# The Symmetric Nature of the Position Distribution of the Human Body Center of Gravity during Propelling Manual Wheelchairs with Innovative Propulsion Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{i}(Figure 3), which enabled the measurement of reaction forces R

_{i}which was the effect of loading the scale with the wheelchair, including a man.

_{i}, based on which, with the defined distances between strain gauge scales (L, H), the position of the human body center of gravity was determined f

_{ij}(1–4) by the rotational balance on four planes π

_{1}–π

_{4}in relation to the coordinate system from originating in the scale W

_{1}(Figure 4 and Figure 5).

_{ij}(Figure 4), they were marked on the sides of the rectangle drawn on the plan of the locations of the strain gauges W

_{i}, which are also the points of application of the reaction forces R

_{i}. Then two straight lines were drawn through the points Pi marked on the sides of the right angle. These lines intersected at one point on the horizontal XY plane (Figure 5). The x (5) and y (6) coordinates of this point are the searched position of the center of gravity of the human body CG.

_{COG}and y

_{COG}, semi-axis a, semi-axis b and the ellipse inclination angle α (Figure 6). The position of the ellipse center was determined by calculating the average value of the coordinate x and y of the points measured. The semi-axis length α constituted the double value of the standard deviation (2σ) of the coordinate x of the points measured, whereas, as far as the semi-axis b is concerned, its length corresponding to the double standard deviation (2σ) of the coordinate y of the points measured. Assuming the ellipse dimensions as the double standard deviation ensured the ellipse covering 95.4% of all the points measured. The ellipse inclination α corresponded to the inclination of the trend line determined based on all the measured points [5,18].

## 3. Results

## 4. Discussion

## 5. Conclusions

## 6. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Dimensions of the areas of variability in the position of the center of gravity of individual patients during the operation of a wheelchair with a multispeed drive for three angles of inclination of the wheelchair k.

**Figure A2.**Dimensions of the areas of variation in the position of the center of gravity of individual patients during the operation of the wheelchair with a hybrid drive for three inclination angles of the wheelchair k. Patient 2 refused to perform the test for the angle of inclination k = 14°.

**Figure A3.**Dimensions of the areas of variability in the position of the center of gravity of individual patients during the operation of a wheelchair with a classic drive for three angles of inclination of the wheelchair k.

## References

- Smith, E.M.; Mortenson, W.B.; Mihailidis, A.; Miller, W.C. Understanding the task demands for powered wheelchair driving: A think-aloud task analysis. Disabil. Rehabil. Assist. Technol.
**2020**, 1–8. [Google Scholar] [CrossRef] [PubMed] - Veeger, E.H.; Van Der Woude, L.H.; Rozendal, R.H. Effect of handrim velocity on mechanical efficiency in wheelchair propulsion. Med. Sci. Sports Exerc.
**1992**, 24, 100–107. [Google Scholar] [CrossRef] [PubMed] - Coutts, K.D. Kinematics of sport wheelchair propulsion. J. Rehabil. Res. Dev.
**1990**, 27, 21–26. [Google Scholar] [CrossRef] [PubMed] - Mulroy, S.J.; Gronley, J.K.; Newsam, C.J.; Perry, J. Electromyographic activity of shoulder muscles during wheelchair propulsion by paraplegic persons. Arch. Phys. Med. Rehabil.
**1996**, 77, 187–193. [Google Scholar] [CrossRef] - Wieczorek, B.; Kukla, M.; Warguła, Ł. Methods for measuring the position of the centre of gravity of an anthropotechnic human-wheelchair system in dynamic conditions. Mater. Sci. Eng. Conf. Ser.
**2020**, 776, 012062. [Google Scholar] [CrossRef] - Chien, C.-S.; Huang, T.-Y.; Liao, T.-Y.; Kuo, T.-Y.; Lee, T.-M. Design and development of solar power-assisted manual/electric wheelchair. J. Rehabil. Res. Dev.
**2014**, 51, 1411–1426. [Google Scholar] [CrossRef] - Boninger, M.L.; Souza, A.L.; Cooper, R.A.; Fitzgerald, S.G.; Koontz, A.M.; Fay, B.T. Propulsion patterns and pushrim biomechanics in manual wheelchair propulsion. Arch. Phys. Med. Rehabil.
**2002**, 83, 718–723. [Google Scholar] [CrossRef] - Vanlandewijck, Y.C.; Theisen, D.; Daly, D. Wheelchair Propulsion Biomechanics. Sports Med.
**2001**, 31, 339–367. [Google Scholar] [CrossRef] - Mâsse, L.C.; Lamontagne, M.; O’Riain, M.D. Biomechanical analysis of wheelchair propulsion for various seating positions. J. Rehabil. Res. Dev.
**1992**, 29, 12–28. [Google Scholar] [CrossRef] [Green Version] - Russell, I.M.; Wagner, E.; Requejo, P.; Mulroy, S.; Flashner, H.; McNitt-Gray, J. Characterization of the shoulder net joint moment during manual wheelchair propulsion using four functional axes. J. Electromyogr. Kinesiol.
**2019**, 102340. [Google Scholar] [CrossRef] - Koontz, A.M.; Roche, B.M.; Collinger, J.L.; Cooper, R.A.; Boninger, M.L. Manual Wheelchair Propulsion Patterns on Natural Surfaces During Start-Up Propulsion. Arch. Phys. Med. Rehabil.
**2009**, 90, 1916–1923. [Google Scholar] [CrossRef] [PubMed] - Kirby, R.L.; Sampson, M.T.; Thoren, A.F.; Macleod, A.D. Wheelchair stability: Effect of body position. J. Rehabil. Res. Dev.
**1995**, 32, 367–372. [Google Scholar] [PubMed] - Soltau, S.L.; Slowik, J.S.; Requejo, P.S.; Mulroy, S.J.; Neptune, R.R. An Investigation of Bilateral Symmetry During Manual Wheelchair Propulsion. Front. Bioeng. Biotechnol.
**2015**, 3, 86. [Google Scholar] [CrossRef] [PubMed] - Goosey, V.L. Symmetry of the elbow kinematics during racing wheelchair propulsion. Ergonomics
**1998**, 41, 1810–1820. [Google Scholar] [CrossRef] [PubMed] - Wieczorek, B.; Warguła, Ł.; Rybarczyk, D. Impact of a Hybrid Assisted Wheelchair Propulsion System on Motion Kinematics during Climbing up a Slope. Appl. Sci.
**2020**, 10, 1025. [Google Scholar] [CrossRef] [Green Version] - Wieczorek, B.; Warguła, Ł. Problems of dynamometer construction for wheelchairs and simulation of push motion. MATEC Web Conf.
**2019**, 254, 01006. [Google Scholar] [CrossRef] - Van Der Woude, L.H.V.; Veeger, H.E.J.; Rozendal, R.H.; Sargeant, A.J. Optimum cycle frequencies in hand-rim wheelchair propulsion. Graefe’s Arch. Clin. Exp. Ophthalmol.
**1989**, 58, 625–632. [Google Scholar] [CrossRef] - Wieczorek, B.; Kukla, M. Effects of the performance parameters of a wheelchair on the changes in the position of the centre of gravity of the human body in dynamic condition. PLoS ONE
**2019**, 14, e0226013. [Google Scholar] [CrossRef] - Zhang, R.; Vogler, C.; Metaxas, D. Human gait recognition at sagittal plane. Image Vis. Comput.
**2007**, 25, 321–330. [Google Scholar] [CrossRef] - Finley, M.A.; Rasch, E.K.; Keyser, R.E.; Rodgers, M.M. The biomechanics of wheelchair propulsion in individuals with and without upper-limb impairment. J. Rehabil. Res. Dev.
**2004**, 41, 385. [Google Scholar] [CrossRef] - Goosey-Tolfrey, V.L.; Vegter, R.J.K.; Mason, B.S.; Paulson, T.A.W.; Lenton, J.P.; Van Der Scheer, J.W.; Van Der Woude, L.H. Sprint performance and propulsion asymmetries on an ergometer in trained high- and low-point wheelchair rugby players. Scand. J. Med. Sci. Sports
**2018**, 28, 1586–1593. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gutierrez-Farewik, E.M.; Alm, M.; Hultling, C.; Saraste, H. Measuring seating pressure, area, and asymmetry in persons with spinal cord injury. Eur. Spine J.
**2003**, 13, 374–379. [Google Scholar] - Cooper, R.A.; Boninger, M.L.; Shimada, S.D.; Lawrence, B.M. Glenohumeral joint kinematics and kinetics for three coordinate system representations during wheelchair propulsion. Am. J. Phys. Med. Rehabil.
**1999**, 78, 435–446. [Google Scholar] [CrossRef] [PubMed] - Mulroy, S.J.; Newsam, C.J.; Gutierrez, D.D.; Requejo, P.; Gronley, J.K.; Haubert, L.L.; Perry, J. Effect of Fore-Aft Seat Position on Shoulder Demands During Wheelchair Propulsion: Part 1. A Kinetic Analysis. J. Spinal Cord Med.
**2005**, 28, 214–221. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Time-lapse photos depicting the change of the human body position in the push phase (

**A**) and return phase (

**B**). The dashed green line shows the hand trajectory during its contact with the pushrim; the dashed red line shows the hand trajectory during free return movement.

**Figure 2.**Wheelchairs used during the tests: hybrid manual-electric (

**A**), multispeed with the planetary transmission (

**B**), typical semi-active with the pushrim drive (

**C**); where: 1—pushrims, 2—BLCD (brushless DC motor) electric motor embedded in the hub, 3—planetary transmission embedded in the hub, 4—drive wheel.

**Figure 3.**The used test stand with the indicated strain gauge scales W

_{1}–W

_{2}and the force of reactions in the scale supports R

_{1}–R

_{2}.

**Figure 4.**The outline specifying the data required for determining the position of the center of gravity, where $CG$—the center of gravity of the human body, π

_{i}—one of four side planes, R

_{1}, R

_{2}, R

_{3}, R

_{4}—a reaction in the scale support, f

_{ij}—the position of the center of gravity on one of the side planes, L—scale length, H—scale width. For the used model R

_{x}= 0 and R

_{y}= 0.

**Figure 5.**The scheme of the method for determining the location of the center of gravity on the XY horizontal plane, the description of symbols is given in the text.

**Figure 6.**The outline which illustrates drawing the ellipse determining the position variability of the human body center of gravity based on the measured points of the position of the center of gravity in the exemplary test sample.

**Figure 7.**An example of the ellipse decomposition depicting the variability of the human body center of gravity (

**A**) on the ellipse geometry (

**B**), ellipse center position $COG$ (

**C**), and the ellipse inclination angle (

**D**).

**Figure 8.**The outline of the positioning of the analyzed ellipses within the tested patient body, where: a—ellipse which is the variability area of the position of the human body center of gravity, b—ellipse center, c—directional line, d—measured positions of the human body center of gravity during the measurement test.

**Figure 9.**The graphs of the ellipse directional lines, depending on the wheelchair inclination angle k for (

**a**) wheelchair with the multispeed manual propulsion system, (

**b**) hybrid propulsion system, (

**c**) typical manual propulsion, where α

_{k=0}

_{°}—directional line inclination angle during propelling the wheelchair inclined at 0°, α

_{k=7}

_{°}—directional line inclination angle during propelling the wheelchair inclined at 7°, α

_{k=14}

_{°}directional line inclination angle during propelling the wheelchair inclined at 14°.

**Figure 10.**The ellipse diagrams describing the variability of the position of the human body center of gravity depending on the wheelchair inclination angle k for (

**a**) wheelchair with multispeed manual propulsion system, (

**b**) hybrid propulsion system, (

**c**) typical manual propulsion system, where α

_{k=0}

_{°}—the length of the semi-axis in the directional axis during propelling the wheelchair inclined at 0°, α

_{k=7}

_{°}—the length of the semi-axis in the directional axis during propelling the wheelchair inclined at 7°, α

_{k=14}

_{°}—the length of the semi-axis in the directional axis during propelling the wheelchair inclined at 14°, b

_{k=0}

_{°}—the length of the semi-axis perpendicular to the directional axis during propelling the wheelchair inclined at 0°, b

_{k=0}

_{°}—the length of the semi-axis perpendicular to the directional axis during propelling the wheelchair inclined at 7°, b

_{k=0}

_{°}—the length of the semi-axis perpendicular to the directional axis during propelling the wheelchair inclined at 14°.

**Figure 11.**The diagrams of the position of the ellipse center describing the position variability of the human body center of gravity depending on the wheelchair inclination angle k for (

**a**) wheelchair with multispeed manual propulsion system, (

**b**) hybrid propulsion system, (

**c**) typical manual propulsion system, where x

_{k=0}

_{°}and y

_{k=0}

_{°}—the coordinates of the position of the ellipse center during propelling the wheelchair inclined at 0°, where x

_{k=7}

_{°}and y

_{k=7}

_{°}—the coordinates of the position of the ellipse center during propelling the wheelchair inclined at 7°, where x

_{k=14}

_{°}and y

_{k=14}

_{°}—the coordinates of the position of the ellipse center during propelling the wheelchair inclined at 14°.

**Table 1.**Comparison of anthropometric features and the level of experience in wheelchair operation of the test subjects.

Patient No. | Height | Weight | Age | Push Force ^{2} | Experience ^{1} |
---|---|---|---|---|---|

(-) | cm | kg | years | N | (–) |

Patient 1 | 186 | 88.4 | 32 | 315 | ●●●●● |

Patient 2 | 176 | 60.8 | 27 | 244 | ●●●●○ |

Patient 3 | 186 | 79.4 | 34 | 282 | ●●●○○ |

^{1}qualitative assessment of the driving skills of the wheelchair, where the ○ representing the user’s first contact with the manual drive.

^{2}right limb repulsion force, all patients declared right-handedness. ● qualitative assessment of the driving skills of the wheelchair, where the ○ representing the user’s first contact with the manual drive.

**Table 2.**The comparison of the ellipse parameters describing the variability area of the position of the human body center of gravity during propelling the wheelchair with the multispeed propulsion system; where: a—the length of the semi-axis parallel to the direction of the trunk movements, b—the length of the semi-axis perpendicular to the direction of the trunk movements, α—the ellipse inclination angle in relation to the human body sagittal plane, x and y—the coordinates of the position of the ellipse center in relation to the rotation axis center of the wheelchair drive wheels.

k = 0° | k = 7° | k = 14° | M | Δ | ||
---|---|---|---|---|---|---|

a | (mm) | 91.89 | 107.65 | 126.05 | 108.53 | 17.08 |

b | (mm) | 29.75 | 36.57 | 39.02 | 35.11 | 4.63 |

α | (°) | −8.27 | −5.10 | −7.40 | −6.92 | 2.73 |

x | (mm) | 182.27 | 113.37 | 47.90 | 114.51 | 67.19 |

y | (mm) | −10.82 | −15.90 | −4.87 | −10.53 | 8.05 |

**Table 3.**The comparison of the ellipse parameters describing the variability area of the position of the human body center of gravity during propelling the wheelchair with the hybrid propulsion system; where: a—the length of the semi-axis parallel to the direction of the trunk movements, b—the length of the semi-axis perpendicular to the direction of the trunk movements, α—the ellipse inclination angle in relation to the human body sagittal plane, x and y—the coordinates of the position of the ellipse center in relation to the rotation axis center of the wheelchair drive wheels.

k = 0° | k = 7° | k = 14° | M | Δ | ||
---|---|---|---|---|---|---|

a | (mm) | 58.22 | 67.99 | 65.99 | 64.07 | 5.89 |

b | (mm) | 43.52 | 30.91 | 27.12 | 33.85 | 8.20 |

α | (°) | 1.99 | −2.22 | −1.45 | −0.56 | 2.49 |

x | (mm) | 319.77 | 244.28 | 171.35 | 245.13 | 74.91 |

y | (mm) | −28.03 | −18.21 | −38.48 | −28.24 | 15.04 |

**Table 4.**The comparison of the ellipse parameters describing the variability area of the position of the human body center of gravity during propelling the wheelchair with the typical propulsion system; where: a—the length of the semi-axis parallel to the direction of the trunk movements, b—the length of the semi-axis perpendicular to the direction of the trunk movements, α—the ellipse inclination angle in relation to the human body sagittal plane, x and y—the coordinates of the position of the ellipse center in relation to the rotation axis center of the wheelchair drive wheels.

k = 0° | k = 7° | k = 14° | M | Δ | ||
---|---|---|---|---|---|---|

a | (mm) | 69.20 | 92.91 | 92.45 | 87.19 | 15.13 |

b | (mm) | 32.75 | 23.88 | 21.49 | 26.04 | 5.63 |

α | (°) | −9.24 | −3.48 | −0.91 | −4.55 | 4.17 |

x | (mm) | 127.52 | 69.73 | 4.84 | 67.36 | 61.34 |

y | (mm) | 12.38 | −16.19 | 4.84 | 0.34 | 24.80 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wieczorek, B.; Kukla, M.; Warguła, Ł.
The Symmetric Nature of the Position Distribution of the Human Body Center of Gravity during Propelling Manual Wheelchairs with Innovative Propulsion Systems. *Symmetry* **2021**, *13*, 154.
https://doi.org/10.3390/sym13010154

**AMA Style**

Wieczorek B, Kukla M, Warguła Ł.
The Symmetric Nature of the Position Distribution of the Human Body Center of Gravity during Propelling Manual Wheelchairs with Innovative Propulsion Systems. *Symmetry*. 2021; 13(1):154.
https://doi.org/10.3390/sym13010154

**Chicago/Turabian Style**

Wieczorek, Bartosz, Mateusz Kukla, and Łukasz Warguła.
2021. "The Symmetric Nature of the Position Distribution of the Human Body Center of Gravity during Propelling Manual Wheelchairs with Innovative Propulsion Systems" *Symmetry* 13, no. 1: 154.
https://doi.org/10.3390/sym13010154