Modulation of Impedance and Muscle Activation of the

Upper Limb Joints while Simultaneously Controlling

Manual-grasping and Walking

Joseph Mizrahi

, Navit Roth

and Rahamim Seliktar

Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa, Israel

School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA, U.S.A.

Keywords: Mechanical Impedance, Muscle Activation, Motor Control, Manual-grasping, Balanced Walking,

End-effector, Joint Constraints.

Abstract: The design of spring-based artificial and robotic arm joints presents a challenge in problems of transportation

of manually-held objects during walking. For maintaining stability of these objects, stiffness and damping of

the arm joints have to be adjusted by continuously tuning muscle activation. This necessitates knowledge

about the mechanisms by which stiffness and damping (mechanical impedance) are being modulated in

walking movement. The paradigm employed in this study consisted of modeling the impedance adjustments

from input data obtained in simultaneously controlled grasping and walking experiments. While walking on

a treadmill, tested subjects held a cup filled with liquid and were asked to aim at minimizing liquid spillage.

Monitoring liquid spillage served to quantify stability of the hand as the end-effector of the upper limb.

Kinematic data were obtained for the shoulder, elbow and wrist joints. Accelerometer data were obtained for

the wrist and for the knee. Electro-myography (EMG) data were collected for the wrist flexor and extensor

muscles. Based on the measured data, regressive functions were used to express stiffness and damping as a

function of angle and angular velocity. The joints of the upper limb were thereafter successively constrained

to study the effect of joint immobilization on joint impedance and muscle activation. The obtained results

indicate the nonlinearity of the joint impedances as required in tasks of manual grasping of objects during

locomotion, with and without joint constraints.

1 INTRODUCTION

Walking while grasping a cup filled with liquid (e.g.

tea, water) is a common daily activity necessitating

coordination of locomotion and prehension. Clearly,

the aim in this task is to navigate the moving hand in

space, so as to avoid or minimize spillage or dripping

of liquid from the cup. Following unintended

perturbations, it would also be desirable that the

grasping hand regains its stability through motion of

the joints of the upper limb. Thus, an interesting

question is how our body controls these joint

movements in order to perform the task in question.

Studying this question would provide an insight

into the mechanisms, by which the stiffness and

damping are adjusted to accommodate changes taking

place during manual transport of objects while

walking, if stability of the held object is to be

maintained.

Mechanically, the upper limb can be represented

by three major segments including the arm, forearm

and hand, connected through the shoulder, elbow and

wrist joints. Through the motion of its joints, the

upper limb provides the output to the terminal

segment or end-effector: the self-navigating free hand

grasping the cup of liquid being subjected to an

oscillatory-like motion.

The complex relationship between torque, angular

position and angular velocity, termed mechanical

impedance, defines the stiffness and damping

characteristics of the joint. Controlling the

mechanical impedance of the upper limb joints is an

important feature of the neuromuscular system

enabling to stabilize hand-held objects in space, or to

minimize the effect of externally applied forces

(Stroeve, 1999).

Past studies on the combined control of the

locomotor and prehensile systems have suggested

that locomotion and reaching are closely connected

motor activities (Georgopoulos and Grillner, 1989).

More recently, mechanical aspects of the interaction

between grasping and walking were reported (Roth et

194

Mizrahi J., Roth N. and Seliktar R.

Modulation of Impedance and Muscle Activation of the Upper Limb Joints while Simultaneously Controlling Manual-grasping and Walking.

DOI: 10.5220/0006239101940199

In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2017), pages 194-199

ISBN: 978-989-758-216-5

al, 2011). Muscle activity was not included in this

latter study.

The present study deals with the analysis of

motion of the hand grasping a cup filled with liquid

while walking. In order to explore the relative role of

each of the joint to the mechanical impedances,

different joint disabilities were simulated by the

successive immobilization of each of the shoulder,

elbow and wrist joints. Activation of the major

muscle groups of the elbow joint was also studied by

monitoring their EMG signals. Since impedance-

based control strategies require information on the

continuous nonlinear behavior of the joints, the

results of the present research should have

implications on the design of spring based artificial

and robotic arms.

2 METHODS

Subjects (n=4), aged 28-57 (average 35.5, SD 14.3)

provided informed consent to participate in the study

according to the University’s ethical committee’s

guidelines. The subjects walked on a treadmill

(Woodway PPS55-Med) at a constant speed of 1.25

m/s while holding in their right hand a cup filled with

liquid and fixing their look at a mark positioned in

front of them at eye level. While walking, the subjects

were instructed to maintain the liquid surface as level

as possible, to minimize "liquid spillage" from the

cup.

The walking tests, each of duration of 30 seconds,

were performed in the following testing conditions:

unrestricted joints of the upper limbs, followed by the

successive restriction of each of the right wrist, elbow

and shoulder joints. Joint restrictions were applied in

order to immobilize each joint (wrist 180 degrees,

elbow 90 degrees and shoulder 0 degrees). The

restrictions were accomplished by means of

constraining braces or straps. The tests were repeated

five times at each condition with a resting period of 2

min between the tests.

3 INSTRUMENTATION

3.1 Apparatus for Liquid Spillage

Quantitation

To observe the target of minimum liquid spillage, an

instrumented cup was designed to monitor liquid

level within the cup as follows, to simulate “liquid

spillage”. A plastic cup was wired at its inner surface

with circular conductive stripes, parallel to each other

and to the bottom of the cup, to indicate different

levels for the liquid. A signal was generated when the

liquid (salted water) level raised as a result of the

subject's motion and made contact with any of the

circular stripes to short a circuit.

3.2 Kinematics

Since the joint angles served as inputs for the model,

goniometers (Biometrics Ltd, Gwent, UK) were used

for two-dimensional measurements of elbow and

wrist angles. For kinematic measurements in the

sagittal plane video data were collected by two-

reflective markers located at the upper arm, near the

shoulder and elbow joints, as shown in Fig. 1.

Figure 1: Positioning of sensors (blue=positioning marker,

purple=goniometer, light green=EMG, yellow=accelero-

meter; the cup is shown in green color).

To monitor the foot-strike event, a light-weight

accelerometer (Kistler PiezoBeam, type 8634B50)

was attached onto the skin in closest position to the

bony prominence of the tibial tuberosity and was

aligned along the longitudinal axis of the tibia to

provide the axial component of the vertical impact

acceleration on the shank.

The signals from the accelerometer were fed to the

PC-based data acquisition system at a sampling rate

of 1000 Hz. A high sampling rate was required to

pick-up the timings of the spike acceleration resulting

from foot strike.

3.3 Electromyography (EMG)

Surface EMG signals from the right biceps and

triceps muscles were monitored to indicate the

activation of the major muscle groups of the elbow

joint. The signals were measured by means of two

pairs of bipolar Ag/AgCl disposable snap electrodes

(10mm diameter), amplified (Atlas Research Ltd.,

Hod-Hasharon, Israel) and sampled at 1000 samples/s

Modulation of Impedance and Muscle Activation of the Upper Limb Joints while Simultaneously Controlling Manual-grasping and Walking

195

(National Instrument AT-MIO-16E). The signals

were processed as follows: in the time domain, the

signals of each muscle were filtered (2-500 Hz),

normalized to their respective maximal voluntary

contraction (MVC) value, after which the root mean

squares (RMS) were calculated. The co-contraction

value of both muscles was calculated (Winter, 2009).

In the frequency domain, steadiness of the median

frequency was used to indicate the possible presence

of muscle fatigue.

4 BIOMECHANICAL MODEL

The input to the system in Figure 1 are the periodic

displacement signals due to the walking body-

movement, as transmitted to the upper limb through

the shoulder girdle, and the output of the system is the

self-navigated free hand holding the cup-of-liquid.

The model segments are assumed to be rigid bodies,

with known mass and inertia properties. The joint

angles are as defined in Fig. 2. The shoulder angle Øs

is defined between the upper arm and the vertical.

Angles Øe and Øw represent the elbow and wrist joint

angles, respectively, and their corresponding θ’ are

the external angles of these joints. Angles θ (no

prime) are between segments and the horizontal. The

model segments are connected together by the joints

via lumped impedances representing damped springs.

The damped spring coefficients are expressible in

terms of joint angles and angular velocities (Mizrahi,

2015).

Thus,

()

jjjjjjjj

kkkk

02010

φφφφφ



−+−+=

(1)

()

jjoint of stiffness−

() ( )

jjjjj

bbb

010

φφφ



−+=

(2)

()

jjoint of damping−



The reference angle

0 j

was taken in the neutral

position of each joint.

These coefficients are related to joint torques M

as follows:

∂

(3)



∂

(4)

Figure 2: Sagittal view of segments and joints of the upper

limb: A=upper arm, in relation of vertical axis of the body

representing the walking body; B=forearm; C=hand.

The joint torque is M

obtainable by integration

and by summing up the elastic and damping torques.

=+=

btjstjtj

MMM

()()

+−+−

jtj

jtjj

φφφφ

()

[]

+−−

jtjjtjj

002

φφφφ



()()

jtj

jtjj

φφφφ



−+−

(5)

The torques of the wrist, elbow and shoulder

joints were obtained by solving the inverse dynamics

for the upper limb using Kane’s method (Kane and

Levinson, 1985). These torques were thereafter used

for the calculation of the stiffness and damping

coefficients at each joint.

4.1 Parameter Estimation and

Reduction of the Model

The stiffness and damping coefficients in Eqs. (5)

were resolved from the calculated torques in the

dynamic model by parameter estimation using

optimization procedures. Parameter estimation was

performed by using quadratic programming-

LSQLIN. Comparison between the various testing

conditions was carried out by using T-test for

repeated measures and statistical significance was

established at p-value p<0.05. Parameter identificati-

on was made to reveal the joint impedance model

which best fits all the tests made with and without

joint restrictions, and to indicate whether the general

impedance expressions could be reduced to a simpler

form. To ensure correct parameter estimation, all

predictor variables in the multiple linear regression

analysis must be uncorrelated and the model

BIODEVICES 2017 - 10th International Conference on Biomedical Electronics and Devices

196

parameters should be independent of each other.

Multiple collinearity diagnostic criteria combined

with F-test (Rapoport et al 2003) were used to reveal

dependencies and eliminate redundancies in the

numerical solution of the stiffness and damping

coefficients and reduce the variables in the stiffness

and damping functions. The reduction procedure of

the basic model was made separately for each joint.

5 RESULTS

In all four subjects, the liquid level did not reach the

highest conductive stripe during steady-state motion.

This indicated that the subjects succeeded in

stabilizing their end-effector, irrespective of whether

or not restrictions were introduced to the joints.

5.1 Joints Angles

Fig. 3 shows typical traces of the upper limb joint

angles while walking and holding the cup-of-liquid.

The traces shown are for the shoulder, elbow and

wrist angles. The dark dots designate heel-strike

events of the right foot.

5.2 Model Reduction

By applying the multiple collinearity diagnostic

criteria, the most significant stiffness coefficients

(with p-value p<0.05) were k

and k

, for the elbow

and shoulder joints and k

for the wrist joint (Eq 1).

The damping coefficient b

(Eq 2) was significant

only in the wrist joint. Thus, it was concluded that

reducing the optimal model to a 3-parameter model,

with nonlinearly variable stiffness and constant

damping would be sufficient, as follows:

For the wrist joint:

()

(6)

(

)



(7)

For the elbow and shoulder joints:

()

(

)

jjjjj

kkk

020

φφφ



−+=

(8)

Table 1 presents values of the overall stiffness

(Eqs. 6,8), in N*m/rad, with and without joint

restriction. The values designate averages of 5 tests,

each over the period of 30 s. The 'no restriction' case

served as a reference for comparisons (t-test), with

significance p level of p<0.05.

During the tests with no restriction, the overall

stiffness values were higher in the shoulder joint than

Figure 3: Typical traces of shoulder, elbow and wrist angles

during test. The dark dots designate heel-strike events of the

right foot.

Table 1: Overall stiffness (for the wrist, elbow and

shoulder, expressed in N*m/rad) with and without joint

restrictions. The values presented are averages of 5 tests,

each over the period of 30 s (SD).

Wrist Elbow Shoulder

SubjectRestriction

3.53 (0.01) 3.02 (0.05) 46.63 (12.83)

1.74 (0.01) 1.66 (0.36) 18.33 (0.45)

2.141(0.03)2.05 (0.24) 42.02 (8.39)

8.97 (0.00) 2.10 (0.14) 21.02 (1.16)

22.26 (0.06)2.90 (0.49) 57.36 (8.42)

Wrist

1.42 (0.02) 1.73 (0.14) 36.28 (3.99)

16.86 (0.27)1.99 (0.08) 54.74 (6.56)

126.65 (0.35)1.99 (0.16) 19.58 (1.57)

2.50 (0.01) 4.28 (0.43) 39.39 (4.14)

Elbow

1.90 (0.04) 3.39 (0.26) 47.61 (2.44)

1.42 (0.00) 2.51 (0.24) 53.84 (5.73)

4.14 (0.01) 3.03 (0.06) 19.70 (1.39)

2.67 (0.00) 3.60 (0.11) 64.91 (1.07)

Shoulder

5.82 (0.19) 1.95 (0.49) 26.52 (1.89) 2

2.18 (0.04) 1.72 (0.28) 52.77 (3.42) 3

6.58 (0.02) 2.67 (0.08) 59.92 (8.74) 4

in the elbow and wrist joints. Wrist restriction

resulted in an increase in stiffness (and damping) in

that joint in 3 out of the 4 subjects. The effect on the

elbow stiffness was a decrease in 3 out of 4 subjects.

The effect on the shoulder stiffness was an increase

in 3 out of 4 subjects. Elbow restriction demonstrated

a stiffness increase in that joint. The effect on the

wrist was a decrease in stiffness in 3 out of the 4

subjects (the effect on damping was not uniform).

Elbow restriction did not cause any uniform effect on

Modulation of Impedance and Muscle Activation of the Upper Limb Joints while Simultaneously Controlling Manual-grasping and Walking

197

the stiffness of the shoulder. Shoulder restriction

resulted in an increase in stiffness on that joint. In 2

subjects this restriction resulted in a decrease in

stiffness in the wrist and in 3 subjects an increase in

stiffness in the elbow.

5.3 EMG Results

EMG traces (linear envelope of filtered data) of the

biceps muscle alongside the elbow joint angle

variation and elbow stiffness during a typical test

without joint constraint are demonstrated in Fig. 4.

The heel-strike signals are also shown by the red dots.

It is seen that biceps EMG and elbow overall stiffness

are opposite in phase. No correlation, however, was

observed between EMG and joint angle. It should be

remembered that stiffness is estimated from the

model and is not directly expressed by the angle.

Summary of time-domain processing of the root

mean square (RMS) values of the EMG signals is

presented in Table 2 for one of the tested subjects. It

is noted that activation intensity of the triceps is

nearly 50% of that of the biceps. The results indicate

that activation of both the biceps and the triceps were

not significantly affected by constraining any of the

wrist, elbow or shoulder joints. Likewise was the case

for co-contraction of these two muscles. Median

frequency results did not indicate development of

fatiguing during the course of the tests.

Figure 4: Filtered EMG signal of biceps (linear envelope)

with no joint restriction (Blue line = EMG, light blue =

elbow joint stiffness, black line = elbow joint angle, red dots

= heel-strike events of right foot).

Table 2: Representative RMS values of the EMG results

(normalized to MVC) of Biceps and Triceps muscles and of

co-contraction. Both unconstrained and joint-constrained

cases are reported.

Joint

constraint

Biceps RMS Triceps RMS Co-contraction

No 3.284 (0.0130) 1.659 (0.0090) 68.20 (0.080)

Wrist 3.284 (0.0086) 1.664 (0.0037) 68.25 (0.080)

Elbow 3.274 (0.0082) 1.655 (0.0041) 68.15 (0.045)

Shoulder 3.266 (0.0078) 1.653 (0.0057) 68.21 (0.093)

6 DISCUSSION

Although coordination between locomotion and

control has been studied in the past (Georgopoulos

and Grillner, 1989; van der Wel and Rosenbaum

2007, Roth et al 2011), no works were found dealing

with adjustment of the mechanical impedance by

continuously tuning muscle activation during

simultaneous control of grasping and walking.

The basic muscle-tendon model used was made to

include elastic and damping elements. The elastic

element depended on angular displacement and

angular velocity (Woo and Young, 1991) and the

damping element depended on angular velocity

(Milner and Cloutier, 1998). By checking for multi

co-linearity, this model was separately reduced and

adapted to each of the joints, in accordance with the

goodness of fit of parameter estimation.

The wrist joint was found to have constant

stiffness and damping (Eqs 6,7), and no regulation of

these coefficients was necessary during the gait cycle.

It should be reminded, however, that the finger joints

were not represented in the end-effector and this

segment was considered a rigid body attached to the

wrist joint. This representation was consistent with

the two-dimensional assumption of the model. The

other two joints had non-linear stiffness representa-

tions (Eq 7). Non-linear models are widespread in the

description of human joints (Rakheja et al 1993;

Karniel and Inbar, 1999; Konczack et al, 1999;

Rapoport et al 2003). Both in the elbow and shoulder

joints, stiffness included a constant coefficient as well

as an angular velocity-dependent coefficient.

The EMG results did not confirm a definite

relation between any of the elbow stiffness or elbow

joint angle and the activation of the flexor and

extensor muscles studied. It should be mentioned that

intensity of these muscles relative to their respective

MVC was only around 5% for the triceps and 10% for

the biceps muscles. This low activation suggests that,

most probably, other muscles (not monitored in this

study) also take part in controlling the elbow joint,

hindering the correlation sought. From the data of

stride timing versus biceps EMG it can be noted that

activation of this muscle decreases upon heel-strike

and increases again towards the next strike. In view

of the obvious presence of additional muscles in the

process of elbow control, this particular behavior of

the biceps should not be considered representative of

the other muscles. Siegler et al (1985) also reported

that joint torque and muscle activation are not

uniquely correlated.

We did not find in this study a pre-activation of

the muscles studied, prior to the impact loading

BIODEVICES 2017 - 10th International Conference on Biomedical Electronics and Devices

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introduced by heel strike. Previous studies have

indicated the presence of pre-activation in non-

repetitive activities such as ball-catching (Lacqaniti et

al, 1993). In the present study, loading was rather

repetitive, due to the cyclic nature of steady walking.

7 CONCLUSIONS

We investigated how the stiffness and damping of the

upper limb joints are being modulated in combined

activity of hand grasping and locomotion. Kinematic

data from the upper limb and of EMG from the wrist

extensors and flexors were obtained with the joints

unconstrained and after successively immobilizing

each of the joints. Stiffness and damping values of

each of the joints were obtained as a function of joint

angle, for the shoulder and elbow joints. The wrist

joint was found to have constant stiffness and

damping, and no regulation of these coefficients was

necessary during the gait cycle. The results also

showed how joint immobilization affects the joint

impedance behavior. The EMG results did not

confirm a definite relation between any of the elbow

stiffness or elbow joint angle and the activation of the

flexor and extensor muscles studied. The wide

variability in the impedance results obtained

indicated that the compensatory mechanisms

exercised by each subject to regulate the mechanical

impedance to overcome the joint restriction were

individual, not necessarily indicating to a common

pattern.This study sheds light on the mechanisms of

stabilization of grasped objects during walking and

the results obtained, despite their variability, may be

relevant for the future designing of artificial arms and

robots and for the development of more accurate

control strategies of combined hand grasping and

walking.

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