SUGISAKAMASANORI

Journal of Robotics, Networking and Artificial Life
Vol. 9(1); June (2022), pp. 59–65
ISSN (Online): 2352-6386; ISSN (Print): 2405-9021
https://alife-robotics.org/jrnal.html

Research Article

Flexible Bar Geometric Designs for Personalized Knee Orthoses
Inspired by Compliant Mechanisms
Pancho Dachkinov1, Shintaro Kasai1, Kohei Tanaka1, Hiroaki Wagatsuma1,2
Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-Ku, Kitakyushu, 808-0196, JapanRIKEN CBS, Japan

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2

ARTIC LE INFO
Article History
Received 25 November 2021
Accepted 12 March 2022

Keywords
3D Printing
Flexible Bars t
Compliant Mechanisms
Knee Supportive Orthoses
Customized Design

ABSTRACT

Recently, 3D printed compliant mechanisms have been expected not only in engineering purposes,
but also in supportive devices of human motions especially for human joint problems. On theother hand, the establishment of a systematic design principle is the issue to provide an actual
solution for the target body problem, i.e. the personalization. In the present study, we proposed asystematic method to design flexible bars to reduce the burden of the human joint. The proposed
concept was verified in computational analyses and the 3D printer productions were demonstrated
in an actual implementation as prototypes. In computational analyses, larger deformations of thebars were analyzed to absorb the stress occurring a flexing action in joint’s motion. Theoreticalanalysis and experiments were demonstrated its flexibility and support functions during theflexion and extension of the knee motion. It indicates that high importance of the geometricalanalysis of the orthosis design in the sense of compliant mechanisms.

© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

significantly reduces the number of parts to assemble andsolve complex maintenance issues and allows to provide
a simple fabrication and realize an ideal deformation to
execute the target motion.
Thus, a controllable elasticity in the repetitive cycle
motion can be derived from those compliant mechanisms
replying on the geometry and the infill density, andpattern. According to the unique property, compliant
mechanisms can be assured candidates for orthotic
devices applications. The 3D printing compatibility ofthem allows a fine customization with respect torequirements in individual patients.
The rest of this article is structured as follows: Section 2
gives the research background, the methodology fordeveloping various the designs is described in Section 3,
Section 4 explains and summarizes the results, Section 5gives a discussion, Section 6 concludes the paper.

1. Introduction
3D printing methodology is getting to be extended invarious types of additive manufacturing in research
perspectives and applications. According to thosedevelopments, models in the prototyping stage candirectly be tested in the actual field as 3D functional parts.
In this sense, additive manufacturing has been widelyadopted in industries from engineering purposes such as
space engineering and automotive to medical purposes
and arts. With respect to the conventional technology, theproduction process is a high flexibility of the geometry
to maximize the desired function. The mass production
is outdated currently, and a high-mix low-volume
production is expected. The concept of compliant
mechanisms is suitable for such a direction, which

Corresponding author’s E-mail: dachkinov.pancho-nikolaev608@mail.kyutech.jp, kasai.shintaro660@mail.kyutech.jp,
tanaka.kohei886@mail.kyutech.jp, waga@brain.kyutech.ac.jp

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2. Related Work: Compliant Mechanisms

knee flexion and extension if the lateral stability of theknee joint is accursed.

In the viewpoint of flexible materials and its function, thetopology was initially investigated in Murphy et al.
(1996) [1], followed by the related study [2], which
discussed the design of parallel-guiding mechanisms.
Trease et al. (2005) [3] demonstrated a possibility oflarge displacement compliant joints, which is an
important proposal of a revolute and a translational
solution of joints with large range of motion. Jingjun etal. (2009) [4] designed a compliant building block for
micro/nano positioning and related works [5], [6] and [7]presented the design and applications of spread type ofcompliant joint as a cross-spring pivot.
In addition, advancements of the compliant joints
reached the compatibility of the 3D printing materials
and their properties as an issue to be solved in the senseof potential functions of the mechanisms. The 3D printed
structures have a property of deformations, which isderived from a flexible filament with varied relative
density (infill) [8]. Xiao and Gao (2017) [9] discussed
properties and functions in the medical use of TPU
materials. In the orthopedics application of the 3D
printing, orthotic device can be provided as demonstrated
by Chen et al. (2020) [10] and Lin et al. [11] and [12].
Therefore, the methodology of designing for orthotic
devices has further extended in the large medical andsupportive system such as the result of Chaparro-Rico etal. (2021) [13].

Fig. 1. Bar Groups

All bars were provided by using the Fused Deposition
Modeling (FDM) technology on a 3D printer Anycubici3 Mega with a flexible Thermoplastic Polyurethane(TPU) filament called Ninjaflex commercially [14]. The
samples were printed under the same condition andparameter, as shown in Table 1. It shows configurations
for the slicing software Ultimaker Cura. The orientation
for a sample on the 3D printing platform is given in thesame condition, which means that the models are flatwith their surface in the platform. As shown in Table 1,
the samples were printed with infill density of 90% andinfill pattern known as Cross 3D, which was referred by
the description of the slicing software Ultimaker Cura[15]. It suggests that it is a robust infill way for 3D
deformations.
Therefore, the infill density percentage is highly
important related to stiffness of the parts. In principle, thehigher infill density, the stiffer the part is. On the other
hand, when the infill density is getting to be high, thesample becomes heavier as shown in Figure 2. It showsthat the time duration of the printing process grows
linearly up to 90% and it increases significantly at a
100% at last. Therefore, 90% was selected for infill
density in this study to avoid unnecessary processing
time with a certain strength.

3. Methodology
3.1. Flexible Bars and 3D Printing Parameters
Proposed beams were designed in Autodesk Inventor
Professional 2021. In the first place, types were divided
into four groups (A, B, C and D) associated with
common geometrical features. For bars in Group A, thegeometry was changed morphologically from a simple
beam design annotated with 0. In bars in Groups B, C
and D, the geometry was changed to add an additional
beam part in forms of 1) a half regular polygon withdifferent number of the sides, 2) square, 3) hexagon and4) half circle respectively. All bars were designed withthe same length l=160 [mm] and a square cross-section
a=10 [mm]. Thus, the compliant hinging geometry wasvaried depending on the bars. Individual groups with all
bar variations were shown in Figure 1. The dimensionsof given groups were marked on the figure. Once a 3D
printing was completed, the physical pretotypes of thebars can be attached laterally of the knee byimplementing int a cloth bracket. Since the bars aredesigned to match certain requirements as compactness,the supportive function is expected to provide during the60Table 1. 3D printing Processes
Parameter
Values3D printer
Anycubic i3 Mega
Slicing Software
Ultimaker Cura
3D printing
Ninjatek Ninja Flex
Material
TPU Filament
Printing
230 (Recommend for
Temperature [℃]
the material)
Platform
60
Temperature [℃]
Supporting Material
No
Infill Density[%]
90
Infill Type
Cross 3D
Layer Height [mm]0.1
Printing Speed
30[mm/s]

Fig. 3. Loads on the Bars

The results of the Finite Element Analysis (FEA) were
demonstrated by individual deformations of the bars
under the same set of boundary conditions. The beams
having a property to exceed an enough level of thedeformation are suitable for parts of knee assistive
devices.

4. Results
All beam models were analyzed in FEA in the non-linear
static stress environment of Autodesk Inventor Nastran,
where a 3-point bending test as shown in Figure 3. We
focused on the large deformations in a non-linear elastic
material. As shown in Figure 4, all beams were loadedwith the force F=150 [N] in negative Y direction. The
mechanical properties of the material were provided with
the Ninjaflex TPU filament, which has Young’s Modulus
as 12 [MPa], Tensile Strength as 26 [MPa] and PoisonsRatio as 0.35. The computer experiment of each sample
was done with 20 increments. In the present study, thehighest deformation of each beam is the target
phenomenon to investigate and how it works well in thesame loading force, which changes depending on thegeometry. The non-linearities contribute to large
deformations of the model with the anisotropic material.
Figure 4 showed the setup of the analysis and the results
for all models.

Fig. 2. Relationship between the 3D printing Infill Density
and the Printing Duration

The processing time was shown in Figure 2, which wasa case of Group A Bar 0 and other processing time havea similar tendency.
3.2. Load Analysis of the Bars
For sake of the lowest resistance when supporting the
motion in the knee flexion, the bar is bending to provide
a resistance force preventing lateral motion. The fullrange of motion of the human knee joint has to beconsidered to be ranging from fully extended knee as 0°
degree to fully flexed knee at 140° degree. In this sense,
the designed compliant beam needs to provide adeformation in the range. On the other hand, according
to its symmetry, each side of the joint is required todeform at an angle of 70° approximately. In the analysisof the deformation, the samples were tested in non-linear
environment by using Autodesk Inventor Nastran.
The models were illustrated in Figure 3, which represent
with a schematic view of the loading conditions. The
terminal points of the bars were fixed, and a given force
was applied at the middle of the models.

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(a) Group A Bar 0

Table 2. Mechanical Behavior of the Bars
Displacements
Stress 𝝈𝝈𝑴𝑴𝑴𝑴𝑴𝑴
Name∆ [mm][MPa]
Group A Bar 0
33.75
1.684
Group A Bar 1
45.13
6.119
Group A Bar 2
62.73
16.5
Group B Bar 1
30.04
0.7827
Group B Bar 2
39.17
3.996
Group C Bar 1
34.47
1.819
Group C Bar 2
46.58
7.942
Group D Bar 1
35.37
1.806
Group D Bar 2
4.681
0.2599(b) Group A Bar 1(c) Group A Bar 2(d) Group B Bar 1(e) Group B Bar 2(f) Group C Bar 1(g) Group C Bar 2(h) Group D Bar 1

As shown in Figure 5, the samples with highest values ofthe stress and the displacements were analyzed in casesof Group A bars 3, 2 and 4. Lowest values were found insamples from Group B as bars 1 and 3. Similarly, thedisplacements with highest values were observed inGroup A Bar 2 and Group C Bar 2, the lowest was foundin Group D bars 2.
As we expected, the highest deformations were observedin highest levels of the stress in the samples.

Fig. 5. Mechanical Behaviors of the Bars Based on theGeometry

In consideration of the applicability for an orthotic
device, an appropriate balance of the stress and the strain(displacements) relationship is necessary. In this sense,
possible candidates were Group A Bar 2 and Group C
Bar 2 in the set of our designs.
In all beams, force-displacement relationships insimulation were shown in Figure 6, which imply nonlinear behavior of the models. For some beams such asGroup A Bar 0, Group B Bar 1 and Group D Bar 2, theload of 150 [N] was not significant enough to deformthem out of the linear elastic region.
All 9 samples were provided by 3D printing withparameters in Table 1. The physical prototypes weremade from TPU filament as shown in Figure 7.

(i) Group D Bar 2
Fig. 4. Non-linear Static Stress Analysis of the Bars with
the Largest Deformations

The values of the stress and the displacements were given
in Table 2. In Figure 5, the stress and the displacementsof the beams during the FEA bending test were presented,
which the parameter values were arranged from thesmallest to the largest.

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In design and evaluation processes, all the parameters
have to be carefully balanced. Table 3 showed asummary of all bars as the applicability criterion. The
evaluation criteria were considered as high level of thedisplacements (high flexibility), low level of the stress,
low duration of the printing process and mass of the
prototype. These four parameters were labeled as G as
“good”, o as “average” and x as “poor” which
respectively rated with points 1, 0 and -1 in this criterion
panel. The result of the panel suggests the best beamsuitable for the implementation into the compliant hingeof an orthotic device for the knee joint.

Fig. 6. Non-linear Deformation of the Bars – FEA Results

Name
A0
A1
A2
B1
B2
C1
C2
D1
D2

Fig. 7. Sample 3D printed from Flexible TPU Filament

The measured 3D printing time and the measured massof the physical samples were respectively shown in
Figure 8(a) and (b). Group B Bar 1 takes more 2 hours
longer than the other samples. By focusing on
compactness and low mass for an actual use as alightweight attachment, the mass of the models is also
important. Group B Bar 1 was the model with the highest
mass as 21 [g], 6 [g]heavier than the next beam Group D
Bar 1.

Table 3. Evaluation of the Samples
Stress
Displace
Time
Mass
ments
x
x
G
G
G
G
G
G
G
G
G
G
x
x
x
x
o
o
x
o
o
o
o
o
G
G
o
x
o
o
x
x
x
x
o
o

Score
0
4
4
-4
-1
0
1
-2
-2

According to the criterion panel, Bars 1 and 2 fromGroup A and Bar 2 from Group C were the models withpositive points and therefore those are appropriate for thetask.

5. Discussion
In the present study, we investigated the potential offlexible compliant beams in the additive manufacturingin the field of orthopedics as a knee supportive device.
In order to achieve the purpose, 9 models were proposed
and analyzed in non-linear FEA accounting for the large
displacements. For more assured analysis, the results ofcomputer simulations should be evaluated in comparison
with data from physical tests from real materials,
especially in the stress-displacement relationships if themodels have flexible properties due to their geometries.
The prototype support device was shown in Figure 9,
which includes an extended behavior (a) and flexedbehavior (b). In the sense of the three-dimensional
deformation, an out-of-plane deformation has to beanalyzed such as a lateral stability of the knee in this case.
Those issues will be addressed in future missions.
Interestingly, in the physical analysis, as shown in Figure
9, the out-of-plane stability of Bar 2 from Group C canbe expected. There is a possibility of the extended design
based on the hybrid style, by using a 3D printed partmade from the PPGW material (Figure 10). It allows free(a) 3D Printing Time of the Samples(b) Mass of the 3D Printed Samples

Fig. 8. Duration of the 3D Printing and Mass of the Samples

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6. Conclusion

motion in bending and stabilizes the joint motion during
walking.

The mechanical behavior of 3D printed flexible beams
was analyzed with application as an orthotic device. The
bars inspired by compliant mechanisms were verified in
the required motion having hinging mechanisms. A nonlinear FEA accounting for the anisotropic material andthe large deformations of the flexible models wereconducted on all beams to determine the mostappropriate for the application. In analyses of 3D
printing time and the mass of the samples, the criterion
panel was clarified to rank scores to evaluate objectively
how much a beam is appropriate for the applicability.
Advantages of proposed beams were the low-cost, lowmass and compactness in comparison to traditional
solutions such as mechanical parts. The simple andreplaceable attachment has a large benefit for the
implementation into support devices with different
stiffness depending on rehabilitation stages of patientswith joint problems.
According to the proposed method as the basement, theevaluation table will be extended including moreparameters such as various cross-section geometries,
infill patterns and densities and multi-material
assemblies, which combine flexible and stiff materials inthe design of supportive devices.
Capabilities of the additive manufacturing processes areconstantly increasing, and 3D printing allows various
fabrications in the wide range including complex
geometries with turned stiffness for the target issue. It
will extend an opportunity for realization of devices fit
for individual personal requirements in the field of
orthoses. It helps in strengthening the important link of
the patient-doctor relationship aiming for improving thequality of life.

(a)(b)
Fig. 9. Physical Prototype Used in Orthotic Support

As part of the future plans, the lateral deformations needfurther improvements of models with larger resistances.
A systematic idea to improve the lateral stiffness isshown on Figure 10 (a) by replacing the square crosssection with a “I-type beam” cross-section andincreasing the range of motion is illustrated in (b). Figure
10 (c) and (d) represents a multi-material assembly of thebeam combining a stiffer PPGW and TPU filament toprovide a larger lateral stability and higher control overthe stiffness.
Another unique opportunity can be provided by theadditive processes and the infill density variability
contributes to allow a local control of the stiffness of themodel. A combination of those factors will open a further
potential of the additive manufacturing for customizable
solutions to fit for individual requirements.

(a)

(b)

(c)

Acknowledgements
This work was supported in part by EU Horizon 2020
MSCA RISE project “Cyber-Physical Systems for
PEdagogical Rehabilitation in Special Education(CybSPEED),”JSPS
KAKENHI(16H01616,
17H06383) and the New Energy and Industrial
Technology Development Organization (NEDO),
Project on Regional Revitalization Through Advanced
Robotics (Kyushu Institute of Technology/Kitakyushu
city, Japan) and Kitakyushu Foundation for the
Advancement of Industry, Science and Technology(FAIS).

(d)Fig. 10. 3D Representation of the Beam

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Authors Introduction
Mr. Pancho Dachkinov
He received his Master’s degree inEngineering in 2018 from theTechnical University of Sofia,
Bulgaria. He worked in the Instituteof Robotics – Bulgarian Academy of
Sciences 2016-2019. He is currently
a doctoral student in Kyushu Instituteof Technology, JapanMr. Shintaro Kasai

Mr. Kohei Tanaka

He received his Bachelor’s degree inEngineering in 2021 from the Facultyof Engineering, Kyushu Institute oftechnology in Japan. He is currently amaster student in Kyushu Institute ofTechnology, Japan

He is currently a fourth grade
undergraduate
studentin
Department of Mechanical andControl Engineering, Faculty ofEngineering, Kyushu Institute ofTechnology, Japan. He is interested
in 3D printing and compliant
mechanisms.

Dr. Hiroaki Wagatsuma
He received his M.S., and Ph.D.
degrees from Tokyo Denki
University, Japan, in 1997 and 2005,
respectively. In 2009, he joined
Kyushu Institute of Technology,
where he is currently an Associate
Professor of the Department of
Human Intelli- gence Systems. His
research interests include nonlinear dynamics and robotics. He is a member of IEEE.

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