Dynamic Ease Allowance in Arm Raising of Functional Garment

Transaction

Roger Ng ＊1,Leung-fu Cheung ＊2 and Winnie Yu ＊1

＊1 Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Hong Kong ＊2 Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

Abstract :The functional garments are important protective devicefor the disciplinary forces, such as police, fireman and soldier. Typical protective garments are made of special non-stretchable fabric and hence can restrict the movement of the wearer if the garment is not designed properly. A protective garment that can ensure maximal range-of-motion can be a difference of life and death when the disciplinary force is on duty. There are many aspects of range-of-motion. In the current study, we address the question of the appropriate amount of dynamic ease allowance (movement ease) required for any given height that the arm is supposed to reach.The relationship among the dynamic ease allowance, under arm sleeve length, and side seam length was derived, by using the rod joint model of the human being and assuming the motion is a cross-sectional one along the frontal plane. Sixty subjects wore the special net garment to record the reference of zero dynamic ease allowance, and then the adjustable garments of different scye depth, which is related to the dynamic ease allowance. The subjects were asked to move their arm along a vertical plane, from rest position to the maximum height that they can reach. Such motions were recorded by a motion capturing system. The experimental data was compared to the theoretical prediction. Since the analysis was conducted using the 3-D data and the garment measurements must be converted from the 3-Denvironment (when the garment is worn) to the 2-D environment (when the garment is not worn). The conversionapproximation is also presented. Consequently, when the required posture is known, the required scye depth and the required dynamic seam allowance can be found. The armhole can be designed accordingly. (Received 14 February, 2007, Revised 25 April 2008)

1. Introduction garment surface along the cross-section of the key body landmarks. In the current study, the dynamic ease In garment pattern design, the extra spacing between allowance at the armhole is defined as the difference the garment and the wearer is called the ease allowance. between the scye depth of the arm and the vertical Ease allowances can be classified according to three thickness of the arm at the armhole along the cross- different functions and can be defined in two different sectional plane that is perpendicular to the frontal plane. ways. Firstly, the basic movements, such as breathing and This definition is related to the radial definition, because sitting, require static ease allowance (also known as the difference between the scye depth and the thickness is comfort ease). Secondly, an extreme posture, such as considered in this article as the cross-sectional radial ease raising one’s toe to hit one’s head, needs dynamic ease allowance along the plane of the shoulder joint, allowance (also known as movement ease). Thirdly, the containing the top shoulder point, bottom shoulder point garment itself needs styling ease, which is the extra and the underarm. spacing to conform to the required silhouette. Moreover, In this article, the focus is on the measurement of the two common conventions of defining the ease allowance armhole of a functional garment with dynamic ease include the circumferential definition [1] and the radial allowance by finding out the shape of the garment pattern definition [2, 3]. In the circumferential definition, the that allows the wearer to perform certain given extreme tailors define the ease allowance by the excess girth postures. From the theoretical point of view, both the measurement at the key body landmarks, such as bust, body and the garment are considered as free-formed waist and hip. This definition is the most popular and surfaces, with a planar cross-section at the armhole. widely used in the industry. On the other hand, the The study commenced with a selection of the critical researchers define the radial ease allowance by measuring extreme postures. There were a total of twenty five the radial distance between the body surface and the critical postures selected for study. One of them is the

236 SEN’IGAKKAISHI（報文）Vol.64, No.9(2008) （52） raising of the arm to the highest possible height, which is such as [11, 12, 13, 14, 15, 16]. All of these studies are one of the common movements performed by the experimental in nature. The theoretical formulation of the disciplinary force. Initially, a yoga master was invited to ease allowance with respect to the postures has not been demonstrate these extreme postures and to make reported. recommendation as well as guidelines for the subjects. Then, sixty subjects were invited to repeat these postures 3. Posture definition under a safe condition, meaning that these subjects only tried their best without hurting themselves by over In biomechanics, the set of maximum reachable stretching. Each subject tried the adjustable garments with points of a subject is called the range-of-motion. Such different scye levels, while keeping their personal range-of-motion forms an envelop surface. The complete underarm and sleeve length. The motion was captured by range-of-motion is the union of range-of-motion of each the Vicon™ motion capturing system for data analysis. part of the body. In the case where the body remains in The mathematical model of the dynamic ease allowance, the same place, the body is assumed to be in balance. which is based on the position of shoulder point, under Such complete range-of-motion is defined by a series of side wrist point, side waist point, the side seam length, balanced postures. and the under side sleeve length was derived. The In the extreme posture selection process, the postures theoretical prediction of the scye depth that allows a must achieve the range-of-motion, and/or maximum given height of the under side wrist point arm is stretch of muscles. The postures must also be commonly compared to the experimental results for verification. performed by the disciplinary force, such as firemen, Finally, the discussion is presented. policemen, and soldier during their duty. Then, the postures were classified into three groups : (1) motion of 2. Literature review arm, (2) motion of leg, (3) motion of trunk. These extreme postures can also be classified into 2- The study of the dynamic ease allowance is D postures and 3-D postures. In the 2-D postures, all the equivalent to the study of the fitting problem in motion or movements are restricted on a motion plane, while 3-D kinetic comfort. If a wearer considers the garment fit to be postures are not restricted at all. In this article, the focus is comfortable while doing exercises, there must be on the 2-D posture of maximum arm height to be reached. appropriate amount of spacing between the body and the It is mainly because many of the motion can be garment, which is known as the dynamic ease allowance. partitioned according to the joints of the human subject. The study of dynamic ease allowance can be qualitative Once the origin of the local coordinate system is defined and/or quantitative, such as using statistical analysis. at the joint, the motions of the limbs are reduced to a local Tomita [4] examined the movement ease of the pants, by plane containing the limb. These basic motions are thus measuring the clearance distance between the body the simple cases and they can be combined as the building surface and the pants surface using moiré topography. blocks of the more complicated cases. Makabe [5] reported on the part and amount of ease In the final stage of the posture definition process, a required for upper limb motion. Hirokawa [3] revealed yoga master was invited to try out all the extreme the movement ease on the jacket and concluded the width postures. The yoga master reported the level of stretching across body is an important factor. Prevatt [7] asked the and which muscles were under stretch. The comments subjects to wear selected protective garments to perform a were compiled into a precaution procedure. series of postures and body movements and subjectively Atotalof twenty five postures were selected. A evaluate the comfort level. Larmour [8] studied the best- selected posture showing the restriction of the arm fit garment for senior citizens between the ages of 65 and movement by the sleeve is displayed in Fig. 1, which 74, based on the body measurements. Similarly, Burke [9] shows how the garment can restrict the range-of-motion developed four different prototypes of fit-modified of a subject. Apparently, the armhole is too big. So when garment for ambulatory women between 68 and 94 years the wearer raises her arm, the sleeve is under stretch. The of age to identify the best-fit prototypes. Cho [10] crease lines indicate the direction of the stretch. The designed and studied the mobility of the hospital gowns. figure illustrates a very important difference between the The qualitative analysis was based on the interviews and static ease allowance and the dynamic ease allowance. survey of the female nurses. Furthermore, range-of- For static ease allowance, more space implies less motion and fit is evaluated subjectively and statistically, restriction on the movement, while the dynamic ease

（53） SEN’IGAKKAISHI（報文）Vol.64, No.9(2008) 237 Fig. 4 Positioning of light reflecting balls.

Fig. 1 Raising of arm. Table 1 Properties of Sample Fabric allowance at the armhole is on the contrary (refer to Fig. 6 for the locus of armhole).

4. Design of the adjustable garment

The number of subjects was targeted as 60. It is not feasible to manufacture tailor-made trial garment for each of them,asthatwouldimply300(60x5scyedepth) garments. Therefore, two sets of five adjustable garments were designed. The garment is made of 100% polyester woven fabric with the property stated in Table 1. In each set, the scye depth of the bodice of the garments varies from 20 cm to 40 cm, with a step size of 5 cm. There are shoulder straps to control the shoulder width, detachable and replaceable segments of sleeves to control the sleeve length, wrist straps to control the wrist closure (Fig. 2), Table 2 Summary of subjects detachable and replaceable segments of bodice to control the bodice fitting and body trunk girth measurement, waist straps to control the waist fitting, side hip strap to control the hip fitting, side thigh strap to control the thigh fitting (Fig. 3).

5. Data collection of armhole movement

Sixty subjects, 37 female and 23 male, were invited

to participate this research project. The summary range of their data is listed in Table 2. The motions of the subjects were captured with the motion capturing system. They wore their own underwear with a net garment on top (Fig. 4). This initial set of data defines the reference frame of zero dynamic allowance. This is an important reference, because it is the minimum scye depth acceptable for each subject. This data is the lower bound for the computation. The light reflecting balls were secured to the net garment. They captured the shape of the subject, when the subjects raised their arms from the relaxed position to the highest Fig. 2 Top view Fig. 3 Side view possible point along the frontal plane, without

238 SEN’IGAKKAISHI（報文）Vol.64, No.9(2008) （54） overstretching the garment (Fig. 1). There are four abandoned because that means we shall put adjustable important light reflecting balls for the current study, Velcro straps at the armhole. Correspondingly, we need to which are located at the top shoulder point, the side seam put adjustable Velcro straps on the armhole of the sleeve. of the waist, the bottom of the scye, and the underside of This would make the armhole too bulky and affect the the wrist. Since, the light reflecting balls were located movement of the arm. along the seam of the net garment, there was not any The accuracy of the positioning of the light reflective length extension if the garment was not stretched. balls is within 0.5 cm. The shoulder point is defined as Then, each subject tried the adjustable garments (Fig. the highest outward edge of the shoulder bone along the 1) with scye depth variations from 20 cm to 40 cm with frontal plane. The side seam, underarm point and the an increment step of 5 cm. In each of adjustable garments, lower wrist are defined on the same plane by comparing the scye depth is fixed, but the shoulder width, sleeve their location along a vertically aligned and flat board of length, waist girth, side seam length can be adjusted so 0.5 cm thickness. The subject should be watching the arm that subjects with different body frame can be movement to ensure the movement is aligned with the accommodated. The use of adjustable scye depth was reference board. Finally, 300 valid data were collected.

Table 3 List of variables

depth is derived. The origin of the local Cartesian 6. Mathematical model coordinate system is defined at the top shoulder point (sht) with the x-axis along the horizontal direction, the y- Asimplegeometric mechanical model is used to axis along the vertical direction, and z-axis along the model the raising of the arm (Fig. 5). The definitions of depth direction. This definition is essential, because when the variables are listed in Table 2. The arm raising angle, the arm is raised, the shoulder muscle contracts, and the t θ wr,between the side seam of the bodice and the topside top shoulder point moves towards the neck. of the sleeve can represent the height of the arm. When t the arm is raised, this angle θ wr increases. Yet, the scye sht =(0,0) (1) depth may restrict the raising of the arm. So, the relationship between the arm raising angle and the scye The arm has a thickness of (sht − shu). The arm is

（55） SEN’IGAKKAISHI（報文）Vol.64, No.9(2008) 239 fixed at the carm and can rotate from the rest position || sht − wrt || = slt (7) (wrist at the lowest height) to the highest reach position u (wrist at the highest reachable height) along the frontal θ wr =angle between y-axis and ( ahu − wru )(8) plane, xy-plane, dividing the front and back. The controlling parameter, position of the ahu,is carm =(-||sht − shu || / 2, 0) (2) defined by the shape of the sleeve. However, the distance between sht and ahu must be larger than the reference Moreover, the top side of the sleeve is assumed to be scye depth to avoid the collision of the sleeve and the coincident with the top side of the arm. The wrt is related body . t to aht by the angle θ wr,measured between y-axis and sl2. || sht − ahu || = scye >||sht − shu || (9) t t wrt = sl1 (SIN(π−θ wr), COS (π−θ wr)) (3) Assuming further that the arm is straight and the The cuffofthesleeveisatthesame size of the wrist. wrist is perpendicular to the sleeve along the top side, the t The sleeve is further assumed to be perpendicular to the position of the arm can be defined using the angle, θ wr, top sleeve centre line. between the wrist and the y-axis. When the arm is at rest, t t horizontal position and highest position, θ wr =0,θ wr = t || wrt − wru || = cuff (4) π/2 and θ wr =πrespectively. AHU, the relationship between the input factors and ( wrt − sht ).(wrt − wru )=0 (5) the dynamic ease allowance, dea, can be modelled. AHU can be expressed as the solution to the optimization The garment is fixed to the body at the waist line. problem described in equation 11 to 14.

wa =fixedpoint (6) AHU : (sht, wru, wa) →dea (10)

Finally, the sleeve is assumed to be grown-on Minimize || sht − ahu ||, subjected to (11) (extension of the bodice), the reference point ahu is used to identify the bottom of the armhole. The armhole curve {|| wru − ahu || !underarm length (sl2), (12) is defined as the geodesic curve connecting sht and ahu. The actual shape of the shoulder seam of the set-in sleeve || wa − ahu || !side seam length (sl1), (13) (separate piece sewn to the bodice) can be defined arbitrarily by the fashion designer based on the grown-on || sht − ahu || "arm thickness || sht − shu || } (14) version. The top sleeve length is measured from the shoulder point to the wrist, while the under sleeve length Since the thickness of an individual is considered as is measured from the waist to the wrist along the side constant in the calculation, the AHU can also expressed seam. as the mapping to dea or ahu.The design of dynamically fitted garment can be solved analytically under equality

Fig. 5 Rods model of raising arm problem Fig. 6 Position of ahu as arm is raised

240 SEN’IGAKKAISHI（報文）Vol.64, No.9(2008) （56） Fig. 8 List plot of predicated dea (x) and dea Fig. 7 Trajectory of the arm movement of wru observed (y) [Unit : mm] [Unit : mm] condition in equation 12 and 13 [16]. Yet, the closed form is too long for the publication in an article, but it can be generated by a series of Mathematica™ commands (Appendix). A sample of the locus of the ahu is plotted (under normalized unit with origin at sht) with different height of wru in Fig. 6. Fig. 9 Cross-sectional view of armhole 7. Experimental verification measured by comparing the predicted dea and the actual The verification involves three steps. Firstly, the dea is 0.89 cm. The average relative root-mean-square input parameters were recorded. The distances between error with respect to the mean local ordinates of the the sht and ahu, sht and wru, wa and shu, wru and ahu reference data points is 4.52%. The Pearson coefficient of were measured directly from the subject using measuring correlation of the predicted values to the observed values tapes and the Martin-type instruction. During the motion, is 0.98 and is significant. The scatter plot is displayed in the distances were calculated from the data that were Fig. 8. The unit is in mm. captured by the motion capturing system. A sample trajectory of the arm movement is displayed in Fig. 7. 8. Mapping 3-D measurements to 2-D Atotal of 300 valid data were recorded. Once the measurements data was ready, the first step of processing the data is to shift the local coordinate system to match the sht as the The prediction of dea or scye is based on sht, sl1 origin. It is because when subject raise his/her arm, the and sl2 measured when the garment is already worn. shoulder point will move towards the neck, as the Since this preceding analysis is based on the 3-D shoulder muscle contracts. environment, and the measurements must be mapped to Then, together with the other three points, wa, wru the 2-D environment, namely when the garment is flat, so and ahu,itispossible to define a best fit frontal plane, that the measurement can be used for pattern making. which is typically slightly tilted, because the light The values of sl1 and sl2 are the same as that on the reflective ball may shift during movement. Finally, all garment. However, the scye changes when the garment is reference points are projected onto this best fit frontal worn. Yet, they can be estimated by considering the arm plane for further analysis. cross-section to be made up of arc segment of a circle of At the extreme positions, the distance between ahu radius r and the ahu is at a distance of d away from the and wa, ahu and wru, are at the maximal. Depending on centre which is located at carm.Therequired cross- the height of wru,distance between ahu and sht are sectional circumferential length (ccl )ofthearmhole typically at the maximal too, unless the arm has already when being worn is listed in equation 15, in which, ct is t reached the highest height (θ wr =π). Therefore, in the the point satisfying the tangential requirement of (ct − reference case of maximal dynamic ease allowance, all carm) ⊥ (ahu − carm), as in Fig. 9. When β represents subjects can raise their arm to vertical position. the angular ordinates of ct,β*r becomes the arc length The average root-mean-square (RMS) error from sht to ct along the circular arc while GEO (ct, ahu)

（57） SEN’IGAKKAISHI（報文）Vol.64, No.9(2008) 241 is the distance from ct to ahu. not restrict the wearer to perform his or her duty. Designers need to determine the dynamic ease allowance ccl =β*r + GEO( ct , ahu ) (flattened scye) (15) (movement ease), which is the key to the restriction of the movement. In the current study, we focus on the arm

The (rss)between the scye depth (2-D) and the scye depth raising. (3-D) is defined in equation 16. An estimated mean value The study of the relationship between the dynamic of rss is about 90%, or 10% reduction, varying from 69% ease allowance proceeded with the direct formulation of (small armhole) to 96% (large armhole). relationship between the dynamic ease allowance at the armhole, which is the difference between the scye depth

rss = scye (2-D) / scye (3-D) = (ccl) /(2r + d )(16) of garment and body, and sleeve length, side seam length together with the position of under arm point. The Furthermore, the measurements of cross-sectional cuff theoretical prediction was compared with the data that width changes when the garment is worn. Yet, the ratio were collected via the motion capturing system. The

(rsc)betweenthecuff(2-D) and cuff (3-D) can be average root mean square error between the predicted and estimated using equation 17, assuming that the cross- the measured dynamic ease allowance is 0.89 cm. The section of the wrist is circular. An estimated mean value average relative root-mean-square error with respect to of rsc is about 64%, or 36% reduction. the mean local ordinates of the reference data points is 4.52%. The Pearson coefficient of correlation of the

rsc =(π r)/(2r)=π/2=0.64(17) predicted values to the observed values is 0.98 and is significant. 9. Discussion on trivial cases Once the dynamic ease allowance and scye depth is known in the 3-D local coordinate system, they can be The above analysis is based on the assumption that mapped back to the 2-D measurements that are used for the protective cover all functional garment has a closure garment making. When designing a cover all protective at the wrist and the movement of the waist line is also garment, there is additional information such as the restricted as in the cover all garment. When the cuff is dynamic ease allowance of at the crotch area, to be used. larger than the largest circumference of the arm, and the The study of dynamic ease allowance of the crotch area subject raises the arm, the sleeve can fall down, and hence, will be reported later. Then, required garments can be movement is unrestricted. Moreover, if the waist line is made. free to move up, when the subject raises the arm, the whole bodice can be pulled up. Finally, if the garment is Acknowledgment made of stretchable fabric, with sufficient extensibility, movement is not restricted. The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong 10. Limitation Kong Special Administrative Region, China (Project No. PolyU 5284/03E). There are limitations in this study. Firstly, some assumptions on the anatomy of the subject have been References simplified, such as the position of the arm joint is estimated at the mid way of the arm, and the arm is 1. R. Ng, “Discovering Garment Pattern Design, Vol considered as a straight rod, rather than a two segmented 1: Basic Concept”, Coman Publishing, 46-48, rods. Since, the results from the experiments match very (2000). well with the predication model (Pearson coefficient of 2. Z. Wang, E. Newton, R. Ng, W. Zhang, J, T. I., 97, correlation at 0.98), the assumptions are acceptable. 3, 247-256, (2006). 3. T. Hirokawa, M. Miyoshi, M., J. Japan R. Assoc. 11. Conclusion Text. End., 38, 218-226, (1997). 4. A. Tomita, Y. Nakaho, J. Japan R. Assoc. Text. End., In the design of a functional garment, such as the 30, 133-141, (1989). uniform of the disciplinary forces, the movement of the 5. H. Makabe, H. Momota, J. Japan R. Assoc. Text. wearer is of primary concern, because the uniform should End., 32, 34-42, (1991).

242 SEN’IGAKKAISHI（報文）Vol.64, No.9(2008) （58） 6. M. B. Prevatt, “Fit and sizing evaluation of limited- Assoc. J., 56,4,333-40, (1995). use protective coveralls (garment fit) ”, Virginia 11. S.P. Ashdown, M. DeLong, App. Ergo., 26,1,47-54, Poly. Inst. State U., (1991). (1995). 7. M. S. Larmour, “Astudy of body measurements 12. P. Chan, H.Tam,A.Mak,K.K.Chan,Proc.3rd ATC, relating to the fit of clothing for 65 to 74 year old 343-347, (1995). women”, U. of Arizona, (1988). 13. J. E. Smith, “The evaluation and optimization of 8. B. F. Burke, “Satisfaction of women over 65 years of sensorial comfort”, U. of Salford, (1987). age with a fit-modified garment (women elderly) ”, 14. H. T. Chen, “Factors affecting perception of fit of Texas Woman’s U., (1994). jeans”, U. of North Texas, (1987). 9. K. Cho, “User-centered design and evaluation of 15. J. Huck, App. Ergo., 19,3,185-190, (1988). functional hospital gowns”, Kansas State U., (2001). 16. R. Ng, W. Yu, L.F. Cheung, Proc. CESA 2006, T1- 10. P. S. Adams, W. M. Keyserling, Amer. Ind. Hyg. 44-0370.

Appendix Listing of the computation of DEA using the program written in Mathematica™

(* Section 1 : Deviation of the General Formula of DEA (denoted as AHU) *) (* Define distance between two points v1, v2 ; Sqrt is the square root function ; . is the cross product of 2 vectors *) disXY[v1_, v2_] : = Sqrt[(v1 - v2) . (v1 - v2)] ; (* define origin and other variables *) sht = {0,0} ; wa = {xwa, ywa} ; wru ={xwru,ywru} ; ahu = {xahu, yahu} t (* Note : theta = θ wr and take on the range of [0, Pi] * ) wrt = {xwrt, ywrt} = slt {Sin[Pi - theta], Cos[Pi - theta]} ; (* calculate wru *) ansWRT = Solve[{disXY[wrt, wru] == cuff, (sht -wrt).(wrt - wru) == 0}, {xwru, ywru}] ; xwru = Evaluate[FullSimplify[ansWRT[[2, 1, 2]]]] ; ywru = Evaluate[FullSimplify[ansWRT[[2, 2, 2]]]] ; (* calculate ahu = {xahu, yahu} *) ansAHU = Solve[{disXY[wru, ahu] == sl1, disXY[ahu, wa] == sl2}, {xahu, yahu}] xahu = ansAHU[[2, 1, 2]] ; yahu = ansAHU[[2, 2, 2]] ; (* Closed Form definition of dea, which is denoted as AHU in the formula *) AHU[slt_, theta_, wa_, cuff_, sl1_, sl2_] : = disXY[ahu, sht] (* The closed form can be displayed by the following commend *) AHU[slt, theta, wa, cuff, sl1, sl2] (* Section 2 : Deviation of the Specific Formula of DEA forexperiment (denoted as AHU). From the experiment, sht defines the origin, wru and wa are recorded So, we only need to compare the calculated ahu to the experimental ahu. The t u angle θ wr andθ wr can be used to check the consistency of the data. *) (* calculate ahu = {xahu, yahu} *) ansAHU = Solve[{disXY[wru, ahu] == sl1, disXY[ahu, wa] == sl2}, {xahu, yahu}] xahu = ansAHU[[2, 1, 2]] ; yahu = ansAHU[[2, 2, 2]] ; (* Closed Form definition of dea, which is denoted as AHU in the formula. Ahu is defined by both wru and wa *) AHU[wru_, wa_, sht_] : = disXY[ahu, sht]

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