Page 408 - IJB-9-3

International Journal of Bioprinting Cellular metamaterial flexure joints

in robotic grippers/hands and anthropomorphic hand the bending stiffness of the finger joints has not been
prostheses [4-6] . investigated. A soft robotic gripper with compliant cell
[16]
The most commonly used flexure-based compliant stacks has been used for part handling although the
revolute joints for soft robotic fingers are single-axis single- unit cells only considered at the surface of the gripper
flexure notch-type joints with rectangular, right-circular for the shape adaptation, not in the joint structure.
corner-filleted, or circular/elliptical shapes [6-8] . Altering Other soft robotic gripper designs based on mechanical
[17,18]
the geometrical parameters of these joints will result in metamaterial have been proposed , which have a large
different stiffness values. These designs are fabricated using deformation capacity but only provide a single constant
bending stiffness all through the range of motion. The
molding or 3D printing of flexible materials. The continuum properties of the most common soft flexure joint are
and homogeneous structure of these joints makes them summarized in Table 1.
easy to design, model, and fabricate. However, this also
results in a single constant stiffness for the whole range of In this paper, we propose a revolute flexure joint based
rotation, lacking the advantages of the joints with stiffness on the auxetic cellular mechanical metamaterials with a
variation along their range of motion in providing multiple heterogeneous structure. The heterogeneous structure of
characteristics, such as more stable grasp at high stiffness the proposed soft, compliant flexure joint enables: (i) Large
range, safer interactions and higher conformability at low range of rotation without requiring a large notch in the
stiffness range, and high impact absorption capability at structure; and (ii) tunable multi-level bending stiffness.
quasi-zero stiffness range [9,10] . The type of unit cells considered in the structure of the
joint has auxetic properties, which expand laterally when
The conventional flexure joints also have a limited stretched longitudinally . In addition, the geometrical
[19]
range of motion. To increase their range of motion, they parameters of these unit cells are different in the inner and
require a large notch in their structure, which will make outer sides of the joint. These result in large expansion and
them prone to undesired out-of-rotational-axis motions. contraction of the joint under tension and compression
Compensating the out-of-axis motion through increasing forces, respectively, producing large range of joint rotation
the flexure stiffness will result in high stiffness all through similar to human finger joint.
the range of motion as they can only provide a constant
stiffness for the whole range of rotation. The multi-level bending stiffness of the proposed flexure
joint is due to the multi-stage internal self-contact of the
In this work, we investigated utilizing cellular unit cells, and the interaction between inner and outer
mechanical metamaterials in design of the compliant sides of the joint, which provides a mechanically tunable
flexure joints. Cellular mechanical materials, also known as joint based on the passive mechanical metamaterials. The
architectured materials, are a class of artificial materials that desired stiffness behavior can be encoded in the joint
can provide different mechanical properties mainly based structure through changing the geometrical parameters of
on their structure/architecture, rather than the constitutive the unit cells. Therefore, the bending stiffness variation does
base material characteristics [11,12] . They consist of unit not require external stimulus similar to field-responsive or
cells distributed in periodic or non-periodic fashion. The active mechanical metamaterials [17,20] ; however, the encoded
geometrical parameters of the unit cells and their spatial stiffness behavior cannot be altered after fabrication. The
distribution/configuration can be altered to achieve the capabilities of the proposed metamaterial flexure joints
desired mechanical properties or functional behavior. The (MFJs) have been demonstrated through applications in
inherent heterogeneous structure of cellular mechanical soft robotic grasping and manipulation.
metamaterials provides the ability to locally tune the
mechanical properties, including stiffness, that cannot 2. MFJ design
be afforded by homogeneous structures [13,14] . Therefore, Here, the design of the proposed flexure-based revolute
the compliant flexure joints based on cellular mechanical joint and its mechanical metamaterial architecture have
metamaterials can potentially address the aforementioned been presented. The overall architecture of the proposed
limitations of the conventional flexure joints.
MFJ is inspired by the human finger joints, which have large
The applications of cellular mechanical metamaterials expansion in the extension (outer) side and large contraction
in compliant flexure joints and soft robotic fingers have in the flexion (inner) side, as shown in Figure 1A. Three-
been investigated in only a limited number of studies. dimensional model of the proposed flexure joint, as shown
The three-dimensional (3D) unit cells with dual material in Figure 1B, consists of auxetic re-entrant unit cells in its
have been used in a soft robotic gripper ; however, mechanical metamaterial architecture. While re-entrant
[15]
the structure of the 3D-designed cellular fingers cannot type auxetic unit cells are mainly investigated under
provide the large range of bending angle, and additionally compression force conditions [12,19] (for energy absorption

Volume 9 Issue 3 (2023) 400 https://doi.org/10.18063/ijb.696