SUGISAKAMASANORI

Journal of Advances in Artificial Life Robotics
Vol. 3(2); September (2022), pp. 66–72
ON LINE ISSN 2435-8061; ISSN-L 2435-8061
https://alife-robotics.org/jallr.html

Research Article

A Multi-Material Joint System as a Three-Dimensional SpringDamper Compliant Mechanism Toward Functional Versatility
Pancho Dachkinov1, Anirudha Bhattacharjee2, Bishakh Bhattacharya2, Hiroaki Wagatsuma1,3
1

Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-Ku, Kitakyushu, 808-0196, Japan
Indian Institute of Technology Kanpur, Kanpur-208016, India
RIKEN CBS, Japan

2
3

ARTICLE INFO
Article History
Received 25 November 2021
Accepted 11 August 2022
Keywords
Cross-spring pivot

ABSTRACT
3D printed material designs have a large capability in the functional aspect. A cross-spring
compliant joint is a hot topic in the sense of multipurpose applications in various engineering
fields. A combination of flexible materials embedded in the structural form performs a motion of
the system according to deformation of parts elastically, which may fit to a specific engineering
purpose. In the present study, a traditional cross-spring pivot (CSP) was improved to provide
effectively frictionless and wear free in-plane motion. The behavior of the joint was analyzed
based on a non-linear FEA computer analysis to focus the properties with various loading
conditions. Improved compliant joints will open a new door for designs of high-precision
actuators and robotic manipulators.

Compliant mechanisms
FEA simulation
Multi-material joint© 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/).

structures fabricated from thermoplastic polyurethane(TPU). TPU models are flexible and have large
deformation properties in the elastic region. Therefore,
those factor combinations may provide an uniquecapability to control the geometry of the model frominside, especially on its orientation and density beyond
traditional technologies. It implies that 3D printing
significantly contributes for applications in the design ofcompliant mechanisms to provide an expected range of
motion based on a large deformation. On the other hand,following challenging issues remain unsolved inconsideration of suitable compliant mechanisms:

1. Introduction
In compliant mechanisms, the deformation is caused by
an external loading to perform a motion. Recently, theimplementation of compliant mechanisms is of interestfor engineers to obtain multi-purpose functions based on
3D printing, for fabricating complex geometry [1]. The
advancements in the Additive Manufacturing (AM) lead
not only to realization of complex geometry but also to
the development to variety of new filaments withdifferent behavior and properties. Poly Lactic Acid
(PLA) is a frequently used material, which is relatively
low cost and environmentally friendly filament in the
Fused Deposition Modeling (FDM) 3D printing. As
Aveen et al. (2018) [2] and Catana et al. (2021) [3]discussed, PLA tensile and flexural mechanicalproperties have been examined in the comparison withother popular 3D printing filaments such as Acrylonitrile
Butadiene Styrene (ABS) [4]. Płatek at al. (2020) [5]investigated the relative density of flexible cellular• Non-linearities in the geometry and the material whena large displacement occurs,• Variation of the stiffness of the parts in the system inorders of magnitude, depending on the orientation of
the load,• Examining of the balance between stiffness andflexibility as a complex design problem

Corresponding author’s E-mail: dachkinov.pancho-nikolaev608@mail.kyutech.jp, anirub@iitk.ac.in, bishakh@iitk.ac.in, waga@brain.kyutech.ac.jp66• Prevention of plastic deformations due to fatigue ofthe material, which are frequently caused by highstress concentrations,development of precise instruments with high resolutionof positioning.
Th other sections of this paper are structured as follows:
Section 2 explains methodology of the design and themathematical modelling of the multi-material joint;
Section 3 focuses on the results; Section 4 gives thediscussion and Section 5 concludes this paper.

• Finding desired motion parameters for target
mechanisms.
In rigidly articulated joints, the clearances between thecomponents causes backlash in the assemblies.
Furthermore, a friction due to relative motion is
unavoidable by wearing the parts and increasing theclearances and generating heat in the joint [6].
Disadvantages in the above list result in insufficientaccuracy and performance.
Interestingly, those issues provided hints on thecompliance of the joints rather than restricting suchdeformations. Compliant joints provide adaptive andmonolithic motion, avoiding entirely the assembly
process.
Flexural hinges have been widely studied in the literatureand several applications in machine design which harness
the advantages of flexure-based design elements havebeen realized. Being monolithic in structure and with theadvent in AM techniques, it is even simpler nowadays todesign, prototype, test and verify the performance of
these hinges in various applications, especially in thefield of Precision Engineering (PE). The most popular
type of flexural hinge is CSPs, commercially known as
free-flex joints.

2. Methodology
2.1. Design of the Compliant Joint
As discussed in the previous section, compliant
mechanisms and joints are becoming a replacement of the
traditional equivalents in certain applications regarding
their benefits. In the current study, a new compliant typeof universal joint realized from two materials is proposed.
Rigidly articulated universal joints have two
perpendicular axes of rotation where two pin joints areconnected. The motion occurs as two rotations inorthogonal planes.
The compliant multi-material joint consists of two CSPs
rotated at the right angle according to the Z-axis of theorigin coordinate system as shown in Figure 1.

Primitive flexural joints primarily consist of leaf-type ornotch-type configurations, but they have their own
inherent limitations. Notch-type hinges have highstiffness in transverse directions and the rotation
capability is limited by stress concentrations. However,the leaf-type flexures provide large rotations but at
expense of drifting rotation centers. In-order to mitigate
these issues several complex flexural hinges have been
proposed like the cartwheel hinges [7], butterfly hinges[8]. While these hinges provide greater benefits overconventional leaf or notch type, CSPs are relatively
simpler and versatile in applications. The diversity ofthese flexures stems from the fact that they wereextensively explored in the literature for decades. They
were first studied analytically [9], [10]. Goncalvesprovides a thorough theoretical formulation and laser
based optical experiments to characterize theperformance of CSPs .
Such accuracy provided by compliant pivots is useful forsmall displacement in precise mechanisms andinstruments [11]. Relaying on material deformation,
flexure joints have become major component in

Fig. 1. Orientation of CSPs compounding the universal
compliant joint

That type of orientation allows the joint to deform
according to X- and Y-axis and provides stability for outof plane movements and moments around the Z-axis.
Another advantage of the configuration is minimal axial
drift of the center of the joint.
2.2. Modelling and Physical Prototype
As illustrated in Figure 2 below, in XY plane the modelof the joint consists of three beams oriented at 60º angle(α) from each other (beams A, C and E shown later).
Another identical unit is attached to it at a perpendicularorientation around Z-axis. All bars of the joint have same
dimensions: length (L), and square cross-section (a). The
offset between beams from a single cross-spring joint isalso equal to (a) and the beams do not intersect. A generalview representation of the joint is shown in Figure 2. The
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joint has two platforms as top and bottom (1) and fivebeams (2).

Ultimaker Cura. The 3D model was designed in
Autodesk Fusion 360 CAD software. The flexible TPU
filament is called Ninjaflex from the company Ninjatek
and according to their recommendations the appropriate
3D printing temperature of the nuzzle (extruder) is 230ºC [12]. The infill pattern used for the beams is called
Cross 3D described in the slicing software as suitable for
3D deformations and flexible material prints [13].

2.3. Analysis of the Loading Conditions
The performance of joint has been analyzed undervarious loading conditions illustrated alongside with thedeformations (Figure 4) such as a) compression, b)
tension, c) bending of the model. On the right side of the
figure, the platforms are removed, and the direction of theforces is annotated for the different loading cases.
To better visualize the position and orientation of thejoint components in the space, the top and bottom
platforms are removed (Figure 5), and the beams arecolor coded and annotated with letters. The coordinate
systems in the different orientations are given as well.

Fig. 2. General View of the Compliant Joint

Figure 3 showed a) a 3D rendered model and b) a
physical 3D printed prototype of the compliant multimaterial joint. The platforms are printed from a solidmaterial PLA and the beams from a flexible filament –TPU. This multi-material combination provides uniquecapabilities. The platforms that attach to othercomponents are rigid but the beams that execute themotion throughout deformation are flexible.

Table 1: 3D printing Configurations
Parameter

Fig. 3. A model and 3D printed prototype of the compliant
multi-material joint

Filament

PLA

3D printer

Anycubic i3 Mega s

Slicin SoftwareThis two-material approach provides diversity for
combining and experimenting with different materials
pairs. However, this joint is not a single unit, theplatforms and the beams have been 3D printed separately
and later assembled.
Technology, chosen for rapid prototyping of thisspecimen is FDM. The filament used for printing themodel is PLA and TPU with diameter of 1.75 mm. The
3D printer used for fabricating the sample is Anycubic i3
Mega S, a desktop type machine. 3D printing process is
described in Table 1. As discussed by Henein et al.
(2003) [8], 3D printing parameters could impact theanisotropic behavior of the fabricated parts. Therefore,
the configuration set up of the working process isessential for the properties of the physical prototypes. For
configuring the printing process is used slicing software

TPU

Ultimaker Cura

Layer Height

0.1 mm

0.1 mmInfill Density, %

100

100

Infill Pattern

Grid

Cross 3D

210

230

60

60

Print Speed, mm/s

4530

SupportyesnoPrinting
Temperature, ºC
Building Plate
Temperature, ºC

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Value of the Printing
Parameter
Platforms
Beams

Fig. 6. Loads acting on the individual beams

2.4. Mathematical Modelling of CSPs

Fig. 4. Loading conditions of the joint

The proposed design can be modelled as an assembly of
two CSPs with free center of rotations. Behavior of CSP
is widely studied in literature analytically [9], [10] andexperimentally [10], [11]. In Figure 5, beams A and E
corresponds to the leaf springs of the pivot 1 and beams
B and D, rotated at 90 degrees along the Y-axis consistsof pivot 2. The beam C at the center of the joint acts as a
stiffener and provides additional rotational stability to thejoint.

Fig. 5. Position and orientation of the beams

Figure 6 illustrated all unique loading condition of thebeams taken from Figure 6 tension, compression andbending. There are three beams that have different force
distribution and using the annotation (Figure 5; A, B and
C). Beams D is symmetrical to B and E is sumetrical to
A and therefore, forces with same magnitude anddirection are acting on them.

Fig. 7. Generalized forces and moments acting on the CSP

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Figure 7 illustrated the generalized forces and moments
acting on the CSPs and the behavior is described by 11
variables [14]. The load rotational relationship of a CSP
under a generalized loading condition M-couple, Fhorizontal loads, P- vertical loads is characterized by 11
variables (θ, PA , PE , FA , FE , MA , ME , ΔYA , ΔYE , Δ
XA andΔXE ). Similarly, the pivot 2 is characterized by
the same set of variables corresponding to beams B and
D. For each pivot a system of 11 equations is required tosolve the problem. Five are obtained from theequilibrium conditions of forces in X and Y directions,the moment balance, and the compatibility at the edgesof beams A and E. The remaining six are obtained fromcurvature equations for each beam as given in equation 1.
𝐸𝐼

𝑑 2 𝑦⁄
𝑑𝑥 2

3

2 2
𝑑𝑦
[1+( ⁄𝑑𝑥) ]Fig. 8. Illustrates of the strains induced due to axial loading (a,b) and transverse loading (c, d).

= 𝑃𝐴(𝐸) 𝑦 + 𝑀𝐵𝐴(𝐸) − 𝐹𝐴(𝐸) 𝑥(1)
As illustrated a non-linear behavior of the model can beobserved when large deformations occur due to the nonlinear properties of the joint.

where subscripts A and E refers to the beams as shown in
Figure 7.
Table 2: Materials Properties used in the FEA
Material
PLA
TPU

Young’s
Modulus3.5 GPa15.6 MPa

Poisson
Ratio
0.3
0.346

Density
1.24 g/cm3
1.23 g/cm3

3. Results
Simulation studies were carried out in Comsol
Multiphysics (CM). The material properties used for the
analysis are described in Table 2.
Figure 8 showed the result from the studies for tension a)and b) and bending c) and d). As it can be observed, in b),
there is a rotation of the top platform due to the tensile
forces. The results for compression are like the tension
with the reversed direction of the rotation.
The displacements corresponding to axial load ranging
between 2 N and 20 N with the increment of 2 N are
shown on the plots in Figure 9 (a). Figure 9 (b) showed
the displacements related to the transverse load are given,
the range of which is 0.05 N to 0.2 N with the step sizeof 0.05 N.

Fig. 9. Displacement vs load plot.
a) Axial loading (tension/compression);b) Transverse loading (bending)

4.

Discussion

The FEA simulation studies yields conforming results tothe physical behavior of the design. The proposed
configuration of the CSP provides greater rotational
stability due to the additional center leaf placed along theaxis of the joint. However, in transverse plane when axial
forces applied additional rotation can be observed about
Z-axis. Designing such compliant joint for specificapplications can be improved by parameterization of70

5. Conclusion

center-shift phenomenon and characterizing themechanical properties of the flexible 3D printing
materials.
The proposed design of a cross-spring joint has geometry
like the ligaments of the human knee joint. The ligaments
are tissue made from small fibers of collagen, twisted likea rope that attaches bones to other bones in the humanbody and provides stability of the joint. The applicationof the proposed compliant multi-material joint has been
inspired by the knee ligament application since theirgeometrical similarities such as precision adjustments
unbalanced forces in small displacement sensitive
instruments. The proposed improved design of a CSP is
an ideal candidate owing to the degree of compliance it
provides.

In the present paper, compliant multi-material joints wereclearly improved. The joint consists of two cross-spring
compliant joints perpendicular to each other. The pivot
has two rotations around its center according to X-axis
and Y-axis. It has relatively small axial drift and stability
in other planes of motion.
The design and methodology of creating the joint aredescribed and 3D printing parameters were presented.
The forces have been dissolved for all beams individually,
depending on the various loading conditions ascompression, tension and bending. A static FEM analysis
has been conducted to demonstrate the behavior of themodel.
Those models were highlighted in its compactness suchas the rotational axis has matching center points. Itscompliance leads to frictionless and free motion, which
preserves the reliability and durability in time. The multimaterial pairing can be varied, and different material
couple can be considered depending on the requirements.
Another advantage of its compliance is the adaptivity
according to the flexibility of the elastic deformations.
Several challenges need to be considered in the design
stage. Further experimental investigations clarify its
performance on determination of the flexure from plastic
buckling due to greater forces. Another important factor
is a fatigue of the material, which will be examined
fatigue testing of the joint in individual cases. An
advancement of AM is expected to fabricate the complex
geometry. It enhances the rapid development of 3D
printing and expands a possibility to creative designs in
the context of the Industry 4.0.

In addition, the joint can be 3D printed as one monolithic
unit avoiding the assembly process as shown in Figure 10[14]. This prototype, made from PLA has the purpose toillustrate the model can be fabricated at once without
assembling the parts. This can be especially applicablefor 3D printer using metal powder such as SLS (selective
laser sintering) machines.

Fig. 10. Single 3D print prototype

The plans for future development of the current design
extends to conduct experimental studies of a 3D printed
prototype by 3D Laser Doppler Vibrometer (LDV) to
validate its performance characteristics such as stress,
displacements, rotational stiffness, natural frequency, etc.
Both single and multi-material samples will be studied inthis context as well. The frequency analysis will
determine the vibration damping responses of the joint,
to be used for stabilizing purposes. To optimize thestabilizing properties of the joint, 3D printing parameters- infill density, infill geometry, layer thickness, etc. - canbe tuned. Firbman et al. (2016) [15] and Dachkinov et al.
(2020) [16] discussed that the infill orientation, geometry
and density could impact the stress performance of theprinted samples [17].

Acknowledgment
This work was supported in part by Bilateral Joint
Research Project (DST-JSPS/India-Japan), 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 ofIndustry, Science and Technology (FAIS).
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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 Institute of
Robotics – Bulgarian Academy of
Sciences 2016-2019. He is currently adoctoral student in Kyushu Institute ofTechnology, Japan.

Mr. Anirudha Bhattacharjee
He received his M.E. degree in
Production Engineering in 2014 fromthe Faculty of Engineering andTechnology, Jadavpur University inIndia. He is currently working as
Research Associate at SMSS
Laboratory in Department of
Mechanical Engineering at Indian
Institute of Technology Kanpur. His
research interest is Robotics and Computational Geometry.
Dr. Bishakh Bhattacharya
He is a Professor, Department of
MechanicalEngineering at
IIT
Kanpur, India. He is currently
the HAL Chair for the period of Feb
2021 - Jan 2024. He received his Ph.
D. in Aerospace Engineering fromIISc Bangalore, India in 1998. His
area of research encompasses: Active
and Passive Vibration Control, Structural HealthManagement, Design of Energy Harvesting System,
Intelligent System Development and Child-Robot
Interaction Design.
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 non-linear
dynamics and robotics. He is a member of IEEE.

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