A NOVEL DEVICE FOR MEASURING MECHANICAL

IMPEDANCE DURING DYNAMIC TASKS

Hossein Mousavi Hondori and Ling Shih-Fu

School of Mechanical and Aerospace Engineering, Nanyang Technological University,50 Nanyang Avenue, Singapore

Keywords: Dynamic measurement, Assessment of human motor function, Rehabilitation, Mechanical impedance.

Abstract: Mechanical impedance is an important factor that the central nervous system takes into account while

coordinating a motion. This research work thus aims to develop a new measurement for monitoring

dynamic changes of mechanical impedance. The method is introduced and validated in the context. The

results show that device correctly measures the dynamic force and impedance of an eccentric linear spring.

Furthermore, 62 measurement trails on two human subjects (31 trials on each) confirmed that the value of

mechanical impedance changes with adaptation. Finally, we propose a method for the assessment of motor

recovery in the stroke patients undergoing rehabilitation sessions.

1 INTRODUCTION

Assessment of human motor function has remained a

challenge for years; this is because of the complexity

of human brain and the subjective nature of the

assessment. On the other hand with its numerous,

important applications such as assessment of

functional capabilities in post-stroke rehabilitation,

motor function assessment undeniably needs

improvements and new methods. Although several

scoring methods such as Fugl-Meyer (Fugl-Meyer et

al, 1975) or NIH stroke scale (Goldstein et al, 1989)

already exist, they are generally subjective or

qualitative; thus not quite suitable for accurate and

scientific studies of motor functions. For clinical

purposes, though, these methods are still widely

used because of their simplicity. Researchers

recently tried to use robots for the assessment

besides the physical therapy (Palazzolo et al, 2007)

and (Loureiro et al, 2003). Their robots were

basically designed for performing physical therapy

exercises and because of the capabilities of a robot

(Palazzolo et al, 2007) they tried to use the same

robot for assessment purposes. Having measured

forces with respect to displacement, they measured

stiffness of the arm. They assumed a two-DoF model

of mass-spring-damper for the arm and tried to

estimate stiffness, mass, and damping matrices.

However, their method was not a direct, real time,

and in-situation measurement. On the other hand, a

robot might be very complicated and expensive;

setup and maintenance of it can be very difficult as

well. Hence, there still remains a room for a more

reliable, convenient, and efficient tool for the

assessment of motor function. Furthermore, what the

robot measures is also a very important issue for the

assessment.

Hogan (Hogan, 1984) showed that the value of

mechanical impedance for the upper arm, which is

set at the elbow joint, is very important. He

examined the postulate that antagonist muscle’s co-

activation is to generate mechanical impedance and

therefore this is necessary to perform some tasks. A

typical case with necessity of the antagonist

activation is performing a dynamically unstable

task. Burdet (Burdet et al, 2001) showed that human

learns to stabilize unstable dynamics by optimizing

mechanical impedance. Darainy (Darainy et al,

2008) has recently reported that the EMG patterns of

dynamic learning reveals a considerable portion of

co-activation in mechanically stable tasks.

Therefore, this is not only in case of unstable

dynamics that the CNS co-contracts the antagonists

to control the impedance of the limb, but also in

other case of other tasks, with learning the efficient

co-activation, it is practically regulating and

controlling the mechanical impedance of the limb.

Regarding the importance of mechanical impedance

and incapability of the conventional methods to

measure it, this research aims to develop a novel

method for measuring human arm’s mechanical

Mousavi Hondori H. and Shih-Fu L. (2010).

A NOVEL DEVICE FOR MEASURING MECHANICAL IMPEDANCE DURING DYNAMIC TASKS.

In Proceedings of the Third International Conference on Biomedical Electronics and Devices, pages 64-68

DOI: 10.5220/0002697100640068

 SciTePress

impedance which is usable for the assessment of

motor function of patients going under

rehabilitation.

2 SENSING CUM ACTUATING

It is known that mechanical impedance is a measure

of how much a structure resists motion when

subjected to a given force. Hence, in order to

measure mechanical impedance, one needs to

measure the force and the velocity and calculate the

ratio of them.

Measurement of impedance of a limb is usually done

using a robot that applies a perturbation to the limb.

Then sensors located at the same robot measures the

force and the velocity; some notable examples are

(Palazzolo et al, 2007), (Burdet et al, 2001), and

(Darainy et al, 2008). In general, a robotic device is

used so as to measure the force (during motion) and

the speed. The two values are then correlated.

Besides the traditional approach discussed above,

Ling et al (Ling et al, 2001, 2004, and 2006) have

proposed a creative method for impedance. The idea

is to make use of simultaneous sensing cum

actuating (SSA) property of the electrical motors.

Although the method was initially designed for the

industrial applications an experimental study

(Mousavi et al, 2009) showed that a reversion of it

works very well for the medical applications. In this

paper, the same method is further modified and then

used for measuring arm’s mechanical impedance.

According to Figure 1, an electric motor is

considered to have four ports: two inputs and two

outputs.

Motor

Transduction

Matrix

Figure 1: An electromechanical system as a four-pole

block.

The input and output are considered two vectors

each having two elements. E and I (i.e. voltage and

current) are elements of the input vector. T and ω

(i.e. toque and angular velocity) are elements of the

output vector. The transfer function, relating the

input and the output, is a two-by-two matrix which

is called Transduction Matrix. As the name suggests,

it transfers electrical the entries to the mechanical

entries and vice versa.

⎭

⎬

⎫

⎩

⎨

⎧

⎥

⎦

⎤

⎢

⎣

⎡

⎭

⎬

⎫

⎩

⎨

⎧

2221

1211

(1)

In order to obtain the transduction matrix

use an experimental procedure to measure E and I

while the motor runs at measurable T and ω. Once a

number of T and ω versus E and I are attained,

matrix

is found using least square approximation.

⎥

⎦

⎤

⎢

⎣

⎡

⎥

⎦

⎤

⎢

⎣

⎡

⎥

⎦

⎤

⎢

⎣

⎡

ωω

2221

1211

(2)

Using the transduction matrix, we are able to find

the mechanical output based on measuring the

electrical input. In other words, T and ω are found

once E and I are measured.

⎭

⎬

⎫

⎩

⎨

⎧

⎥

⎦

⎤

⎢

⎣

⎡

⎭

⎬

⎫

⎩

⎨

⎧

−

2221

1211

(3)

Afterwards, mechanical impedance,

, is obtained

by dividing ∆T over ω.

(4)

TTT

−

(5)

Where T

is the torque measured at unloaded

condition.

3 EXPERIMENTAL STUDY

A typical shoulder wheel, shown in Figure 2, is

widely known as a common rehabilitation device.

Shoulder wheels are simply found in the market for

inexpensive prices and can be installed and used

easily. Therefore, prescription of such equipment is

welcomed by patients who need physical exercises

on their upper limb. These patients normally suffer

from muscle atrophy and/or a loss in their ranges of

motion. Their practice with a shoulder wheel

involves rotating the shoulder wheel while the

physiotherapist can adjust the radius of the circular

motion. Sometimes they attach some mass blocks to

the wheel such that the patient has to apply more

torque to rotate and control the wheel. Through the

exercise, patients adapt to the motion and their

A NOVEL DEVICE FOR MEASURING MECHANICAL IMPEDANCE DURING DYNAMIC TASKS

control over the muscles would improve; hence they

recover.

3.1 Apparatus Design

Here, we use a shoulder wheel equipped with a DC

motor as the measurement apparatus, shown in

Figure 3. The set also involves a current and a

voltage probe, and a dynamic signal analyzer, which

is depicted in Figure 4.

The set-up was used for measuring human arm’s

mechanical impedance while the subject was

exercising with the shoulder wheel, illustrated in

Figure 2.

Figure 2: Subject exercising with the wheel.

Figure 3: A photograph of the experimental set-up.

Figure 4: The SSA system in diagram.

Using the apparatuses we have designed, we can

measure mechanical impedance of the arm

accurately during motion. Study of human motor

learning will then be possible; with designing

appropriate experiments, we can examine a number

of issues in neuroscience i.e. learning, consolidation,

motor forgetting, retention and transfer of tasks. The

quantification of motor function provides a very

good tool for science and many other applications

such as robotics, physical medicine, and

physiotherapy.

3.2 Method Verification

To validate the method, before measuring human

arm’s mechanical impedance, we challenged our

method by attaching a linear spring according to

Figure 5. The elongation force of the spring

generates mechanical impedance that can be

measured and compared to an analytical prediction.

If the two quantities are comparable, the method is

confirmed to be correct. Then we can apply the

method to direct measurement of human arm’s

mechanical impedance.

Figure 5: Shoulder wheel with the eccentric spring.

The moment about at the centre, O, caused by the

spring generates the mechanical impedance at the

rotating wheel. Based on conventional mathematical

and mechanical calculations, we can predict the

mechanical impedance of the wheel.

All constant values such as r, d, and l are measured

from the experimental setup. Spring stiffness, K is

obtained by adding mass, measuring displacement of

the spring and then using least square fitting. The

stiffness was found to be 155.50 N/m.

Moreover, based on transduction matrix theory,

mechanical impedance was measured in an

experiment where the spring is attached to the

shoulder wheel. In Figure 6, the theoretical data and

the experimental data can be compared. We can see

that they have a very obvious similarity.

As it is observable in Figure 6, there is a good

agreement between the measured value and the

analytical solution. This supports and validates the

accuracy of the measurement method. Now the

method is prepared to use for direct measurement of

the human arm’s mechanical impedance.

BIODEVICES 2010 - International Conference on Biomedical Electronics and Devices

0 50 100 150 200 250 300 350

-0.04

-0.02

0.02

0.04

(degree)

(N.m.s)

Experiment

Theory

Figure 6: Experimental result (solid blue) of the

mechanical impedance of a spring as compared to the

theoretical solution (dashed red).

3.3 Arm’s Impedance

While performing the one-dimensional rotary task

with constant speed, the subjects change their arm’s

mechanical impedance on the wheel to synchronize

their arm’s movement with the rotation. Figure 7 to

Figure 10 show the measurement results of the same

experiment on two right-handed healthy subjects, a

man and a woman both of which do the task with

their right hand.

For both subjects, we observed the adaptation

process in form of changes in mean cycle of the

mechanical impedance, as well as ∆T and ∆ω.

Where ∆ω is the value of ω minus ω0 which is the

angular velocity measured at unloaded condition.

Figure 7 shows arm mechanical impedance of the

two subjects where each performed the task 31

times. Curves in solid line are those of subject 1

while measurements on subject 2 are shown in

dashed lines. We can see that density of the data is

more near the axis Zm=0. This can be explained by

the nature of the task that the subject is asked to

follow the motion without resistance or assistance

which means the velocity of the subject’s hand

should be equal to that of the wheel. Should any

discrepancy occurs, it is considered an error that is

represented in terms of excessive mechanical

impedance.

0 0.2 0.4 0.6 0.8 1 1.2

-0.3

-0.2

-0.1

0.1

0.2

0.3

0.4

Time (sec)

(N.m.s)

Subject 1

Subject 2

Figure 7: Arm mechanical impedance of two subjects;

each subject performed the trial 31 times. Curves in solid

line are those of subject 1 while measurements on subject

2 are shown in dashed lines.

In order to have a better understanding of how

mechanical impedance changes during adaptation,

mean value of the impedance curves are shown in

Figure 8; in the graphs the error-bar represents the

standard deviation of the impedance in each cycle.

0 5 10 15 20 25 30

-0.2

-0.1

0.1

0.2

Number of trials

Mean(Z

) (N.m.s)

Subject 2

Subject 1

Figure 8: Mean value of arm mechanical impedance of

two subjects doing 31 trials. Curves in solid line are those

of subject 1 while measurements on subject 2 are shown in

dashed lines.

Please note that the relatively high standard

deviation is mainly because of the stochastic

temperament of the biomechanical system.

Mechanical impedance is a product of T divided by

ω thus an intrinsic property of a mechanical system.

However in this biomechanical system, this property

changes with neural signals. For example, when the

neural signal is low density, the muscles are less stiff

hence we expect that the impedance is lower

comparing to a posture with high density neural

signals. The value of ∆T measured in our experiment

is proportional to the interaction force between the

subject’s hand and the wheel’s handle. The

interaction force, in turn, has to do with each single

muscle’s force. So if we study the changes of the

measured mechanical impedance, we will have some

clue about how neural signals of the muscles

regulated to control the motion of the arm.

0 5 10 15 20 25 30

-1

-0.5

0.5

Number of trials

Mean(

T) (Rad/s)

Subject 1

Subject 2

Figure 9: Mean value of the interaction torque of two

subjects in 31 trials. Curves in solid line are those of

subject 1 while measurements on subject 2 are shown in

dashed lines.

A NOVEL DEVICE FOR MEASURING MECHANICAL IMPEDANCE DURING DYNAMIC TASKS

Mean value and standard deviation of the torque,

∆T, is shown in form of an error-bar graph in Figure

9. In Figure 10 also, we can see the error-bar graph

of mean value and standard deviation of ∆ω.

0 5 10 15 20 25 30

-0.9

-0.8

-0.7

-0.6

-0.5

Number of trials

Mean(

Δω

) (Rad/s)

Subject 1

Subject 2

Figure 10: Mean value of hand velocity of two subjects in

31 trials. Curves in solid line are those of subject 1 while

measurements on subject 2 are shown in dashed lines.

4 AN IMPEDANCE BASED

INDICATOR

In this paper we used an electromechanical

simultaneous sensor cum actuator to propose a

method and a device which is capable of the

measuring impedance, the torque, and the velocity

during motion. In comparison with existing

methods, this methodology is much simpler to use.

More importantly, we can measure the impedance,

the torque, and the angular velocity during any

motion profile accurately. In conventional methods

of impedance measurement, one needs to apply

perturbation while our method does not require

perturbation in a sense of an externally applied

force. In our experiments, we applied a constant

speed to the subject’s limb while their actual

reaching speed profile is always a bell-shape

function. Then we measured impedance based on the

resulted interaction force and the changes in the

initial speed.

The experimental results showed that during

adaptation to a rotational motion with constant

speed, subjects adapted their arm’s mechanical

impedance with changing their interaction force and

velocity.

The tests will be soon available to some stroke

patients before, during, and after upper limb

rehabilitation. The values of impedance, torque, and

velocity will be analyzed and compared to Fugle-

Mayer motor function assessment test in order to

give the evaluators a quantifying tool to help them

with an objective assessment.

ACKNOWLEDGEMENTS

Hereby we would like to acknowledge the School of

Mechanical and Aerospace Engineering at Nanyang

Technological University and the M&C Lab in

especial. We shall also thank Professor Etienne

Burdet for his comments. Last but not least Mrs.

Maryam Khademi’s help with reviewing the paper is

appreciated.

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BIODEVICES 2010 - International Conference on Biomedical Electronics and Devices