Development of Wrist Bending Rehabilitation Robot

Hyeon-Min Kim

, Tae-Kyung Hong

, Hyung-Je Cho

and Gab-Soon Kim

Department of Control & Instrumentation Engineering (ERI), Gyeongsang National University, Jinju, South Korea

YESON Rehabilitation Hospital, Seoul, South Korea

Keywords: Four-axis Force/Moment Sensor, Interference Error, Wrist Rehabilitation Robot, Rehabilitation Exercise.

Abstract: This paper describes the wrist bending rehabilitation robot using a four-axis force/moment sensor. The robot

can be used to exercise the wrist bending rehabilitation for severe stroke patients lying in bed wards or at

home. The manufactured four-axis force/moment sensor which can detect two directional force Fx, Fy and

two directional moment Mx, My, was attached to the developed rehabilitation robot and allows the

rehabilitation robot to measure a bending force (Fx) exerted on a wrist, the signal force Fy and moments

Mx, My which in turn allows the device to be used safely. The results of a characteristics test for the

developed rehabilitation robot showed that it was safely operated while the wrist bending flexibility

rehabilitation exercise was performed. Therefore, it is thought that the developed rehabilitation robot can be

safely used with severe stroke patients.

1 INTRODUCTION

The numbers of patients with severe strokes are

increasing rapidly in the world, and their wrists must

receive rehabilitation exercises so that they can be

used in everyday life. The wrist bending flexibility

rehabilitation exercise bends the wrist in a counter-

clockwise direction (right hand) or clock wise

direction (left hand) based on the wrist, like with

rehabilitation therapist, it conducts rehabilitation

exercises until the patient starts feel pain, and then

the robot pauses the exercise for a while (about 4s).

It then bends back the wrist again in the opposite

direction, and then pauses for a while. Rehabilitation

therapists, nurses and physicians for rehabilitation

find it very difficult to deal with the number of

severe stroke patients and because of this some of

the severe stroke patients don’t receive adequate

rehabilitation exercise. Therefore, the wrist bending

rehabilitation robot has been developed for safe and

adequate wrist bending rehabilitation and to ease the

burden on rehabilitation therapists, nurses and

physicians.

Pan developed three degrees of freedom

rehabilitation robot for mild stroke patients sitting in

a chair attached to a robot, that provided elbow

rehabilitation exercise. Both Pan and Culmer did

research on how to control the robot using the fuzzy

theory. Kim developed the six degrees of freedom

robot for upper limb rehabilitation of the minor

stroke patients, and this robot was able to perform

the rehabilitation exercises for mild stroke patients’

upper limbs. Li developed an upper limb

rehabilitation robot that could be used to exercise

bending and straightening of a patients arm. The

robot can measure the moment needed to the bend of

the patient's arm and the control of the robot is

performed using measured moment. Culmer

developed a six degrees of freedom rehabilitation

robot to rehabilitate patient's upper limb using two

robots, and he researched the control of the robot for

mild stroke patient's upper limb rehabilitation

exercise.

These robots can perform the rehabilitation

exercise for mild patients’ wrists, but can't perform

that of severe stroke patients’ wrists. Thus, a wrist

bending rehabilitation robot, such as rehabilitation

therapist, that helps rehabilitate severe stroke

patients lying in bed wards or at home by providing

wrist rehabilitation exercises must be developed.

The Rehabilitation robots must measure the

moments of wrist rotated to counter-clockwise and

clockwise, and be controlled using the measured

moments. A four-axis force/moment sensor

measures x, y directional force Fx, Fy and moment

Mx, My, and it is composed of a body in order to

reduce the size of the sensor in general. The four-

axis force/moment sensor built into a wrist bending

rehabilitation robot should be suitable in the size,

with a rated capacity and price, and it should be easy

272

Kim H., Hong T., Cho H. and Kim G..

Development of Wrist Bending Rehabilitation Robot.

DOI: 10.5220/0005007402720279

In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2014), pages 272-279

ISBN: 978-989-758-040-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

to attach to the robot. Current developments of a

multi-axis force sensor [Nagai, Kim and Kim] are

not suitable for a wrist bending rehabilitation robot

in terms of size, price and additional conditions.

Therefore, the wrist bending rehabilitation robot

needs to be developed for severe stroke

rehabilitation lying in bed wards or at home.

In this paper, the wrist bending rehabilitation

robot using a four-axis force/moment sensor was

developed. The four-axis force/moment sensor was

designed and fabricated for measuring the applied

force (Fx) of patient's wrist and force Fy and

moment Mx, My for a safe control of movement.

And then a robot body was designed and

manufactured. The characteristic test of a wrist

bending flexibility rehabilitation exercise of a

normal people and a stroke patient was carried out

using the developed the robot.

2 DESIGN

AND MANUFACTURING

OF WRIST BENDING

REHABILITATION ROBOT

2.1 Design and Manufacturing of Wrist

Bending Rehabilitation Robot

Figure 1 shows the manufactured wrist bending

rehabilitation robot, it was designed and

manufactured to perform the rehabilitation exercise

of a wrist for a stroke patient lying in a hospital

ward. The rehabilitation robot was composed of a

robot body, a hand fixing block, a hand fixture

Velcro, an arm fixing block, an arm fixture Velcro,

an up-down supporter, a wrist bending motor, a

four-axis force/moment sensor, a high-speed

controller and so on. The robot body was

manufactured using aluminum square rods (size:

40mm40mm), and its size is 800mm 600mm

400mm, and most of the robot’s parts were fixed to

the robot body. The hand fixing block and the hand

fixture Velcro were designed to be fixed to the

patient's hand safely, and they were also fixed to the

four-axis force/moment sensor that transmits the

bending force (Fx) of the wrist bending motor to

patient's wrist. The arm fixing block and arm fixture

Velcro were designed to be fixed patient's arm

safely, and they were also fixed to the robot body

and the up-down supporter. The up-down supporter

was designed to be adjusted the height of the

patient's bed and to the height of the robot body with

one side being fixed to the wrist bending motor and

other side being fixed to the four-axis force/moment

sensor. The wrist bending motor applies the bending

force to patient's wrist, and it was fixed to the up-

down supporter.

The four-axis force/moment sensor was designed

and manufactured, it measures the bending force

(Fx) applied to a patient's wrist during the

rehabilitation exercise and also measures force Fy

and moments Mx, My in case of emergency. The

manufactured four-axis force/moment sensor is

described in detail in the next section. The high-

speed control system was manufactured to measure

the forces and moments from the four-axis

force/moment sensor, and to control the wrist

bending motor with the measured force Fx, and also

returns the robot to the initial position of the wrist

bending motor using the measured force Fy and

moments in case of an emergency situation.

Figure 1: Manufactured rehabilitation robot for wrist

bending exercise.

The wrist rehabilitation exercise using the wrist

bending rehabilitation robot is conducted by, first,

fixing patient's arm with the arm fixing block and

the arm fixture Velcro. The patient's hand is then

fixed to the hand fixing block and hand fixture

Velcro, after which the stroke patient lies in bed.

The robot bends the wrist counter-clockwise and

clockwise by the rotating of the bending motor

repeatedly, and the bending force exerted on the

wrist (force Fx) is measured by the four-axis

force/moment sensor. The robot is controlled with

the reference of the measured bending force (Fx). In

an emergency situation, the patient applies any force

to the robot, the four-axis force/moment sensor

measures forces Fx, Fy and moments Mx, My at the

same time, and the high-speed control system stops

the robot from using the forces and moments. The

robot is then returned to the initial position of the

motor.

DevelopmentofWristBendingRehabilitationRobot

273

2.2 Design and Manufacture of the

Four-Axis Force/Moment Sensor

Figure 2 shows the structure of the four-axis

force/moment sensor, and the sensor detects forces

Fx, Fy, and moments Mx, My simultaneously. The

sensor is composed of a force/moment transmitting

block, F/M, two

fixing block, F1 and F2, two

moving block, M1 and M4, four parallel plate beam,

PPB1~PPB4. PPB1 and PPB2 are for perceiving

force Fx and moment My, and PPB3 and PPB4 are

for force Fy and moment Mx. The sizes of the plate-

beams composed of PPB1 and PPB2 are width

b ,

thickness

t , length

l , those for PPB3 and PPB4 are

width

, thickness

, length

. The size of the

sensor is 104mm20mm20mm. Theoretical

equations should be derived to determine the size of

the sensor.

Figure 2: Structure of four-axis force/moment sensor.

Figure 3 shows the free body diagram of plate beams

for a four-axis force/moment sensor under the forces

Fx(or Fy). When the force Fx is applied to the point

O of the force/moment transmitting block, force

Fxx

and moment

Fxy

M are generated on the end of

the plate-beam. The force

Fxx

F and moment

Fxy

can be derived from the equations of force and

moment equilibrium-condition



 0Fx ,





0Fy

and



 0

of the force/moment transmitting

block and the moving block M1. And the equations

UFx



and

LFx



for analyzing the strains on the

upper and lower surfaces of the plate-beams are

derived by substituting the derived force

Fxx

F and

moment

Fxy

M into the equation of bending moment

EZM

/



, and they can be written as

)

hEb

UFx







(1)

where,

is the modulus of longitudinal elasticity.

Figure 3: Free body diagram of plate beam for a four-axis

force/moment sensor under the forces Fx(or Fy).

Figure 4 shows the free body diagram of plate beams

for a four-axis force/moment sensor under the

moment My(or Mx). When the moment My is

applied to the point O of the force/moment

transmitting block, forces

Myx

F ,

Myz

F and moment

Myy

M are generated on the end of the plate-beam.

The forces

Myx

F ,

Myz

F and moment

Myy

M can be

derived from the equations of force and moment

equilibrium-condition



 0Fx ,



 0Fy and





M of the force/moment transmitting block

and the moving block M1. And the equation of the

rotational angle of force/moment transmitting block



can be derived using forces

Myx

F ,

Myz

F and

moment

Myy

M .

)

(

484

)

(

211

EdAl

dEI







(2)

And the equations

UMy 



and

LMy



for analyzing the

strains on the upper and lower surfaces of the plate-

beams are derived by substituting the derived forces

Myx

F ,

Myz

F and moment

Myy

M into the equation of

bending moment

EZM





and the equation of

tension and compression

/ld





 , and they can be

written as

211

))

(

))

(

dld

UMy









(3)

The design variables of the modeled the four-axis

force/moment sensor are the size of body, the rated

output of each sensor, the rated forces and moments

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274

Figure 4: Free body diagram of plate beam for a four-axis

force/moment sensor under the forces My(or Mx).

of each sensor, the size (width

b , thickness

t ,

length

) of plate-beams of PPB1 and PPB2, the

size (width

b , thickness

t , length

l ) of plate-

beams of PPB3 and PPB4. And,

d is the distance

between the vertical center-line of the force/moment

transmitting block and the right end point of PPB1,

is the distance between the horizontal center-line

of the force/moment transmitting block and the right

end point of PPB1. The processing of the sensor

design is as follow, first the size of sensor's body,

the rated output of each sensor and the rated load of

each sensor are determined. And then the width

thickness

t , length

l , width

b , thickness

t ,

length

l ) of plate-beams are calculated by

substituting the determined them into the equations

(1) and (3).

Wheastone bridges are made for each sensor in

the four-axis force/moment sensor. The rated strain

of each sensor under each rated force or moment is

determined from the strain values of the attached

strain-gages to each sensor. Total strain of

Wheastone bridge can be calculated as following

equation.

112 2TCT C



 



(4)

where,



is total strain from Wheastone bridge,



is strain of a tension strain-gage

T ,



is strain of

a compression strain-gage

C ,



is strain of a

tension strain-gage

T ,



is strain of a

compression strain-gage

C .

And, the rated output can be calculated as below

equation.





(5)

where,

E is the input voltage of Wheastone bridge,

E is the output voltage of Wheastone bridge,

the factor of strain-gage (about 2.0),



is total strain

gotten from equation (4).

The rated outputs of the variables for designing

the four-axis force/moment sensor is determined by

about 0.5

VmV / respectively, the rated force and

moment of each sensor of the four-axis

force/moment sensor are Fx=Fy=100N, Mx=6Nm

and My=7Nm, the size of the sensor is

104mm

20mm20mm, the attaching locations of

strain-gages in length-direction is 1.5mm from the

end of the plate-beam, the attaching locations of

strain-gages in width-direction is on the center line

of the plate-beams, and the rated strain at the

attaching location of strain-gage is about 250

mm /



The sizes of sensing elements of the four-axis

force/moment sensor are determined by substituting

the determined variables into equations (1) and (3).

The lengths

l and

l are 10mm respectively, the

widths

and

are 20mm and 12mm, the

thicknesses

t and

t are 1.14mm and 1.36mm, the

distance

d and

d are 12mm and 5.34mm

respectively. The material of the sensor id Al 2024-

T351.

Figure 5 shows the attachment locations of strain

gages on each sensing element of four-axis

force/moment sensor. The attaching locations for

each sensor in the four-axis force/moment sensor

were determined in consideration of the results of

theoretical analysis. The attaching locations of

strain-gages for Fx sensor are S1~S4, those for Fy

sensor are S5~S8, those for Mx sensor are S13~S16,

those for My sensor are S9~S12. The attaching

location of each strain-gage is 1.5mm from the end

of plate-beam in the length-direction, and that in the

width-direction is the center line of plate-beam.

These locations were determined in consideration of

the interference error 0% calculated by equation (4).

The rated strains of each sensor in the four-axis

force/moment sensor at each attachment location of

strain-gages were calculated by theoretical analysis.

The rated strains for Fx sensor and Fy snsor were

992

mm /



, and those for Mx sensor and My sensor

were 992

mm /



and 968 mm /



respectively. The

maximum error of each sensor was less than 3.2%,

reflecting the fact that the sensing element is

0.01mm thick, taking the manufacturing processing

into consideration.

DevelopmentofWristBendingRehabilitationRobot

275

Figure 5: Attachment locations of strain gages on each

sensing element of four-axis force/moment sensor.

The four-axis force/moment sensor was fabricated

by using the bond (M-200) and the strain gauges

(N2A-13-S1452-350, made in Micro-Measurement

Company, gauge constant 2.03, size 3

5.2mm), and

constructed Wheatstone bridge. Figure 6 shows a

photograph of the manufactured four-axis

force/moment sensor, the rated forces of Fx sensor

and Fy sensor are each 100N, and the rated moments

of Mx sensor and My sensor are each 6.00Nm and

7.00Nm. The size of the four-axis force/moment

sensor is 104mm

20mm20mm. The characteristic test

of the manufactured four-axis force/moment sensor

must be carried out to get the rated output, the

repeatability error, the non-linearity error and the

interference error of each sensor. The characteristic

test was performed with a multi-axis force/moment

sensor calibration system [Kim] and a measuring

device (DMP40).

Figure 6: Manufactured four-axis force/torque sensor.

In order to detect the rated output of each sensor and

the interference error of the four-axis force/moment

sensor, the moment and the force from each sensor

was measured under the rated force and the moment

of each sensor and it was repeated three times, and

the rated output of each sensor was derived by

averaging the values. Table 1 shows the rated output

from theoretical analysis and characteristic test of

each sensor of four-axis force/moment sensor. The

rated outputs from theoretical analysis were by

substituting the gage factor 2.03 of strain-gage and

the calculated rated strain from equation (4) into the

equation (5). The rated outputs of Fx sensor, Fy

sensor, Mx sensor and My sensor were 0.4927mV/V,

0.5145mV/V, 0.5084mV/V and 0.4893mV/V

respectively. The maximum error of the rated output

from theoretical analysis and characteristic test was

less than 2.21%. Table 2 shows the interference error

of each sensor of four-axis force /moment sensor,

The maximum interference error of the four-axis

force/moment sensor was less than 0.96%.

In order to get the repeatability error and the

non-linearity error of each sensor, the force and the

moment from each sensor was measured under the

force and the moment 10%~100% of the rated force

and the moment with 10% step of each sensor and it

was repeated three times. The maximum

repeatability error and the maximum non-linearity

error of each sensor were less than 0.03%

respectively. Therefore, the four-axis force/moment

sensor manufactured in this paper is similar to the

multi-force sensors previously developed [Kim and

ATI INDUSTRIAL AUTOMATION] in level of the

errors. Thus, it is thought that the manufactured

four-axis force/moment sensor can be used for the

wrist bending rehabilitation robot. The developed

four-axis force / moment sensor is suitable for use in

rehabilitation robotics, because it is inexpensive, and

its size is 104

2020mm.

Table 1: Rated output from theoretical analysis and

characteristic test of each sensor of four-axis force

/moment sensor.

Sensor

Rated output )/( VmV

Theo. Exp. Error(%)

Fx 0.5034 0.4927 2.13

Fy 0.5034 0.5145 -2.21

Mx 0.5034 0.5084 0.99

My 0.4913 0.4893 0.41

Table 2: Interference error of each sensor of four-axis

force /moment sensor.

Sensor

Force

Interference error(%)

Fx Fy Mx My

Fx=100N - 0.23 0.52 0.96

Fy=100N 0.31 - 0.27 0.38

Mx=6Nm 0.48 0.18 - 0.62

My=7Nm 0.59 0.31 0.24 -

The four-axis force/moment sensor with the high-speed

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276

control system was calibrated using the multi-axis

force/moment sensor calibration machine [Kim] to

measure the forces and moments. The calibration was

performed as follows: first, in order to calibrate Fx

sensor of the four-axis force/moment sensor, the

calibration machine applied the rated force of

Fx=100.0N to x-direction, and the indicated value of

Fx sensor was adjusted to 100.0N (resolution: 0.2N).

The Fy sensor, Mx sensor and My sensor were

calibrated as that of the Fx sensor, and they were

adjusted to 100.0N (resolution: 0.1N), 3.00Nm

(resolution: 0.01Nm), 5.00Nm (resolution: 0.01Nm)

respectively.

3 THE CHARACTERISTIC TEST

OF A WRIST BENDING

REHABILITATION ROBOT

AND ITS FINDINGS

3.1 Characteristic Test of Wrist

Bending Flexibility Rehabilitation

Exercise

Figure 7 shows the characteristic test for the wrist

bending flexibility rehabilitation exercise using the

wrist bending rehabilitation robot. The wrist bending

flexibility rehabilitation exercise is performed as

follows; first, a person's wrist and arm are safely

fixed using the fixtures and Velcro. The reference

bending force and the reference bending angle (the

measured bending angle add 5

) in counter-

clockwise and clockwise are then measured and are

inputted into the high-speed control system. The

initial position (the reference angle (0

)) of the hand

fixture and person's right hand is that the palm is

straight in the axial direction of the arm and vertical

with the ground, when person was lying in bed. The

method of wrist bending flexibility rehabilitation

exercise is as follows; first, the right hand is bended

to counter-clockwise from the bending force of 0.0N

(the initial position) to the reference bending force

using the motor attached to the robot, the robot is

controlled with the reference bending force for about

4s. Then it is rotated to clockwise like counter-

clockwise. Such a process carried out continuously.

Figure 8 shows the results of the characteristic

test for the wrist bending flexibility rehabilitation

exercise using the wrist bending rehabilitation robot.

The two forces and two moments are outputs from

the four-axis force/moment sensor during the wrist

bending flexibility rehabilitation exercise. The force

Fx is the generated force that the robot pushes the

Figure 7: Photographs of characteristic test for wrist

bending flexibility rehabilitation exercise using the wrist

bending rehabilitation robot (right hand).

Figure 8: Graphs of characteristic test for wrist bending

flexibility rehabilitation exercise using the wrist bending

rehabilitation robot (right hand).

palm or the back of hand, The force Fy is the

generated force that the hand presses the hand fixing

block in upward and downward, the moment Mx is

the generated moment that the end of fingers or the

part of hand presses the hand fixing block in upward

and downward (y-direction), and the moment My is

the generated moment that the end of fingers or the

part of hand presses the hand fixing block left and

right direction (x-direction). As the results of the

measurement tests of subject, the reference bending

force (Fx) and the reference angle in counter-

clockwise were -14.1N and 90.5

 respectively. And

in clockwise, they were each 18.8 and 89.3

.

Therefore, the reference bending force and the

reference bending angle (the measured bending

angle add 5

) in counter-clockwise and clockwise

are then measured and are inputted into the high-

speed control system.

As shown in Figure 8, the reference wrist

bending forces (Fx) were applied to subject's right

hand in counter-clockwise and clockwise during the

DevelopmentofWristBendingRehabilitationRobot

277

wrist bending flexibility rehabilitation exercise, and

then the PI control at the reference bending force

was performed for about four seconds. The force Fy

at reference bending force in counter-clockwise was

2.5N, and 6.2N in clockwise. The moment Mx at

reference bending force in counter-clockwise was -

0.07Nm(-7Ncm), and -0.35Nm(-35Ncm) in

clockwise. The moment My at reference bending

force in counter-clockwise was 0.02Nm(2Ncm), and

-0.15Nm(-15Ncm) in clockwise. The generated

forces and moments in clockwise were greater than

those in counter-clockwise, because the wrist

withstand greater force in counter-clockwise

(bending to backward). And the generated force Fy

and the moments Mx, My were that the fixing block

pushes the palm to the end of finger direction.

Thus, the Fx sensor of the four-axis

force/moment sensor attached to the robot can be

used to control for performing the wrist bending

rehabilitation exercise by measuring the bending

force (Fx) of wrist, and the Fy sensor and Mx sensor

can be used to sense the fixing situation of patient's

arm during the wrist bending rehabilitation exercise

by measuring forces Fx, Fy and moments Mx, My.

3.2 Characteristics Test of Wrist

Bending Flexibility Rehabilitation

Exercise of Severe Stroke Patient

The characteristics test of the wrist bending

flexibility rehabilitation exercise was carried out to

confirm applying the wrist bending rehabilitation

robot for severe stroke patient. The characteristic

test was carried out at YESON Rehabilitation

Hospital, and a severe stroke patient who was almost

unable to move the right hand participated in the

test. She received her wrist bending flexibility

rehabilitation exercise using the wrist bending

rehabilitation robot for thirty minutes each day.

Figure 9 shows the stroke patient's characteristic

test for the wrist bending flexibility rehabilitation

exercise using the wrist bending rehabilitation robot.

Figure 10 shows the outputs of the two forces and

the two moments from the four-axis force/moment

sensor in a severe stroke patient's wrist bending

flexibility rehabilitation exercise using the wrist

bending rehabilitation robot(for three days). At the

results of rehabilitation exercise for eight days, the

reference bending forces in counter-clockwise and

clockwise were -5.4N and 9.4N, and the reference

bending angles were 48.23

 and 47.97 respectively.

The bending force after eight days was 3.1N bigger

than after three days in counter-clockwise, and that

in clockwise was 4.5N bigger. And the bending

Figure 9: Photographs of stroke's characteristic test for

wrist bending rehabilitation exercise using the wrist

bending rehabilitation robot (right hand).

Figure 10: Graphs of stroke's wrist bending flexibility

rehabilitation exercise using the wrist bending

rehabilitation robot (right hand).

angle after eight days was 0.72 bigger than after

three days in counter-clockwise, and that in

clockwise was 3.33

 bigger. The reference bending

forces from the sensor and the reference bending

angles were determined when the robot rotated the

patient's wrist until she felts pain in counter-

clockwise and clockwise in the everyday. To reveal

bigger moment Mx=-0.09Nm(9.00Ncm) was fixed

to the patient's wrist axis in discord to the central

axis of the hand fixture, and the part of wrist pushed

the wrist fixing block as shown in Figure 9. It is that

the four-axis force/moment sensor was composed of

a body.

4 CONCLUSIONS

In this paper, the wrist bending rehabilitation robot

using the four-axis force/moment sensor was

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278

developed. The four-axis force/moment sensor of the

wrist bending rehabilitation robot was designed and

manufactured, and the interference error of the four-

axis force/moment sensor and the maximum

repeatability error and the maximum non-linearity

error of each sensor are similar to that of the

developed sensor [Kim and ATI INDUSTRIAL

AUTOMATION]. Thus, the four-axis force/moment

sensor can be used for the wrist bending

rehabilitation robot. In the characteristic test of the

wrist bending flexibility rehabilitation exercise, the

robot was accurately operated with the reference

bending force in counter-clockwise and clockwise

motions. The robot was safely operated when severe

stroke patient received the wrist bending flexibility

rehabilitation exercise. Therefore, it is thought that

the developed wrist bending rehabilitation robot can

be applied to severe stroke patient for the wrist

bending flexibility rehabilitation exercise.

ACKNOWLEDGEMENTS

This research was supported by Basic Science

Research Program through the National Research

Foundation of Korea(NRF) funded by the Ministry

of Education (2012R1A1A2A10041417)

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