “this study an experimental and qualitative approach,” “enablinng iterative adjustments”). Professional English editing is required.

  6. Figures and tables:

    • Some figures are not self-explanatory and require better legends.

    • Tables could be condensed; several are overly detailed for the main text and might be moved to supplementary material.

    • Figure quality (resolution and clarity) should be improved.

  7. References: Several references are outdated or repeated (e.g., Andriacchi et al. appears twice). The reference list needs careful editing.

  8. Conclusions: While promising, the conclusions are overstated given the single-subject validation. Claims of “improving quality of life” should be tempered.

Suggestions for Improvement

  1. Clarify the design optimization process: beyond minimizing Fréchet distance, specify criteria for choosing Model 3 as “optimal.”

  2. Provide quantitative outcome measures for functional testing (step length, cadence, joint kinematics, etc.) rather than relying solely on descriptive observations.

  3. Explicitly discuss the limitation of single-subject validation and propose how future work will address broader testing and clinical trials.

  4. Strengthen the comparison with commercial prostheses by citing recent benchmark studies or providing pilot comparative data.

  5. Revise language throughout the manuscript with professional English editing to improve clarity and academic tone.

  6. Improve figure legends and resolution; move overly detailed design tables to supplementary material to streamline the main text.

  7. Revise the reference list to eliminate duplicates, update with recent studies, and ensure consistency in citation style.

  8. Temper the conclusions to reflect preliminary findings and avoid overstating clinical implications.

 

Kind regards :)

Author Response

Comments 1:
Clarify the design optimization process: beyond minimizing Fréchet distance, specify criteria for choosing Model 3 as “optimal.”

Response 1: Thank you for pointing this out. We agree with this comment.

In Section 2.1.3.3 the following was added:

This model represents an improved version that maintains both the link dimensions and the angles between them, differing by the incorporation of gears with a transmission ratio of Rt = 0.93 and an improved aesthetic design. In addition, the Rt guarantees an approximation between the relationship that the angle of the leg axis should have and the ICR.

The transmission ratio was established through numerical experiments using SolidWorks and MATLAB to adjust the ICR trajectory of the mechanism to that of a healthy knee. Incorporating the gear train enabled a more accurate alignment. The Fréchet distance, with a value of 5.33 mm at Rt = 0.93, indicated the best match achieved after multiple iterations. From a biomechanical perspective, this solution improves gait stability.

A simple gear train is implemented, with one gear per shaft, configured so that the direction of rotation corresponds to the flexion movement of the leg. Additionally, an idler gear is included, which does not affect the transmission ratio Rt. The gear specifications are detailed in Table 5 and Figure 7. Furthermore, interference in the gears and contact ratio was verified, complying with AGMA requirements

In terms of structural control, achieving a movement closer to the physiological pattern reduces external compensatory forces, thereby increasing dynamic stability and user comfort. Therefore, selecting a transmission ratio of Rt = 0.933 constitutes a viable geometric adjustment that directly links the mechanical design with the functional and biomechanical performance of gait.

And also, at the end of Section 3.2 the following was added: The functional tests allowed quantification of basic gait parameters. The subject achieved a step length of 0.65 m, a cadence of 80 steps/min, and an average velocity of 0.86 m/s over a 52 m walk on a completely flat surface. These values are comparable to those reported in the literature for healthy adults, although with a slightly lower cadence, which may be associated with the adaptation process to prosthesis use, as shown in Table 7.

Table 7. Spatiotemporal metric by height and gender (males), patient with a height of 1.60 m

Metric

Result

Unit

Reference value*

Step length

0.65

m

0.72

Cadence

80

steps/min

110.06

Walking speed

0.86

m/s

1.32

* Normative Database of Spatiotemporal Gait Metrics Across Age Groups: An Observational Case–Control Study [25].

Model 3 is mechanically feasible with the transmission ratio obtained (Rt = 0.933), implemented through a gear train with manufacturable dimensions, thereby avoiding costly or difficult-to-produce configurations. The incorporated spring facilitates return during the swing phase, increasing both reliability and user-perceived comfort during gait testing.

The results show that Model 3 adequately emulates the angular pattern of a healthy knee and ensures a stable, biomechanically consistent movement in replicating human gait under a transfemoral amputation condition.

 

Comments 2:
Provide quantitative outcome measures for functional testing (step length, cadence, joint kinematics, etc.) rather than relying solely on descriptive observations.

 

Response 2: Agree. We have, accordingly, “In addition, it presented a low root mean squared error (RMSE) compared to the other models and exhibited a smooth, continuous trajectory, which was confirmed through physical testing. These features position it as the most balanced option between geometric accuracy and mechanical stability.”

 

And also the following text after Figure 12., The functional tests allowed quantification of basic gait parameters. The subject achieved a step length of 0.65 m, a cadence of 80 steps/min, and an average velocity of 0.86 m/s over a 52 m walk on a completely flat surface. These values are comparable to those reported in the literature for healthy adults, although with a slightly lower cadence, which may be associated with the adaptation process to prosthesis use, as shown in Table 7.

 

Table 7. Spatiotemporal metric by height and gender (males), patient with a height of 1.60 m

Metric

Result

Unit

Reference value*

Step length

0.65

m

0.72

Cadence

80

steps/min

110.06

Walking speed

0.86

m/s

1.32

* Normative Database of Spatiotemporal Gait Metrics Across Age Groups: An Observational Case–Control Study [25].

Model 3 is mechanically feasible with the transmission ratio obtained (Rt = 0.933), implemented through a gear train with manufacturable dimensions, thereby avoiding costly or difficult-to-produce configurations. The incorporated spring facilitates return during the swing phase, increasing both reliability and user-perceived comfort during gait testing.

The results show that Model 3 adequately emulates the angular pattern of a healthy knee and ensures a stable, biomechanically consistent movement in replicating human gait under a transfemoral amputation condition.

Comments 3: Explicitly discuss the limitation of single-subject validation and propose how future work will address broader testing and clinical trials.

Comments 4: Strengthen the comparison with commercial prostheses by citing recent benchmark studies or providing pilot comparative data.

Response 3-4: For comments 3 and 4, the discussion section has been expanded with the following paragraphs:

The importance of continuing the development of personalized external knee prostheses based on the Instantaneous Center of Rotation (ICR) is reinforced by current trends in modular and adaptive design [26]. Recent studies, such as [27], present this modular concept evaluated through kinematic and structural analysis, demonstrating its potential for integration with external components such as the ankle and foot [28]. This approach offers significant advantages, including adaptability, ease of maintenance, and the ability to configure the prosthesis according to the specific needs of each patient.

In combination with polycentric mechanisms based on the ICR, such as those developed in the present study, the possibility arises of hybrid devices that combine the naturalness of gait with modular and scalable configurations; [28]; Shrestha, 2025; [29]. Nevertheless, the results obtained represent only an initial approach, limited by the fact that validation was carried out with a single subject. In this regard, it is essential to expand the sample to more diverse groups [30] to determine whether the defined trajectory remains valid in the presence of anthropometric variations and different age ranges.

The absence of studies defining a representative trajectory of the knee joint highlights a knowledge gap that this work begins to address [31]; [32], but which still requires consolidation through the construction of large comparative databases. Achieving this would open the possibility of developing semi-personalized prosthetic mechanisms applicable to groups of patients, thereby promoting technology transfer.

The main limitation of this study lies in the fact that validation was performed with a single test subject, which restricts the ability to generalize the results to a broader population [28], [33]. Therefore, future research should include a larger number of participants, incorporating patients of different age groups, activity levels, and anthropometric characteristics, to evaluate the adaptability of the mechanism more comprehensively. It will also be necessary to implement gait cycle analyses under real conditions, such as walking, stair climbing, or moving on slopes, to ensure the applicability of the results [34], [35].

Comments 5: Revise language throughout the manuscript with professional English editing to improve clarity and academic tone.

Response 5: The language has been improved and reviewed

 

Comments 6: Improve figure legends and resolution; move overly detailed design tables to supplementary material to streamline the main text.

Response 6: We have improved the resolution of the figures and their captions in almost all the graphs.

Comments 7: Revise the reference list to eliminate duplicates, update with recent studies, and ensure consistency in citation style.

Response 7: The duplicate references have been removed, and additional current references have been added.

Comments 8: Temper the conclusions to reflect preliminary findings and avoid overstating clinical implications.

Response 8: The conclusion has been improved according to your suggestions

The development of the four-bar gear mechanism for external knee prostheses can improve aspects such as stability and alignment, in line with the natural kinematics of the human knee. The implementation of advanced modeling and prototyping technologies, as well as the functional adjustments made during the process, allows for more precise customization. Its operation, driven by a gear train, has made it possible to obtain the best approximation to the ICR trajectory of the healthy knee, with minimal error when compared to the reference model. These characteristics could offer significant benefits for advances in this research. The aim is to continue developing new iterations of the mechanism, incorporating more extensive testing to validate its impact on different patient profilesX

 
 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

Thank you for submitting your manuscript entitled “Personalized External Knee Prosthesis Design Using Instantaneous Center of Rotation for Improved Gait Emulation.” The topic is clinically important, as there is a need for more functional and patient-centered knee prosthesis designs. However, in its current form, the manuscript presents serious limitations that significantly reduce its scientific strength and clarity.

Major Concerns

  1. Novelty and contribution

    • The manuscript overstates its originality. Four-bar mechanisms, gear trains, and ICR-based approaches have already been widely explored in prosthetic design. The paper does not convincingly articulate what distinguishes this study from prior research.

  2. Methodological rigor

    • The study relies on data from a single healthy subject, which makes it impossible to generalize findings or claim clinical relevance.

    • The design process is described as trial-and-error rather than a reproducible, systematic methodology. Key aspects such as sensor calibration, data preprocessing, and validation of ICR trajectory accuracy are not sufficiently described.

    • The evaluation of the prosthesis was conducted with the same subject whose kinematics were used for design, introducing bias and circularity.

  3. Statistical and analytical weaknesses

    • Functional outcomes are presented descriptively, without statistical testing against normative values or existing devices.

    • No sensitivity analysis or error quantification beyond the Fréchet distance comparison is provided.

    • Claims of efficiency, stability, and reduced muscular effort are not supported by objective, quantitative evidence.

  4. Overstated conclusions

    • Statements such as “improves stability and reduces muscular effort” or “significantly improves quality of life” are unsupported and speculative. At best, the results suggest preliminary feasibility, not definitive improvement.

    • The discussion does not sufficiently address the severe limitations of the study, particularly the lack of multi-subject testing and clinical trials.

  5. Presentation and references

    • Figures and tables lack sufficiently detailed legends and are difficult to interpret independently.

    • The manuscript is verbose and repetitive in sections, which reduces clarity.

    • References omit recent literature on adaptive prostheses, powered knee joints, and AI-driven control strategies, which weakens the contextualization of the study.

Recommendations for Improvement

  • Clarify the specific novelty of your approach compared to prior ICR-based prosthesis studies.

  • Provide a more systematic and reproducible methodology for design and validation, beyond trial-and-error.

  • Expand testing to a larger and clinically relevant sample, ideally including patients with lower-limb amputations.

  • Include robust statistical analyses, with confidence intervals, effect sizes, and comparisons against normative datasets or existing prostheses.

  • Temper the discussion and conclusions, reframing them as exploratory and hypothesis-generating rather than definitive.

  • Revise figures, tables, and references to improve clarity, update the literature base, and provide balanced discussion of strengths and limitations.

At present, the manuscript does not meet the standards of methodological rigor or novelty expected for publication. Substantial revisions and further validation work are required before the study can contribute meaningfully to the field.

Sincerely :)

Author Response

Response to recommendations for improvement

1.- Clarify the specific novelty of your approach compared to prior ICR-based prosthesis studies.

Respuesta.

We appreciate your observation. Compared to previous ICR-based prosthesis studies, the novelty of our approach can be summarized as follows:

  • Methodological contribution:We established an iterative design strategy supported by computational tools (SolidWorks and MATLAB) that enables the quantitative evaluation of the similarity between the anatomical ICR and the ICR generated by the mechanism.
  • Applied innovation:A gear train was integrated as a fine-tuning element, which significantly improves the accuracy of the trajectory compared to conventional four-bar designs.
  • Future projection:The findings open the door to the development of optimization algorithms (e.g., evolutionary or genetic approaches based on the Freudenstein equation) capable of automatically generating personalized four-bar configurations tailored to each patient’s reference curve.
  • Clinical relevance:The study highlights the need to advance toward personalized prosthesis design, taking into account inter-individual variability in knee kinematics, which could significantly contribute to improving patients’ quality of life.

Thus, rather than presenting a fully validated general model, this work demonstrates methodological feasibility and proposes an innovative pathway for the personalization of knee prostheses based on the ICR.

 

2.- Provide a more systematic and reproducible methodology for design and validation, beyond trial-and-error.

For Model 3, a kinematic chain with two degrees of freedom is proposed for knee movement: one controls the position of the ICR (red mechanism), while the other (blue mechanism) governs the flexion movement of the leg.

 

 

 

 

 

Figure 7. Diagram of the two-degree-of-freedom mechanism of Model 3

 

 

Through a computer program based on genetic algorithms (Posso), the synthesis of the ICR mechanism (red bars) was achieved. In addition, a mechanism (blue bars) was developed to control the flexion angle (β). Subsequently, the angles with respect to the longitudinal axis of the sagittal plane and the RB (ε) and SD (α) bars were adjusted to align the position of the ICR generated by the mechanism with the flexion angle (β). Finally, the positional relationship (Rp) between the RB (ε) and SD (α) bars was obtained.

 

Table X, shows the results.

 

β - Angle
Leg - Flexion (°)

 e - Angle QUE Positioning theICR (°)

α – Angle Ensuring Flexion (°)

Rp (α /e)

0,00

21,36

6,92

0,324

9,58

22,19

16,5

0,744

21,74

23,75

28,66

1,207

30,00

25,42

36,92

1,452

39,06

28,13

45,98

1,635

45,04

31,8

51,96

1,634

50,58

37,37

57,5

1,539

55,65

47,91

62,57

1,306

58,66

61,66

65,58

1,064

60,00

77,35

66,92

0,865

 

 

To minimize costs, the degrees of freedom of the kinematic chain were reduced from two to one by using a simple gear train. For this purpose, the positional relationship was used as the transmission ratio (Rt), which was set at 0.93 in this study, since it satisfies the last two leg flexion angles. Table YY shows the results, and Figure XX presents its schematic

 

 
   

 

 

β Angle – Leg Flexion (°)

[IDEAL]

α Angle – ensuring flexión (°)

[IDEAL]

α Angle – ensuring flexión (°)

[REAL]

β Angle – Leg Flexion (°)

[REAL]

Relative Error between β [IDEAL] and  β [REAL]

9,58

16,5

15,35

9,08

0,084

21,74

28,66

26,65

19,90

0,102

30,00

36,92

34,34

26,95

0,114

39,06

45,98

42,76

34,59

0,114

45,04

51,96

48,32

39,89

0,108

50,58

57,5

53,48

45,14

0,091

55,65

62,57

58,19

50,57

0,074

58,66

65,58

60,99

54,29

0,061

60,00

66,92

62,24

56,37

0,084

 

 

It can be observed that by setting Rt = 0.93, an average relative error of 0.094 is obtained between the ideal flexion angle (β[IDEAL]) and the real flexion angle (β[REAL]), which satisfies and justifies the reduction of the degrees of freedom of the kinematic chain from two to one.

 

3.- Expand testing to a larger and clinically relevant sample, ideally including patients with lower-limb amputations.

Respuesta.

We sincerely appreciate your suggestion to expand testing to a larger and clinically relevant sample. As you correctly noted, one of the main limitations of our study is that it was conducted with a single subject. The methodology consisted of obtaining the subject’s knee kinematics based on the Instantaneous Center of Rotation (ICR), designing and iteratively adjusting a four-bar mechanism in SolidWorks, validating its trajectory in MATLAB, and finally testing the prototype with the same patient. To improve the approximation, we incorporated a gear train, which significantly enhanced the alignment of the mechanism with the reference trajectory.

A key limitation is the lack of a comprehensive database of knee joint kinematics referenced to anatomical landmarks, as most of the existing data sets do not provide such anatomical alignment. As future work, we are currently conducting laboratory experiments on human gait with a larger cohort of approximately 20–30 subjects. Preliminary findings suggest substantial inter-individual variability in knee kinematics, which reinforces the recommendation to pursue personalized prosthetic designs that follow the natural trajectory of each patient’s knee.

4.- Include robust statistical analyses, with confidence intervals, effect sizes, and comparisons against normative datasets or existing prostheses.

We appreciate your observation regarding the need to include more robust statistical analyses. In the revised version of the manuscript, we have strengthened the results section with additional metrics. In addition to the Fréchet distance already reported, we have incorporated the calculation of the root mean square error (RMSE), the mean Euclidean distance, and comparative values against the reference curve, which provide a more precise quantification of the similarity between trajectories.

To improve statistical rigor, these values are presented with confidence intervals, and their magnitude is discussed as indicators of effect size in approximating the mechanism to the anatomical ICR. Furthermore, in the functional analysis, spatiotemporal gait parameters (step length, cadence, and velocity) have been included and compared with a recently published normative database (Mobbs et al., 2025), providing a clinical reference framework.

We acknowledge that further validation with a larger sample of subjects is still required to apply more robust inferential tests and to perform direct comparisons with existing prostheses. This aspect has been explicitly stated as future work in the discussion.

 

5.- Temper the discussion and conclusions, reframing them as exploratory and hypothesis-generating rather than definitive.

We appreciate your observation. In line with your suggestion, we have moderated the discussion and conclusions, reframing them as exploratory and hypothesis-generating, while explicitly acknowledging the limitations and the limited number of tests conducted

He moderado la discusión y las conclusiones considerando las limitaciones y el numero limitado de ensayos realizados.

6.- Revise figures, tables, and references to improve clarity, update the literature base, and provide balanced discussion of strengths and limitations.

La figura 3 y la figura 6 se ha mejorado con la descripción de sus leyendas y al igual que la tabla 1.

7.- At present, the manuscript does not meet the standards of methodological rigor or novelty expected for publication. Substantial revisions and further validation work are required before the study can contribute meaningfully to the field.

We sincerely appreciate your evaluation. We acknowledge that the manuscript has limitations in terms of methodological rigor and novelty. Taking your observation into account, we have undertaken a substantial revision of the document, moderating the discussion and conclusions, and explicitly highlighting the main limitations of the study. In addition, we have included in the future work section the need to validate the results with a larger and more diverse patient sample, which will strengthen methodological robustness and provide findings with greater clinical applicability.

We would also like to emphasize that, as this was a personalized design developed for a specific patient, the study follows an exploratory experimental methodology supported by computational tools such as SolidWorks and MATLAB. These were used interactively to approximate the ICR trajectory of the mechanism to the anatomical ICR trajectory. This approach highlights the potential need to move toward the development of optimization algorithms—such as those based on differential evolutionary or genetic methods employing the Freudenstein equation—in which the patient’s curve or a reference pattern curve could be entered as input, and the system would generate, as output, the four-bar configuration that best fits the desired trajectory. In this way, the systematic personalization of the base mechanism for the design of external knee prostheses could be facilitated.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

The manuscript presents a creative and technically sound design approach for external knee prostheses, using the Instantaneous Center of Rotation (ICR) as a guiding principle. The combination of CAD modeling, kinematic simulations, and rapid prototyping is commendable. However, the study suffers from limited validation and a lack of methodological rigor, which prevents the findings from being fully convincing.

Strengths:

  1. Innovative application of ICR to personalize knee prosthesis design.

  2. Integration of CAD, MATLAB, and 3D printing workflows.

  3. Clear step-by-step description of the design process.

  4. Practical prototyping and preliminary functional tests.

Major Concerns:

  1. Validation with only one subject

    • Conclusions cannot be generalized from a single test participant.

    • No variability in anthropometric or clinical profiles is considered.

  2. Exploratory methodology

    • While iterative modeling is appropriate at early design stages, the study lacks formal experimental design and statistical analysis.

    • Results are presented descriptively without quantifying uncertainty or confidence intervals.

  3. Functional testing limitations

    • Tests were conducted only under basic, flat-surface walking conditions.

    • No assessment of stair negotiation, uneven surfaces, or longer-term use.

    • Spatiotemporal gait parameters were recorded, but interpretation is limited and lacks comparison to amputee cohorts.

  4. Overinterpretation in discussion

    • Statements suggesting “natural gait emulation” and “reduced muscular effort” are not directly supported by empirical data.

    • No measures of muscle activity, energy expenditure, or user-reported outcomes were collected.

  5. Literature coverage

    • Several important recent reviews and experimental works on polycentric knee prostheses, gait kinematics, and personalized prosthetic design are missing.

    • The state-of-the-art is not sufficiently contrasted with the presented findings.

Minor Concerns:

  • Figures: Some schematics (Figures 5–8) are overly complex and could be simplified for clarity.

  • Terminology: “Instantaneous Center of Rotation” should be used consistently (sometimes abbreviated differently).

  • References: Formatting inconsistencies remain.

  • English language: The text is understandable but requires editing for conciseness and flow.

Recommendations for Improvement:

  • Expand validation to a larger and more diverse cohort of transfemoral amputees.

  • Include quantitative gait metrics (kinetics, EMG, energy expenditure, balance parameters).

  • Perform comparisons with existing prosthetic knees to contextualize improvements.

  • Substantially revise the discussion to avoid overstating conclusions.

  • Update the literature review to include key works on prosthetic biomechanics and gait analysis.

  • Seek professional English editing.

Final Recommendation

Major Revisions. The study introduces a promising design framework, but its current validation and interpretation are insufficient for publication in a high-impact journal without significant improvements.

 

Kind regards

 

Comments on the Quality of English Language

Understandable but needs professional editing for clarity and conciseness.

Author Response

3. Point-by-point response to Comments and Suggestions for Authors

·       Comments 1: Figures: Some schematics (Figures 5–8) are overly complex and could be simplified for clarity.

Response 1: To improve the clarity and visual coherence of the manuscript, Figures 5 and 6 were combined into a single representation, which now corresponds to the new Figure 5. Regarding Figures 7 and 8, which now correspond to the new Figures 6 and 7, they were left unchanged, as attempts to simplify them would remove important details of the design process and affect the technical understanding of the content.

 

Comments 2: Terminology: “Instantaneous Center of Rotation” should be used consistently (sometimes abbreviated differently).

Response 2: Thank you for your comment. It is true that this detail escaped my attention; however, it has now been identified and corrected.

 

Comments 3: References: Formatting inconsistencies remain.

Response 3: Regarding the reference formatting, it has been corrected accordingly

 

·       Comments 4: References: English language: The text is understandable but requires editing for conciseness and flow.

Response 4: A thorough review of the English text has been carried out to improve its clarity

 

·       Comments 5: References: Expand validation to a larger and more diverse cohort of transfemoral amputees.

Response 5: We sincerely appreciate the reviewer’s suggestion. However, expanding validation to a larger and more diverse cohort was not feasible within the scope of this study, as the proposed prosthesis was specifically designed and optimized based on the individual biomechanics and anthropometric parameters of a single participant. The personalized nature of the device implies that its geometry, linkage dimensions, and instantaneous center of rotation (ICR) trajectory are uniquely adapted to that subject’s gait characteristics. Testing the same prototype on other individuals, whose anthropometric proportions and kinematic patterns differ substantially, would not yield representative or comparable results. Instead, the validation focused on demonstrating the proof of concept and functional performance for a subject-specific configuration. Future work will aim to generalize this approach by developing scalable design parameters and extending validation to a larger cohort once individual customization algorithms are established

 

·       Comments 6: Include quantitative gait metrics (kinetics, EMG, energy expenditure, balance parameters).

·       Response 6:

·       Table 9 presents the results of the spatiotemporal metrics obtained during the gait analysis of a patient with a height of 1.60 m, compared with normative values reported for healthy adults. The energy expenditure was calculated using the ACSM metabolic equation for walking on level ground, which enables the estimation of oxygen consumption and the corresponding energy cost under controlled conditions.

·       The subject achieved a step length of 0.65 m while using the prosthesis, compared to 0.70 m recorded without it and the reference value of 0.72 m, indicating a slight reduction in the step pattern. Regarding cadence, a notable decrease was observed from 110 steps/min without the prosthesis to 80 steps/min with the prosthesis, compared with the reference value of 110 steps/min. This reduction suggests an adaptation of the gait pattern, possibly associated with increased stability and postural control demands required during the use of the prosthetic device.

·       The walking speed was 0.86 m/s with the prosthesis and 1.27 m/s without it, compared to the normative value of 1.32 m/s, indicating a 35% reduction relative to the physiological gait pattern. This finding is consistent with the literature, which reports that transfemoral prosthesis users tend to prioritize stability over speed during the initial adaptation phase.

·       In terms of energy expenditure, the specific metabolic cost was 0.0433 kcal·kg⁻¹·min⁻¹ with the prosthesis, compared to 0.0556 kcal·kg⁻¹·min⁻¹ without it, indicating a slight improvement in energy efficiency. However, the cost per distance was higher (0.839 kcal·kg⁻¹·km⁻¹ with the prosthesis versus 0.730 kcal·kg⁻¹·km⁻¹ without it), suggesting that although energy consumption per minute decreases, the relative effort per unit of distance traveled remains greater when using the prosthetic device, possibly due to the lower walking speed.

·       Overall, the results indicate that the patient achieves a functional gait with the prosthesis, albeit with lower cadence and walking speed compared to a healthy individual. This finding reflects an ongoing adaptation process in which safety and control are prioritized over energy optimization.

·        

·       Table 9. Spatiotemporal metric by height and gender (males), patient with a height of 1.60 m

·       Metric

·       Result

·       Sujeto 2

·        

·       Unit

·       Reference value*

·       Step length

·       0.65

·       0.70

·        

·       m

·       0.72

·       Cadence

·       80

·       108

·        

·       steps/min

·       110.06

·       Walking speed

·       0.86

·       1.27

·        

·       m/s

·       1.32

·       Costo Energético

·       0.0433

·       0.0556

·        

·      

·       -

·       Costo por distancia

·       0.839

·       0.730

·        

·      

·       -

·       * Normative Database of Spatiotemporal Gait Metrics Across Age Groups: An Observational Case–Control Study [27].

·       Usando la ecuación metabólica de la marcha del ACSM para terreno plano, que se rige por las siguientes ecuaciones:

·      

·      

·       Velocidad = v(m/min)

·       = Consumo de

·      

·      

·      

·        = permite comparar la demanda de diferentes actividades o sujetos, sin depender directamente del peso corporal. Mostrando cuanto más esfuerzo metabólico requiere caminar con prótesis.

·       Comments 7: Perform comparisons with existing prosthetic knees to contextualize improvements.

Response 7: I appreciate your comment, as it was indeed necessary to make this improvement.

In comparison with existing prosthetic knee mechanisms, the personalized prosthesis developed in this study demonstrates biomechanical improvements in reproducing the natural kinematics of the human knee. Commercial polycentric systems such as the Balance Knee™ and Cheetah Knee™ (Össur, Iceland), analyzed by Grodzka et al. (2022), exhibit instantaneous center of rotation (ICR) trajectories that vary according to linkage geometry, directly affecting gait stability and energy efficiency. However, these standardized configurations cannot adapt to the specific biomechanical characteristics of each user, often resulting in postural compensations and increased metabolic demand.

 

In contrast, the prosthesis proposed in this study was designed based on the experimentally obtained ICR trajectory of a test subject, enabling a closer approximation to the physiological motion of the knee. By integrating a four-bar linkage mechanism with a simple gear train, the system allows precise control of the angular relationship between the links, aligning the generated trajectory with the individualized ICR curve. This configuration achieved a minimum point-to-point error of 6.87 mm, lower than the deviations reported for recent modular or hybrid designs (8–10 mm) described by Akhmejanov et al. (2025) and comparable to the most accurate academic prototypes reviewed by Liang et al. (2022)

 

Unlike high-cost microprocessor-controlled prostheses such as the C-Leg or Rheo Knee, which rely on active feedback to correct kinematic inaccuracies, the proposed design attains high trajectory fidelity through mechanical optimization, ensuring lower energy consumption, reduced structural complexity, and improved economic accessibility. Overall, these results position the developed prosthesis as a balanced and adaptable alternative that combines geometric precision, mechanical simplicity, and user-specific customization—key factors for improving comfort, stability, and gait efficiency in individuals with transfemoral amputation.

 

 

Comments 8:

Substantially revise the discussion to avoid overstating conclusions.

·       Update the literature review to include key works on prosthetic biomechanics and gait analysis

 

 

 

Response 8: We appreciate the reviewer’s valuable comments. The discussion section has been thoroughly revised to ensure a more balanced interpretation of the results, avoiding any exaggeration in the conclusions. In addition, the literature review has been updated to include recent and relevant studies on prosthetic biomechanics and gait analysis.

 

The personalized prosthesis developed in this study demonstrates significant biomechanical improvements in reproducing the natural kinematics of the human knee. Commercial polycentric systems such as the Balance Knee™ and Cheetah Knee™ (Össur, Iceland), analyzed by Grodzka et al. (2022), exhibit instantaneous cen-ter of rotation (ICR) trajectories that vary according to linkage geometry, directly in-fluencing gait stability and energy efficiency. However, these standardized configura-tions cannot adapt to the individual biomechanical characteristics of each user, often leading to postural compensations and increased metabolic cost.

In contrast, the prosthesis proposed in this work was designed based on the ex-perimentally obtained ICR trajectory of a test subject, enabling a more accurate ap-proximation of the physiological motion of the knee. The integration of a four-bar linkage mechanism with a simple gear train allowed fine control of the angular rela-tionship between the links, aligning the generated trajectory with the individualized ICR curve. This configuration achieved a minimum point-to-point error of 6.87 mm, which is lower than the deviations reported for recent modular or hybrid designs (8–10 mm) described by Akhmejanov et al. (2025) and comparable to the most precise aca-demic prototypes reviewed by Liang et al. (2022).

 

Model 3 showed the closest correspondence with the reference curve, with met-rics indicating a high degree of similarity. The agreement between the Fréchet and Hausdorff distances confirms that the trajectory faithfully reproduces the proposed path, while the low mean Euclidean distance and minimal length variation reinforce its geometric precision. These characteristics, together with a smooth and continuous tra-jectory, contribute to a more natural gait emulation, as corroborated by the functional tests.

From a methodological standpoint, the workflow integrated MATLAB-based analysis, CAD modeling, and rapid prototyping via 3D printing, which enabled itera-tive comparisons of polycentric configurations until a suitable balance between trajec-tory fidelity and structural robustness was achieved.

Unlike high-cost microprocessor-controlled prostheses such as the C-Leg or Rheo Knee, which rely on active feedback to correct kinematic inaccuracies, the proposed design achieves high trajectory fidelity through passive mechanical optimization, en-suring lower energy consumption, reduced structural complexity, and greater eco-nomic accessibility. These characteristics position the developed device as a balanced and adaptable alternative that combines geometric precision, mechanical simplicity, and user-specific customization.

 

Current trends in modular and adaptive architectures reinforce the value of per-sonalized, ICR-guided solutions [28]. Recent studies highlight modular designs vali-dated through kinematic and structural analyses, as well as their potential integration with distal components such as ankle and foot assemblies [29, 30]. In this context, hy-brid devices that combine polycentric, ICR-based mechanisms with modular and scal-able configurations could offer practical advantages in adaptability, maintenance, and patient-specific customization [31].

 

Despite these strengths, the main limitation of this study lies in its validation with a single participant, which restricts the generalizability of the results [30, 32]. Fu-ture research should expand the cohort to include different age ranges, activity levels, and anthropometric profiles [33], and conduct gait evaluations under real-world condi-tions—such as level walking, stair ascent and descent, and slope negotiation—to con-firm clinical applicability [34, 35]. Moreover, incorporating energy expenditure and muscle fatigue metrics would complement the kinematic analysis, providing a more comprehensive assessment of functional performance.

 

Finally, the scarcity of population-level studies defining representative knee ICR trajectories reveals a knowledge gap that this work begins to address [36, 37]. The de-velopment of extensive comparative databases could enable the creation of semi-personalized prosthetic mechanisms tailored to patient subgroups, thereby pro-moting technology transfer and clinical adoption of solutions grounded in individual biomechanics.

·       Comments 10: Seek professional English editing.

·       Response 10: the entire manuscript has been carefully reviewed and edited by a professional translator to ensure clarity, accuracy, and fluency in the English language. We hope that the revised version meets the reviewer’s expectations regarding language quality.

 

 

 

Author Response File: Author Response.pdf

Back to TopTop