Passive Exoskeletons to Support Human Locomotion - a

computational study

Marta Sofia Galrito Pintomartagpinto@tecnico.ulisboa.pt

Instituto Superior Tecnico, Lisboa, Portugal

October 2017

Abstract

Human gait is one of the most optimized motions through human evolution. It is by the detailedstudy of gait that it is possible to diagnose motion pathologies and to find solutions for their correctionthrough support systems like orthoses. This work consists of an inverse dynamic analysis of anon-pathological gait and later in the optimized gait analysis with the help of a passive exoskeletonimplemented in a computational way. Data was collected from the human gait movement at theLaboratorio de Biomecanica de Lisboa (LBL) and later treated. For its analysis, a 3D biomechanicalmodel of the entire body was created and then implemented in accordance with the studied subject.Later, a computational model of the exoskeleton under study was created, whose function is to reducethe leg effort in the execution of the gait task of making the foot to push the ground raising the heel.It was observed, comparing the results of the two analyzes, a decrease of the moment produced by thebiological ankle with the use of the exoskeleton. This decrease was on average 24.2%. These resultsreinforce the idea that, with the help of passive exoskeletons, without the use of external energy sourcesapplied in the human body system, it is possible to reduce the moments-of-force at some joints.Keywords: Biomechanics of movement, Gait, Passive exoskeleton, Inverse dynamic analysis

1. IntroductionLocomotion is an essential task for all humans. It isthrough the combined set of our skeletal, muscularand nervous systems that we are able to efficientlywalk in our daily activities. Through evolution, hu-mans became experts in walking, naturally choos-ing, for example, the length of each step and thearm movement that minimizes energy expenditure[1]. Despite its high efficiency it is still of greatinterest to study gait improvement strategies.

The present work will focus on the possibil-ity of reducing the metabolic energy cost of non-pathological human locomotion with the use ofpassive elements. Such achievement could bring,when well studied and systematized, a long-termprevention/retardation of joint wear or other lo-comotion pathologies without needing expensivepower sources and control elements.

1.1. ObjectivesThe main objective of this work is the computa-tional study and analysis of a passive external solu-tion for non-pathological gait augmentation. Morespecifically, this dissertation work aims to constructa computational model of a passive exoskeletonbased on the prototype solution proposed by Saw-icki et al. [1]. This experimentally tested passive

exoskeleton, provides support to the ankle functionduring propulsion of the foot push the ground withthe use of a clutch-spring system. Further in thisdocument this device is explained in more detail.

In order to reproduce the results of Sawicki etal. [1], the method here presented consists in thestudy of a natural non-pathological gait motion andits consequent dynamic analysis. Once the analysisis done, then the exoskeleton information is addedcomputationally, making it possible to simulate areal person motion with the influence of the ex-oskeleton. A comparison analysis is then made withthe results of both situations: with and without theexoskeleton influence.

Throughout the work there will be several goalsto be achieved and are stated as follows:

• Study the human natural gait cycle.• Collect experimental data for natural gait.• Create a biomechanical model for the entire

body.• Carry out the inverse dynamic analysis of nat-

ural gait.• Develop a computational model of a passive

exoskeleton to study the improvement in theenergetic performance of natural gait.• Carry out the inverse dynamic analysis of gait

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optimized by the implementation of the device.

2. State of the artThe research in the area of gait support devices isvery broad based on various types of applicationsaccording to their function and modes of operation.The two main fields where the use of exoskeletonsare present nowadays are on augmenting the ca-pabilities of able-bodied individuals and support-ing/correcting people with motion pathologies.

In this research area the powered devices becamethe most studied type of exoskeletons, mainly dueto the technological evolution of sensors, actuatorsand control systems of the past decades [2] and alsoby the huge capacity in terms of power that theycould bring for many functions. By contrast, morerecently it became of great interest to some researchunits to make use of the wasted energy by the hu-man motions using passive elements with the aimof reducing cost and weight of powered systems.

2.1. Sawicki et al. studyThe research on passive elements for locomotionsupport is quite recent. Passive elements, such assprings, started to appear in active exoskeletons asa way to reduce the need of external power sourcesfor the operation [3]. But the idea to totally re-move the external power sources making use of allthe energy wasted in human-machine overall systemstarted to appear [1].

In this experimental study [1], it is exposed thedesign of a lightweight passive exoskeleton (see Fig-ure 1) that reduces the metabolic rate while walk-ing, helping the lower limb system on the task ofpushing the ground, reducing the needed biologicforce of the system composed by the calf musclesand the Achilles tendon.

Figure 1: Passive exoskeleton design for reducingthe energy cost of walking [1].

The device consists in a lightweight elastic device

Figure 2: Sawicki et. al. work. Net metabolic rateresults of this study, showing the larger reductionwith the use of a spring with stiffness coefficient of180 N m rad−1 [1].

that acts in parallel with the user’s calf muscles,off-loading muscle force and thereby reducing themetabolic energy consumed in contractions. Thedevice uses a mechanical clutch to hold a springas it is stretched and relaxed by ankle movementswhen the foot is on the ground. The exoskeletonconsumes no chemical or electrical energy and deliv-ers no net positive mechanical work, yet reduces themetabolic cost of walking by 7.2 ± 2.6% for healthyhuman users under natural conditions (observed inFigure 2), comparable to savings with powered de-vices. This work will be studied in great detail,from the computational point of view, in this dis-sertation.

3. Background

In order to assist human locomotion it is necessaryto understand the human physiology during gait,to later understand how the human biology inter-acts with the projected device. Biomechanics is amultidisciplinary science responsible for the studyof human motion. It is through the laws and con-cepts of Mechanics that we are able to study thebehaviour of biological systems [4].

3.1. Biomechanics of walking

Gait is commonly described in the literature bythe lower limbs movements which occur during onestride and that are repeated during human locomo-tion. Figure 3 shows a representation of a gait cy-cle with the main phases and events on the sagittalplane, the dominant plane of gait motion named ac-cordingly with the Biomechanics terminolgy. Gaitdata is often represented along the stride percent-age, as the timing of the labelled events is approx-imate, and varies across individuals and conditions[5]. The gait cycle is divided into two main phases- the stance phase, which corresponds to the periodwhen the foot is in contact with the ground andthe swing phase, when the foot is airborne. Start-ing with the initial contact (IC), the point when theheel first touches the ground and ending in the same

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point of the next stride, thus completing the cycle.The principal moments of the gait cycle are: Ini-tial Contact; Foot Flat (FF, instant of stance phasewhen the foot is totally flat in the ground); Heel Off(HO, instant of stance phase when the heel leavesthe ground); and Toe Off (TO, first instant of swingphase when the foot totally leaves the ground)

Figure 3: Gait cycle representation. Here are themain phases of the cycle as well the definition of themain moments in the cycle, starting on heel strikeand ending on the same foot heel strike [5]

Some important parameters when analysing gaitare joint angles, moments and mechanical powervariation along stride. While walking data may dif-fer somewhat across subject and condition, yet thequalitative nature of data remains similar [5], forexample being possible to identify the main jointmovements along the stride. By observing gait datapatterns it is possible to distinguish between normaland pathological gait, making this a clinical analy-sis tool that can be used to support medical decisionand pathology diagnosis [6].

4. Multibody system inverse dynamics anal-ysis

A multibody system is defined as an assembly ofbodies that are joined together by kinematic joints,having the possibility of relative movement betweenthem due to the application of external forces [7].There are two main types of analyses that can beperformed within a multibody systems formulation:a kinematic analysis and a dynamic analysis. Thefirst accounting only for the motion apart forces in-volved, and the second adding the influence of theforces and accelerations that are present in the sys-tem. A multibody system can exhibit a complex be-havior when driven by external and internal forces.An inverse dynamic analysis consists on the recon-struction of the internal forces and/or torques fromthe known movements and external forces. Thistype of analysis allows calculating the forces andtorques that produce a specific movement. Apply-ing the calculations of inverse dynamics to humanmotion data it is possible to analyze the momentsof force associated with biological joints temporallyalong the associated motion.

To perform an inverse dynamic analysis, the stud-ied motion need to be already known and consistent

through time with the kinematic constraints used todescribe the mechanical system. That is, the tra-jectories of the generalized Natural coordinates, q(the type of coordinates used in this work) of themodel need to be first obtained, being consistentwith the kinematic constraint equations, Φ (equa-tion 1). In order to obtain a consistent generalizedcoordinates vector the procedure here used is to in-terpolate the trajectories of each generalized coor-dinate using cubic splines and then obtaining theirvelocity and acceleration using spline differentiationtechniques.

Φ(q, t) =

Φ1(q)Φ2(q)

...Φns+nr(q, t)

= 0 (1)

where nh is the total number of constraints.To solve an inverse dynamics problem there are

several methods that could be applied in order toobtain the forces involved in a mechanical system.In this work only the Lagrange multipliers methodwill be exposed. Using this method the equationsof motion are solved with respect to the Lagrangemultipliers vector as in equation 2.

ΦTq λ = g −Mq (2)

With this method the Lagrange multipliers as-sociated with the driving constraints are used tocalculate the external forces associated with eachdegree of freedom. The remaining Lagrange multi-pliers are used to calculate the internal forces de-veloped in the kinematic joints and rigid bodies.

4.1. Apollo softwareThe analysis software used for this work was theacademic software Apollo, a multibody dynamicssoftware with Natural coordinates developed in For-tran, that was created at Instituto Superior Tcnico[8].

To perform an inverse dynamic analysis of an in-dividual motion is necessary to provide the position,velocity and acceleration of the biomechanical sys-tem and all the external forces applied [7]. Morespecifically the necessary data is following informa-tion:

• Anthropometric information - anatomical seg-ments lengths, center of mass location, inertialproperties and mass.• Kinematic information - trajectories of the

anatomical joints and extremity points.• Dynamic information - forces applied through

the motion under analysis.

With the creation of files containing detailed in-formation about the created model, along with all

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the necessary information about the desired simu-lation, the Apollo software provides the necessaryresults to analyze a mechanical system motion alongthe simulation time.

5. ImplementationA biomechanical model consists of a mathematicalapproximation of a given biological real system [4],in this case the human body. The analysis donein this work was an inverse dynamics analysis ofhuman gait within the framework of multibody sys-tems in which the creation of a full body biomechan-ical model is relevant. The biomechanical modelcreated for this work has 28 rigid bodies and 62points. The human joints in multibody systemsanalysis with natural coordinates are defined be-tween rigid bodies points and also with rigid bodiesunit vectors. For the creation of this biomechani-cal model two types of mechanical joints are repro-duced: the revolute joint and the universal joint.To better understand the method used to imple-ment kinematic joints in this biomechanical model,two good examples are the elbow and wrist joints.

Figure 4: Right arm model: Revolute joint in theelbow and universal joint at the wrist - Main typesof joints used in the full body biomechanical modelcreation.

The elbow is here described as two revolute joints:the first allowing the lower arm flexion and the otherallowing its internal rotation. In another way, thewrist joint is described as a universal joint, allowingfor the hand flexion and extension and medial andlateral movements. Figure 4 represents the rightupper limb of the model. With this representation itis possible to see that with the use of inner productconstraints between vectors and/or segments, andwith superposition constraints between points it ispossible to mathematically define biological joints.

In the case of the elbow joint the four correspon-dent points (P44, P46, P47, P49) are superposed andthe vectors v28 and v30, having the direction of theelbow flexion/extension axis, are constrained to beparallel with the use of a scalar product constraint.

Here lower arm internal rotation is described withthe addition of a second rigid body that may be seenas a mobile rigid body (M) that rotates around afixed one (F) only via the superposition of the pairof points P47/P49 and P48/P50, which naturally cre-ate the revolute joint. Adding a second rigid bodyto describe an internal rotation is a useful methodthat can be found here in the definition of severalsegments of the human body.

At the level of the wrist, vectors v31 and v32 areconstrained to be orthogonal along time and thepoints P48, P50 and P51 are superposed, only al-lowing the flexion/extension and radial/ulnar devi-ations of the hand. The hand rigid body needs to beconstrained with the lower arm mobile rigid body inorder to reproduce the hand natural motion whichfollows the lower arm rotation.

This is how it is possible to reproduce the move-ment of the human body mathematically, applyingthis type of constraints throughout all the other bi-ological joints. By reproducing the biological jointsmotion restrictions it is possible to obtain approx-imately the same degrees of freedom of the humanbody gross movement.

Figure 5: Biomechanical 3D model developed hasentry for the Apollo software. Detailed point andrigid body numeration.

The entire body model is illustrated in Figure 5,where it is seen all the defined bodies, rigid andmobile ones, and correspondent points. Most of therigid bodies are defined here by two points, yet thereare also 3 point bodies (in the case of the head,

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pelvis, and feet) and 4 point bodies (in the case ofthe mobile trunk).

5.1. Kinematic drivers

In order to prescribe motion to the biomechanicalmodel it is necessary to mathematically define eachof the existent degrees of freedom. Now that, withsuperposition and inner product constraints, the de-grees of freedom are defined, kinematic drivers needto be defined in order to then guide the system alongtime.

The created model has a total of 42 degrees offreedom including rotation and translation ones.This means that 42 joint driving actuators areneeded to fully describe the model kinematics.

The degrees of freedom need to be guided withangular and translation drivers defined in theApollo software. The calculation of the driver val-ues along time is done with the Matlab programdeveloped created to analyze the experimental datafrom the laboratory. The Apollo software allows thedriver definition in several different types. In thecase of angular drivers, an angle can be defined be-tween: unit vectors, rigid body segments, one unitvector and one segment. Regarding the translationones, its definition is made by the global coordi-nates of a point or a vector. Along with the modeldescription (modulation file) at Apollo it is neces-sary to describe the system drivers.

5.2. Database

For the construction of a biomechanical model inaccordance with a specific individual it is necessaryto consult databases with information about the an-thropometry of the human being, making a properapproximation of the biological system to the math-ematical one. The information consulted for therealization of this model was, for each anatomicalsegment, the relative position of the CM, the rela-tive mass and the inertia parameters.

6. Data processing

Before creating the files needed for motion simu-lation, is necessary to fully treat and process thedata from the laboratory of movement. For thatis necessary to create a set of Matlab functionsand scripts capable to process the Qualysis TrackManager (QTM) software data and generate the re-quired information for the Apollo simulation.

6.1. Joints location determination

The data acquired in the QTM software, regardingthe markers coordinates along time and the corre-spondent external forces measured with the forceplatforms, can be exported to *.tsv format files.Further the data is processed accordingly with thenecessary information to the creation of Apollo in-put files.

The data processing starts with the use of a 3rdorder low pass Butterworth filter in order to at-tenuate high frequency noise signals which can bepresent in the trajectories of the markers. Primarilyit is necessary to process the markers coordinates inorder to have the model points coordinates, that isthe human body joints and extremity points. Foreach rigid body is also necessary to define 3 localvectors defining x, y and z directions of the body.This directions are approximately chosen to, whenthe individual is in the anatomical reference posi-tion, the local coordinate system corresponds to theglobal coordinate system.

It is through the local vectors and model point co-ordinates determination in each frame of the move-ment acquisition, that it is possible to withdrawinformation about the defined kinematic drivers.

6.2. Static trial

In order to acquire anthropometric data about theindividual under study a static acquisition is madefirst. In this work the static trial was made beingthe individual in the anatomical reference position.Then the generated static data is processed in orderto find the individual anatomical segments lengths.With the use of the anthropometry databases, theCM location for each rigid body of the model cannow be calculated, as well as the rigid bodies pointslocal coordinates. Knowing the subject mass, withthe relative segments masses from the databases,each rigid body mass is prescribed in the model.After this, for each anatomical segment of the indi-vidual, the inertia parameters for the 3 main direc-tions are calculated.

6.3. Two rigid bodies approach

In the biomechanical model here created some hu-man segments are described as a set of two, onemobile and one fixed, appearing when an internalrotation needs to be defined. For those cases themass of the human segment needs to be distributedamong the two representative rigid bodies, as wellas the inertia properties. The method used for thispurpose was a division into two rigid bodies con-sidering that the fixed one has the properties of acylinder with mass equal of 1/6 the mass of the totalbiological segment, and the mobile one correspond-ing to the remaining part of the human segment.

It is also imposed for the fixed rigid body (F ) az direction inertia of 0.01 kg m2 . Then the iner-tia values on the x and y directions of body F arecalculated with the cylinder tabulated equation,{

IFx,y = 14m

F r2 + 112m

FL2

IFz = 0.01 [kg m2](3)

where mF corresponds to the mass of the fixed rigidbody, r represents the cylinder radius and L its

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Figure 6: Inertia and mass distribution among thetwo bodies of the representation, one mobile (M)and one fixed (F )

length (corresponding to the length of the consid-ered anatomical segment).

At this stage the database is consulted to obtainthe correspondent inertia values of the human bio-logical segment in order to find body M correspon-dent part.

ITz = IMz + IFz (4)

Regarding the z direction inertia values, as thetotal and body F values are known, the body Mvalue can be determined by the equation 4 pre-sented above.

For the calculation of body M inertia parametersin the x and y directions it is used the parallel-axistheorem as follows,

Ix,y = IFx,y + mF dF2

+ IMx,y + mMdM2

(5)

where dF and dM respectively represent the dis-tances from the fixed and mobile rigid bodies centerof mass to the entire anatomical segment center ofmass (as it can be seen in the illustration presentedin Figure 6). The parameter mM corresponds tothe mobile rigid body mass, that is 5/6 of the totalmass of the anatomical segment in question.

It is also necessary the system center of massequation as follows,

rTCM =rFCMmF − rMCMmM

mF + mM(6)

from where the CM location of the mobile rigidbody (rMCM ) can be withdraw once the remainingconstituents of the equation are known.

With the use of the parallel-axis theorem togetherwith the center of mass equation the following equa-tions are obtained making it possible to determinethe inertia values for the three directions.

IMx = IMy = ITx − IFx −mF ‖rFCM − rTCM‖2

−mM‖rMCM − rTCM‖2

IMz = ITz − IFz(7)

6.4. Dynamic trials

The dynamic trials corresponds, in this experimen-tal work, to natural cadence continuous gait, fur-ther divided into strides and chosen only the rightones for the analysis. The model points and localvectors coordinates are determined for each frameof acquisition. The set of these local vectors alsodefine the rotation matrix for each rigid body, thatnow can be calculated for each frame of the acquisi-tion. The rigid bodies initial accelerations and ini-tial euler angles are calculated through the rotationmatrices values.

From the dynamic data it is also necessary to takethe drivers values for each frame of the acquisitionfor further creation of *.dat files for the Apollo sim-ulation. As described above, the created model has38 angular drivers and 3 translation drivers whichcan be defined in several different ways. For angu-lar drivers calculation, it is only necessary to definethe corresponding vectors (being unit vectors or di-rection vectors of a segment) and then determinethe angle between them. In the case of translationdrivers they correspond to one vector or one pointglobal coordinates. To the creation of *.dat files itis necessary the time vector and the correspondentdriver value for each frame.

There are 38 angle drivers which are calculatedwith the Matlab functions between the same vectorsdefined in the Apollo software. The other threedrivers are translation ones which corresponds toP1 and vectors v1 and v2 translations along time.

The external forces data is also processed in away of define, for each frame of the acquisition, thecorrespondent rigid body where the force is beingapplied.

6.5. Exoskeleton specifications

The passive exoskeleton implemented herein maybe summarized by adding the influence of a springbetween the leg and the foot (as illustrated in Fig-ure 7) within a specific interval of the stride period.Along one stride the spring engagement and disen-gagement instants are triggered by the ankle anglepattern [1], where the engagement corresponds tothe first peak and the disengagement instants be-fore the second peak. In this way, being the springengaged at foot flat (first peak of plantar flexion)and disengaged at toe off (second peak of plantarflexion), the spring will be loaded during its stretch-ing along the dorsiflexion period and then, duringthe next plantar flexion period, the spring will recoilreleasing energy to the system. This will interactwith the muscles crossing the ankle biological jointreducing the net mechanical positive power in thisjoint.

In the case of this computational study the lo-cations of the two additional points on the model

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(the two points to which the spring is connectedrepresented in Figure 7 by PL and PF ), taking ac-count the Sawicki et al. [1] prototype dimensions,are approximataly scaled to have the same relativedimensions in relation to the individual leg studiedhere.

6.6. Fortran routine

In order to add the exoskeleton influence into theanalysis of the normal gait an additional Fortranroutine to the Apollo software was implemented.This routine reproduces the clutch task of connectand disconnect the spring at the necessary momentsalong the stride.

Figure 7: Model developed for the addition of theexoskeleton influence in natural gait. Schematicrepresentation of the main necessary distances andvectors for the creation of the implemented Fortranroutine

This routine needs to apply the influence of theexoskeleton spring between the two plantar flexionmaximums (between FF and TO) and, on the re-maining time, has to assume the influence of thespring to be null. Looking to the resultant anglevariation from the natural gait experimental resultsit is possible to take the percentage values of thestride where these peaks are appearing. In this way,the additional routine needs to have has input thetwo instants so that the spring is applied at thecorrect interval.

To reproduce the spring influence, the routineneeds to perform calculations regarding the forceof the spring applied. First, the direction vectorbetween the two points where the spring will be at-tached needs to defined.

rFL = rPF − rPL (8)

The vector rFL goes from the foot point PF tothe leg point PL where the spring is being connectedas illustrated in the Figure 7 presented above.

Other important quantity is the length betweenthese two points that corresponds the spring length.

This value will vary along the stride has the springstretches and recoils.

LFL = |rFL| (9)

Now, it is possible to calculate the force doneby the spring (FS) between this two points usingHooke’s law for a linear spring as follows,

FS = k(LFL(t)− L0), L0 = LFL(t0) (10)

where k is the spring stiffness coefficient, L0 thespring length at the moment of the engagement andt0 the correspondent instant of first peak of the an-kle angle.

FS = FSrLF

LLF(11)

Equation 11 defines the force vector done by thespring at point PF , with the direction of rFL. Anopposite force vector is applied at point PL.

The additional routine in Fortran will be respon-sible to calculate the force applied between thesetwo points at each frame of the analysis, consider-ing the spring length variation along time and thestiffness constant k.

This new routine will have has inputs the follow-ing variables: spring stiffness k, number of the legrigid body, number of the point of appliance on theleg, number of the foot rigid body, number of thepoint of appliance on the foot, initial instant, finalinstant.

6.7. Ankle joint moments balanceTo a proper results analysis it is necessary to un-derstand the forces and moments of force present inthe ankle joint.

First, while the system is under the influence ofthe exoskeleton, the spring force (FS) is being ap-plied generating the correspondent moment in theankle joint. The exoskeleton produced torque τ wascalculated as the cross product of spring force FS

and the lever arm vector r, assuming constant lever-age, as follows,

τ = r × FS (12)

Taking τ norm along stride is possible to rep-resent the exoskeleton moment value contributionalong stride.

Looking to Figure 8 it is possible to see a repre-sentation of the main forces and moments involvedin the foot and leg during the period which is beingapplied the exoskeleton influence.

In the case of natural gait the resultant momentthat the ankle joint will have to do (MA) corre-sponds to the following equation.

MA = MGR = bGRFGR (13)

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Figure 8: Representation of the main moments andforces involved in the leg-foot system under the ex-oskeleton influence.

In this case the only moment that the ankle jointneeds to counteract is the ground reaction forceFGR correspondent moment, MGR. In the equation13 above, bGR stands for the perpendicular distancefrom the rotation axis to the line of action of theforce, also known as lever arm.

Under the exoskeleton spring influence the neces-sary ankle joint moment changes to,

MA = MGR −MS = bGRFGR − bSFS (14)

where the ankle moment calculation is made nowwith the influence of spring moment also calculatedwith the correspondent lever arm bS and springforce FS (determined as explained above).

In this case the spring moment MS actuate inthe same direction as the ankle moment, also sup-porting the ground reaction forces. Equation abovedemonstrates the reduction of the ankle momentwith the application of the exoskeleton spring.

With these set of equations and concepts, it ispossible to make a relevant comparison between theanalysis results with and without the influence ofthe exoskeleton.

7. Results and discussion

In the case of the natural gait, through inverse dy-namic analysis, the result of the Apollo softwarefor the ankle moment corresponds to the momentthe joint would need to produce to withstand theground reaction forces.

When the influence of the exoskeleton is added tothe simulation the result for the ankle joint momentwill then be changed. In this case, the resulting mo-ment for the ankle will be the one that counterbal-ances the two contributions of the external forces,those of the exoskeleton and those of the groundreaction. Equation 14 illustrates this result.

7.1. Natural gait

Ten right strides were studied for the same subject.It was taken the average over strides for some rel-evant results for example the three main leg jointsangles of the hip, knee and ankle, and then it wascalculated the standard deviation. The observationof the ankle angle pattern (observed in Figure 9)is what triggers the choice of the interval in whichthe clutch allows the spring influence in the leg sys-tem. The spring is engaged at foot flat moment(FF) and disengaged at toe off moment (TO). Thenthe spring is stretching between FF and HO (heeloff) taking advantage of movement of the leg to eas-ily stretch. This spring mechanisms during the gaitcycle are further represented in Figure 10.

0 10 20 30 40 50 60 70 80 90 100

Stride (%)

-5

0

5

10

15

Ank

le a

ngle

(º)

Spring engages Spring disengages

Figure 9: Ankle angle average variation along stridewithout the influence of the exoskeleton. Standarddeviation is also represented.

7.2. Application of the exoskeleton influence and re-sults comparison

The results obtained in the Apollo software and pro-cessed with the Matlab software for graphical rep-resentation are presented hereafter. As seen above(Figure 9) the time interval in which the spring in-fluence will be added in the system is triggered bythe two minimum peaks at the ankle angle vari-ation along stride. The spring is engaged on FFand disengaged at TO, which correspond approxi-mately to the interval 8%-63% of the stride period.An illustration of the gait cycle with the influence ofthe exoskeleton can be seen in Figure 10 in whichthe stretching and recoil phases of the spring arepointed out.

Figure 10: Illustration of the gait cycle with theinfluence of the exoskeleton.

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The results presented below were obtained fromthe analysis done in the Apollo software for the tenright strides acquired. The mean curve was thenobtained for each analysis type with and withoutthe influence of the exoskeleton. The spring stiffnessused was the optimal value observed by Sawicki et.al [1], corresponding, in that study, to the one thatproduced a greater reduction in the net metaboliccost observed.

With this optimal stiffness value (7.9 k N m−1)it was here obtained, through the inverse dynamicanalysis performed in the Apollo software, an av-erage reduction of about 24.2% with respect to thebiological ankle moment curve for the natural gait(see Figure 11).

0 10 20 30 40 50 60 70 80 90 100

Stride (%)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Bio

logi

cal a

nkle

mom

ent (

N m

kg

-1)

Spring engages Spring disengages

Without exoskeleton

k = 7.9 k N-1

Figure 11: Ankle moment average (normalized tobody weight) along stride percentage for the analy-sis without the exoskeleton and with the exoskele-ton being with the optimal value for spring stiffness(observed by Sawicki et. al [1]).

The used Fortran routine in the Apollo softwarehad as input variable the spring stiffness coefficientwhich allowed to make the simulation analysis forthe several coefficient stiffness studied in Sawicki etal. [1]. The obtained results are further presentedin Figure 12 where it is possible to see the expectedconsecutive reduction of the ankle moment with theincrease of the spring stiffness.

0 10 20 30 40 50 60 70 80 90 100

Stride (%)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Bio

logi

cal a

nkle

mom

ent (

N m

kg

-1)

Spring engages Spring disengages

Without exoskeleton

k = 5.6 kN m-1

k = 7.9 kN m-1

k = 10.5 kN m-1

k = 13.3 kN m-1

k = 17.2 kN m-1

Figure 12: Ankle moment average (normalized tobody weight) values for each stiffness coefficientused along stride percentage.

Using equation 12 and then taking the torque vec-

tor norm for each analysis made among the differentvalues of spring stiffness used here the graphic rep-resentation of the exoskeleton produced torque canalso be obtained (illustrated below in Figure 13).

0 10 20 30 40 50 60 70 80 90 100

Stride (%)

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Exo

skel

eton

mom

ent (

N m

kg-1

)

Spring engages Spring disengages

k = 5.6 kN m-1

k = 7.9 kN m-1

k = 10.5 kN m-1

k = 13.3 kN m-1

k = 17.2 kN m-1

Figure 13: Exoskeleton produced moment average(normalized to body weight) along stride percent-age. With the increase of the spring stiffness coef-ficient the exoskeleton moment also increases.

An important result to analyze an anatomicaljoint and its motion is the mechanical power. Thisparameter summarizes the muscles role of absorp-tion and generation of mechanical energy necessaryto accomplish the movement observed [6]. The anal-ysis of the mechanical power variation at humanjoints during gait provides a perception of the en-ergy expenditure during the gait cycle [9].

The mechanical power is defined as the work per-formed per unit time and is calculated as follows,

PA = MA ωA (15)

where PA is the mechanical power done by the anklejoint, MA corresponds to the ankle joint momentand ωA is the angular velocity at the ankle joint.

By observing Figure 14, comparing the resultswith and without the exoskeleton influence, it ispossible to see an increase of the ankle joint me-chanical power on the negative work phase and sub-sequently a reduction on the positive work phase.This means that the ankle joint moment is greaterin order to stretch the spring (approximately un-til 50 % of the gait cycle), although this movementis easy to do due to the phase of stride in ques-tion. Then, in the positive work phase, there is areduction of the mechanical power that the musclescrossing the ankle joint need to generate in order toperform the heel elevation.

8. Conclusions and future workWith this work it was possible to understand themethodology involving the creation of a 3D biome-chanical model as well as its broad potential on mo-tion analysis.

Throughout the work a wide variety of informa-tion was gathered. Starting with the study of natu-

9

0 10 20 30 40 50 60 70 80 90 100

Stride (%)

-0.8

-0.4

0

0.4

0.8

1.2

1.6

2B

iolo

gica

l ank

le p

ower

(W

kg

-1)

Spring engages Spring disengages

Without exoskeleton

k = 5.6 kN m-1

k = 7.9 kN m-1

k = 10.5 kN m-1

k = 13.3 kN m-1

k = 17.2 kN m-1

Figure 14: Ankle joint average mechanical power(normalized to body weight) along stride.

ral human gait and its characteristics, it was possi-ble to understand the reference patterns of motionalong strides and its meaning regarding the ener-getics of gait.

Looking at the state of the art in the area of ex-oskeletons devices, one can find several different so-lutions with a variety of technologies to support oraugment human locomotion. The possibility of us-ing passive elements in a device of this type, reduc-ing the need for external power supply and reduc-ing the device overall weight, was one of the reasonsthat led to this study.

Learning more about the passive exoskeleton de-vice under study, the device developed by the Saw-icki et al. [1], it can be seen the potential of apassive device on natural human gait augmentationshowing a 7% reduction on the human net metabolicenergy expenditure. One of the results shown bythis researchers was that with the use of this ex-oskeleton it can be seen a reduction of about 14%on the averaged biological ankle moment contribu-tion along stride. This is the main parameter toaccomplish in this study. The obtained result herewas a reduction of approximately 24.2% on average.This greater value, in comparison with the resultsobtained by Sawicki et. al [1], may have been ob-tained due to energy losses at experimental levelor, in another way, some failures at the exoskeletoncomputational model approach (regarding dimen-sions for example) to the experimental prototypethat was being reproduced.

In a near future, with continued research, it is ex-pected to obtain a sharper decrease in the metabolicdemands of walking or running, with both activeand passive exoskeletons. And thus reducing fa-tigue with a significant order of magnitude, in thosetasks.

An optimal future research and developmenton lower limbs exoskeletons design should focuson the characteristics of used materials, human-machine interfaces, safety, energy efficiency andcost-effectiveness of exoskeletons [10]. An interest-

ing goal is the development of an well-suited ex-oskeleton, that doesn’t bring any discomfort to thesubject wearing it by being extremely adapted to aspecific person [2].

More specifically with regard to studies on Saw-icki et al. work, in further studies of the presentwork it would be of great interest to add the musclesinfluence on the dynamic analysis. Another inter-esting research would be the computational study ofa similar exoskeleton application to other leg jointswith the objective to augment their functions dur-ing gait also with not entering with external powersources.

Still in this framework, the biomechanics researchgroup at IST intends to soon replicate the proto-type developed by Sawicki et. al [1] to be testedat the laboratory of movement and contribute withmore results for metabolic net energy measuring theoxygen consumption and carbon dioxide productionrates.

References[1] S. H. Collins, M. B. Wiggin, G. S. Sawicki,

Nature 522, 212 (2015).

[2] H. Herr, Journal of neuroengineering and re-habilitation 6, 1 (2009).

[3] C. J. Walsh, K. Endo, H. Herr, InternationalJournal of Humanoid Robotics 4, 487 (2007).

[4] M. Silva (2004).

[5] A. M. Dollar, H. Herr, IEEE Transactions onrobotics 24, 144 (2008).

[6] D. A. Winter, Biomechanics and motor controlof human gait: normal, elderly and pathological(1991).

[7] J. G. De Jalon, E. Bayo, Kinematic and dy-namic simulation of multibody systems: thereal-time challenge (Springer Science & Busi-ness Media, 2012).

[8] M. T. Silva, Human motion analysis us-ing multibody dynamics and optimization tools(IST, 2003).

[9] S. Goncalves, Master thesis (2010).

[10] B. Chen, et al., Journal of Orthopaedic Trans-lation 5, 26 (2016).

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