Development of a Bolt Type Force Sensor
using Strain Gauges for Sport Climbing
Akihiro Kawamura1 , Takato Nakashima2 , Masakado Danjo2 , and Ryo Kurazume1
Abstract— This paper proposes a novel bolt type force sensor
that measures forces applied to an object fixed by the sensor.
This sensor consists of a iron bolt and four strain gauges andcan be made inexpensively compared to a 6-axis force sensor.
Due to the feature of the bolt type sensor, it can measure theforce applied to the object without dedicated holds, extra jigs,
gaps between holds and walls. Therefore, the sensor can beapplied to existing climbing holds without changes of difficultyof climbing problems. In this paper, the structure of the sensor
is introduced and its calibration method is discussed. Finally,a force measurement experiments are conducted, and it wasconfirmed that the sensor is able to achieve highly accurate
force estimation in practical situations.

ZYX

Hold

HoldwallBolt type force sensor

Bolt type force sensor

Fig. 1.
Bolt type force sensor
mounted on the wallFig. 2. Cross-sectional view of theinstallation of a hold using the bolt
type force sensor

I. INTRODUCTION
Sport climbing is a sport in which athletes climb artificiallyconstructed walls by grasping on the holds attached to thewalls. In several studies, researchers have measured the force
applied to the holds in order to measure and record theclimbing movement of athletes[1] – [7]. In these studies,
force is measured either by dedicated climbing holds with abuilt-in sensor or by inserting a sensor between the hold andthe wall. However, the former restricts variations of climbing
holds. Also, the latter changes and restricts the difficulty ofclimbing problems since the distance between the hold andthe wall changes depending on the thickness of the force
sensor.
This paper proposes a new type of force sensor whichsolves the problem of thickness of force sensors without
any changes of holds and walls, extra jigs and gaps. The
bolts used to attach the holds to the wall are converted into
force sensors as shown in Figs.1 and 2. This bolt type force
sensor has four strain gauges and can measure triaxial force.
For highly accurate force estimation, calibration method
is important. Various studies have been conducted on themethod of calibration for force sensors[8] – [12]. For example, R.Tamura et al. proposed a calibration method for force
sensor with strain gauges affixed to a flexure element with a
Maltese cross structure [13]. In these researches, geometricfeatures of sensors must be considered for calibrations.
However, climbing holds have a variety of sizes and shapes.
Therefore, a calibration method which does not need any
information about holds is applied in this paper.
In the following sections, the design of the bolt type
triaxial force sensor is introduced. Next, a calibration strategy
1 Akihiro Kawamura and Ryo Kurazume are with Faculty of Information and Electrical Engineering, Kyushu University, Fukuoka, Japan

kawamura@ait.kyushu-u.ac.jp
2 Takato Nakashima and Masakado Danjo are with Graduate school ofInformation and Electrical Engineering, Kyushu University, Fukuoka, JapanFig. 3.

Bolt type force sensor

for the sensor by using other triaxial force sensor is proposed.
Finally, a force measurement experiments are conducted toshow the performance of the proposed sensor.
II. B OLT T YPE F ORCE S ENSOR
The bolt type force sensor consists of a metal bolt and four
strain gauges (Tokyo Measuring Instruments Laboratory Co.,
Ltd., FLK-1-11) as shown in Fig. 3. The surface of the shaft
is shaved by 1.8 mm and covered with an oxide film. Fourstrain gauges are arranged evenly around the shaft and affixed
to the bolt. The cables coming out of the strain gauges passthrough holes drilled in the bolt head. The four strain gauges
detect the deformation of the bolt as force is applied to theaffixed climbing hold. The bolt type sensor are tightened
at a constant torque using a torque wrench. The sampling
rates of this sensor is 1000 Hz due to the sampling rates ofstrain gauges. It is presumed that 100 [kg] is sufficient as
the measuring range of this sensor on sport climbing due tobody weight of climbers.

Z

Bolt type force sensor
YForceXHold

6-axis forcesensor

Fig. 5.
Fig. 4.

Strain data

Configuration of the device during calibration

Next, a calibration method for the proposed sensor isdescribed. The force measured by a 6-axis force sensor isutilized for the calibration as a true value. The 6-axis force
sensor (Leptrino Co. Ltd.) is commercially available. Figure
4 shows the configuration of the calibration system which
includes the bolt type sensor and the 6-axis force sensor.
The calculation process of the conversion equation between
strains on the gauges and forces on the 6-axis force sensor
is shown below. The forces fx , fy and fz acting on the centerof the strain gauges are defined by using the coefficients Cxx ,Cxy , Cxz , Cyx , Cyy , Cyz , Czx , Czy and Czz as well as e1 , e2 , e3
and e4 . The variables e1 , e2 , e3 and e4 denote the outputs ofthe four strain gauges on the bolt.

Cxx Cxy Cxz
B = Cyx Cyy Cyz (1)Czx Czy Czz

Fig. 6.

Transient responses of f x

Fig. 7.

Transient responses of f y

Fig. 8.

Transient responses of f z

The resulting conversion equations are expressed in (2), (3)and (4).
e2 − e412fx =|B| Cyx
Czx
Cxx
1 e2 − e4
fy =|B|2Czx

e1 − e32Cyy
CzyCxye1 − e32Czy

e1 + e2 + e3 + e4
4Cyz
Czz
Cxz
e1 + e2 + e3 + e4
4Czz

(2)

(3)

Cxx
CxyCxz
1Cyx
CyyCyzfz =(4)|B| e2 − e4 e1 − e3 e1 + e2 + e3 + e4
224
In this calibration process, the hold and the bolt type sensor
are regarded as a rigid body. Therefore, force data measured
by the 6-axis force sensor is utilized as fx , fy and fz . The
coefficients Cxx to Czz are determined by using three pairs ofstrain and force data at the same time.

III. EXPERIMENTS
In this section, two experiments using the proposed bolt
type sensor are conducted. The first experiment is force
estimation with point contact using a metal rod. The second
experiment is that force estimation on sport climbing. A force
applied to a climbing hold by a climber is estimated ona climbing wall. In this experiment, the climbing hold isgrasped with multiple contacts by fingers and a palm.

Bolt typeforce sensor

6-axisforce sensor
ZA. FORCE ESTIMATION WITH POINT CONTACT
A force estimation experiment using the proposed bolt
type sensor is conducted. The experimental setup is shownin Fig. 4. The target force is applied to the climbing hand
hold by using a metal rod with point contact. The 6-axis
force sensor is installed to calibrate the bolt type sensor andto get true force values for evaluation.
Figure 5 shows the output of the strain gauges. Figures 6- 8 show the results from comparing the output of the 6-axis
force sensor with the estimation results of the bolt-type forcesensor. The results confirm that the force can be estimatedwith high accuracy in the case of point contact.

XFig. 9.

6-axisforce sensor

Climbing wall

HoldBolt typeforce sensor
ZYX

B. FORCE ESTIMATION ON SPORT CLIMBING
Force estimation experiment on sport climbing is conducted on the climbing wall in our laboratory shown inFig. 9. In this experimental setup, the 6-axis force sensor
is installed between the bolt type sensor and the wall shownin Fig. 10 for evaluation though the 6-axis force sensor is
not necessary to measure the force by using the bolt typesensor except for calibration. The force is applied with barehands as in a climbing movement shown in Fig. 11. It meansthat the force to the climbing hold is applied with multiplecontacts.
Figure 12 shows the output of the strain gauges. Figures
13 - 15 show the results from comparing the output of the 6axis force sensor with the estimation results of the bolt-typeforce sensor. The results show that even in sport climbing
movements where the influence of moments is large, highly
accurate force estimation can be achieved.

Fig. 10.

Experimental setup on the wall

IV. CONCLUSIONSIn this study, a bolt-type force sensor using strain gauges
was developed. This sensor overcomes the conventional
problems in motion measurement of sport climbing due to thegap to install force sensors. Firstly, the structure of the sensor
was presented and the calibration method was introduced.
Secondly, two types of experiments were conducted. Then,the accuracy of the proposed bolt type sensor is confirmed
from the two experimental results.
In future, the performance of the proposed sensor will beevaluated deeply. In addition, the wiring of the sensor will
be redesigned not to interfere climbing movement.

Fig. 11.

Sport climbing movement performed in the experimentY

ACKNOWLEDGMENT
This work was partially supported by JSPS KAKENHI
Grant Number JP21K11468. I would like to thank Mr. Sugioka from Tec Gihan Co.,Ltd. for supporting the developmentof the bolt-type force sensor.
R EFERENCES

Fig. 12.

Strain data for sport climbing movementFig. 13.

Transient responses of f x for sport climbing movement

Fig. 14.

Transient responses of f y for sport climbing movement

Fig. 15.

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