# CardioVR-ReTone—Robotic Exoskeleton for Upper Limb Rehabilitation following Open Heart Surgery: Design, Modelling, and Control

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## Abstract

**:**

## 1. Introduction

- Actuator type: the actuator types can be DC servo, electro-hydraulic disk brakes; AC servo motor; stepper motor; BLDC motors; or cable system driven by BLDC motor, with harmonic or planetary gearboxes.
- Control type/Feedback: the control type and feedback include incremental encoder; position and force sensors; EMG optical incr. encoder; electroencephalographic (EEG); and electrooculographic (EOG).
- Movements: the parts of the body that the exoskeleton augments are shoulder–elbow, shoulder–elbow–wrist, or shoulder–elbow–wrist–hand.
- DoFs: the degrees of freedom of the analyzed exoskeletons vary from 1 to 7, and they can be active or passive depending on the type of mechanism used.
- Rehabilitation type: in terms of rehabilitation modalities, there are several approaches, such as active and/or passive assistance provided by the exoskeleton.

## 2. Materials and Methods

#### 2.1. CardioVR-ReTone Design Overview

#### 2.2. Forward Kinematics

#### 2.2.1. Geometrical Modeling of the CardioVR-ReTone Exoskeleton

#### 2.2.2. Development of Kinematical Modeling for CardioVR-ReTone Exoskeleton

#### 2.3. Actuators, Electrical, and Electronic Design

#### Torque Requirements Calculation

^{©}3D modeling software. Every link connects two exoskeleton joints, as mentioned in the subscript. Joints J2 and J3 are interconnected by link L

_{2,3}. Table 6 presents an overview of the upper limb anthropomorphic characteristics of Romanian male subjects, and defines a relation between the exoskeleton joints that have to sustain the load introduced by a specific body segment.

_{jexo}(34) represents the torque required by a specific exoskeleton joint to maintain equilibrium with the associated exoskeleton segment, T

_{jbody}(34) represents the torque required by a specific exoskeleton joint to maintain equilibrium with the associated human body segments, and K

_{s}is an oversize safety coefficient.

- $LinkLengt{h}_{j}$ = length of the link between exoskeleton j and j + 1
- $Lin{k}_{C{G}_{j}}$ = distance from the starting point of the link up to link j center of gravity
- ${F}_{{G}_{j}}$ = gravity force acting on a link j
- ${\varnothing}_{{M}_{j}}$ = diameter of actuator that drives joint j
- $C{G}_{{M}_{j}}$ = center of gravity of the actuator driving joint j
- ${F}_{G{M}_{j}}$ = gravity force acting on actuator j$${T}_{jbody}=\left({{\displaystyle \sum}}_{j=E{J}_{G}}^{segments-1}\left({{\displaystyle \sum}}_{k=j+1}^{segments}SegmentLengt{h}_{j}\times {F}_{{G}_{k}}\right)\right)+{{\displaystyle \sum}}_{j=E{J}_{G}}^{segments}SegmentLengt{h}_{j}\times Lin{k}_{C{G}_{j}}\times {F}_{{G}_{j}}$$

#### 2.4. Control Architecture Design

#### 2.5. Patient Extrinsic Motivation with VR

#### 2.5.1. Operating and Control Application: Interaction Scenarios

#### 2.5.2. Operating Software Architecture

#### 2.5.3. Gaming Components

**The VR game:**to make the entire rehab journey easily understandable and fun, a VR game is being developed to act as an avatar “host” for the patient. It conveys information such as the current progress, what is coming next, and medical information related to the patient’s disease, cure, and recommended lifestyle. When presenting the next exercise level, the avatar explains the movements to be made and trains the patient to do them, while also providing feedback.

**The level games**: to build enthusiasm, introduce fun into a rehab level, and to distract from potential pain, a simple game can be played while performing the exercises. To avoid boredom and to be able to adapt to each patient, any game (for which a valid license exists) can be used in this step.

## 3. Results

#### 3.1. Differential Motion Equations for CardioVR-ReTone—6R Structure

#### 3.2. Working Process of Kinetic Joints Using $\left(3n\right)-type$ Polynomial Functions

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ruiz-Olaya, A.F.; Lopez-Delis, A.; da Rocha, A.F. Upper and Lower Extremity Exoskeletons. In Handbook of Biomechatronics; Segil, J., Ed.; Elsevier Inc.: London, UK, 2018. [Google Scholar]
- Mocan, M.; Răhăian, R.; Mocan, B.; Blaga, S.N. Multi-Marker Evaluation of the Cardio-Metabolic Risk. Atherosclerosis
**2017**, 263, E201–E202. [Google Scholar] [CrossRef] - Hamaya, M.; Matsubara, T.; Noda, T.; Teramae, T.; Morimoto, J. Learning assistive strategies for exoskeleton robots from user-robot physical interaction. Pattern Recognit. Lett.
**2017**, 99, 67–76. [Google Scholar] [CrossRef] - Martínez, G.M.C.; Zuniga Avilés, L.A. Design Methodology for Rehabilitation Robots: Application in an Exoskeleton for Upper Limb Rehabilitation. Appl. Sci.
**2020**, 10, 5459. [Google Scholar] [CrossRef] - Mocan, M.; Mocan, B. Cardiac rehabilitation for older patients with cardiovascular pathology using robotic systems—A survey. Balneo Res. J.
**2019**, 10, 33–36. [Google Scholar] [CrossRef] - Schabron, B.; Desai, J.; Yihun, Y. Wheelchair-Mounted Upper Limb Robotic Exoskeleton with Adaptive Controller for Activities of Daily Living. Sensors
**2021**, 21, 5738. [Google Scholar] [CrossRef] - Mocan, M.; Chiorescu, R.; Banc, O.N.; Mocan, B.; Anton, F.; Stoia, M.; Farcas, A.D. Cardiac rehabilitation protocols outcome in frail patients undergoing transcatheter aortic valve implantation. BALNEO Res. J.
**2018**, 9, 401–405. [Google Scholar] [CrossRef] - Wu, Q.; Wu, H. Development, Dynamic Modeling, and Multi-Modal Control of a Therapeutic Exoskeleton for Upper Limb Rehabilitation Training. Sensors
**2018**, 18, 3611. [Google Scholar] [CrossRef] [Green Version] - Galofaro, E.; D’Antonio, E.; Patané, F.; Casadio, M.; Masia, L. Three-Dimensional Assessment of Upper Limb Proprioception via a Wearable Exoskeleton. Appl. Sci.
**2021**, 11, 2615. [Google Scholar] [CrossRef] - Liu, C.; Liang, H.; Ueda, N.; Li, P.; Fujimoto, Y.; Zhu, C. Functional Evaluation of a Force Sensor-Controlled Upper-Limb Power-Assisted Exoskeleton with High Backdrivability. Sensors
**2020**, 20, 6379. [Google Scholar] [CrossRef] - Rosen, J.; Brand, M.; Fuchs, M.B.; Arcan, M. A myosignal-based powered exoskeleton system. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum.
**2001**, 31, 210–222. [Google Scholar] [CrossRef] [Green Version] - Fanin, C.; Gallina, P.; Rossi, A.; Zanatta, U.; Masiero, S. NeRebot: A wire-based robot for neurorehabilitation. In Proceedings of the 9th International Conference on Rehabilitation Robotics, Taejon, Korea, 23–25 April 2003; pp. 23–27. [Google Scholar]
- Nef, T.; Mihelj, M.; Kiefer, G.; Perndl, C.; Müller, R.; Riener, R. ARMin—Exoskeleton for arm therapy in stroke patients. In Proceedings of the ICORR’07, 2007 IEEE 10th International Conference on Rehabilitation Robotics, Noordwijk, The Netherlands, 13–15 June 2007; pp. 68–74. [Google Scholar] [CrossRef]
- Garrec, P.; Friconneau, J.P.; Méasson, Y.; Perrot, Y. ABLE, an innovative transparent exoskeleton for the upper-limb. In Proceedings of the 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, Nice, France, 22–26 September 2008; pp. 1483–1488. [Google Scholar] [CrossRef] [Green Version]
- Brackbill, E.A.; Mao, Y.; Agrawal, S.K.; Annapragada, M.; Dubey, V.N. Dynamics and control of a 4-dof wearable cable-driven upper arm exoskeleton. In Proceedings of the 2009 IEEE International Conference on Robotics and Automation, Kobe, Japan, 12–17 May 2009; pp. 2300–2305. [Google Scholar] [CrossRef] [Green Version]
- Rahman, M.H.; Kittel-Ouimet, T.; Saad, M.; Kenné, J.-P.; Archambault, P.S. Development and control of a robotic exoskeleton for shoulder, elbow and forearm movement assistance. Appl. Bionics Biomech.
**2012**, 9, 275–292. [Google Scholar] [CrossRef] [Green Version] - Stienen, A.H.A.; Hekman, E.E.G.; Prange, G.B.; Jannink, M.J.A.; Aalsma, A.M.M.; Van Der Helm, F.C.T.; Van Der Kooij, H. Dampace: Design of an exoskeleton for force-coordination training in upper-extremity rehabilitation. J. Med. Devices
**2009**, 3, 031003. [Google Scholar] [CrossRef] - Naidu, D.; Stopforth, R.; Bright, G.; Davrajh, S. A Portable Passive Physiotherapeutic Exoskeleton. Int. J. Adv. Robot. Syst.
**2012**, 9, 137. [Google Scholar] [CrossRef] - Pirondini, E.; Coscia, M.; Marcheschi, S.; Roas, G.; Salsedo, F.; Frisoli, A.; Bergamasco, M.; Micera, S. Evaluation of a New Exoskeleton for Upper Limb Post-stroke Neuro-rehabilitation: Preliminary Results. Biosyst. Biorobotics
**2014**, 7, 637–645. [Google Scholar] [CrossRef] - Zhou, L.; Bai, S.; Andersen, M.S.; Rasmussen, J. Modeling and design of a spring-loaded, cable-driven, wearable exoskeleton for the upper extremity. Model. Identif. Control
**2015**, 36, 167–177. [Google Scholar] [CrossRef] [Green Version] - Islam, M.R.; Assad-Uz-Zaman, M.; Brahmi, B.; Bouteraa, Y.; Wang, I.; Rahman, M.H. Design and Development of an Upper Limb Rehabilitative Robot with Dual Functionality. Micromachines
**2021**, 12, 870. [Google Scholar] [CrossRef] - Gull, M.A.; Thoegersen, M.; Bengtson, S.; Mohammadi, M.; Struijk, L.A.; Moeslund, T.; Bak, T.; Bai, S. A 4-DOF Upper Limb Exoskeleton for Physical Assistance: Design, Modeling, Control and Performance Evaluation. Appl. Sci.
**2021**, 11, 5865. [Google Scholar] [CrossRef] - Huamanchahua, D.; Vargas-Martinez, A.; Ramirez-Mendoza, R. Kinematic of the Position and Orientation Synchronization of the Posture of a n DoF Upper-Limb Exoskeleton with a Virtual Object in an Immersive Virtual Reality Environment. Electronics
**2021**, 10, 1069. [Google Scholar] [CrossRef] - Chen, C.-T.; Lien, W.-Y.; Chen, C.-T.; Wu, Y.-C. Implementation of an Upper-Limb Exoskeleton Robot Driven by Pneumatic Muscle Actuators for Rehabilitation. Actuators
**2020**, 9, 106. [Google Scholar] [CrossRef] - Zhao, Y.; Liang, C.; Gu, Z.; Zheng, Y.; Wu, Q. A New Design Scheme for Intelligent Upper Limb Rehabilitation Training Robot. Int. J. Environ. Res. Public Health
**2020**, 17, 2948. [Google Scholar] [CrossRef] - Buongiorno, D.; Cascarano, G.D.; Camardella, C.; De Feudis, I.; Frisoli, A.; Bevilacqua, V. Task-Oriented Muscle Synergy Extraction Using An Autoencoder-Based Neural Model. Information
**2020**, 11, 219. [Google Scholar] [CrossRef] [Green Version] - Badesa, F.J.; Diez, J.A.; Catalan, J.M.; Trigili, E.; Cordella, F.; Nann, M.; Crea, S.; Soekadar, S.R.; Zollo, L.; Vitiello, N.; et al. Physiological Responses During Hybrid BNCI Control of an Upper-Limb Exoskeleton. Sensors
**2019**, 19, 4931. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chen, W.; Li, Z.; Cui, X.; Zhang, J.; Bai, S. Mechanical design and kinematic modeling of a cable-driven arm exoskeleton incorporating inaccurate human limb anthropomorphic parameters. Sensors
**2019**, 19, 4461. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chaparro-Rico, B.D.M.; Cafolla, D.; Ceccarelli, M.; Castillo-Castaneda, E. NURSE-2 DoF Device for Arm Motion Guidance: Kinematic, Dynamic, and FEM Analysis. Appl. Sci.
**2020**, 10, 2139. [Google Scholar] [CrossRef] [Green Version] - Bond, S.; Laddu, D.R.; Ozemek, C.; Lavie, C.J.; Arena, R. Exergaming and Virtual Reality for Health: Implications for Cardiac Rehabilitation. Curr. Probl. Cardiol.
**2021**, 46, 100472. [Google Scholar] [CrossRef] [PubMed] - The Top 15 Examples of Gamification in Healthcare. Available online: https://medicalfuturist.com/top-examples-of-gamification-in-healthcare/ (accessed on 1 October 2021).
- Dithmer, M.; Rasmussen, J.O.; Grönvall, E.; Spindler, H.; Hansen, J.S.; Nielsen, G.D.; Sorensen, S.B.; Dinesen, B.I. “The Heart Game”: Using Gamification as Part of a Telerehabilitation Program for Heart Patients. Games Health J.
**2016**, 5, 27–33. [Google Scholar] [CrossRef] [Green Version] - Ingadottir, B.; Jaarsma, T.; Klompstra, L.; Aidemark, J.; Askenäs, L.; Bahat, Y.; Ben Gal, O.; Berglund, A.; Berglund, E.; Höchsmann, C.; et al. Let the games begin: Serious games in prevention and rehabilitation to improve outcomes in patients with cardiovascular disease. Eur. J. Cardiovasc. Nurs.
**2020**, 19, 558–560. [Google Scholar] [CrossRef] - Stuart, A.G. Exercise as therapy in congenital heart disease—A gamification approach. Prog. Pediatr. Cardiol.
**2014**, 38, 37–44. [Google Scholar] [CrossRef] - Lee, J.G.; Choi, Y.; López, J. A Review and Evaluation of Smartphone Applications to Support Virtual Cardiac Rehabilitation. J. Am. Coll. Cardiol.
**2020**, 75, 3644. [Google Scholar] [CrossRef] - Ambrosetti, M.; Abreu, A.; Corrà, U.; Davos, C.H.; Hansen, D.; Frederix, I.; Iliou, M.C.; E Pedretti, R.F.; Schmid, J.-P.; Vigorito, C.; et al. Secondary prevention through comprehensive cardiovascular rehabilitation: From knowledge to implementation. 2020 update. A position paper from the Secondary Prevention and Rehabilitation Section of the European Association of Preventive Cardiology. Eur. J. Prev. Cardiol.
**2020**, 28, 460–495. [Google Scholar] [CrossRef] [Green Version] - Doyle, M.P.; Indraratna, P.; Tardo, D.T.; Peeceeyen, S.C.S.; Peoples, G.E. Safety and efficacy of aerobic exercise commenced early after cardiac surgery: A systematic review and meta-analysis. Eur. J. Prev. Cardiol.
**2019**, 26, 36–45. [Google Scholar] [CrossRef] [PubMed] - Katijjahbe, M.A.; Granger, C.L.; Denehy, L.; Royse, A.; Royse, C.; Bates, R.; Logie, S.; Ayub, A.N.; Clarke, S.; El-Ansary, D. Standard restrictive sternal precautions and modified sternal precautions had similar effects in people after cardiac surgery via median sternotomy (“SMART” Trial): A randomised trial. J. Physiother.
**2018**, 64, 97–106. [Google Scholar] [CrossRef] - Mocan, M.; Vlaicu, S.I.; Farcaș, A.D.; Feier, H.; Dragan, S.; Mocan, B. Cardiac Rehabilitation Early after Sternotomy Using New Assistive VR-Enhanced Robotic Exoskeleton—Study Protocol for a Randomised Controlled Trial. Int. J. Environ. Res. Public Health
**2021**, 18, 11922. [Google Scholar] [CrossRef] [PubMed] - Negrean, I.; Kacso, K.S.; Schonstein, C.; Duca, A. Mecanică: Teorie şi Aplicaţii; UT Press: Cluj-Napoca, Romania, 2012. [Google Scholar]
- Negrean, I.; Duca, A.; Negrean, C.; Kacso, K.S. Mecanica Avansată în Robotică; UT Press: Cluj-Napoca, Romania, 2008. [Google Scholar]
- Schonstein, C.; Negrean, I.; Kacso, K. Using of Polynomial Functions in Modelling of the Working Process of Mobile Robot RmITA. Acta Tech. Napoc. Ser. Appl. Math. Mech. Eng.
**2014**, 57, 195–200. [Google Scholar] - Negrean, I.; Kacso, K.; Schonstein, C.; Duca, A.; Rusu, F.; Cristea, F.; Haragas, S. New Formulations on Acceleration Energies in Analytical Dynamics. Appl. Mech. Mater.
**2016**, 823, 43–48. [Google Scholar] [CrossRef] - Negrean, I.; Schonstein, C.; Duca, A. Dynamic Model for the Mobile Robot RmITA. Acta Tech. Napoc. Ser. Appl. Math. Mech. Eng.
**2014**, 57, 159–164. [Google Scholar] - The Robot Operating System (ROS). Available online: https://www.ros.org/ (accessed on 10 October 2021).
- Çubukçu, B.; Yüzgeç, U.; Zileli, R.; Zileli, A. Reliability and validity analyzes of Kinect V2 based measurement system for shoulder motions. Med. Eng. Phys.
**2020**, 76, 20–31. [Google Scholar] [CrossRef] [PubMed] - Chaparro-Rico, B.D.M.; Cafolla, D.; Castillo-Castaneda, E.; Ceccarelli, M. Design of arm exercises for rehabilitation assistance. J. Eng. Res.
**2020**, 8, 203–218. [Google Scholar] [CrossRef] - van Diest, M.; Stegenga, J.; Wörtche, H.J.; Postema, K.; Verkerke, G.J.; Lamoth, C.J.C. Suitability of Kinect for measuring whole body movement patterns during exergaming. J. Biomech.
**2014**, 47, 2925–2932. [Google Scholar] [CrossRef] - Schonstein, C. Kinematic Control Functions for a Serial Robot Structure Based on the Time Derivative Jacobian Matrix. Acta Tech. Napoc.
**2018**, 61, 219–224. [Google Scholar] - Negrean, I. New Formulations in Analytical Dynamics of Systems. Acta Tech. Napoc. Ser. Appl. Math. Mech. Eng.
**2017**, 60, 49–56. [Google Scholar] - Negrean, I.; Schonstein, C.; Kacso, K.; Duca, A. Formulations in advanced dynamics of mechanical systems. Mech. Mach. Sci.
**2014**, 17, 185–195. [Google Scholar] [CrossRef]

**Figure 1.**The designed CardioVR-ReTone exoskeleton. Isometric 3D view (

**left)**; kinematic structure (

**right**).

**Figure 8.**Mass parameters for the CardioVR-ReTone exoskeleton. (

**a**) Joint 4—mass properties. (

**b**) Joint 5—mass properties.

Reference/Year | Rehab Type | Movements | DoFs | Control Type/Feedback | Actuator Type | Clinical Tests |
---|---|---|---|---|---|---|

Rosen et al. [11]/2001 | Active assist | Shoulder, elbow | 1A + 1P | EMG optical incr. encoder | DC servo and gearbox | No |

Fanin et al. [12]/2003 | Passive or active assist | Shoulder, elbow | 3A | Incremental encoder | Wire driven by BLDC motor | Yes |

Nef et al. [13]/2007 | Passive or active assist | Shoulder, elbow | 4A + 6P | Position and force sensors | DC motor and HD gearbox, cable drive linear module | Yes |

Garrec et al. [14]/2008 | Passive or active assist | Shoulder, elbow | 4A | Force sensor | Ball–screw and cable driven by electric motor | No |

Brackbill et al. [15]/2009 | Active assist | Shoulder, elbow | 4A | Encoder | Cable system driven by BLDC motor | No |

Frisoli et al. [16]/2009 | Passive or active assist | Shoulder, elbow, wrist | 4A + 1P | Force feedback, VR optical encoder | DC motor driving a system of pulleys and ball bearings | Yes |

Stienen et al. [17]/2010 | Passive assist | Shoulder, elbow | 4A + 3P | Load sensor | Electro-hydraulic disk brakes | No |

Naidu et al. [18]/2012 | Passive | Shoulder, elbow, wrist | 4A + 3P | Joint angle | Electric actuators | No |

Pirondini et al. [19]/2014 | Passive or active assist | Shoulder, elbow, wrist | 4A + 2P | EMG, force control | No info provided | No |

Zhou et al. [20]/2015 | Passive assist | Shoulder, elbow | 4 | No info provided | Not applicable | No |

Wu et al. [8]/2018 | Active assist | Shoulder, elbow, forearm, wrist | 7A + 2P | EMGs, force sensor, potentiometer, virtual reality | Cable system driven by AC servo motor | Yes |

Islam et al. [21]/2021 | Active or passive assist | Shoulder, elbow, forearm, wrist | 7A + 2P | Force sensors, Hall sensor encoders | Electric motor coupled to HD gear | No |

Schabron et al. [6]/2021 | Active assist | Shoulder, elbow | 3A | Hand gesture control, EMGs | Stepper motor | No |

Gull et al. [22]/2021 | Active assist | Shoulder, elbow | 3A + 1P | Trajectory tracking, encoders | BLDC motor coupled to HD gear | No |

Huamanchahua et al. [23]/2021 | Passive assist | Shoulder, elbow | 4A + 1P | Virtual reality tracking | No motors | No |

Galafaro et al. [9]/2021 | Active or passive assist | Shoulder, elbow | 4A + 2P | Impedance control | BLDC motors | No |

Liu et al. [10]/2020 | Active assist | Shoulder, elbow | 2A + 4P | Force sensor, EMGs, joint angle | BLDC with belt pulley and gear reducer | No |

Chen et al. [24]/2020 | Passive assist | Shoulder, elbow | 3A + 1P | Position control, joint angle, encoder | Pneumatic muscle actuator | No |

Curz et al. [4]/2020 | Passive assist | Shoulder, elbow, wrist | 7A | PLC contro | Linear and rotary electric motors | No |

Zhao et al. [25]/2020 | Active or passive assist | Shoulder, elbow, wrist | 3A | Stereo vision, auditory sensor, EMG, force sensor, proximity, encoder | Cable driven by DC servo motors | No |

Buongiorno et al. [26]/2020 | Active or passive assist | Shoulder, elbow, wrist | 4A + 1P | EMG, autoencoder, force sensor | Cable with gear driven by electric motor | No |

Badesa et al. [27]/2019 | Active assist | Shoulder, elbow, hand, wrist | 4A + 8P | Electroencephalographic (EEG), electrooculographic (EOG) | No data | No |

Chen et al. [28]/2019 | Active assist | Shoulder, elbow | 4A | Encoders, inertial measurements unit | Cable driven by DC electric motors | No |

Chaparro et al. [29]/2020 | Passive or active assistance | Shoulder, elbow | 2A | Encoder | DC motor and planetary gearhead | No |

${\mathit{M}}_{\mathit{v}\mathit{n}}^{\left(0\right)}\in 6\mathit{R}\left(\mathbf{Right}\right)$ | |||||||
---|---|---|---|---|---|---|---|

Joint $\mathit{i}=1\to 6$ | Joint Type $\left\{\mathit{R}\hspace{0.17em};\hspace{0.17em}\mathit{T}\right\}$ | ${\overline{\mathit{p}}}_{\mathit{i}}$ | ${\overline{\mathit{k}}}_{\mathit{i}}$ | ||||

$@{\overline{\mathit{p}}}_{\mathit{x}\mathit{i}}$ | $@{\overline{\mathit{p}}}_{\mathit{y}\mathit{i}}$ | $@{\overline{\mathit{p}}}_{\mathit{z}\mathit{i}}$ | ${\overline{\mathit{k}}}_{\mathit{x}\mathit{i}}$ | ${\overline{\mathit{k}}}_{\mathit{y}\mathit{i}}$ | ${\overline{\mathit{k}}}_{\mathit{z}\mathit{i}}$ | ||

1 | R | 0 | ${l}_{0}$ | ${l}_{1}$ | 0 | 1 | 0 |

2 | R | 0 | $-{l}_{2}$ | ${l}_{3}$ | 0 | 0 | 1 |

3 | R | ${l}_{4}$ | $-{l}_{5}$ | $0$ | 0 | 0 | 1 |

4 | R | $0$ | ${l}_{6}$ | $0$ | 0 | 0 | 1 |

5 | R | ${l}_{7}$ | $0$ | $-{l}_{8}$ | 1 | 0 | 0 |

6 | R | $-{l}_{9}$ | $0$ | $-{l}_{10}$ | 1 | 0 | 0 |

7 | - | $0$ | ${l}_{11}$ | $0$ | 1 | 0 | 0 |

Joint | Right | Left | Kinetic Link Orientation Vector |
---|---|---|---|

i | ${\Delta}_{\hspace{0.17em}i}=1$ | ${\overline{k}}_{i}\equiv \left\{{\overline{x}}_{i},\hspace{0.17em}{\overline{y}}_{i},\hspace{0.17em}{\overline{z}}_{i}\right\}$ | |

1 | y | ${\overline{k}}_{i}\equiv {\overline{y}}_{i}={\left[\begin{array}{ccc}0& 1& 0\end{array}\right]}^{T}$ | |

2, 3, 4 | z | ${\overline{k}}_{i}\equiv {\overline{z}}_{i}={\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}^{T}$ | |

5, 6 | x | ${\overline{k}}_{i}\equiv {\overline{x}}_{i}={\left[\begin{array}{ccc}1& 0& 0\end{array}\right]}^{T}$ |

Characteristic | CPU-14 | CPU-17 | CPU-20 | CPU-25 | CPU32 |
---|---|---|---|---|---|

Gear ratio | 100 | 100 | 100 | 100 | 100 |

Repeated peak torque (Nm) | 28 | 54 | 82 | 157 | 333 |

Average torque (Nm) | 11 | 39 | 49 | 108 | 21 |

Rated torque (Nm) | 7.8 | 24 | 40 | 67 | 137 |

Momentary peak torque (Nm) | 54 | 110 | 147 | 284 | 647 |

Gear weight (kg) | 0.54 | 0.79 | 1.3 | 1.95 | 3.9 |

Motor weight (kg) | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

Joint Number j | Link between Joints L _{j,j+1} | Length (cm) | Center of Gravity (cm) | Weight (kg) |
---|---|---|---|---|

1 | L_{1,2} | 15 | 7.5 | 0.3 |

2 | L_{2,3} | 19.8 | 8.11 | 0.427 |

3 | L_{3,4} | 35.63 | 15.61 | 0.847 |

4 | L_{4,5} | 17.3 | 8.64 | 0.292 |

5 | L_{5,6} | 37.2 | 17.57 | 1.209 |

6 | L_{6,E} | 22.170 | 15.87 | 0.923 |

Exoskeleton Joint Groups EJ_{G} | Body Segment Number j | Body Segment | Length (cm) | Center of Gravity (cm) | Weight (kg) |
---|---|---|---|---|---|

1: J1- > J2 | 1 | Shoulder | 14 | 7 | 3.47 |

2: J3- > J5 | 2 | Upper arm | 29.425 | 14.92 | 3.73 |

3: J6 | 3 | Forearm | 28.375 | 11.83 | 2.06 |

4 | Hand + joystick | 10.125 | 5.17 | 1.0 |

Joint | T_{jexo}(Nm) | T_{jbody}(Nm) | Ks | T_{j}(Nm) | Actuator | |||
---|---|---|---|---|---|---|---|---|

Type | Average Torque (Nm) | Repeated Peak Torque (Nm) | Weight (Kg) | |||||

6 | 1.44 | 5.69 | 1.25 | 8.91 | CPU-17 | 39 | 54 | 1.29 |

5 | 12.09 | 19.97 | 1.25 | 40.07 | CPU-17 | 39 | 54 | 1.29 |

4 | 20.95 | 19.97 | 1.25 | 51.15 | CPU-20 | 49 | 82 | 1.8 |

3 | 46.90 | 19.97 | 1.5 | 100.30 | CPU-25 | 108 | 157 | 2.45 |

2 | 64.76 | 31.68 | 1.5 | 144.66 | CPU-25 | 108 | 157 | 2.45 |

1 | 88.96 | 31.68 | 1.25 | 150.80 | CPU-25 | 108 | 157 | 2.45 |

Joint i | Seq. j = 4,5 | Configuration k = 10→15 | Joint Rotation Reported to Previous Position (°) | Coordinates Values ${\mathit{q}}_{\mathit{i}\mathit{j}\mathit{k}}\hspace{0.17em}\left[\mathit{r}\mathit{a}\mathit{d}\right]$ | Duration ${\mathit{t}}_{\mathit{i}}\hspace{0.17em}\u2329\mathit{s}\u232a$ | $\mathbf{Time}{\mathit{\tau}}_{\mathit{j}\mathit{k}}\hspace{0.17em}\u2329\mathit{s}\u232a$ |
---|---|---|---|---|---|---|

4 | 4 | 9 | 0 | 0 | 0 | 6.77832 |

10 | 60 | 1.047197551 | 0.8334 | 7.61172 | ||

11 | 120 | 2.094395102 | 0.8334 | 8.44512 | ||

12 | 180 | 3.141592654 | 0.8334 | 9.27852 | ||

5 | 5 | 12 | 0 | 0 | 0 | 9.27852 |

13 | 75 | 1.308996939 | 1.04175 | 10.32027 | ||

14 | 150 | 2.617993878 | 1.04175 | 11.36202 | ||

15 | 225 | 3.926990817 | 1.04175 | 12.40377 |

Sequence j = 4,5 | Interval k = 1→3 | Coordinate | Expressions for Generalized Positions, Velocities, and Accelerations | ||
---|---|---|---|---|---|

$\begin{array}{c}{\mathit{q}}_{\mathit{i}\mathit{j}\mathit{k}}\\ [\mathit{r}\mathit{a}\mathit{d}]\end{array}$ | $\begin{array}{c}{\dot{\mathit{q}}}_{\mathit{i}\mathit{j}\mathit{k}}\\ [\mathit{r}\mathit{a}\mathit{d}/\mathit{s}]\end{array}$ | $\begin{array}{c}{\ddot{\mathit{q}}}_{\mathit{i}\mathit{j}\mathit{k}}\\ \hspace{0.17em}[\mathit{r}\mathit{a}\mathit{d}/{\mathit{s}}^{2}]\end{array}$ | |||

4 | 1 | ${q}_{4}$ | $0.912\cdot {\left(\tau -6.78\right)}^{3}-1.05\cdot {10}^{-19}\cdot \tau +7.4\cdot {10}^{-19}$ | $2.74\cdot {\left(\tau -6.78\right)}^{2}-1.085\cdot {10}^{-19}$ | $5.47\cdot \tau -37.09$ |

2 | $1.82\cdot {\tau}^{3}+43.77\cdot {\tau}^{2}-348.47\cdot \tau +918.73$ | $-5.46\cdot {\tau}^{2}+87.54\cdot \tau -348.48$ | $87.54-10.91\cdot \tau $ | ||

3 | $0.89\cdot {(\tau -9.28)}^{3}+3.14$ | $2.69\cdot {(\tau -9.28)}^{2}$ | $5.37\cdot \tau -49.86$ | ||

5 | 1 | ${q}_{5}$ | $\begin{array}{l}0.5808109\xb7{(\tau -9.28)}^{3}-5.421010\cdot {10}^{-20}\cdot \tau +\\ +5.03\cdot {10}^{-19}\end{array}$ | $1.743\cdot {(\tau -9.28)}^{2}-5.5\cdot {10}^{-20}$ | $3.49\cdot \tau -32.34$ |

2 | $-1.162\cdot {\tau}^{3}+37.77\cdot {\tau}^{2}-406.665\cdot \tau +1450.95$ | $-3.485\cdot {\tau}^{2}+75.55\cdot \tau -406.667$ | $-6.97\cdot \tau +75.56$ | ||

3 | $2.169\cdot {10}^{-19}\cdot \tau +0.581\cdot {(\tau -12.4)}^{3}+3.92$ | $1.743\cdot {(\tau -12.4)}^{2}+2.17\cdot {10}^{-19}$ | $3.49\cdot \tau -43.22$ |

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## Share and Cite

**MDPI and ACS Style**

Mocan, B.; Schonstein, C.; Neamtu, C.; Murar, M.; Fulea, M.; Comes, R.; Mocan, M.
CardioVR-ReTone—Robotic Exoskeleton for Upper Limb Rehabilitation following Open Heart Surgery: Design, Modelling, and Control. *Symmetry* **2022**, *14*, 81.
https://doi.org/10.3390/sym14010081

**AMA Style**

Mocan B, Schonstein C, Neamtu C, Murar M, Fulea M, Comes R, Mocan M.
CardioVR-ReTone—Robotic Exoskeleton for Upper Limb Rehabilitation following Open Heart Surgery: Design, Modelling, and Control. *Symmetry*. 2022; 14(1):81.
https://doi.org/10.3390/sym14010081

**Chicago/Turabian Style**

Mocan, Bogdan, Claudiu Schonstein, Calin Neamtu, Mircea Murar, Mircea Fulea, Radu Comes, and Mihaela Mocan.
2022. "CardioVR-ReTone—Robotic Exoskeleton for Upper Limb Rehabilitation following Open Heart Surgery: Design, Modelling, and Control" *Symmetry* 14, no. 1: 81.
https://doi.org/10.3390/sym14010081