Page 409 - IJB-9-3

International Journal of Bioprinting Cellular metamaterial flexure joints

Table 1. Comparing mechanical properties and performance of the state-of-the-art passive flexure joints and the proposed
metamaterial flexure joint
References Fabrication Material Actuation Range of bending Variable stiffness over
method motion the range of motion?
[5] 3D printing TPU Cable driven ~80° Yes – but not
mechanically tunable
[6] Molding Polyurethanes (IE90A) Cable driven ~70° Yes – but just the
torsional stiffness
[8] 3D printing TPU Cable driven 90° No
[15] 3D printing TPU-PLA Cable driven - No
[18] 3D printing Flexible photocurable Cable driven ~45° No
polymers
[25] Multi-material Elastomer (Agilus30) Shape memory alloy ~90° -
3D printing and Polymer
[26] 3D printing TPU Cable driven - No
[27] 3D printing TPU-PLA Pneumatic driven 100° @60 mm No
length of joint
Our design 3D printing TPU Cable driven 95° @30 mm Yes
length of joint
TPU: Thermoplastic polyurethane

A B C

D E F

Figure 1. Metamaterial flexure joint design. (A) Human finger; (B) 3D CAD model; (C) architecture of the auxetic unit cells in the joint structure and
geometrical parameters of a single unit cell; (D) FE simulation of the bending behavior of the auxetic unit cell; (E) FE simulation of the joint; (F) 3D-printed
joint when force applied through the tendon cable.

applications), here we use them for bending dominant horizontal struts, and θ is the re-entrant angle. The value
situation. of θ should be <90° to represent an auxetic behavior . In
[11]
this architecture, the unit cells of the flexion and extension
Figure 1C shows the 2D model of the MFJ and the sides of the joint are decoupled to ensure maximum
tunable geometrical parameters of the joint where w is contraction and expansion in the flexion and extension
the length of re-entrant struts, t is the thickness of struts, sides of the joint. The geometrical parameters of the flexion
l is the length of the vertical struts, δ is the thickness of and extension sides of the joint can be different to provide

Volume 9 Issue 3 (2023) 401 https://doi.org/10.18063/ijb.696