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Tian, et al.

Figure 3. Demonstration of the actuation system of our previous design (left) and the simplified one used in this paper (right). The
simplification is feasible due to our multi-layer design. The remaining structures are labeled in green.

of the tissue tube, to control the deformation modulus A
of the tissue layer. This is feasible as the larger σ is, the
harder it is to deform the tissue layer. The 3D tissue
model with the thickness of σ can be generated easily
by shrinking the outer hull by σ, while expanding the
inner hull by σ as well. In this way, the tissue layer
is modeled by 2 concentric tubes, as demonstrated
in Figure 4. To determine the optimal value of σ,
this method records the curves of normal forces and
contact surfaces [31] with different values of σ, and sets
σ as the one with the curve being closest to that of the
human finger.
Here, we summarize the steps of our fast template B
matching method as follows:
(i) Acquire the human hand model by 3D scanning;
(ii) Import the 3D models for bones and hand to Maya;
(iii) Manually place the landmarks of 5 fingertips; C
(iv) Place the landmarks of joints;
(v) Place the hand bones based on landmarks;
(vi) Cut the hand into 5 fingers by bonding boxes;
(vii) Generate the tissue layer; Figure 4. (A) Modeling the tissue layer as a concentric tube
(viii) Cut each finger tissue into 3 pieces. structure. (B) Demonstration of tissue tubes with different
The codes and demonstration of the modeling thicknesses. (C) Supports for stabilizing the structure.
process are available in the Appendix (refer to “Maya them can be described with a nonlinear elastic model; while
Script.zip” and “V4 3D Modeling Process.mp4”). for a tiny object, considering the fact that the object can be
Compared with existing robotic hand modeling method, enclosed by the finger, a cage based model is more suitable.
the proposed fast template matching method provides a The nonlinear elastic surface model is proposed by
simple and fast way to generate 3D printable parts. Xydas et al. [32,33] , which extends the Hertzian model for
2.5. Deformation and contact model describing the contact surface of a soft finger as follows:
Due to the deformability of our tissue layer, objects with a = cF n/(2 n + )1 (4)
various sizes can be grasped with different gestures. In this
case, it is insufficient to describe the contact-mechanics where c is a constant determined by the properties
model of our robot hand merely based on a single model. To of the fingertip, such as the material and shape. F is the
tackle this problem, we propose to categorize the contacts normal force pressed on the fingertip, n is the strain
with objects into two types based on the sizes of objects. hardening exponent of the material, and a is the radius
Specifically, for grasping an object with normal size, of the contact surface, which is assumed to be circular.
multiple contact surfaces may be generated, and each of However, we obverse from experiments that most contact

International Journal of Bioprinting (2022)–Volume 8, Issue 1 13