FLEXIBLE THREE-DIMENSIONAL LOAD MEASUREMENT SENSOR USING
AN ELASTIC SPHERE
Kenji TORII
Graduate School of Akita Prefectural University
84-4 Tsuchiya-Ebinokuchi, Yurihonjo, Akita 015-0055, Japan
Email: [email protected]
Noboru NAKAYAMA, Jianhui QIU, Tetsuo KUMAZAWA
Akita Prefectural University
84-4 Tsuchiya-Ebinokuchi, Yurihonjo, Akita 015-0055, Japan
Email: [email protected], [email protected], [email protected]
ABSTRACT
In the present paper, the development of a flexible three-dimensional load measurement sensor using an elastic sphere was
investigated. This load measurement sensor has many microswitches that arranged from a few millimeters electrode interval.
The arbitrary load changes with time and can be divided into the normal load and the shearing load. If the normal load loads to
a sensor, an elastic sphere will change. Therefore, an increase of the normal load increases the contact area of an elastic
sphere and a load measurement layer. That is, the normal load is measured by measuring the contact area. If the shearing
load loads to a sensor, the spherical center is moved from a datum point. Therefore, an increase of the shearing load
increases the distance from a datum point. That is, the shearing load can be measured for by measuring the distance from a
datum point. From the above result, the flexible three-dimensional load measurement sensor using an elastic sphere has been
developed.
Introduction
Numerous products are manufactured by robots. At present, the surfaces of robots are generally made of metal (especially
robot arms). Therefore, there is a risk of injury if a human unexpectedly comes into contact with a robot. Since robots will
almost certainly be used for medical treatment and welfare in the near future, the possibility of contact between robots and
humans will increase greatly. In the future, increased contact between robots and humans will necessitate the development of
a sensor that will allow flexible modification. Although the two-dimensional distribution load measuring method using flexible
material has been proposed, a sensor that can detect load in three dimensions has not yet been developed [1]-[2].
In addition, most current three-dimensional load measurement sensors use image processing systems [3]. However, such
systems have a disadvantage in that image processing systems require a great deal of time because too much information is
collected using this detection method.
In this case, since information processing for load measurement is time consuming, it is difficult for a robot to stop suddenly
upon coming in contact with a human. Therefore, a method of electrical processing to improve the processing speed must be
devised.
In the present paper, the development of a flexible three-dimensional load measurement sensor using an elastic sphere was
investigated. First, the transformation and movement of an elasticity sphere were investigated quantitatively for normal load
P(t) and shearing load W(t). Second, the normal load P(t) and the shearing load W(t) were applied to a sensor and these loads
were measured.
Principle of the flexible tactile sensor
Figure 1 shows the principle of load measurement of the developed sensor. The arbitrary load changes with time and can be
divided into the normal load P(t) and the shearing load W(t), as shown in Figure 1. If the normal load P(t) is applied to a sensor,
the elastic sphere will be deformed. Thus, an increase in the normal load P(t) increases the contact area AC(t) of the elastic
sphere and the load measurement layer. That is, the normal load P(t) can be determined by measuring the contact area AC(t).
If the shearing load W(t) is applied to the sensor, the spherical center is moved from a datum point (center). Thus, an increase
in the shearing load W(t) increases ∆x(t) (the amount of movement from a datum point). That is, the shearing load W(t) can be
determined by measuring ∆x(t).
Load
Normal Load P(t)
Shearing Load W(t)
skin layer
＝
elastic sphere
＋
load measure layer
Δx(t)
Ac(t)
datum point
datum point
datum point
Figure 1 Principle of load measurement
Figure 2 shows a flowchart of the normal load measured with the developed sensor. If the normal load P(t) is applied to a
sensor, the elastic sphere will be deformed. Thus, an increase in the normal load P(t) increases the contact area AC(t) between
the elastic sphere and the load measurement layer. If contact area AC(t) increases, microswitch S(n) is turned on. Microswitch
S(n) is an electrode that is arranged in constant space ∆l(t). In addition, each microswitch S(n) has a resistance of R = 100 Ω.
If microswitch S(n) is tuned on, resistance R and voltage V(t) will change.
P(t)
Ac(t)
V(t)
S(n)
Ac(t)
P(t)
α Δr(t)
P(t)
δ
Ac(t)
β
Δl γ
(a)
(b)
Figure 2 Detection method of normal load measurement
Figure 3 shows a schematic diagram of the contact area AC(t) and ∆x(t) (the sensor loaded arbitrary load). The contact area
AC(t) of the elastic sphere is circular. The load measurement layer is divided into four zones, labeled α through δ and can
detect points of contact A(t) through D(t) by measuring voltage V(t) in each zone. Radius ∆r(t) and the center of the circle are
calculated by the least squares method from points of contact A(t) through D(t). The contact area AC(t) of the elastic sphere
and the load measurement layer is calculated as follows:
(1)
A c ( t ) = π ⋅ ∆ r ( t )2
The normal load P(t) can be detected by the contact area AC(t). Furthermore, the shearing load W(t) and the load direction are
detected based on ∆x(t) as calculated from the center of the circle.
α
datum point
A(t)(0,a(t))
δ
D(t)(d(t),0)
Δｘ（ｔ）
B(t)(b(t),0)
β
Ac(t)
C(t)(0,c(t))
γ
Figure 3 Schematic diagram of circumcircle
Figure 4 shows the structure of the developed sensor. The developed sensor consists of an elastic sphere and a load
measurement layer. The material of the elastic sphere is natural rubber, and the elastic sphere was filled with silicone oil (120
ml). The diameter of the elastic sphere was 60 mm. The load measurement layer consists of an upper plate, a spacer, and a
lower plate. If a load is applied to the elastic sphere, the electrode of the upper plate comes into that of the lower plate, turning
on microswitch S(n). The material of the upper plate is an etched polyimide. Therefore, the upper plate has electrode. The
spacers of thickness 0.05 mm made by polyester are placed between upper plate and lower plate. If the developed sensor is
no-load condition, the electrode of the upper plate is not in contact with the electrode of the lower plate. The spacers are
separated by 20 mm so that placement of the upper plate was easy. The material of the lower plate is an etched glass
composite, and the lower plate also contained an electrode. In this study, in order to check whether the load of the sensor
developed was measured exactly, it was compared with the load of the sensor developed and the load in the load cell.
Therefore, the load cell sets upper part in this sensor.
P(t)
load cell
high cis-polyisoprene
copper electrode
upper plate
spacer
lower plate
20mm
Figure 4 Structure of the tactile sensor
Figure 5 shows a diagram of the connection of the upper and lower plates. The developed sensor is switched on when the
upper plate is superimposed on the lower plate. The load measurement layer is divided into four zones of from α to δ. The
developed sensor detects a coordinate by measuring the voltage V(t) in each zone. The space ∆l of the copper wiring printed
on the lower plate is 2 mm. If ∆l of this copper wiring changes, the load resolution will change. Figure 6 shows a schematic
diagram of the microswitch in the sensor (α zone). The developed sensor is a parallel circuit. An increase in the normal load
P(t) increases the contact area AC(t) of the elastic sphere and the upper plate. When the upper plate (contact part) descends,
the electrode of the upper plate contacts that of the lower plate. Microswitch S(n) is then turned on. The increase in the normal
load P(t) increases the contact area AC(t), so resistance R, which depends on the normal load P(t), increases to “n” units. The
combined resistance of “n” units, which is given by Rs(n), and the combined resistance of the zones α – δ, given by Rsα(n) Rsδ(n), were defined. The α zone is representative in that the combined resistance Rsα(n) of the α zone is calculated using Eqn.
(2). In addition, the voltage V(t) calculated based on the combined resistance Rsα(n) is calculated using Eqn. (2), and the
constant current is calculated using Eqn. (3). Because values of combined resistance Rsα(n) decrease as switches S(n) are
turned on, the voltage V(t) decreases. Other zones can be calculated in the same manner as the α zone.
n
1 / R sα (n) =
∑ 1 / Rα (k )
(α zone)
(2)
k =1
V = IRsα (n) (I = constant)
upper plate
α
β
δ
γ
(3)
lower plate
+
overall view
=
elastic sphere
Figure 5 Substrate and wiring of tactile sensor (above and below)
～
～
S(n)
S(3)
S(2)
S(1)
Rα(n)
Rα(3) Rα(2) Rα(1)
～
～
Figure 6 Schematic diagram of the switch in the sensor (αzone)
Normal load measurement of the developed sensor
Experiment and results
The relationship between the normal load P(t) and the voltage V(t) was investigated using a newly developed sensor. The
normal load P(t) and the voltage V(t) vary with time. A normal load P(t) was applied to the developed sensor (the displacement
speed was constant at 2 mm/min) using a universal materials testing machine from Instron. The load cell was placed in the
upper part of the developed sensor, and the actual normal load was measured. The voltage was supplied by a stable power
supply. The initial voltage applied to the circuit was controlled to be constant at 9 V. The resistance was R = 100 Ω. The
variations in the normal load P(t) and the voltage V(t) with load were recorded on a PC using an AD converter. Figure 7 shows
the normal load P(t) applied in the experiment. The normal load P(t) was applied over time. The elastic sphere was varied with
the increase in normal load P(t). Thus, the contact area AC(t) increased. Figure 8 shows the relationship between the normal
load P(t) and the contact area AC(t). The contact area AC(t) was proportional to the normal load P(t). If contact area AC(t)
increases, microswitch S(n) (S(n) was set in zones α - δ) is turned on. If microswitch S(n) is turned on, the voltage V(t)
changes because the combined resistance Rs(n) changes. Figure 9 shows the change in voltage V(t) for each zone. The
microswitch was turned on as a result of the increase in the contact area AC(t), and the voltage V(t) was changed. The
developed sensor can detect the number of ON-switches S(n) from the voltage V(t). Figure 10 shows the number of ONswitches S(n) (where S(n) was calculated by the voltage V(t)). thus, the coordinate A(t) - D(t) was measured based on the
number of ON-switches S(n) in each zone (Figure 3). The contact area AC(t) was calculated by the least squares method from
the point of contact A(t) - D(t). Figure 11 shows the change in the contact area AC(t) with time. The contact area AC(t) was
changed with the number of the ON-switches. Figure 12 shows the relationship between the contact area AC(t) and the normal
load P(t) in this case. The contact area AC(t) is proportional to the normal load P(t). Therefore, the normal load P(t) was
measured based on the detected contact area AC(t). Figure 13 shows the normal load P(t) obtained by the load cell and the
developed sensor. The results obtained by the developed sensor and the load cell were approximately the same, indicating
that the developed sensor can measure the normal load P(t). In addition, the normal load resolution of the new sensor was
approximately 0.96 N.
Normal Load P(t) (N)
20
10
0
0
100
Time (s)
200
Figure 7 Relationship between time and normal load (∆l=2)
Contact Area A c (mm 2)
1000
500
0
0
10
Normal Load P (N)
20
Figure 8 Relationship between normal load and contact area (∆l=2)
Voltage V (V)
10
α
β
γ
δ
8
6
4
2
0
0
100
Time (s)
200
Number of ON-Switches S(n)
Figure 9 Relationship between time and voltage (∆l=2)
α
β
γ
δ
6
4
2
0
0
100
Time (s)
200
Contact Area Ac (mm2)
Figure 10 Relationship between time and number of ON-switches (∆l = 2)
1000
500
0
0
100
Time (s)
200
Figure 11 Relationship between time and contact area (∆l = 2)
Normal Load P (N)
20
10
0
0
500
1000
2
Contact Area A c (mm )
Figure 12 Relationship between contact area and normal load (∆l = 2)
20
Normal Load P (N)
Load cell
Sensor
10
0
0
100
Time (s)
200
Figure 13 Relationship between time and normal load (∆l = 2)
Shearing load measurement using the developed sensor
Experiment and results
The constant normal load P(t) and the shearing load W(t) were applied to the newly developed sensor. The distance of the
datum point of the elastic sphere ∆x(t) was then investigated. The shearing load W(t) was applied to the developed sensor
(starting at δ and ending at β). The displacement speed was a constant 2 mm/min. The normal loads P(t) = 10 N, P(t) = 12.5 N,
and P(t) = 15 N, and the shearing load W(t) were applied to the newly developed sensor. The effect of the normal load P(t) on
the shearing load W(t) was investigated. Figure 14 shows the relationship between the shearing load W(t) and the voltage V(t)
(P(t) = 15 N). The voltage V(t) was varied in each zone. The voltage V(t) shows the number of ON-switches. The coordinate
A(t) - D(t) was thus calculated by the voltage V(t) in each zone. The contact area AC(t) and the datum point of the elastic
sphere can be calculated by the coordinate A(t) - D(t) using the least squares method. Figures 15(a) - 15(d) show the drawing
of the datum point of the elastic sphere moving with the increase in the shearing load (P(t) = 15 N). Figure 16 shows the
relationship between the shearing load W(t) and the distance of the datum point of the elastic sphere ∆x(t). The distance of the
datum point of the elastic sphere ∆x(t) was proportional to the shearing load W(t). In addition, the changes in the normal load
P(t) and the shearing load W(t) tended to be constant. Equation (4) shows the relational expression among the distance ∆x(t),
the normal load P(t), and the shearing load W(t).
W(t) = 0.1∆x(t) + 0.044P(t) - 0.06
(4)
The shearing load W(t) was determined using Eqn (4) (which takes this tendency into account). Figure 17 shows the measured
result of the shearing load W(t) and distance of the datum point of the elastic sphere ∆x(t) (P(t) = 10 N, P(t) = 12.5 N, and P(t)
= 15 N). The experimental result and the shearing load W(t) calculated using Eqn. (4) were equal. Therefore, the newly
developed sensor can measure the shearing load W(t).
Voltage V(t) (V)
4
3
2
α
β
γ
δ
1
0
0
0.2
0.4
0.6
0.8
Shearing Load W(t) (N)
1
Figure 14 Relationship between shearing load and voltage (P(t) = 15 N)
α
α
Δx(t)
δ
β
δ
β
Ac(t)
Ac(t)
5mm
5mm
γ
(a)　W(t) = 0 N
γ
(b)　W(t) = 0.7 N
α
α
Δx(t)
δ
Δx(t)
β
δ
β
Ac(t)
5mm
γ
(c)　W(t) = 0.8 N
Ac(t)
5mm
γ
(d)　W(t) = 0.9 N
Figure 15 Relationship between shearing load and datum point (P(t) = 15 N)
Distance Δ x(t) (mm)
5
4
3
P(t) = 10 N
P(t) = 12.5 N
P(t) = 15 N
2
1
0
0
0.2
0.4
0.6
0.8
1
Shearing Load W(t) (N)
Figure 16 Relationship between shearing load and distance
Shearing Load W(t) (N)
1
0.8
0.6
0.4
P(t) = 10 N
P(t) = 12.5 N
P(t) = 15 N
0.2
0
0
1
2
3
4
Distance Δx(t) (mm)
5
Figure 17 Relationship between distance and shearing load
Conclusions
In the present paper, the development of a flexible three-dimensional load measurement sensor using an elastic sphere was
investigated. The following conclusions were obtained:
(1) The normal load P(t) was proportional to the contact area AC(t).
(2) The shearing load W(t) was proportional to the distance to the datum point of the elastic sphere ∆x(t).
(3) The newly developed sensor can measure the normal load P(t) and the shearing load W(t).
As a result, a flexible three-dimensional load measurement sensor that uses an elastic sphere was developed.
The elastic nature of this sensor will enable its use in robot that will be used for medical treatment that requires human contact.
In particular, it will be set wheelchairs and bed for medical care.
Acknowledgments
This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young
Scientists (B), 16700187, 2004-2005.
References
1.
2.
3.
R.Tajima et al., Advanced Robotics, Vol. 16, No. 4, 381-397, 2002.
Jonathan.E, et al., J. Micromech. Microeng. Vol. 13, 359-366, 2003.
M.Ohka, et al., Advances in Information Storage System, Vol. 10, 314-325, 1999.