IEEE Robotics & Automation Magazine - September 2016 - 57

Due to the importance of
hands and the prevalence
of hand issues, there is an
increasing effort toward
developing hand orthotics.

holes molded into the wrist side of the glove. The tubes are
connected to a pressure source via inexpensive three-position (pressurize, hold, and drain) electrical solenoid valves.
Actuator Motion Analysis
In this orthotic, each of the five fingers is made of a series of
interconnected hollow spherical chambers. Figure 3(a) and
(b) shows a single finger in two configurations: 1) its rest state,
when the gauge pressure-the difference between the interior
and exterior pressure-is zero, 3 p = 0 ; and 2) bent to a curvature, l = 1/t , caused by both the pressure difference,
3 p 2 0, and the bending load that the finger carries. To
approximately calculate the curvature l in terms of other
parameters, we further simplify the finger model into a bending thin-wall cylindrical pressure vessel. The hoop strain (the
increase in diameter of the cylindrical finger) is constrained
by the struts (the walls between the spheres) [Figure 3(b)].
We model the strut structures by assuming the hoop strain is
constrained [Figure 3(c)]. We model the whole cylindrical
finger (the elastomer, stiff fabric at the bottom, gas pressure,
and radial constraint) using a composite-beam model.
We presume the fabric at the finger bottom to be inextensible; thus, the beam-neutral axis is at the finger bottom.
We assume that any external axial load is at the neutral axis
so that it does not enter the bending calculations. For simplicity, we assume that the cylinder wall thickness t is much
less than the finger radius r (t 11 r) and that the elastomer
is linear and isotropic. The net moment MN about the neutral axis is due to the axial elastic tension stress in the elastomer vaxial (acting on the hollow cylinder with the radius
r, thickness t, and moment of inertia about the neutral axis
of I N = 3rr 3 t ), and that due to the gas pressure 3 p (acting
on the area rr 2 a distance r from the neutral axis)
M N =- #

v axial

ydA + r $3 p $ (rr 2).

e axial

(2)

= ly .

(3)

The linear elastic material properties of the elastomer are
= v axial /E - o v hoop /E - o v radial /E,
e hoop = v hoop /E - o v axial /E - o v radial /E,
e axial

(4)

where the elastomer elastic modulus is E and Poisson's
ratio is o.
Optical Fiber
Interconnected
Pressure Chambers

Nylon Fabric

Optical Fiber-LED
Holder

Photodetector

LED
Elastomer

Pressure-Tube
Clamp

(1)

The equilibrium of the cylinder in the y direction [Figure 2(d)] gives a modified version of the standard thinwalled pressure-vessel formula
3 p $ r = v hoop t + Ts ,

where v hoop is the hoop stress in the elastomer and Ts is a force
per length that comes from the restraint against the hoop strain
(against cylinder bulging). In the model here, the restraint represents the sidewall struts of the spheres. It could also represent
restraint from the circumferential fibers [20] or from the interior foam [21]. As per conventional composite beam theory,
we assume that the plane normal sections remain plane and
normal, and, hence, the elastomer axial strain is given by

Tube
Figure 2. A schematic of the glove. Each component is labeled
and exists on each finger: LEDs, pressure-chambers, optical
fibers, photodetectors, nylon fabric, clamps, air-supply tubes, and
optical-component holders.

September 2016

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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57
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2016
