Analysis of Elbow-Joints Misalignment in Upper-Limb Exoskeleton

Matteo Malosio, Nicola Pedrocchi, Federico Vicentini, Lorenzo Molinari TosattiInstitute of Industrial Technologies and Automation, Italian National Council of Research

via Bassini 15, 20133 Milano, Italymatteo.malosio@itia.cnr.it

Abstract— This paper presents advantages of introducingelbow-joints misalignments in an exoskeleton for upper limbrehabilitation. Typical exoskeletons are characterized by axesof the device as much as possible aligned to the rotational axesof human articulations. This approach leads to advantages interms of movements and torques decoupling, but can lead tolimitations nearby the elbow singular configuration. A properelbow axes misalignment between the exoskeleton and thehuman can improve the quality of collaborative rehabilitationtherapies, in which a correct torque transmission from humanarticulations to mechanical joints of the device is required toreact to torques generated by the patient.

Index Terms— Exoskeleton; elbow singularity-free; human-robot axes misalignments; robot-assisted rehabilitation.

I. INTRODUCTION

Exoskeleton robotized prostheses and devices for reha-bilitation are typically designed to match and align theirmechanical joints to human limb articulations, to achievejoint decoupling and a good coverage of the whole arm rangeof motion. The development of upper-limb exoskeletonsneeds to face important problems related to the complexshoulder movement. For this reason methodologies to de-sign exoskeletons with improved ergonomic performances interms of adaptability and human-robot joint self-alignmentare presented in [1], [2], [3].

Moreover, singularities can play a significant role in defin-ing the actual exploitable range of motion of mechanicalchains. Exoskeleton singularities typically occur if rotationaljoint axes are aligned during their movement.

Some developed solutions have been optimized to faceand limit singularities drawbacks at the shoulder, in orderto exploit as much as possible the human shoulder range ofmotion [4]. On the other side, few emphasis has been giventill now to the singularity affecting the upper limb and theexoskeleton at the elbow joint.

Modern medical rehabilitation robotic devices are charac-terized by force feedback in order to interact with the patienton the basis of the actual exchanged force and proper controltechniques. Force is typically measured by torque sensors incorrespondence with robot joints, or measuring motors over-currents. In both cases the mechanical kinematics and jointdisposition need to guarantee that force/torque generated athuman arm joint space is correctly transmitted to the robotjoint space: torques generated by human muscles have tobe transmitted to robot joints. Human-robot joint alignmentguarantees that torques generated by human muscles actselectively on correspondent mechanical joints, but kinematic

singularities can influence actual transmitted torques to themechanical device.

Experimental studies [5], [6] highlighted that some func-tional daily movements (e.g.reaching movements), are char-acterized by a complete extension of the elbow articulation.If a complete human-robot joint alignment is achieved atthe elbow (typical condition of a number of pre-existing ex-oskeletons [7], [8], [9], [10]) a double singularity affects boththe exoskeleton and the human-arm kinematic chain in theelbow extended configuration [11]. Problems and limitationscan consequently arise during collaborative rehabilitationtherapies, in which torques generated by patient (typicallyweak for impaired people) have to be transferred from humanarticulations to exoskeletal joints.

In this paper the misalignment between the exoskeletonand the human joints is investigated and the advantagefrom the controllability point of view of a proper elbowjoint misalignment is shown. The kinematical structure refersto an innovative upper-limb exoskeleton currently beingdeveloped. The kinematic model of the human upper limband of the exoskeleton being analyzed is reported in SectionII. In Section III aspects related to elbow singnularities areidentified and described, illustrating the advantages of intro-ducing a proper joint misalignament, obtained by the peculiarmechanical structure of the conceived exeskeleton nearby theelbow. Finally, Section IV draws conclusions about already

Fig. 1. Exoskeleton setup: a Cartesian holder for setting the gross positionof shoulder joint; the human shoulder center stays floating w.r.t. the holdingstructure thanks to the peculiar exoskeleton kinematics.

2011 IEEE International Conference on Rehabilitation Robotics Rehab Week Zurich, ETH Zurich Science City, Switzerland, June 29 - July 1, 2011

978-1-4244-9861-1/11/$26.00 ©2011 IEEE 456

TABLE IUpper extremity range of motion

Degree of freedom Min MaxPlane of elevation

{φ1, uh,1

}0 135

Angle of elevation{φ2, uh,2

}-90 90

Internal rotation{φ3, uh,3

}-55 70

Elbow flexion{φ4, uh,4

}0 140

Angle of pronation{φ5, uh,5

}5 160

Fig. 2. Human arm kinematic model

completed design activities and further development steps.

II. KINEMATIC MODELS

Hereafter, kinematic chains and symbology of the humanarm and of the exoskeleton are introduced. An alternativekinematic description and symbology to ISB description [12]is introduced to better highlight human arm and exoskeletonjoint correspondence.

A. Human arm

Referring to Fig. 2 let us denote by:1) xy, yz and xz the coronal, transverse and sagittal planes,

respectively.2) Oh,s = (Xh,s,Yh,s,Zh,s) and Oh,e = (Xh,e,Yh,e,Zh,e) the

shoulder and elbow centers. Oh,s can translate freelywith respect to the chest, due to the shoulder girdlemovement.

3) uh,i the rotational axis of the i-th joint of the humanlimb chain and φi denotes the value of its angle. Referto Table I for joint names in medical nomenclature andtheir typical range of motion (see [13], [14], [15]).

Two singularity conditions may occur in the model:• shoulder singularity (uh,1 //uh,3) not representing an ac-

tual singularity in the human upper extremity shoulder,but exclusively due to the representation of shoulderjoint by three serial rotation axes;

• elbow singularity (uh,3 //uh,5) actually occurring whenthe upper arm and the forearm are aligned (human elbowcompletely extended).

B. Exoskeleton

The mechanism design has been optimized to cope withtwo distinct and relevant aspects of upper limb rehabilitation:

• adaptability and compensation of shoulder displace-ments to prevent undesired shoulder internal stresses dueto joint axes misalignements (shoulder adaptability);

• optimization of the elbow usable workspace and dexter-ity, limiting singularities drawbacks (topology optimiza-tion).

Shoulder adaptability is achieved by a hybrid kinematicmechanism and a proper set of compliant links. (Fig. 3).

Topology optimization is achieved by a peculiar joint axesdisposition at elbow level. Exoskeletons usually reproduceshoulder and elbow articulations by a spherical joint centeredon the humeral head and a revolute joint aligned to theelbow rotational axis. The solution here presented, on thecontrary, features two Cardan joints centered respectivelyon the humeral head and on the elbow center. Details onadvantages of the presented solution are in Section III.For symbology related to the exoskeleton refer to Fig.3.Actual differences with [16] are related to the position oftranslational joints in the kinematic chain. A comparisonof actual kinematic performances are outside the scope ofthis paper. For a deeper description of the kinematics and ofkinematic equations refer to [11].

III. ELBOW TOPOLOGY AND SINGULARITIES

The kinetostatic relationship between two sets of degreesof freedom of two distinct spaces is defined by the Jacobianmatrix J.

The kinetostatic relation between the degrees of freedomof the upper-limb and the exoskeleton kinematic chains is:

Φ̇ = JΘ̇

denoting as:• Φ the set of coordinates of the human arm• Θ the set of coordinates of the exoskeletonIf a correct and exact alignment between correspondent

degrees of freedom of the two kinematic chains is achieved(i.e. each exoskeleton joint is aligned to its correspondentjoint of the human kinematic chain) the previous relationcan be simplified as:

φ̇i = θ̇i

for each i-th degree of freedom, and the Jacobian matrixdegenerates in the identity matrix:

J = diag(1)

A. Elbow singularity

The elbow is intrinsically characterized by a singular con-figuration. Referring to Fig.2, if uh,3 //uh,5 (complete elbowextension) the human arm kinematic chain is in singularity.If a joint-to-joint alignment is achieved between the limband the exoskeleton, also the exoskeleton is consequently insingularity. The double singularity at the completely elbowextended configuration, which typically characterizes upper-limb exoskeletons due to human-exoskeleton elbow jointsalignment, can lead to a not correct alignment between the

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(a) (b)

Fig. 3. (a) Topological representation and (b) tridimensional view of the exoskeleton hybrid serial-parallel kinematic architecture.

elbow axes of the human uh,4 and of the exoskeleton ue,2. Ifφ4 = 0 (elbow completely extended) the human can performintra-extra rotations of the shoulder uh,3 independently bythe configuration of the exoskeleton [11], without inducinga proper orientation of ue,2.

Referring to (Fig.3), the misalignment between uh,3 andue,1, identified by the α angle, influences the relationship be-tween human and exoskeleton elbow joints kinematics. Thekinetostatic relationship between the human and exoskeletonjoints axes intersecting in the elbow (Oh,e) is:

φ̇3 =∂φ3(θ3, θ4)|α

∂θ3θ̇3 +

∂φ3(θ3, θ4)|α∂θ4

θ̇4,

φ̇4 =∂φ4(θ3, θ4)|α

∂θ3θ̇3 +

∂φ4(θ3, θ4)|α∂θ4

θ̇4;

B. Torques transmitted to exoskeleton joints

Due to the kinetostatic dualism exoskeleton and humanarm joints torque are related by:

Tr = −JT Th

denoting as Tr and Th the torques of robot and human jointsrespectively.

Similarly to velocities, a complete alignment betweenhuman and exoskeleton joints leads to the equation:

Tr,i = Th,i

for each i-th joint.Both in case of sensorized joints and in case of torque

estimation by motor overcurrents measurement and in caseof complete passive exoskeleton movements driven by thepatient, a minimum torque transmitted to joints has to beguaranteed in order to make the resulting joints torque,due to human’s generated torques by muscles, appreciable.This minimal level depends, in general, on the sensibilityof the measuring system and mechanical frictions. Let usdenote this minimum torque for the i-th exoskeleton jointby Tminr,i. If the torque transmitted to the i-th mechanicaljoint is lower than Tminr,i the capability of the exoskeleton

of reacting to human’s generated torque is prevented. Withthese premises the kinetostatic analysis can lead to identifycritical configurations of the elbow articulation in terms ofmovement fluidity and controllability, and to analyze theinfluence of the α angle on torques actually transmitted tothe exoskeleton.

C. Influence of soft tissues and cuffs compliances

The mechanical constraints between the human arm andthe exoskeletal arm are intrinsically compliant due to humansoft tissues and softness of interfacing materials (i.e. cuffs).

Nearby singularities torques generated by cuffs on the hu-man arm can be not sufficient to be transmitted to exoskeletalmechanical joints, resulting in a possible relative rotationbetween the human’s and the exoskeleton arm, without acorrect rotation/reconfiguration of the exoskeleton.

Cuffs can be, simply but exhaustively, modeled as linearand torsional springs, to take into account the effect of softtissues reactions and mechanical compliances. Referring toFig.4, Ca and C f denote the cuffs constrained respectivelyto the arm and the forearm. Forces and torques exerted bycuffs are denoted respectively by (Fc,a,Tc,a) and (Fc, f ,Tc, f )for the arm and the forearm:

Fc,i = klc,i ∗ dlc,iTc,i = ktc,i ∗ dtc,i

where klc,i and ktc,i denote the linear and torsional springcharacteristics, dlc,i and dtc,i denote the linear and torsionaldisplacements.

The total torque the cuffs can exert in constraining thehuman arm with respect to the exoskeleton structure is:

Ts,a = Fc,a ∗ dca + Tc,a ∗ sin δca + Tc, f ∗ sin δc f

and, denoting by Th,i the torque of the i-th human joint, theresulting torque along the arm axis uh,3 is:

Th,3 = Tsa cos δca

Torque components along cuffs axes (uh,3, uh,5) are neg-ligible, due to the extreme compliancy of the human soft

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Fig. 4. Schematic representation of the cuffs reaction forces and torques onthe two-link arm plane defined by shoulder, elbow and wrist center points.

tissues around the bones axes. Approaching the elbow sin-gular configuration, dca, δca and δc f decrease and the totaltorque the cuffs can exert on the human arm consequentlydecreases.

If a torque, exerted by the human, around uh,3 axis,generates torques in exoskeleton elbow joints below theirminimum sensitivity levels (Tminr,3, Tminr,4), a relativerotation between the human and the device can occur, dueto mechanical compliances, without a correct rearrangementof the exoskeleton configuration.

In conclusion, singularity drawbacks occur not strictlyif uh,3//uh,5 but its workspace influence is function ofconstraints and tissues uncompliances. They can lead to arelative intra-extra rotation of the human arm with respectto the exoskeleton arm, causing a misalignment between ue,2and uh,4 and incoherency between human and robot joints.

This aspect emphasizes the importance, previouslymentioned, of introducing the α angle misalignment tounivocally define the elbow exoskeleton configuration duringextended movements and extend the actually exploitablelimb range of motion in collaborative therapies. Thisdrawback and limitation of some existing exoskeletons asbeen confirmed by interviews with physiotherapists.

D. Numerical results

Hereafter the torques transmitted to exoskeletal jointsintersecting in the elbow (ue,1, ue,2) are analyzed. Both theinfluence of intra-extra rotations of the shoulder and flexo-extension movements of the elbow on transmitted torques,as function of the misalignment α, are investigated. Torquetransmission ratios, and not absolute values, are plotted,to illustrate guidelines to follow, independently on actual

exerted torques and sensibility levels. ur,3 and ur,4 will denoterespectively ue,1 and ue,2 to better identify the correspon-dence between human and robot joints.

In Fig.5 the torque transmission ratio to ur,3 and ur,4 dueto a torque applied around the axis uh,3 is plotted. It is worthunderlining that the elbow misalignment α let the trasmittedtorque Tr,3 to be amplified, facilitating the exoskeleton el-bow rearrangement, reducing the risk of incurring in jointmechanical blocks due to friction effects, during shoulderrotational movements nearby the singularity.

In Fig.6 the torque transmission ratio to ur,3 and ur,4 dueto a torque applied around the axis uh,4 is plotted. Thesegraphs are useful to analyze what would happen if a correctrearrangement of elbow joints does not occur; it can be dueto an undesired rotational movement of uh,3 (with respect tour,3) due to soft tissues and cuffs mechanical compliancesnearby the elbow extended configuration. Increasing the αvalue will allow to avoid mechanical blocks with a propertorque trasmission from human elbow to exoskeleton elbowjoints.

Limitations in increasing α are due to the necessity ofkeeping ur,3 axis outside the range of motion of the forearm(α < 40◦), not to incur in singularities during elbow flexionalmovements (ref. Table I). For this reason the quantitativeanalysis has been performed for 0◦ < α < 30◦.

IV. CONCLUSIONS

Most of currently available exoskeletons for upper limbneuro-rehabilitation are affected by shoulder uncompliancyand lack of adaptability in terms of movements criticalconditions (i.e. singular configurations). For these reasonsan innovative mechanism as been conceived in order toface these two widespread problems. In this work a par-ticular focus has been put on relevant torques transmissionaspects from the human articulations to the exoskeletalaxes, leading to improvements in robot controllability by thehuman and torque transmission nearby the elbow singularity.Modern exoskeletons require to collaborate with the patientin achieving the final goal of the therapy and, consequently,a significant transfer of torques from the human articulationsto the mechanical joints of the exoskeleton is required. Lowlevel of torques transmitted to mechanical joints can lead tomechanical problems in following the patient’s action, dueto mechanical frictions and joints minimum sensitivities. Inthis study, the influence of joints misalignment nearby theelbow is investigated, highlighting the advantages in termsof torque transmission ratio to the exoskeletal joints nearbythe elbow singularity. Nearby the elbow extended position thehuman arm can rotate freely with respect to the exoskeletonaround the arm axis, due to mechanical compliances typicalof human tissues and cuffs employed to constrain the armto the exoskeleton. Compliances lead to have the elbow axisof the human misaligned with respect to the elbow axis ofthe robot. This undesired and unavoidable rotation can becorrectly faced by a proper singularity-free mechanical elbowin the range of motion of the human arm. This study willbe employed for the correct dimensioning of an innovative

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0 10 20 30 40 50 60 70 80φ3

1.0

1.5

2.0

2.5

3.0

3.5

φ̇3/θ̇

3 T

r,3/Th,3

[φ4=

10.0

◦]

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α=−10.0 ◦

α=−20.0 ◦

α=−30.0 ◦

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1

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◦]

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α=−30.0 ◦

(a) (b)

0 10 20 30 40 50 60 70φ3

1.0

1.2

1.4

1.6

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2.2

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Tr,

3/Th,3

[φ4=

20.0

◦]

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0 10 20 30 40 50 60 70φ3

0.0

0.5

1.0

1.5

2.0

φ̇3/θ̇ 4

Tr,

4/Th,3

[φ4=

20.0

◦]

α=−0.0 ◦

α=−10.0 ◦

α=−20.0 ◦

α=−30.0 ◦

(c) (d)

Fig. 5. Torque transmission ratios of Th3 at different flexion angles: (a-b) φ4 = 10◦; (c-d) φ4 = 20◦

exoskeleton currently being developed. The theoretical di-mensioning phase will be followed by experimental resultsto assess the improved quality of motion transmission forhuman-driven complex movements with the elbow almostextended.

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0 10 20 30 40 50 60 70 80 90φ3

0.6

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3/T

h,4

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0.1◦

]

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h,4

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0.1◦

]

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α=−10.0 ◦

α=−20.0 ◦

α=−30.0 ◦

(a) (b)

0 10 20 30 40 50 60 70 80φ3

0.5

0.4

0.3

0.2

0.1

0.0

φ̇4/θ̇ 3

Tr,

3/Th,4

[φ4=

5.0◦

]

α=−0.0 ◦

α=−10.0 ◦

α=−20.0 ◦

α=−30.0 ◦

0 10 20 30 40 50 60 70 80φ3

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4/Th,4

[φ4=

5.0◦

]

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α=−10.0 ◦

α=−20.0 ◦

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10.0

◦]

α=−0.0 ◦

α=−10.0 ◦

α=−20.0 ◦

α=−30.0 ◦

(e) (f)

Fig. 6. Torque transmission ratios of Th4 at different flexion angles: (a-b) φ4 = 0.1◦; (c-d) φ4 = 10◦; (e-f) φ4 = 20◦

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