Page 411 - IJB-9-3

International Journal of Bioprinting Cellular metamaterial flexure joints

A B

Figure 2. Comparing stiffness characteristics of: (A) Conventional flexure joint commonly used in soft robotic fingers; (B) the proposed metamaterial
flexure joint.

multi-stiffness behavior of the MFJ can be tuned through unit cells include the length of the re-entrant struts (w),
altering the geometrical parameters of the unit cells. the thickness of the re-entrant struts (δ), the thickness of
vertical struts (t), the length of the vertical struts (l), and
4.1.2. Large range of bending motion
the re-entrant angle (θ). The range of these parameters are
The large range of bending motion of the MFJ is mainly constrained with the desired size of the joint, including
due to the auxetic characteristics of the re-entrant unit length (L), width (W), and depth (D), and the geometrical
cells used in its architecture, which is also known as relation between them to ensure that the joint is realizable
negative Poisson ratio . The structures with auxetic with the tuning parameters. Therefore, the bending
[11]
unit cells contract under compression and expand under stiffness of the MFJ can be represented as:
tension. In the MFJ, the re-entrant auxetic cells enables
,
f wt l θδ,, ,, ,,
the large contraction under compression loading and K = ( L WD) (I)
α
large expansion under tension loading, which results in
the large range of bending motion. In addition, the inward Figure 3 represents the effect of the length of the joint
contraction of the re-entrant unit cells of the flexion side (Figure 3A and B), the re-entrant angle (Figure 3C and D),
of the joint and their densification creates a pivot point for and the thickness of the vertical struts (Figure 3E and F)
the applied force that results in further stretching of the on the stiffness values at different stages of the bending
extension side of the joint. Therefore, for the same length motion of the MFJ. The joint with L = 25 mm, θ = 60°, and
of the joint, the maximum range of motion of MFJ is t = 0.5 mm is used in all plots for the sake of comparison,
higher than that of conventional flexure joints without the highlighting the effect of different tuning parameters.
need for large notch as required in the conventional flexure The force versus bending angle plots of different
joints (as shown in Figure 2A). The range of the MFJs geometrical parameters of the joint and auxetic unit
depends on the geometrical parameters of the constituent cells show three linear regions corresponding to three
unit cells as discussed in the following section.
approximately constant stiffness values as shown on the
4.2. The effect of unit cell geometrical parameters plots with the unit of N/rad. In the first regions, the joint
on MFJ characteristics starts deflection, then at the second region, the lower slope
As MFJ architecture consists of unit cells, altering their plateau region where the struts are bending until they start
geometrical parameters will result in different multi- getting in contact with each other. At the third region, the
level stiffness variation and range of bending motion. It unit cells are densifying, and unit cells of flexion side of
should be noted that the mechanical property of the base the joint are moving inward and making a pivot point and
material also provides an extra design freedom of the MFJ. lever that further displacement of the tendon cable will
Using different flexible materials for 3D printing can be result in further expansion of the extension side of the joint
considered in the case that we want to change the overall and large bending angle (even more than 90°). The MFJ
stiffness of the flexure joint. In this study, we mainly focused can also produce single linear stiffness behavior similar to
on developing metamaterial structures for the flexure joints the conventional flexure joints. Depending on the tuning
that through manipulating the geometrical parameters of parameters of the unit cells of the joint, the bending
the structure, the local mechanical properties of the joint stiffness values of each of these three regions are different.
can be altered, which results in the desired characteristics. As a result, the bending stiffness can be represented in the
As shown in Figure 1C, the geometrical parameters of the following form:

Volume 9 Issue 3 (2023) 403 https://doi.org/10.18063/ijb.696