**Author details**

*Heat Transfer - Design, Experimentation and Applications*

conditions, such as going up and down stairs.

The authors declare that there is no conflict of interest.

**Acknowledgements**

**Conflict of interest**

work.

**5. Final remarks**

The maximum temperature reached in the motor and harmonic drive was 29.94°C and 29.92°C, respectively, which are within the working limit temperature recommended by the supplier's catalog, up to 125°C and 120°C, respectively. The maximum temperature reached on the surface of the actuator was 30.68°C, which is not harmful to human skin [46]. These results validate the purpose usage of the AMRK as an actuator for knee replacement/assistance for over-ground walking.

This work presented the thermal analysis of the Active Magneto-Rheological Knee actuator (AMRK) for lower-limb prostheses and exoskeletons. The AMRK is composed by a motor unit (EC motor, harmonic drive, and MR clutch), responsible for generating positive work, that works in parallel to a MR brake, used to dissipate energy when the knee is subjected to negative work conditions. The proposed configuration is designed to perform a proper walk with low energy consumption [25, 26]. The thermal model for the components of the MR actuator was presented. EC motor, harmonic drive, MR clutch, MR brake, and bearings were modeled to assess the thermal behavior of the knee when subjected to a long walk over the ground. The results indicate that the proposed operating modes are effective to avoid actuator overheating. The maximum temperatures reached in each component are within the tolerances established by the suppliers and no damage is caused to the system, as well as to the MR fluid. The external steady state temperature of the actuator is about 31°C, which does not represent risk for the user. Future work will consider evaluating the temperature of the system under more severe working

This research was partially funded by grants from FAPES (Fundação de Amparo à Pesquisa e Inovação do Espírito Santo) TO 0480/2015 Project No. 67637574/15, TO 207/2018 Project No. 83276262, and TO 151/2021 Project No. 2021-8GJZ6. The authors honor Marcos Pinotti (in memoriam) for his important contribution to this

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Rafhael Milanezi de Andrade1,2\*, André Palmiro Storch1 , Lucas de Amorim Paulo1 , Antônio Bento Filho1 , Claysson Bruno Santos Vimieiro2,3 and Marcos Pinotti2

1 Laboratory of Robotics and Biomechanics, Department of Mechanical Engineering, Universidade Federal do Espírito Santo, Vitória, ES, Brazil

2 Bioengineering Laboratory, Department of Mechanical Engineering, Graduate Program in Mechanical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

3 Graduate Program in Mechanical Engineering, Pontifícia Universidade Católica de Minas Gerais, Belo Horizonte, MG, Brazil

\*Address all correspondence to: rafhaelmilanezi@gmail.com

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