Development of a Compliant Pediatric Upper-Limb Training Robot Using Series Elastic Actuators

Comments 1: The paper novelty is not so obvious, and it has a more practical focus:

Response 1:     We sincerely thank the reviewer for this valuable observation. While it is true that the manuscript includes practical components such as mechanical design and experimental validation, we would like to kindly emphasize that the main novelty lies in the theoretical and methodological integration of a computed torque controller with dual-spring series elastic actuators (SEAs), specifically tailored for pediatric upper-limb training.

Unlike conventional SEA implementations—which often rely on basic position control or impedance-based strategies—our work demonstrates that a model-based computed torque control scheme can be successfully applied to an elastic and backdrivable system. This integration ensures accurate trajectory tracking during voluntary training tasks, while simultaneously enhancing safety through passive compliance and disturbance rejection.

Furthermore, the entire system was dimensioned and validated for a particularly underserved demographic: children between 2 and 5 years old. As detailed in our literature review (lines 38–109), most robotic training systems in the field target adult users or older children, often overlooking the specific mechanical, functional, and safety requirements of early developmental stages. In contrast, our contribution includes:

·         A complete anthropometric-based mechanical synthesis of a 2-DOF end-effector robot specifically designed for preschool-aged users;

·         The derivation and simulation of its dynamic model under realistic pediatric interaction conditions;

·         The design and modeling of dual-spring SEAs capable of matching expected torque profiles from upper-limb dynamics in small children;

·         And a functional prototype experimentally validated in laboratory settings.

These additions collectively represent a cohesive and original research effort that bridges control theory, dynamics, and safe robotic design for pediatric use. We have now made these contributions more explicit in the revised Abstract and Introduction. Once again, we are grateful for your thoughtful feedback, which helped us better highlight the scientific impact of this work.

Comments 2: The users mention reference 12, but since it is in Spanish, it is difficult to assess how much has been previously published

Response 2: We sincerely appreciate the reviewer’s observation and the opportunity to clarify. Reference [12] corresponds to a short conference paper in Spanish, presented at the Congreso Iberoamericano de Ingeniería Mecánica (CIBIM 2022) within the Mechatronics and Robotics track. That contribution served as the conceptual origin of the present research and introduced the mechanical configuration of a dual-spring SEA designed for upper-limb training applications. It included basic modeling and discussion but was limited in scope and did not cover detailed dynamic simulations, control implementation, or experimental validation.

While Ref. [12] briefly presented the actuator's mechanical layout and preliminary dynamic behavior, the content was not accessible to a broader, non-Spanish-speaking audience. For that reason, and to ensure transparency and completeness, the present manuscript includes a complete rederivation of the SEA’s dynamic model, followed by new simulations under ideal and perturbed conditions. These additions reinforce the theoretical foundation and extend the analysis far beyond what was originally included.

In addition, this manuscript integrates the SEA into a pediatric-oriented 2-DOF training robot, implements a computed torque control strategy with PD+I compensation, and provides experimental validation of compliance, backdrivability, and safety. To enhance clarity for all readers, we have revised the Introduction (lines 99–112) to explicitly state that Ref. [12] only provided the mechanical baseline. A new English-language reference [13] has also been added to support the modeling framework and serve as an accessible benchmark.

We hope this response clarifies the relationship between both works and confirms the originality, depth, and completeness of the current contribution.

Comments 3: The authors have performed a large number of simulations, but some are not clear enough. For example, looking at Fig. 12, which compares the desired vs actual motor position, what motion parameters have been used? Speed and accelerations. Or are these not important? What is the recorded error? Can you specify the RMSE?.

Response 2: We appreciate the reviewer’s concern and would like to clarify that the simulation shown in Fig. 12 was not designed to evaluate tracking performance or controller accuracy, but rather to validate the dynamic model of the training device and establish a torque profile for actuator selection. The reference trajectory was generated using 6th-degree Bézier polynomials, which define position, velocity, and acceleration implicitly based on start/end conditions and a specified time interval. As a result, motion parameters such as peak velocity (1.5 rad/s) and required torques (3.5 Nm and 1.5 Nm for joints 1 and 2, respectively) were extracted directly from the simulation. Since this experiment does not involve closed-loop control, no tracking error (e.g., RMSE) was computed. Instead, the joint positions in Fig. 12(a) illustrate that the model responds smoothly and realistically to the reference motion, while the velocity and torque profiles shown in Fig. 12(b,c) support the physical coherence of the dynamic response. These clarifications have been added to Section 2.2.4 and the figure caption.

Comments 4: In line 207 the authors say that the determined stiffness value for the actuators is 1000 N/m. How was this determined

Response 2: We thank the reviewer for this valuable observation. In the revised manuscript, we have expanded the justification for selecting a spring stiffness of 1000 N/m per actuator (2000 N/m total in antagonistic configuration). This value was determined based on both the torque required to move the pediatric upper limb and the need to ensure passive mechanical deformation under unexpected external forces.

Specifically, we assumed a conservative upper limb mass of 1.2 kg for children aged 2 to 5 years (based on literature-reported average body weights [Refs. 17, 18]) and applied a gravitational force through a 3 cm moment arm. With a factor of safety of 4, this yields a design torque of approximately 1.41 Nm. To limit spring deformation to 4 mm under this worst-case scenario, the minimum required total stiffness would be around 2000 N/m. Therefore, the selected value of 2000 N/m represents a balanced choice that ensures both safe force transmission and compliance. Additionally, the springs were designed using ASTM A228 piano wire, providing appropriate mechanical properties for durability and fatigue resistance.

These details have now been added to the manuscript between lines 248 and 270, Subsection 2.1.2 Design and fabrication on the Elastic Element to clarify the rationale behind the actuator stiffness selection.

Comments 5: I also don’t understand why some of the figures are represented in 3D, while only two dimensions are used (i.e. x and y)?

Response 2: We thank the reviewer for this observation and agree that it is important to clarify the dimensional representation. While the robotic device itself operates in a planar (2D) configuration in the XY plane, some figures—particularly those involving the workspace—are shown in 3D to reflect the anatomical reality of the upper-limb movement. Specifically, Figures 9 and 10 illustrate the human-arm wrist workspace, which originates at the shoulder and is naturally embedded in 3D space. The Z-dimension in these plots helps contextualize the interaction point (i.e., the wrist), whose vertical position is fixed in the robot reference frame but anatomically meaningful in the human kinematic chain. This 3D visualization allows for a more accurate comparison between the anatomical workspace and the robot’s end-effector reachability, which is critical for verifying ergonomic compatibility and coverage.

Comments 6: The experimental validation seems not to be well described. Maybe some figures and details can be added

Response 2: We sincerely appreciate your thoughtful observation regarding the need for a clearer explanation of the experimental validation process. Your feedback prompted us to enhance the description of the setup and clarify how the passive behavior of the system was evaluated.

To better support the reader’s understanding, we have made the following additions to the revised manuscript:

·         Lines 566–573 (Section 3. Results): We now introduce a labeled photograph of the SEA-based prototype in a passive test configuration, showing the fixed motor position and visible spring deformation. This visual aid (now included as Figure 16) helps clarify the mechanical behavior being evaluated during the experiment.

·         Figure 15 Caption: An annotated image now visually illustrates the backdrivability scenario, reinforcing the explanation already present in the results section.

We hope these improvements make the experimental section more intuitive and accessible, and we thank you again for your valuable insight, which helped strengthen the clarity of our work.

Comments 7: Future work is oriented towards using healthy subjects to evaluate the proposed protocol. This is quite a limitation which should be discussed. Not to mention testing the device using real patients.

Response 2: We appreciate the reviewer’s suggestion to further elaborate on the limitations and future directions regarding clinical validation. In response, we have revised the final section of the manuscript to incorporate a more detailed and structured explanation of the regulatory and methodological pathway required for testing medical-grade devices.

Specifically, lines 734–750 now describe that, in accordance with the international conformity assessment principles for medical devices outlined by the Global Harmonization Task Force [Ref. 27], the proposed device is considered a Class II medical device due to its intended use in supporting motor function through rehabilitation. Consequently, its development must adhere to internationally recognized stage-gate processes and Technology Readiness Level (TRL) criteria [Refs. 28, 29].

The revised text clarifies that the results presented in this work correspond to TRL 3 (proof of concept) and TRL 4 (laboratory functional validation). As outlined, testing with healthy subjects (TRL 5) can only be initiated once these stages have been completed and the corresponding technical and safety benchmarks have been satisfied. We also explain that future work will involve collaboration with medical professionals to define the necessary clinical protocols for preclinical and clinical validation phases (TRL 6 and TRL 7).

We trust this added explanation sufficiently addresses the reviewer’s concern regarding the study’s current scope and future applicability in real-world clinical settings.

Comments 1: Usually if elastic elements are used, they must be supplemented with a damping component, otherwise the system may reach resonant frequencies. These damping components are missing from the presentation:

Response 1:     We appreciate your observation regarding the potential for resonance in systems with elastic elements and the importance of including damping components. In response, we have clarified that our system incorporates damping through both passive and control-based means. Specifically:

·         In Lines 46–52, Section 1. Introduction, we now highlight that the derivative gain  in our control strategy introduces virtual damping, which attenuates oscillations resulting from the SEA’s elasticity.

·         In Lines 231–240, Subsection 2.1.1, we elaborate on the internal viscous friction of the Dynamixel MX-64 actuator, and the viscoelastic behavior of the human limb, which together provide sufficient passive damping during physical interaction. These additions make explicit how our approach mitigates resonance without requiring additional mechanical dampers.

Comments 2: Prof. de Luca from the University of Rome (http://users.diag.uniroma1.it/~deluca/rob2_en/15_ImpedanceControl.pdf) has had research and results in the dynamic modeling of robots taking into account impedance. These studies are not mentioned by the authors (missing from the bibliography) nor used as such.

Response 2: We are grateful for your recommendation to incorporate relevant literature on impedance control. Based on your suggestion, we have added a dedicated discussion in Lines 111–119, Section 1. Introduction, and cited the work by De Luca & Book (Ref. [14]) from the Springer Handbook of Robotics. This allowed us to clearly contrast our approach with classical impedance control methods. While impedance control is a well-established strategy to regulate stiffness and damping, our solution introduces mechanical compliance through a dual-spring SEA and relies on passive damping to ensure safe behavior, thus simplifying implementation without compromising physical safety. Your input directly contributed to a more balanced and better contextualized explanation of our methodology. We hope that these additions satisfy your observations and clarify our rationale for the adopted control and actuation strategy. We truly appreciate the time and expertise you devoted to reviewing our manuscript.