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Multi-Layer Deformable Design for Prosthetic Hands
surfaces of the proposed design are more like ellipses, muscles, eight driven cables and four motors (one motor
instead of standard circles. Therefore, we approximate can be shared by two cables) are used in total to control
the contact surface with an unrotated ellipse and apply a finger.
Eq. (4) along its horizontal axis and vertical axis. That is, Due to the proposed multi-layer design, the
let x and y denote the horizontal axis and the vertical axis aforementioned control system can be simplified
of the ellipse, and b be abbreviation of n, we record a and significantly. As the layers of skin and tissue are made of
x
a w.r.t. various F, where a = 1/2||x|| and a = 1/2||x|| , elastic materials, and the ligaments are resilient rubber
y
2
x
y
2
to estimate c , b and c and b . The experimental results bands, they are able to return to their original shapes
x
y
x
y
validate that this nonlinear elastic model depicts the automatically after being flexed, and consequently the
contact model of the robotic hand well: for F = [0, 4] and bones are pulled back to their original positions as well
σ = 0.4, the estimated a = 4.2960, b = 0.3497, a = 5.776, (i.e., through passive movement). Thus, we removed
x
y
x
and b = 0.2203, with the coefficient of determination the cables of the extensor tendon, the lumbrical and
y
(R ) >0.94. interosseous muscles. Furthermore, for the flexor
2
As to tiny objects, such as a M1 screw cap with tendons, we only kept the cable attached to the FDP
the head diameter of 2 mm, they are far smaller than the tendon. As shown in Figure 3, the new underactuated
contact surfaces generated with normal-sized objects. system (marked in green) requires only one cable and
Object grasping in this case can be considered as forming one motor for each finger (except the thumb which uses
an inescapable cage surrounding the target object, and one more motor to realize abduction and adduction). In
current 2-finger/multi-finger caging theories [34,35] can be summary, our underactuated system has 15 DOFs and
adopted for analysis. Particularly, the proposed robotic 6 DOAs. This reduces the complexity and size of our
hand forms a squeezing cage that the object is grasped system remarkably, and hence, our system can be easily
[36]
and remains being caged when the fingers are moving installed on human arms or robotic arms.
closer towards the object. Furthermore, there is an It is noted that the proposed multi-layer structure
interesting action that can be completed by the robotic is a universal design for robotic hand and is not limited
hand, and yet has not been studied in previous caging to the above underactuated system. Highly dexterous
methods: the proposed robotic hand can “press and pick robotic hands can be obtained with other actuation
up” a tiny object with the tip of a single finger. We owe systems that adopts more actuators to achieve various
this to not only the weak adhesive 3D printing material object manipulations .
[37]
of the tissue layer, but also the friction provided by the
contact cage generated by the deformation of fingertip. 3. Experiments and results
2.6. The underactuated system In this section, we validated the effectiveness of the
proposed design via extensive experiments. The complete
In this section, we described the proposed underactuated experimental settings and results as well as multiple
system which simulates joints, ligaments, tendons, demonstration videos can be found in the Appendix.
and muscles of the human hand. Ligaments are fibrous
connective tissues that connect bones to other bones and 3.1. Grasping gesture test
form joints. Tendons are connective tissues as well, but
they are attached to muscles and bones. To mimic the Following previous methods [5,13,15,25,38] , we first
dynamics of human hands, we use cables as tendons, with evaluated the object grasping performance of our robotic
[26]
electric servo motors as muscles to control the motions of hand with the grasp taxonomy defined by Feix et al. ,
the finger. which consists of 33 human grasp types. A successful
Our underactuated system stems from a previous grasp is defined as each static one-hand posture with
design , in which each of the three phalanges (i.e. the which an object can be held securely. Each grasp type
[22]
proximal, intermediate, and distal phalanx) of a finger was tested 10 times and the success rate was used as the
is driven by a cable and all three cables cooperate in evaluation metric in this experiment. Two state-of-the-
completing the movement. Note that there are two groups art robotic hands, including InMoov hand and Nadine’s
of tendons, that is, flexor tendons that bend the finger, and hand V4, were fabricated for comparison because the
extensor tendons that straighten the finger. Consequently, models and hardware specifications of InMoov hand are
such a design requires two groups of the driven system: publicly available while Nadine’s hand V4 is similar to
one for the flexor tendons, including the flexor digitorum the proposed design.
superficialis tendon and the flexor digitorum profundus The results of the object grasping test are reported
(FDP) tendon, while the other one for the long extensor in Figure 5. Methods with success rates >0.8, in [0.2;
tendon, as shown in Figure 3. With the other two driven 0.8] and smaller than 0.2 are labeled in green, yellow, and
cables for simulating the lumbrical and interosseous red, respectively. These results show that the proposed

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