Ergonomic considerations for anthropomorphic

wrist exoskeletons: a simulation study on

the effects of joint misalignment

Mohammad Esmaeili, Kumudu Gamage, Eugene Tan, and Domenico Campolo∗

School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798 Singapore

Abstract—This work focuses on anthropomorphic exoskeletonsfor the human wrist. We consider a 2 dof model for the humanwrist with non intersecting joints and a similar model for theexoskeleton. We assume a viscoelastic attachment between thehuman hand and the handle of the exoskeleton which on one sideallows the different kinematics of the exoskeleton to follow thehuman wrist and, on the other side, induces reaction forces at alljoints, in particular causing discomfort. We quantify discomfortas the amount of potential energy stored in the deformation ofthe viscoelastic attachment.

For a specific exoskeleton implementation, based on kinematicsimulations, we report the kinematic mismatch (i.e. differencesbetween the human joints and the corresponding exoskeletonjoints) as well as the reaction forces arising when the humanjoints assume postures throughout their physiological range ofmotion. Considering a typical distribution of joint offset forhumans (derived from literature) and the asymmetry in thediscomfort function (derived from our simulations) we addressthe ‘one-size-fits-all’ problem and propose an optimal joint offsetfor the exoskeleton, based on the minimization of the aggregateloss function.

I. INTRODUCTION

Human-machine interaction is a central topic in the field

of robotic exoskeletons (exos) and more recently ergonomic

factors are being systematically included since the early phases

of design [1], [2]. Exos can be divided into two main cat-

egories: anthropomorphic and non-anthropomorphic [3]. In

this paper we present ergonomic considerations, based on

kinematic simulations, for anthropomorphic exos meant to act

in concert with the human wrist.

Discomfort in wearing an exo is due to interaction forces

between human and exo arising at those locations where the

exoskeleton is attached to the human limb. Such forces result

from ‘kinematic discrepancies’ [4], due for example to over-

simplified models of human kinematics and/or misalignments

between human and exo joints [5].

Most of the modern approaches propose the use of extra

degrees of freedom (dof) for compensating joint misalign-

ments. Such extra dof are passive, while only the joints which

correspond to the human ones are meant to be actuated. While

introducing extra dof clearly helps reducing or eliminating

kinematic discrepancy (for example, a 6dof structure can

*Corresponding author d.campolo@ntu.edu.sg. This work is sup-ported by the Academic Research Fund (AcRF) Tier1 (RG 40/09), Ministryof Education, Singapore, and the New Initiative Fund 2010 (NTU).

surely adapt to a human wrist, at least within a certain range),

it should be noticed that, when the extra dof are present

but locked during normal operations, a kinematic mismatch

might still arise, i.e. joint angles at corresponding exo and

human joints no longer coincide. Although some recent studies

focused on reaching-movements for robot-assisted rehabilita-

tion for the wrist districts [6], [7], [8], [9], [10], the effect

of kinematic mismatch on robot control strategies, especially

in relation to neurorehabilitation, received relatively less at-

tention. Most control strategies, in fact, assume that driving

(imposing motion or torque) a robotic joint is equivalent to

driving the corresponding human joint.

In this paper, we do consider extra dof only for the

purpose of wearing the exoskeleton, e.g. different subjects

might require different positioning of the handle, but we

will consider that all the extra dof as locked during normal

operation. Therefore, from a kinematic perspective, the wrist

exoskeleton will comprise only 2dof mobility at joints which

are, in principle, aligned with human ones.

We shall consider a physiologically accurate 2dof model of

the human wrist, which comprises an offset between the two

human joints. Such an offset is known to vary from subject to

subject, with a distribution experimentally derived by [11]. In

our study, we assume that the misalignment between human

and exo occurs at the both proximal and distal joints along

the offset between them.

The human hand and the exo handle represent the end-

points1 of two dof structures, for any non-zero misalignment,

the position and orientation of the hand would be obviously

incompatible with the position/orientation of the handle. In

reality, the hand is not a perfectly rigid body, due for example

to the skin compliance and to the possible adjustment in

the grasping. For this reason we hypothesize that contact

between hand and handle is non-rigid and occurs through

some springs. In this study we assume linear springs and

this is clearly a simplification, nevertheless interesting features

such as asymmetry in the reaction forces can be captured, as

discussed next.

As for the structure of this paper, the model of human wrist

and exoskeleton is described in Section II, the prototype of

1The other endpoint is where the exo is attached to the forearm, we assumethis attachment much more rigid than the hand-handle one, see for example[12, Chapter 5].

2011 IEEE/RSJ International Conference onIntelligent Robots and SystemsSeptember 25-30, 2011. San Francisco, CA, USA

978-1-61284-456-5/11/$26.00 ©2011 IEEE 4905

our exoskeleton is presented as well. Then, we present the

simulation and data analysis and show how misalignments

lead to kinematic mismatch between exo joints and human

wrist counterparts. As the results of our study, the reaction

forces in wrist joint and the deformation energy in the hand-

handle attachment points is presented. Subsequently, as ‘one-

size-fits-all’ concept, we compute the optimal joint offset for

exoskeleton to have the least discomfort. Finally, in section

IV, the results are discussed.

a) b)

Fig. 1. Exoskeleton with hand model. a) Configuration of the exoskeletonalongside the wrist. b) SimMechanics model.

II. METHODS

A. Modeling the human wrist

The human wrist is a complex joint with 2 degrees of

freedom (dof) responsible for radial-ulnar deviation (RUD,

distal) and flexion-extension (FE, proximal). Despite small

changes in the instantaneous center of rotation for each joint

during rotations, a widely accepted approximation is to assume

ideal revolute joints for both degrees of freedom. The simplest

models assume a universal joint [13]. In reality, the FE and

RUD axes are almost orthogonal and non-intersecting [14] and

the joint offset of between the RUD and FE axes is known to

vary among subjects. Leonard et al. [11] investigated, with

noninvasive measurements, the distribution of the offset for a

population of 108 subjects and reported a 6.8mm mean inter-

axes offset with a distribution as shown2 in Fig. 2.

−20−16−12−8 −4 0 4 8 12 16 20 24 280

0.5

1

Joint axes offset [mm]

Fre

qu

en

cy

Fig. 2. Normalized frequency distribution of wrist joint rotation axes offset,based on [11].

Based on the above considerations, we developed a kine-

matic model of the human wrist in the SimMechanics (Math-

Works Inc.) environment. As shown schematically in Fig. 3,

2Note: the values were digitized from the original work [11].

Fig. 3. Functional diagram of the wrist and exoskeleton. Through a chain oflinks and joints human wrist is connected to the exoskeleton. Joint offset isconsidered for the both wrist (δ) and exoskeleton (δexo). Misalignment (m)is applied on the exoskeleton joints throughout the simulations.

the model consists of series of three rigid bodies3, the most

proximal being the forearm (fixed) and the most distal be-

ing the hand, connected to one another via revolute joints.

We considered two orthogonal joints ωwristFE (proximal) and

ωwristRUD (distal) and with an offset between the two axes (‘joint

offset’) along the longitudinal axis of the forearm (Y-axis).

Each joint has an associated joint angle: θFE and θRUD

for the FE and RUD axes, respectively. For the joint angles,

we assumed an average range of motion (RoM) as [-50 35]

degrees for θRUD and [-65 70] degrees for θFE .

B. The modeling of the exoskeleton

For the exoskeleton, we considered an anthropomorphic

structure, i.e. a 2dof mechanism with revolute joint axes ωexoRUD

and ωexoFE with a similar proximal-distal order and aligned with

the anatomical counterparts. As for the alignment, as we shall

see next, a variable misalignment will be purposely introduced

to analyze its effects.

The proximal end of the exoskeleton is meant to be attached

to the forearm, and therefore fixed. The distal end of the

exoskeleton is attached to the hand through the handle. While

for the forearm we can resort to optimal attachments methods

which minimize skin motion effects, e.g. see the splinting

proposed in [15], the hand-handle attachment is more prone

to relative motions and, to the authors’ knowledge, much less

analyzed in literature. For this reason, we assumed a perfect

attachment between human forearm and the proximal side

of the exoskeleton while we assumed a non-rigid attachment

between human hand and handle. This non-rigid attachment

is implemented via a set of four non-collinear ideal springs

which are meant to allow some degree of relative motion

between human hand and handle during grasping. This is

clearly a rough approximation and its required experimental

validation by the authors is still on-going at the time of writing.

Nevertheless, we refer to similar approaches performed by

Schiele et al. on [1] although not specifically for the hand-

handle attachment. We heuristically set the stiffness constant

3The middle body is simply used to introduce an offset between the twojoints.

4906

to the four springs equal to 2000 N/m. The use of four

non-collinear springs results in a translational and rotational

stiffness throughout the movements which are considered in

potential energy (see III-C).

Besides the FE and RUD joints which are supposed to mir-

ror the human counterparts, the exoskeleton is also endowed

with a number of ‘passive’ joints. Such passive joints are

required to adapt the exoskeleton itself to the different size

of end users.

Remark: the passive joints are meant to be locked while

the exoskeleton is in use. The model used in our simulations,

described next, takes into account the full structure of the

exoskeleton. This is important for future studies, when the

inertial properties of the exoskeleton will also be considered.

Fig. 4. Prototype of the exoskeleton. Besides, the FE and RUD joints of theexoskeleton which are supposed to mirror the human counterparts, the extrapassive joints are considered to align the exoskeleton with different size ofend users.

C. Simulation and data analysis

Although in this study we are interested in the ergonomics

of the exoskeleton from a kinematic perspective, in our sim-

ulations we implemented the full structure of the exoskeleton

as shown in Fig. 4, comprising the inertial properties of

each element. Given the elastic and the inertial properties

present in the model, transient behaviors would inevitably

arise after each step of the inputs. For this reason, we also

added linear dampers in series to each spring, to dampen

out any mechanical resonance due to the elastic properties

of the springs and the inertial properties of the exoskeleton.

Heuristically, we set the linear damping coefficients to 1.0

N/(ms−1) as this generated overdamped behaviors, quickly

leading to steady-state conditions.

In order to analyze the steady-state conditions for different

human wrist postures, FE and RUD joints in the human wrist

model are actuated according to a sequence of discrete values

corresponding to a 11 × 9 matrix of values covering the RoM

mentioned in II-A.

SimMechanics is a continuous time simulator, so discon-

tinuous, step-like transitions between two discrete values of a

joint angle would elicit long-lasting transient behaviors, while

we are only interested in steady-state conditions. In order to

generate smooth transitions between discrete values of each

joint angle, we used the jtraj function, distributed with

the MATLAB Robotics Toolbox [16], which implements a 7th

order polynomial interpolation.

As seen from Fig. 5, the combined effect of smooth tran-

sitions between discrete values of the human joint angle and

the overdamped response of the system ensures short transient

behaviors. The steady-state conditions of the angles for both

human and exoskeleton joints can be reliably sampled at fixed

time intervals (circles in Fig. 5).

9.7 9.8 9.9 10 10.1 10.2 10.3

−5

0

5

time [s]

θR

UD [deg]

Exo Human Sampling Sampling

Fig. 5. Steady-state sampling represented in time domain. Blue dash-lineis the active movement of wrist followed by exoskeleton (red solid line)passively. Circles are the samples chosen when system is in steady-statecondition.

By sampling at these very fixed time intervals, we were able

to extract the steady-state values for the following variables

(for both the human wrist and the exoskeleton):

• kinematics: angular position, angular velocity and angular

accelerations for FE and RUD joints;

• reaction forces (F r): amplitude4 of generated forces due

to misalignments for FE and RUD joints, computed as

Fr =√

F 2x + F 2

y + F 2z

• discomfort function: for each misalignment, we compute

the mean value over the workspace of the elastic energy

of the springs between hand and handle5 (see Fig. 3);

4Single force components could be analyzed as well, but we found noqualitative difference.

5Although rather arbitrary, we noticed no qualitative difference whenchoosing the mean value of reaction forces or kinematic mismatch betweenhuman and exo joint angles.

4907

Therefore, for each posture of the human wrist, we extracted

the corresponding values for the physical variables described

above.

We repeated the simulation for different possible misalign-

ments between the RUD/FE joint of the exoskeleton and the

RUD/FE joint of the human wrist. In particular, based on the

work of Leonard et al. [11] in Fig. 2, a misalignment distribu-

tion6 was considered. The choice of range of misalignments

was dictated by the aggregate loss calculations explained later.

NOTE: just for programming convenience, the human joint

offset was held constant while the misalignment was generated

by varying the exoskeleton joint offset.

III. RESULTS

A. Kinematic mismatch

We simulated a so-called active mode operation, i.e. de-

sired angles were imposed for the human joints while the

exo passively followed. As expected, except for the case of

perfect alignment, there was a kinematic mismatch between

the exo FE/RUD angles and human counterpart (since the

joint misalignment was for the FE (proximal) joint, the angular

mismatch was obviously found between the human and exo

FE and RUD angles too). Fig. 6 shows a representative

case, for a +12mm joint misalignment. The mismatch grew

approximately linearly with the angle. For the representative

case of +12mm misalignment, there is a 20% relative error,

as shown in Fig. 6.

−50 0 50

−20

−10

0

10

20

θFE

[deg]

θR

UD [

de

g]

Human Exo

Fig. 6. Range of motion of exoskeleton (solid line-crosses) is compared withwrist (dots-circles) for a representative +12mm misalignment on ωexo

FE.

B. Reaction forces at human wrist

Fig. 7 shows the reaction forces at the FE joint of the

human wrist (FrwristFE ) against the range of motion of FE

and RUD joints. These forces are monitored in the presence

of +12mm misalignment between the ωFE of wrist and

exoskeleton. In covering the whole RoMFE , the maximum

amounts of reaction forces occur in the maximum range of

the wrist flexor for the whole RUD joint angles. No reaction

6These misalignments are along the longitudinal axis of the forearm, i.e.in the Y-axis as in Fig. 3.

force is seen throughout the RoMRUD when θFE = 0. For

each FE joint angle the amount of FrFE is almost constant

across RoMRUD .

Note: Since, stiffness of the springs in the attachment points

as well as damping ratio are heuristically selected, we took into

account the normalized values for all forces.

−500

50

−20

0

200

0.5

1

θFE

[deg]θRUD

[deg]

Norm

aliz

ed r

eaction f

orc

eFig. 7. Normalized reaction force on FE joint of wrist over the range ofmotion of FE and RUD for +12mm misalignment on ωexo

FE.

C. Non-rigid attachment

The resulting deformation energy of the four non-collinear

springs, explained in II-B, during movement of the wrist could

be calculated through

U t =4

∑

i=1

1

2ki l

2

i (1)

Where, k is the stiffness and l is the length of each spring

shown in Fig. 3.

−500

50

−20

0

200

0.5

1

θFE

[deg]θRUD

[deg]

No

rma

lize

d d

efo

rma

tio

n e

ne

rgy

Fig. 8. Normalized deformation energy at attachment points of end-effectorfor +12mm misalignment on ωexo

FE.

Fig. 8, illustrates the resulting deformation energy over wrist

RUD and FE angles. It can be seen that, deformation energy

significantly changes across flexion-extension rotations while

it seems less sensitive to radial-ulnar deviations.

4908

Moreover, we calculated the mean values of the deformation

energy for each amount of misalignment and considered the

normalized amount of this deformation energy during move-

ment of wrist as the Normalized discomfort which is shown

in Fig. 9.

−60 −40 −20 0 20 40 600

0.5

1

Misalignment [mm]

No

rma

lize

d d

isco

mfo

rt

Fig. 9. Normalized discomfort over the different amount of misalignments.

D. One-size-fits-all

Since the RUD–FE offset for the exoskeleton cannot be in

principle aligned by simple visual procedures, in this section

we try to estimate which optimal offset, for the exo, would

best fit an entire population, not just a single subject. For this

we shall use the distribution of the joint offsets derived by

Leonard et al. [11] and correlate it with the discomfort caused

by different misalignments, as in Fig. 9.

To this end we shall make use of the concept of ‘aggregate

loss’ [17] which is widely used in the fields of Human

Factors and Ergonomics as well as in Economics. Simply

put: if we have to design a one-size T-shirt meant to fit

an entire population, knowing the anthropomorphic data of

a population and knowing that each individual will claim a

refund proportional to the amount of discomfort (a positive

function of size mismatch), what is the optimal size that will

minimize the total refund (aggregate loss)?

One might be tempted to design a T-shirt that fits the

average size (from the population distribution) any asymmetry

in the population distribution or in the discomfort function

(e.g. better a T-shirt too large rather than too small) might

induce better choices.

In our case, the distribution PDF (δ) of joint offsets (δ)

for the population sampled by Leonard et al. [11], reported

in Fig. 2, does not present remarkable asymmetries, with the

average offset being δ = 6.8mm. On the other hand, the

discomfort U(m), function of misalignment (m), is highly

asymmetric due to mounting the exo in the interior side of

the wrist, as shown in Fig. 9. An exoskeleton with offset δexo

worn by a person whose anatomical offset is δ, would cause a

discomfort U(δexo−δ). Therefore, the aggregate loss L(δexo),for a specific choice of exoskeleton offset, is

L(δexo) :=

∫

PDF (δ)U(δexo − δ) dδ

Fig. 10 shows the aggregate loss numerically estimated from

the data available from Leonard et al. [11] and the simulated

discomfort function.

−20−16−12 −8 −4 0 4 8 12 16 20 24 280

10

20

30

Joint axes offset [mm]

To

tal d

isco

mfo

rt

Fig. 10. Density of total discomfort over the range of wrist axes offset.The mean of total potential energy for a set of misalignment is taken intoconsideration in calculating total discomfort.

The optimal offset for the exoskeleton is numerically found

to be

δexoopt := argminL(δexo) = 4 mm

IV. CONCLUSION

We evaluated the transparency of an exoskeleton in presence

of misalignments between human and mechanical joints. In

particular, we evaluated the response of the exoskeleton in

terms of kinematic mismatch and reaction forces in wrist joint

by simulating imposed movements at the human joints (within

a physiological range of motion). Although the exoskeleton

in Fig. 4 comprises various extra (prismatic) joints, to allow

different users to wear the exoskeleton, during operation all

these extra prismatic joints are meant to be locked. Therefore,

the exoskeleton is a 2dof system. Any misalignment would

make it kinematically incompatible (kinematic discrepancy)

with the human 2dof wrist unless some compliance is allowed.

The distal part of the exo is attached to the hand through a

handle while the proximal part is meant to be attached to the

forearm. We focused on the hand-handle attachment since, is

more prone to relative motion and is less addressed in litera-

ture, to the authors’ knowledge. To do so, we considered a non-

rigid attachment between hand and handle by implementing a

set of four non-collinear springs.

Our simulations quantified the amount of kinematic mis-

match between the human joint angles and the exo counter-

parts caused by joint misalignment.

Such a kinematic mismatch should be taken into account

especially when the exoskeleton is being driven, imposing

movement to the human joints. Typically, it is assumed perfect

match between human and exo joint angles while our simula-

tions show that large errors (e.g. 20% relative error in Fig. 6)

might arise. This suggests that the human joint angles should

be measured separately from the exo joint angles.

Although the exo joints are not actuated in our study,

reaction forces still arise due to kinematic mismatch, as

highlighted by our simulations. As mentioned in [4], kinematic

discrepancy is one of the causes for reaction forces. Since

our exoskeleton is located on the volar side of the wrist, it

causes asymmetric kinematic mismatch between exoskeleton

and wrist for flexion rotations in presence of misalignments.

4909

Therefore, larger amounts of reaction forces occur during wrist

extension, rather than flexion (see Fig. 7). These reaction

forces do not perform work on the human joint but cause

discomfort, or worse, pain.

When a misalignment between human and exo joints is

present, the end-effector does not closely follow the hand

making the non-collinear springs to stretch or compress,

causing deformation energy. Due to the structure of the ex-

oskeleton and its position (volar part of the wrist), deformation

energy has an asymmetric profile with regard to rest position

of FE (θFE = 0) with larger deformation energies during

flexion. To have a natural movement without perturbation, it

is needed to have the least resistance against the motion in

any voluntarily movement over the range of motion of human

joint. The occurrence of the reaction forces on the joint would

cause a perturbation on the movement because of the low

impedance/stiffness of the limb.

Despite the oversimplifications, this work highlighted that

misalignments would result in kinematic discrepancies and

generation of interaction forces in pHRI. Kinematic mismatch

would then make an exoskeleton ‘non-transparent’, causing

movement perturbation. Since, the discomfort is asymmetric,

choosing an offset for the exoskeleton based on the average

offset for the human joints, might not be optimal from a

‘one-size-fits-all’ perspective. Based on the aggregate loss

minimization concept, we numerically found that a 4mm offset

for the exo joints, instead of a 6.8 mm average (as from the

experimental distribution of human offsets), would actually

determine the optimal one-size-fits-all.

REFERENCES

[1] A. Schiele, “An explicit model to predict and interpret constraint forcecreation in pHRI with exoskeletons,” IEEE/ICRA, 2008, pp. 1324–1330.

[2] N. Jarrasse and G. Morel, “On the kinematic design of exoskeletonsand their fixations with a human member,” in Proceedings of Robotics:

Science and Systems, Zaragoza, Spain, June 2010.

[3] F. Sergi, D. Accoto, N. L. Tagliamonte, G. Carpino, and E. Guglielmelli,“A systematic graph-based method for the kinematic synthesis of non-anthropomorphic wearable robots for the lower limbs,” Frontiers of

Mechanical Engineering in China, 2010.

[4] N. Jarrasse, M. Tagliabue, J. Robertson, A. Maiza, V. Crocher, A. Roby-Brami, and G. Morel, “A methodology to quantify alterations in humanupper limb movement during co-manipulation with an exoskeleton,”Neural Systems and Rehabilitation Engineering, IEEE Transactions on,vol. 18, no. 4, pp. 389–397, 2010.

[5] A. Schiele and F. van der Helm, “Kinematic design to improve er-gonomics in human machine interaction,” IEEE Transactions on Neural

Sys and Rehab Eng, vol. 14, no. 4, pp. 456–469, 2006.

[6] D. Campolo, D. Formica, E. Guglielmelli, and F. Keller, “Kinematicanalysis of the human wrist during pointing tasks,” Experimental brain

research, vol. 201, no. 3, pp. 561–573, 2010.

[7] N. Tagliamonte, M. Scorcia, D. Formica, F. Taffoni, D. Campolo, andE. Guglielmelli, “Force control of a robot for wrist rehabilitation: Copingwith human motor strategies during pointing tasks,” RSJ Advanced

Robotics Journal, vol. 25, pp. 537–562, 2011.

[8] D. Campolo, D. Accoto, D. Formica, and E. Guglielmelli, “Intrinsicconstraints of neural origin: Assessment and application to rehabilitationrobotics,” Robotics, IEEE Trans on, vol. 25, no. 3, pp. 492–501, 2009.

[9] F. Sergi, D. Accoto, D. Campolo, and E. Guglielmelli, “Forearmorientation guidance with a vibrotactile feedback bracelet: On thedirectionality of tactile motor communication,” in Biomedical Robotics

and Biomechatronics, 2008. 2nd IEEE RAS & EMBS International

Conference on, pp. 433–438.

[10] D. Campolo, F. Widjaja, M. Esmaeili, and E. Burdet, “Pointing with thewrist: a postural model for donders law,” Experimental Brain Research,vol. 212, no. 3, pp. 417–427, Jun. 2011.

[11] L. Leonard, D. Sirkett, G. Mullineux, G. Giddins, and A. Miles,“Development of an in-vivo method of wrist joint motion analysis,”Clinical Biomechanics, vol. 20, no. 2, pp. 166–171, 2005.

[12] J. Pons, Wearable robots: biomechatronic exoskeletons. Wiley OnlineLibrary, 2008.

[13] D. Williams, H. Krebs, and N. Hogan, “A robot for wrist rehabilitation,”in IEEE/EMBS 2001, vol. 2, 2001, pp. 1336–1339 vol.2.

[14] J. Andrews and Y. Youm, “A biomechanical investigation of wristkinematics,” Journal of Biomechanics, vol. 12, no. 1, pp. 83–93, 1979.

[15] E. Rocon, A. Ruiz, J. Pons, J. Belda-Lois, and J. Sanchez-Lacuesta,“Rehabilitation robotics: a wearable Exo-Skeleton for tremor assessmentand suppression,” in IEEE/ICRA 2005, pp. 2271–2276.

[16] P. Corke, “A robotics toolbox for MATLAB,” Robotics & Automation

Magazine, IEEE, vol. 3, no. 1, pp. 24–32, 1996.[17] C. Hsu, “Developing accurate industrial standards to facilitate production

in apparel manufacturing based on anthropometric data,” Human Factors

and Ergonomics in Manufacturing, vol. 19, no. 3, pp. 199–211, 2009.

4910