Journal of Biomechanics 44 (2011) 455–460

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Journal of Biomechanics

0021-92

doi:10.1

n Corr

E-m

www.JBiomech.com

Prediction of applied forces in handrim wheelchair propulsion

Chien-Ju Lin a, Po-Chou Lin a, Lan-Yuen Guo b, Fong-Chin Su a,n

a Institute of Biomedical Engineering, National Cheng Kung University, Tainan, 1 University Road, Tainan City 701, Taiwanb Department of Sports Medicine, College of Medicine, Kaohsiung Medical University, Kaohsiung, Taiwan

a r t i c l e i n f o

Article history:

Accepted 27 September 2010Researchers of wheelchair propulsion have usually suggested that a wheelchair can be properly designed

using anthropometrics to reduce high mechanical load and thus reduce pain and damage to joints. A

Keywords:

Wheelchair

Handrim force

Model

90/$ - see front matter & 2010 Elsevier Ltd. A

016/j.jbiomech.2010.09.029

esponding author. Tel.: +886 6 2760665; fax:

ail address: fcsu@mail.ncku.edu.tw (F.-C. Su).

a b s t r a c t

model based on physiological features and biomechanical principles can be used to determine

anthropometric relationships for wheelchair fitting. To improve the understanding of man–machine

interaction and the mechanism through which propulsion performance been enhanced, this study

develops and validates an energy model for wheelchair propulsion. Kinematic data obtained from ten

able-bodied and ten wheelchair-dependent users during level propulsion at an average velocity of 1 m/s

were used as the input of a planar model with the criteria of increasing efficiency and reducing joint load.

Results demonstrate that for both experienced and inexperienced users, predicted handrim contact forces

agree with experimental data through an extensive range of the push. Significant deviations that were

mostly observed in the early stage of the push phase might result from the lack of consideration of muscle

dynamics and wrist joint biomechanics. The proposed model effectively verified the handrim contact

force patterns during dynamic propulsion. Users do not aim to generate mechanically most effective

forces to avoid high loadings on the joints.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Although manual wheelchairs are essential for individuals withmobility impairments, propelling a wheelchair has been shown tobe mechanically inefficient (van der Woude et al., 1986; Veegeret al., 1991) and improper wheelchair design could be a risk ofinjuries after long-term propulsion (Boninger et al., 2000; Mulroyet al., 2005; Wei et al., 2003). The kinematics and kinetics ofpropulsion are highly influenced by the user–wheelchair interface.Thus, a prevailing wheelchair propulsion research issue is howwheelchair fitting affects the propulsion mechanism. An analyticalmodel allows subtle alterations of propulsion technique to bedistinguished from changes of physiological and environmentalfactors (Vanlandewijck et al., 2001). Analytical models have beenwidely utilized in the analyses of human movements such aswalking, jumping, and wheelchair propulsion to improve theunderstanding of how the movements are produced (Pandy, 2001).

Van der Helm and Veeger (1996) first adopted quasi-staticanalysis for predicting muscle forces during wheelchair propulsion.They found that, whereas, the stabilization of the shoulder jointduring wheelchair propulsion required large muscle contributions,the input force of the model deviated from actual forces measuredduring dynamic propulsion. Moreover, they pointed out that the

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impact of the angular velocity of a joint should be considered inpredicting muscle forces. Rozendaal et al. (2003) proposed acriterion to quantify the balance of propulsion forces betweenthe mechanical effect and the biomechanical effort. Their findingssuggested that a deviation of the propulsion force direction fromthe tangential direction might be the best solution that themusculoskeletal system can achieve during the guidedmovement. A planar four-bar linkage model for quasi-staticanalysis of wheelchair propulsion was developed (Guo et al.,2002, 2003; Morrow et al., 2003). Guo et al. examined thepotential propulsion moments and predicted propulsion forcesat five hand positions with simplified static conditions. Propulsionmoments were reported to be greater at the initial and end of thepush phase, which differed from actual moment measured duringdynamic propulsion. Morrow et al. (2003) selected the criterion ofmaximizing the moment at the shoulder joint to assess propulsionforces and joint kinematics under various axle positions andhandrim sizes. Although shoulder and elbow joint angles and thefraction of effective forces (FEF) were determined, the assumptionof a fixed shoulder position in the model is inconsistent withdynamic propulsion.

Validated models make it possible to analytically evaluatewheelchair fit and the associated mechanisms of musculoskeletalinjuries resulting from a poor fit. Evaluation of wheelchair fit beforeprescribing a wheelchair may prevent potential injuries. However,above-mentioned studies indicated that predicted forces from astatic condition deviated from actual forces. Besides, effects of

C.-J. Lin et al. / Journal of Biomechanics 44 (2011) 455–460456

velocity were suggested to be taken into consideration to gain moreaccurate predictions. The present study attempts to develop andvalidate a two-dimensional energy model to verify applied han-drim forces during dynamic wheelchair propulsion for novice andexperienced wheelchair users.

2. Materials and methods

This study employed a planar four-bar linkage mechanism, schematized in

Fig. 1, to simulate the movements of the upper limb and the handrim in the sagittal

plane during wheelchair propulsion. This four-bar linkage consists of the vector

from the wheel axle to the shoulder joint, the vector from the wheel axle to the hand

contact point, the forearm, and the upper arm. The wrist joint was assumed to be

fixed in the current model. Given positions of the shoulder joint, wheel axle, and the

wheel angle, kinematic data of the upper extremity joints were obtained using

planar four-bar linkage analysis.

The concept of the model is that users are expected to apply propulsion forces

that maximize efficiency and reduce the required upper extremity joint moments.

Maximizing efficiency is expressed as minimizing the discrepancy between the

work done by the force and the energy change of the whole system. Work W is

defined as the work done on the wheelchair–user system during a time interval:

W¼Moodt, where Mo is the propulsion moment and o is the angular velocity of the

wheel. The energy change includes the kinetic energy of the user–wheelchair

system, the rotational kinetic energy of the two rear wheels, and the energy

consumed by the rolling resistance (FR) between the tires and the floor. Thus, the

formulation of the optimization problem is as follows

Fig. 1. Diagram of the planar four-bar model in the plane of the wheel frame

(S: shoulder joint; E: elbow joint; H: hand position; O: wheel axle; y: wheel angle;

OH,

, SH,

, and EH,

: vectors from the wheel axle, shoulder, and elbow to the hand,

respectively; F: unknown force).

Minimize

w1 � Moodt�½1=2mðv2tþdt�v2

t Þþ2� IDðo2tþdt�o

2t ÞþFRDs�

��

��þw2 � ½ðMsÞ

2þðMeÞ

2�

subject to

Msext oMs oMsflex

Meext oMe oMeflex

where

Mo ¼ 2� OH,� F

FR ¼mg � Crr

Ms ¼ SH,� F

Me ¼ EH,� F

w1 ¼ 1000; w2 ¼ 1

The unknown propulsion force (F) at each instant (t) is determined with the

objective function subject to the physiological constraints of the shoulder and elbow

moments. Ms and Me represent the required shoulder and elbow joint moments,

respectively. Msflex and Msext are the maximum shoulder strengths in flexion and

extension, respectively, and Meflex and Meext are the maximum elbow strengths in

flexion and extension, respectively. Values of the maximum joint strengths were

obtained from previous studies (Guo et al., 2003; Sabick et al., 2004). It was

identified that wheelchair propulsion was an asymmetrical act (Hurd et al., 2008),

but to simplify the model and reduce unknown variables, forces applied to the right

and left wheels were assumed to be symmetrical. OH,

, SH,

, and EH,

represent the

vectors from the wheel axle to the hand, the shoulder joint to the hand, and the

elbow joint to the hand, respectively. The kinetic energy change is computed from

experimental data where ID is the moment of inertia of the rear wheel, m is the mass

of the user–wheelchair system, and v is the linear velocity of the system. The term

DS is the distance that wheelchair has traveled during a time interval. The coefficient

of rolling resistance (Crr) was obtained from experimental results. Two weighting

factors, w1 and w2, are added in our model for solving the multi-objective problem.

The optimization routines were developed in MATLAB.

The effect of Crr on the prediction outcomes was evaluated by testing Crr, Crr+5%,

Crr+10%, Crr�5%, and Crr�10%. In addition, in order to select weighting factors, w1

and w2, several sets of weights, from 1 to 106 in multiples of 10, were evaluated. It

was assumed that conserving energy and reducing the required joint moments had

equal contribution to the applied handrim forces. Due to different units of these two

terms, it was found that when w2 equaled 1 and w1 equaled 1000, minimizing

shoulder and elbow joint loads and minimizing energy consumption had equal

influence on the prediction outcomes. Ratios of w1 to w2 smaller than 1000 increased

the effect of minimizing joint load. Ratios larger than 1000 did not change the

prediction outcomes. Hence, the weighting factors w1¼1000 and w2¼1 were

selected for the multi-objective problems.

Experimental data came from 10 able-bodied individuals and 10 experienced

wheelchair users with spinal cord injuries (Table 1). Subjects with orthopaedic

problems of their upper extremities were excluded. This study was approved by the

National Cheng Kung University Hospital Institutional Review Board. All

participants were informed and gave their consent prior to testing. Distance

from the shoulder to the wheel axle and anthropometric measurements

including body height, weight, and arm length were obtained for all participants.

All users used the same Quickie GP ultralight-weight manual wheelchair with one

instrumented wheel on the right side on level ground paved with a granular canvas

at an average velocity of 1 m/s. Subjects had to complete five successful trials,

defined as stably propelling the wheelchair through a 4-meters pathway in 470.2 s.

The distance between the rear wheels was adjusted according to user’s arm span. An

eight-camera Eagle Motion Analysis System (Motion Analysis Corp., USA)

synchronized with a load cell (Model UFS-4515A, JR3, Inc., Woodland, CA) on the

instrumented wheel was used to collect kinematic and kinetic data during

propulsion. Nineteen reflective markers were attached to the user–wheelchair

system. Detailed marker placements were reported previously (Lin et al., 2009). The

upper extremity was assumed to be a four-segment-linkage system consisting of the

trunk, upper arm, forearm, and hand. Joint kinematics of the upper extremity is

computed using Euler angles to illustrate the orientation of a distal segment

coordinate system relative to a proximal segment coordinate system. The positions

of the shoulder joint, wheel axle, and wheel angle were obtained by projecting the

3-dimensional data on the plane of the wheel frame.

Push phases were defined by exerted force and parameters were analyzed at a

discrete value of 51 of the wheel angle (y) (Fig. 1). The captured hand positions

within a certain range of wheel angles were analyzed together. The number of data

sets varied for each interval of wheel angle. Force directions were evaluated in terms

of the angle (ype) (Fig. 2) between the predicted and experimentally obtained forces,

and the error in force magnitude prediction was determined in absolute values and

as a percentage of the discrepancy within experimentally obtained force magnitude.

Fractions of effective forces (FEF) in novice and experienced wheelchair users were

also analyzed. The FEF is defined as: FEF¼Ft/F; where Ft is the force applied

tangential to the handrim and F is the resultant force.

Table 1Demographic data of subjects (Mean (SD)).

Age (years) Height (cm) Weight (kg) Arm span (cm) Experience of

wheelchair use (years)

Injury level

Inexperienced users (n¼10) 22.1 (1.1) 174.1 (3.8) 70.7 (8.9) 175.3 (6.7) – –

Experienced users (n¼10) 50.1 (14.4) 166.7 (5.8) 65.2 (12.2) 169.6 (6.0) 14.7 (9.4) T3 (n¼1); T5 (n¼1); T10 (N¼1);

T12 (n¼1); L1 (n¼1); L3 (n¼1); L5 (n¼4)

C.-J. Lin et al. / Journal of Biomechanics 44 (2011) 455–460 457

Independent t-test was used to examine the difference in variables between

inexperienced and experienced users and paired t-test was adopted to examine the

difference in FEF between predicted and experimentally obtained values. The

criterion level was set as po0.05.

Fig. 2. Stick diagram illustrating positions of the upper extremities, experimentally

obtained forces, and predicted forces from a representative trial from an experi-

enced wheelchair user (ype: the angle between the predicted force and experimen-

tally obtained force).

3. Results

With the simplified 2-D model, applied handrim forces wereverified at each hand position during propulsion. A stick diagram ofexperimentally obtained forces and predicted forces from a repre-sentative trial is illustrated in Fig. 2. The experimental data showedthat the propulsion angle varied with subject due to differentpropulsion techniques used. Data are shown in 51 increments from1201 to 301 of the wheel angle.

Predicted forces generally agreed with experimentally obtainedforces in direction and magnitude for both inexperienced andexperienced wheelchair users from the middle to the end of thepush phase. Fig. 3 shows that ype ranged from 0.01 to 7.61 and from12.41 to 35.41 for wheel angles in the range 301–1051 forinexperienced and experienced users, respectively. A largedeviation of predicted force directions was noted when the handwas located at a wheel angle larger than 1051. When the hand waspositioned at a wheel angle larger than 1101, ype increased to avalue larger than 1001. Furthermore, during a propulsion cycle, thepeak FEFs for predicted forces were significantly higher than thosefor actual forces in both inexperienced and experienced users. Fromthe experimental results, peak FEFs were 80% and 74% forinexperienced and experienced users, respectively. However,peak FEFs of predicted forces were 96% and 97%, respectively, forexperienced and inexperienced users.

The discrepancies in force magnitude in absolute values andas a percentage of prediction error are shown in Fig. 4. Throughthe entire push phase, the ensemble averages of magnitudediscrepancy were less than 29.7 N, which accounted for 16.9–88.2%and 11.0–91.5% of actual forces for inexperienced and experiencedusers, respectively. Predicted errors varied with hand positions.Large errors were observed at the very end of a propulsive cycle andin the range 75–1101 of the wheel angle.

An evaluation of the effect of the estimated coefficient of rollingresistance (Crr¼0.034) on prediction outcomes (Table 2)demonstrates that when Crr increased or decreased by 10%, thepredicted force magnitude varied by less than 6.13%. When Crr wasincreased or decreased by 5%, the average change in predicteddirection ranged from 0.57% to 2.61%. Crr had large effect on theprediction outcomes for inexperienced users than it did forexperienced users in both force direction and force magnitude.

4. Discussion

The proposed energy model predicted forces which appeared tobe generally compatible with actual forces in the plane of the wheelframe during dynamic propulsion for both novice and experiencedwheelchair users. In terms of force direction, the angles betweenpredicted and experimentally obtained forces were small exceptfor when the hand held the handrim at a wheel angle larger than1051. Predicted forces were tangential to the handrim whereas

forces measured during actual wheelchair propulsion were in thedownward direction. Similar results were obtained in previousstudies (Guo et al., 2003; Rozendaal and Veeger, 2000; Rozendaalet al., 2003; van der Helm and Veeger, 1996). Upward-pointingforce vectors were obtained during static propulsion for handpositions posterior to the top dead center (Guo et al., 2003; van derHelm and Veeger, 1996) because under static propulsion, it isefficient for elbow flexors to generate propulsive force at thesepositions. Additionally, the upwards propulsion force was the mostefficient in the early push phase based on the effect-cost criterion(Rozendaal and Veeger, 2000; Rozendaal et al., 2003). At the start ofthe push phase, the guided movement, limited degrees of freedomof the upper extremity and muscle contributions determinedhandrim force generation. During the early push phase, theelbow joint went from flexion to extension, resulting in quickswitches of muscles activity. However, force generation capacityand dynamics of muscles were not incorporated in the currentmodel, which might partially explain the initial divergence ofpredicted force directions. Except for the initial stage, predictedforce directions were consistent with experimentally obtained

Fig. 3. Results of predicted force direction, represented as mean angle between the predicted force and experimentally obtained force (ype) in each region of wheel angles.

Fig. 4. Results of predicted force magnitude, represented as (a) a percentage and (b) as absolute values of the discrepancy within experimentally obtained force magnitude in

each region of wheel angles.

C.-J. Lin et al. / Journal of Biomechanics 44 (2011) 455–460458

forces through the rest of the push phase especially forinexperienced users. The model predicted forces showed a moreeffective propulsion method than did actual conditions. Peak FEFsobserved in the experiments were below 80% for both

inexperienced and experienced users, which were in agreementwith previous studies (Kotajarvi et al., 2006; van der Woude et al.,2001). As described in previous studies, FEFs were about 73% andincreased with velocity and intensity in wheelchair-dependent

Table 2Variations in prediction outcomes with coefficient of rolling resistance (Mean (SD)).

Force direction Force magnitude

Inexperienced users Experienced users Inexperienced users Experienced users

Change of coefficient of rolling resistance (%) �10 �5 +5 +10 �10 �5 +5 +10 �10 �5 +5 +10 �10 �5 +5 +10

Effect on prediction results (%) 2.61 1.67 1.34 2.40 0.67 0.66 0.57 0.70 6.13 3.03 2.92 5.84 5.35 2.72 2.70 5.30

(2.67) (1.63) (1.30) (2.11) (1.35) (0.89) (0.92) (0.98) (2.02) (1.06) (1.06) (1.99) (2.50) (1.27) (1.30) (2.58)

C.-J. Lin et al. / Journal of Biomechanics 44 (2011) 455–460 459

individuals (Boninger et al., 1997b; Kotajarvi et al., 2006). In thecurrent model, better predictions were observed in inexperiencedusers, which might be explained by the findings that whencompared to inexperienced users, experienced users propelledthe wheel with forces pointed more downward and the shoulderjoints were subject to lower joint moments. It is supposed that forexperienced wheelchair users, reducing joint demands had a higherpriority than generating effective forces while propelling at aleisure velocity. As previously reported, physiologicallywheelchair users do not aim to produce the most effective forceduring propulsion to avoid high joint contact force (Bregman et al.,2009; Desroches et al., 2008).

From the viewpoint of prediction error, great discrepancies inmagnitude of total forces were noted at the early and end stages ofthe push phase. A partial explanation for this may be that predictedforces deviate more at these phases, consequently creating greaterinconsistencies in force magnitude. Another possible explanationfor the large errors is that during the initial contact and releasingphases, the actual applied forces are relatively small compared tothose during the middle of the push phase. A force discrepancy ofaround 28 N could thus result in a huge error. Very little was foundin the literature regarding the accuracy of predicted force magni-tude. A difference in magnitude in the range 46.9–277 N betweenthe predicted and the experimentally obtained forces was pre-viously reported for static propulsion (Guo et al., 2003). In addition,the wrist joint moment toward radial deviation was reported to bearound 3 Nm during initial propulsion (Boninger et al., 1997a). Thelack of consideration in physiological constraints in wrist jointmoment might also result in the errors. Prediction under dynamicpropulsion is more cumbersome than that under static propulsion.Thus, the decreased discrepancy in the present study suggests thatthe proposed model could better verify applied handrim forces.Various coefficient of rolling resistance (Crr) values have beenreported depending on the material and pressure of the tires andthe surface (Kim and Savkoor, 1997; Martin et al., 1998; Mooreet al., 2000). The effect of Crr on prediction outcomes was tested byevaluating Crr values of 75% and 710%. The prediction outcomesfor force direction and magnitude changed by less than 2.61% and6.13%, respectively, with 710% varies in Crr. Therefore, theestimation of the coefficient of rolling resistance in the currentmodel is believed to be accurate.

The proposed simplified 2-dimensional energy model seems toreflect the major movements of the upper extremities that occur inthe plane of the wheel frame during propulsion. Various limitationsshould be noted in the current model. The essential out-of-planearm orientation and the wrist joint in manual wheelchair propul-sion contribute considerably to upper extremity biomechanics.During wheelchair propulsion, the shoulder joint demonstratesgreat range of motion in the frontal and transverse planes (Koontzet al., 2002; Mercer et al., 2006). Movements in the frontal andtransverse planes during propulsion had impacts on forceapplication. Likewise, the muscles that control more thanone degree of freedom might be of importance in predictingmuscle activity during wheelchair propulsion (van der Helm andVeeger, 1996). Wrist injuries are the second most common type of

injury seen in manual wheelchair. Extreme wrist joint movementsusually lead to a heavy burden on the joints (Shimada et al., 2001;Veeger et al., 1998). Nonetheless, the wrist joint was modeled asfixed in the current study and the physiological constraints of thewrist joint were not taken into consideration. Accordingly, a modelof the wrist joint and the consideration of muscle dynamics isrequired to gain better simulations of applied forces.

Wheelchair propulsion is a complex movement involving aman–machine interface. In order to make the proposed modelapplicable under clinical conditions in the future, kinematicsparameters and anthropometric measurements of users are pro-posed as the inputs to the model. Inputting kinematic data, appliedhandrim forces were obtained. Joint kinetics was also acquired.Handrim force prediction in both direction and magnitude duringdynamic propulsion was achieved in this study. Prior studieshighlighted the differences in propulsion techniques, upper extre-mity kinematics, trunk movement, and applied handrim forcesbetween able-bodied and wheelchair-dependent users (Dubowskyet al., 2009; Rodgers et al., 2003; Veeger et al., 1992). However, thecriteria used in this study verified propulsive forces for bothinexperienced and experienced users. The model could befurther applied to examine how changes in wheelchair designand velocity affect applied forces and joint kinetics in propulsion.

Conflict of interest statement

The authors declare that there is no conflict of interest inthis study.

Acknowledgements

This work was supported by the National Health ResearchInstitute, Taiwan, under Grant NHRI-EX98-9617EI. The authorswould like to thank Hsiao-Feng Chieh for her technical support andassistance with data collection. Foreign Language Center inNational Cheng Kung University is appreciated for its editorialassistance.

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