# Investigating the Stiffness Characteristics of a Tendon-Driven Continuum Manipulator Using Sensitivity Analysis: A Case Study in Transoral Laser Microsurgery

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Manipulator Design for TLM and Stiffness Models

#### Design Constraints for Transoral Laser Microsurgery

## 3. Sensitivity Analysis Methodology

- Correlation indices;
- Performance indices;
- Contribution indices.

#### 3.1. Design of Experiments

#### 3.2. PCE-Based Sensitivity Analysis

#### 3.3. DRF-Based Sensitivity Analysis

#### 3.4. SS-ANOVA Sensitivity Analysis

## 4. Sensitivity Analysis Results

#### 4.1. PCE-Based Sensitivity Analysis Results

#### 4.2. DRF-Based Sensitivity Analysis Results

#### 4.3. SS-ANOVA Sensitivity Analysis Results

## 5. Experimental Validation

#### 5.1. Design Selection

#### 5.2. Experimental Setup

#### 5.3. Experimental Procedure

- The four tendons were pretensed to the desired tension using the PID controllers.
- The controller was turned off, and an external load was applied using the Siskiyou micromanipulator.
- The manipulator was loaded by displacing it until reaching the specified distance of 5 mm.
- During the displacement, the external load (measured using the load cell attached to the micromanipulator) and the manipulator displacement (measured using the micromanipulator’s encoder) were continuously recorded.
- Steps 1 to 4 were repeated five times for each design to ensure statistical accuracy and avoid experimental variability or mechanical issues.
- The manipulator stiffness was calculated by determining the slope of the force-versus-displacement graph. To account for the small angular displacement assumption in Model 1, the slope was computed only where the force-versus-displacement graph exhibited a linear relationship.

#### 5.4. Experimental Results

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Kolachalama, S.; Lakshmanan, S. Continuum Robots for Manipulation Applications: A Survey. J. Robot.
**2020**, 2020, 418704. [Google Scholar] [CrossRef] - Dong, X.; Axinte, D.; Palmer, D.; Cobos, S.; Raffles, M.; Rabani, A.; Kell, J. Development of a slender continuum robotic system for on-wing inspection/repair of gas turbine engines. Robot. Comput.-Integr. Manuf.
**2017**, 44, 218–229. [Google Scholar] [CrossRef] [Green Version] - Walker, I.D.; University, C. Use of continuum robots for remote inspection operations. In Proceedings of the 2017 Computing Conference, London, UK, 18–20 July 2017; pp. 1382–1385. [Google Scholar] [CrossRef]
- Wooten, M.; Frazelle, C.; Walker, I.D.; Kapadia, A.; Lee, J.H. Exploration and Inspection with Vine-Inspired Continuum Robots. In Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, QLD, Australia, 21–25 May 2018; pp. 5526–5533. [Google Scholar] [CrossRef]
- Burgner-Kahrs, J.; Rucker, D.C.; Choset, H. Continuum Robots for Medical Applications: A Survey. IEEE Trans. Robot.
**2015**, 31, 1261–1280. [Google Scholar] [CrossRef] - Rodrigues, S.P.; Wever, A.M.; Dankelman, J.; Jansen, F.W. Risk factors in patient safety: Minimally invasive surgery versus conventional surgery. Surg. Endosc.
**2012**, 26, 350–356. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gandaglia, G.; Ghani, K.R.; Sood, A.; Meyers, J.R.; Sammon, J.D.; Schmid, M.; Varda, B.; Briganti, A.; Montorsi, F.; Sun, M.; et al. Effect of Minimally Invasive Surgery on the Risk for Surgical Site Infections: Results From the National Surgical Quality Improvement Program (NSQIP) Database. JAMA Surg.
**2014**, 149, 1039. [Google Scholar] [CrossRef] - McCarrel, T.M.; Woodie, J.B. Update on Laryngeal Disorders and Treatment. Vet. Clin. N. Am. Equine Pract.
**2015**, 31, 13–26. [Google Scholar] [CrossRef] - Peretti, G.; Piazza, C.; Penco, S.; Santori, G.; Del Bon, F.; Garofolo, S.; Paderno, A.; Guastini, L.; Nicolai, P. Transoral Laser Microsurgery as Primary Treatment for Selected T3 Glottic and Supraglottic Cancers: Transoral Laser Microsurgery for T3 Laryngeal Cancer. Head Neck
**2016**, 38, 1107–1112. [Google Scholar] [CrossRef] - Canis, M.; Ihler, F.; Martin, A.; Wolff, H.A.; Matthias, C.; Steiner, W. Results of 226 Patients with T3 Laryngeal Carcinoma after Treatment with Transoral Laser Microsurgery: Laryngeal Carcinoma after Transoral Laser Microsurgery. Head Neck
**2014**, 36, 652–659. [Google Scholar] [CrossRef] - Wang, S.; Li, Q.; Ding, J.; Zhang, Z. Kinematic Design for Robot-Assisted Laryngeal Surgery Systems. In Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, 9–15 October 2006; pp. 2864–2869. [Google Scholar] [CrossRef]
- Chauhan, M.; Deshpande, N.; Barresi, G.; Pacchierotti, C.; Prattichizzo, D.; Caldwell, D.G.; Mattos, L.S. Design and control of a novel robotic microsurgical forceps for Transoral Laser Microsurgery. In Proceedings of the 2017 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Munich, Germany, 3–7 July 2017; pp. 737–742. [Google Scholar] [CrossRef] [Green Version]
- Chauhan, M.; Deshpande, N.; Caldwell, D.G.; Mattos, L.S. Design and Modeling of a Three-Degree-of-Freedom Articulating Robotic Microsurgical Forceps for Trans-Oral Laser Microsurgery. J. Med. Devices
**2019**, 13, 021006. [Google Scholar] [CrossRef] - Piccigallo, M.; Scarfogliero, U.; Quaglia, C.; Petroni, G.; Valdastri, P.; Menciassi, A.; Dario, P. Design of a Novel Bimanual Robotic System for Single-Port Laparoscopy. IEEE/ASME Trans. Mechatron.
**2010**, 15, 5604317. [Google Scholar] [CrossRef] [Green Version] - Lee, H.; Choi, Y.; Yi, B.J. Stackable 4-BAR Manipulators for Single Port Access Surgery. IEEE/ASME Trans. Mechatron.
**2012**, 17, 157–166. [Google Scholar] [CrossRef] - He, X.; van Geirt, V.; Gehlbach, P.; Taylor, R.; Iordachita, I. IRIS: Integrated Robotic Intraocular Snake. In Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 26–30 May 2015; pp. 1764–1769. [Google Scholar] [CrossRef] [Green Version]
- Kim, K.; Woo, H.; Suh, J. Design and Evaluation of a Continuum Robot with Discreted Link Joints for Cardiovascular Interventions. In Proceedings of the 2018 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (Biorob), Enschede, The Netherlands, 26–29 August 2018; pp. 627–633. [Google Scholar] [CrossRef]
- Suh, J.W.; Kim, K.Y.; Jeong, J.W.; Lee, J.J. Design Considerations for a Hyper-Redundant Pulleyless Rolling Joint With Elastic Fixtures. IEEE/ASME Trans. Mechatron.
**2015**, 20, 2841–2852. [Google Scholar] [CrossRef] - Kim, Y.J.; Cheng, S.; Kim, S.; Iagnemma, K. A Stiffness-Adjustable Hyperredundant Manipulator Using a Variable Neutral-Line Mechanism for Minimally Invasive Surgery. IEEE Trans. Robot.
**2014**, 30, 382–395. [Google Scholar] [CrossRef] [Green Version] - Hwang, M.; Kwon, D.S. K-FLEX: A Flexible Robotic Platform for Scar-free Endoscopic Surgery. Int. J. Med. Robot. Comput. Assist. Surg.
**2020**, 16, e2078. [Google Scholar] [CrossRef] [PubMed] - Liu, N.; Abdelaziz, M.E.M.K.; Shen, M.; Yang, G.Z. Design and Kinematics Characterization of a Laser-Profiled Continuum Manipulator for the Guidance of Bronchoscopic Instruments. In Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, QLD, Australia, 21–25 May 2018; pp. 25–31. [Google Scholar] [CrossRef]
- Harada, K.; Bo, Z.; Enosawa, S.; Chiba, T.; Fujie, M.G. Bending Laser Manipulator for Intrauterine Surgery and Viscoelastic Model of Fetal Rat Tissue. In Proceedings of the 2007 IEEE International Conference on Robotics and Automation, Rome, Italy, 10–14 April 2007; pp. 611–616. [Google Scholar] [CrossRef]
- Wang, Y.; Cao, Q.; Zhu, X.; Wang, P. A cable-driven distal end-effector mechanism for single-port robotic surgery. Int. J. Comput. Assist. Radiol. Surg.
**2021**, 16, 301–309. [Google Scholar] [CrossRef] [PubMed] - Dewaele, F.; Kalmar, A.F.; De Ryck, F.; Lumen, N.; Williams, L.; Baert, E.; Vereecke, H.; Kalala Okito, J.P.; Mabilde, C.; Blanckaert, B.; et al. A Novel Design for Steerable Instruments Based on Laser-Cut Nitinol. Surg. Innov.
**2014**, 21, 303–311. [Google Scholar] [CrossRef] - Swaney, P.J.; York, P.A.; Gilbert, H.B.; Burgner-Kahrs, J.; Webster, R.J. Design, Fabrication, and Testing of a Needle-Sized Wrist for Surgical Instruments. J. Med. Devices
**2017**, 11, 014501. [Google Scholar] [CrossRef] [Green Version] - Eastwood, K.W.; Azimian, H.; Carrillo, B.; Looi, T.; Naguib, H.E.; Drake, J.M. Kinetostatic Design of Asymmetric Notch Joints for Surgical Robots. In Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Republic of Korea, 9–14 October 2016; pp. 2381–2387. [Google Scholar] [CrossRef]
- Baykal, C.; Torres, L.G.; Alterovitz, R. Optimizing Design Parameters for Sets of Concentric Tube Robots Using Sampling-Based Motion Planning. In Proceedings of the 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, 28 September–2 October 2015; pp. 4381–4387. [Google Scholar] [CrossRef] [Green Version]
- Dupont, P.; Lock, J.; Itkowitz, B.; Butler, E. Design and Control of Concentric-Tube Robots. IEEE Trans. Robot.
**2010**, 26, 209–225. [Google Scholar] [CrossRef] [Green Version] - Swaney, P.J.; Mahoney, A.W.; Hartley, B.I.; Remirez, A.A.; Lamers, E.; Feins, R.H.; Alterovitz, R.; Webster, R.J. Toward Transoral Peripheral Lung Access: Combining Continuum Robots and Steerable Needles. J. Med. Robot. Res.
**2017**, 02, 1750001. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gifari, M.W.; Naghibi, H.; Stramigioli, S.; Abayazid, M. A Review on Recent Advances in Soft Surgical Robots for Endoscopic Applications. Int. J. Med. Robot. Comput. Assist. Surg.
**2019**, 15, e2010. [Google Scholar] [CrossRef] - Runciman, M.; Darzi, A.; Mylonas, G.P. Soft Robotics in Minimally Invasive Surgery. Soft Robot.
**2019**, 6, 423–443. [Google Scholar] [CrossRef] [Green Version] - Suh, J.W.; Lee, J.J.; Kwon, D.S. Underactuated miniature bending joint composed of serial pulleyless rolling joints. Adv. Robot.
**2013**, 28, 1–14. [Google Scholar] [CrossRef] - Kim, H.; You, J.M.; Hwang, M.; Kyung, K.U.; Kwon, D.S. Sigmoidal Auxiliary Tendon-Driven Mechanism Reinforcing Structural Stiffness of Hyper-Redundant Manipulator for Endoscopic Surgery. Soft Robot.
**2023**, 10, 234–245. [Google Scholar] [CrossRef] [PubMed] - You, J.M.; Kim, H.; Kim, J.; Kwon, D.S. Design and Analysis of High-Stiffness Hyperredundant Manipulator with Sigma-Shaped Wire Path and Rolling Joints. IEEE Robot. Autom. Lett.
**2021**, 6, 7357–7364. [Google Scholar] [CrossRef] - Hwang, M.; Kwon, D.S. Strong Continuum Manipulator for Flexible Endoscopic Surgery. IEEE/ASME Trans. Mechatron.
**2019**, 24, 2193–2203. [Google Scholar] [CrossRef] - Zuo, S.; Iijima, K.; Tokumiya, T.; Masamune, K. Variable stiffness outer sheath with “Dragon skin” structure and negative pneumatic shape-locking mechanism. Int. J. Comput. Assist. Radiol. Surg.
**2014**, 9, 857–865. [Google Scholar] [CrossRef] - Chung, D.G.; Kim, J.; Baek, D.; Kim, J.; Kwon, D.S. Shape-Locking Mechanism of Flexible Joint Using Mechanical Latch with Electromagnetic Force. IEEE Robot. Autom. Lett.
**2019**, 4, 2661–2668. [Google Scholar] [CrossRef] - Lee, D.H.; Hwang, M.; Kim, J.; Kwon, D.S. Payload optimization of surgical instruments with rolling joint mechanisms. In Proceedings of the 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA, 24 October 2020–24 January 2021; pp. 3131–3136. [Google Scholar] [CrossRef]
- Berthet-Rayne, P.; Leibrandt, K.; Kim, K.; Seneci, C.A.; Shang, J.; Yang, G.Z. Rolling-Joint Design Optimization for Tendon Driven Snake-Like Surgical Robots. In Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain, 1–5 October 2018; pp. 4964–4971. [Google Scholar] [CrossRef]
- Wagenmakers, E.J.; Sarafoglou, A.; Aczel, B. One statistical analysis must not rule them all. Nature
**2022**, 605, 423–425. [Google Scholar] [CrossRef] - Saltelli, A.; Ratto, M.; Andres, T.; Campolongo, F.; Cariboni, J.; Gatelli, D.; Saisana, M.; Tarantola, S. Global Sensitivity Analysis: The Primer; John Wiley & Sons: Hoboken, NJ, USA, 2008. [Google Scholar]
- Gkikakis, A.E. Mechanism and Behaviour Co-Optimisation of High Performance Mobile Robots. Ph.D. Thesis, University of Genoa, Genoa, Italy, 2021. [Google Scholar] [CrossRef]
- Esteco. ModeFrontier2021R2. 2021. Available online: https://www.esteco.com/modefrontier (accessed on 15 May 2023).
- Sudret, B. Global sensitivity analysis using polynomial chaos expansions. Reliab. Eng. Syst. Saf.
**2008**, 93, 964–979. [Google Scholar] [CrossRef] - Breiman, L. Random Forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef] [Green Version] - Gu, C. Smoothing Spline ANOVA Models; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013; Volume 297. [Google Scholar]
- Gkikakis, A.E.; Featherstone, R. Robust Analysis for Mechanism and Behavior Co-optimization of High-performance Legged Robots. In Proceedings of the 2022 IEEE-RAS 21st International Conference on Humanoid Robots (Humanoids), Ginowan, Japan, 28–30 November 2022; pp. 752–758. [Google Scholar] [CrossRef]

**Figure 1.**Traditional TLM setup and workspace (used with permission from [12] © IEEE).

**Figure 2.**Rolling joint manipulator: (

**a**) rolling joint manipulator with N = 2; (

**b**) link—side view; (

**c**) link—top view.

**Figure 4.**Sensitivity analysis for Model 1 (Section 2) using three different approaches. The bar-chart plots show the contribution (height of each box) of each factor (x-axis) to the total variance of the stiffness. For each plot, the cumulative sum of the variables in the x-axis equals one. Image (

**c**) also shows the second-order interaction effects. (

**a**) Polynomial chaos expansion-based analysis; (

**b**) distributed random forest-based analysis; (

**c**) smoothing spline analysis of variance sensitivity analysis.

**Figure 5.**Sensitivity analysis for Model 2 (Section 2) using three different approaches. The bar-chart plots show the contribution (height of each box) of each factor (x-axis) to the total variance of the stiffness. For each plot, the cumulative sum of the variables in the x-axis equals one. Image (

**c**) also shows the second-order interaction effects. (

**a**) Polynomial chaos expansion-based analysis; (

**b**) distributed random forest-based analysis; (

**c**) smoothing spline analysis of variance sensitivity analysis.

**Figure 7.**Experimental results—stiffness variation as a function of each design parameter: (

**a**) stiffness versus tension (T); (

**b**) stiffness versus the number of joints N; (

**c**) stiffness versus radius of contact (R); (

**d**) stiffness versus disk thickness (H).

DoF | Discrete | Hyper-Redundant | Continuum | ||
---|---|---|---|---|---|

Material | Hard | Hard | Hard (Continuum) | Soft | |

Actuation | Link-based embedded actuator [14,15] | Tendon-driven hyper-redundant [16,17,18,19,20,21,22,23] | Tendon-driven continuum [24,25,26] | Concentric tube [27,28,29] | SMA tendon electric charges chemical pressurized fluids [30,31] |

Pros | High accuracy, more DoF, high load capacity | Miniaturization, easy control, compliance, variable stiffness | Miniaturization, easy control, compliance, minimal assembly | Miniaturization | High compliance, low weight, high dexterity |

Cons | Low compliance, hard to miniaturize, complex control | Friction, complex assembly | Friction, short life cycle | Unstable, hard to control, friction, planning required | Low accuracy, low load capacity, difficult to control |

Design Variable | Description |
---|---|

N | Number of joints |

R | Radius of contact (mm) |

d | Distance between the central axis and the wire hole (mm) |

H | Disk thickness (mm) |

T | Tendon tension (N) |

$\alpha $ | Half angle, $sin\left(\alpha \right)=\frac{d}{R}$ (rad) |

B | Height of the wire hole: $B=R-\sqrt{{R}^{2}-{d}^{2}}$ (mm) |

Property | Model 1 | Model 2 |
---|---|---|

Reference | Hwang and Kwon [20] | Kim et al. [19] |

Diagram | Figure 3a | Figure 3b |

Assumptions | Tendons fixed at the end; small displacement | Tendon tension maintained; small displacement |

Equations | ${\int}_{o}^{h}F\phantom{\rule{4pt}{0ex}}dh={T}_{o}{\sum}_{1}^{4}\Delta L+\frac{1}{2}{k}_{T}{\sum}_{1}^{4}\Delta {L}^{2}$, where ${T}_{o}$ = initial tension in the tendon and $\Delta L$ = change in tendon length | ${\int}_{o}^{h}F\phantom{\rule{4pt}{0ex}}dh=T\Delta {L}_{p}+T\Delta {L}_{t}$, where T = total tendon tension (pan or tilt) and $\Delta {L}_{p}/\Delta {L}_{t}$ = change in tendon length pan/tilt |

Design Variable | Description | Bounds |
---|---|---|

N | Number of joints | $[3,\phantom{\rule{0.166667em}{0ex}}20]$ |

R | Radius of contact (mm) | $[3,\phantom{\rule{0.166667em}{0ex}}20]$ |

d | Distance between the central axis and the wire hole (mm) | $[0.5,\phantom{\rule{0.166667em}{0ex}}1.5]$ |

H | Disk thickness (mm) | $[1,\phantom{\rule{0.166667em}{0ex}}5]$ |

${\mathrm{T}}_{0}$ | Initial tension (N) | $[0.1,\phantom{\rule{0.166667em}{0ex}}5]$ |

Name | Model 1 | Model 2 | Description |
---|---|---|---|

RSS | $0.101$ | $0.025$ | Residual sum of squares, reflecting the goodness of fit |

Name | Model 1 | Model 2 | Description |
---|---|---|---|

R${}^{2}$ | $0.525$ | $0.432$ | Goodness of fit |

Name | Model 1 | Model 2 | Description |
---|---|---|---|

R${}^{2}$ | $0.738$ | $0.726$ | Goodness of fit |

Stiffness vs. T | Stiffness vs. N | Stiffness vs. R | Stiffness vs. H | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Tension (N) | 2.45 | 4.9 | 7.35 | 9.8 | 4.9 | 4.9 | 4.9 | |||||||||

N | 7 | 4 | 5 | 6 | 7 | 7 | 7 | |||||||||

R (mm) | 18 | 18 | 12 | 18 | 24 | 30 | 18 | |||||||||

H (mm) | 4.5 | 4.5 | 4.5 | 4.5 | 5.25 | 6 | 6.75 | |||||||||

d (mm) | 4.5 | 4.5 | 4.5 | 4.5 |

Sr | Design | Exp_1 | Exp_2 | Exp_3 | Exp_4 | Exp_5 | Mean | Stddev | Model | % Error |
---|---|---|---|---|---|---|---|---|---|---|

1 | Stiffness vs. R (with R = 12) | 0.171 | 0.196 | 0.212 | 0.176 | 0.213 | 0.194 | 0.020 | 0.217 | 10.931 |

2 | Stiffness vs. R (with R = 18) | 0.281 | 0.293 | 0.302 | 0.315 | 0.322 | 0.303 | 0.016 | 0.336 | 10.051 |

3 | Stiffness vs. R (with R = 24) | 0.374 | 0.392 | 0.402 | 0.410 | 0.422 | 0.400 | 0.018 | 0.452 | 11.440 |

4 | Stiffness vs. R (with R = 30) | 0.461 | 0.465 | 0.488 | 0.497 | 0.507 | 0.484 | 0.020 | 0.578 | 16.273 |

5 | Stiffness vs. N (with N = 4) | 1.316 | 1.312 | 1.364 | 1.362 | 1.332 | 1.337 | 0.025 | 1.824 | 26.692 |

6 | Stiffness vs. N (with N = 5) | 0.828 | 0.851 | 0.859 | 0.866 | 0.864 | 0.853 | 0.015 | 1.084 | 21.290 |

7 | Stiffness vs. N (with N = 6) | 0.491 | 0.487 | 0.504 | 0.506 | 0.503 | 0.498 | 0.009 | 0.563 | 11.592 |

8 | Stiffness vs. N (with N = 7) | 0.281 | 0.293 | 0.302 | 0.315 | 0.322 | 0.303 | 0.016 | 0.336 | 10.051 |

9 | Stiffness vs. H (with H = 4.5) | 0.281 | 0.293 | 0.302 | 0.315 | 0.322 | 0.303 | 0.016 | 0.336 | 10.051 |

10 | Stiffness vs. H (with H = 5.25) | 0.187 | 0.214 | 0.212 | 0.209 | 0.206 | 0.206 | 0.011 | 0.240 | 14.269 |

11 | Stiffness vs. H (with H = 6) | 0.148 | 0.150 | 0.160 | 0.166 | 0.157 | 0.156 | 0.007 | 0.181 | 13.804 |

12 | Stiffness vs. H (with H = 6.75) | 0.138 | 0.143 | 0.150 | 0.142 | 0.139 | 0.142 | 0.005 | 0.142 | 0.688 |

13 | Stiffness vs. T (with T = 2.45) | 0.194 | 0.191 | 0.194 | 0.195 | 0.198 | 0.195 | 0.003 | 0.180 | 8.324 |

14 | Stiffness vs. T (with T = 4.9) | 0.281 | 0.293 | 0.302 | 0.315 | 0.322 | 0.303 | 0.016 | 0.336 | 10.051 |

15 | Stiffness vs. T (with T = 7.35) | 0.419 | 0.432 | 0.405 | 0.389 | 0.397 | 0.408 | 0.018 | 0.492 | 17.023 |

16 | Stiffness vs. T (with T = 9.8) | 0.445 | 0.524 | 0.532 | 0.536 | 0.558 | 0.519 | 0.043 | 0.649 | 20.053 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sawant, K.; Gkikakis, A.E.; Mattos, L.S.
Investigating the Stiffness Characteristics of a Tendon-Driven Continuum Manipulator Using Sensitivity Analysis: A Case Study in Transoral Laser Microsurgery. *Machines* **2023**, *11*, 662.
https://doi.org/10.3390/machines11060662

**AMA Style**

Sawant K, Gkikakis AE, Mattos LS.
Investigating the Stiffness Characteristics of a Tendon-Driven Continuum Manipulator Using Sensitivity Analysis: A Case Study in Transoral Laser Microsurgery. *Machines*. 2023; 11(6):662.
https://doi.org/10.3390/machines11060662

**Chicago/Turabian Style**

Sawant, Kapil, Antonios E. Gkikakis, and Leonardo S. Mattos.
2023. "Investigating the Stiffness Characteristics of a Tendon-Driven Continuum Manipulator Using Sensitivity Analysis: A Case Study in Transoral Laser Microsurgery" *Machines* 11, no. 6: 662.
https://doi.org/10.3390/machines11060662