Arm lengths and arm reaches Some interrelationships of structural and functional body dimensions.код для вставкиСкачать
Arm Lengths and Arm Reaches: Some Interrelationships of Structural and Functional Body Dimensions HOWARD W. STOUDT D e p a r t m e n t of Physiology, Hci~vcir-dSchool of Pzihlic H e a l t h , Bostoii, M n s s a c h u s e t t s 021 15 K E Y WORDS Anthropometry . Applied physical ogy . Arm reaches . Measurement prediction. anthropol- ABSTRACT Structural measurements of the human body have for the most part been of little practical use as indicators of such functional body dimensions as arm reaches. These dimensions, which define the area around the body to which a person can reach given certain specified conditions and constraints are often critical for the design and layout of workspaces. However, they are relatively difficult and time-consuming to obtain, usually requiring specially constructed measuring systems for each differing design situation, as well as resurveys for each physically distinct population. An alternate approach, described here, investigates the interrelationships between these two classes of measurements with the aim of predicting functional reaches from structural body dimensions. In the present study traditional structural measurements and 117 functional arm reaches were obtained on 100 subjects. Correlations between the two types of measures are reported. Regression equations are presented which can predict functional arm reaches from two structural body dimensions on anthropometrically differing populations under a fixed set of workspace conditions. Measures of anatomic arm length, such a s shoulder-elbow or elbow-fingertip lengths, have long been included in the battery of dimensions taken in traditional anthropometric surveys. Such measurements, however, while useful for various purposes in human biology, have generally been of relatively little utility to those concerned not primarily with the length of a person’s arms, but rather with what he could do with them, i.e., how far he can reach and perform some specified task. These sorts of data are of considerable importance to the applied physical anthropologist, and to all of those concerned with any aspect of the design and layout of work and living spaces, such as human engineers, industrial designers, and architects. As a partial solution to this problem, some anthropometric surveys have included certain limited kinds of arm reach measurements, usually two or three dimensions on the outstretched arm. Hertzberg et al. (’54), for example, have measured: (1) “arm reach from wall,” a wall-tofingertip dimension taken with both shoulAM. J. PHYS.ANTXAOP.,38: 151-162. ders against the wall and the arm extended horizontally; (2) “maximum reach from wall,” with the left shoulder against the wall and the right shoulder thrust maximally forward; and ( 3 ) “functional reach,” as in (1) above but with the tips of the thumb and forefinger pressed together. Similar reach measurements have also been included in more recent anthropometric surveys (Clauser et al., ’72; White and Churchill, ’71) with the addition of a vertical reach with the arm extended overhead. Such “reach’ dimensions are also unfortunately of only limited use to the designer, since they describe a rather specific type of reach to a single point immediately in front of, or directly above, the subject. These dimensions tell us nothing of what other reaches might be to a myriad of other points surrounding the subject though rough guesses or crude extrapolations can be made in some cases. The kind of functional arm reach, as opposed to anatomic length, with which we are concerned here, can best be defined as 151 152 HOWARD W. STOUDT the distance between some fixed reference point, either anatomic or extra-anatomic, and a point in the area surrounding the body to which a person can reach and perform some task such as touching, grasping or manipulating. These reaches are determined not only by arm lengths, and other measures of body size such as shoulder height, but by many other variables as well. The more critical of these relate to biomechanical considerations such as the range of motion at the joints of the body and, perhaps more importantly, to the position of the body when the reach is being made. Body position, in turn, is affected by a series of non-biologic variables. In the seated position these are: (1) the characteristics of the seat including height above the floor and angulation of seat surface and backrest; (2) constraints, if any, to body movement, i.e., lap belts or shoulder harnesses, or objects in the immediate environment such as control wheels, levers, panels, etc.; (3) the specific reaching task to be undertaken, whether a fingertip button-push, whole hand grasp, or the manipulation of objects with two hands, etc.; and (4) the kind of effort required in the reach, i.e., easy comfortable reach, comfortable maximum reach, absolute maximum reach, etc. Taking into account all the possible interactions of these variables and their resulting effects upon human arm reaches, it can be seen that the measurement of such reaches, and the systematic presentation of the data so that they can be most effectively utilized, is indeed a formidable task. We must remember that the equipment designer needs biologic data on human body movement which can resolve specific questions such as the maximum and minimum permissible limits, as well as the optimum locations, of all controls located i n the workspace. In the past such determinations have usually been made empirically, on a trial and error basis. The results, while often adequate for most people, were also often inadequate for some people. It has become increasingly apparent that for certain design areas at least, a more definite assurance of adequacy for all or virtually all users was needed. Unfortunately, the complexity of the problem, and the seeming impossibility of obtaining any generalized sort of reach data applicable to a variety of different conditions, has required each different design area to have its own special reach study to account for the individual characteristics of that population, in that workspace, performing that task. PREVIOUS RESEARCH The earliest applied anthropometric study that attempted to deal sytematically with this problem was that of King, Morrow, and Vollmer (‘47) who measured 139 subjects to determine the outer boundaries for the operation of manual controls. The subjects were seated in a standard pilot’s seat with a locked lap belt and shoulder harness. The subject kept his back against the backrest cushion, his body in a n “easy sitting position.” The measuring device consisted of a vertical rod on a horizontal support. Each subject reached for and touched points at different levels on the vertical rod as it was moved toward him from different angles to the right or left. Measurements were made at six inch vertical levels from eight inches below to 52 inches above a seat reference point, and at zero degrees and eight other angles to the right and left of the midline. The seat reference point (SRP) was defined by the intersection of the planes of the seat surface and backrest in the midline. The measurements were made horizontally at each level from the vertical axis through the SRP to the maximum point of reach. The resulting data were presented in means and standard deviations for the reaches attained a t each level and angle. A later study extrapolated the values of these reaches to those that could have been made if 18 inches of forward shoulder movement had been permitted (King, ’48). Emanuel and Dempsey (‘55) continued this general approach in a n Air Force study of the effects on arm reach of a partial pressure flying suit. Reaches were made both in shirtsleeves, and while wearing the partial pressure suit, at angular increments of 15” to the right, from 0 ” to 135 along various horizontal planes. The basic measuring device used has been described in detail by Dempsey (‘53). This earlier data on military populations has been largely superseded by the work of O , 153 ARM LENGTHS AND ARM REACHES Kennedy ('64), who determined the outer boundaries of grasping-reach envelopes for a shirt-sleeved operator. Utilizing twenty male subjects, right arm reach was measured on each of 12 horizontal planes separated by five inch intervals from five inches below to 50 inches above the SRP. On each of these planes the measurements were taken at angular increments of 15" to the right of the midline, 0" to 180°, and to the left of the midline to 165'. Hence, measurements were made at a total of 24 vertical planes intersecting with 12 horizontal planes, or 288 measurements for each of the 20 subjects. The measuring apparatus consisted of a hard wooden seat which rotated under a wooden arch with measuring staves radiating toward the seated operator a t 15" intervals. The task of each subject was to grasp a knob on the end of each of these staves and then to push the stave away as far as he could until his arm was fully extended without pulling his right shoulder away from the backrest. The resulting data were presented in tabular and graphical form for the first, fifth, fiftieth, and ninety-fifth percentile reaches along horizontals radiating out from a vertical line through the SRP. Dempster and his associates (Dempster, '55; Dempster, Gabel and Felts, '59) have presented a n excellent theoretical and methodological approach to the problem of functional reaches and "kinetospheres," or the three-dimensional space envelopes that surround the body, and which define the limits of reach of the hands or feet. While invaluable for a n understanding of the biomechanical basis of reach, these studies were not primarily concerned with obtaining reach data for specific applications and hence have been of limited practical utility. A somewhat different mechanical device for obtaining arm reaches has been described by Wright ('63), but without applicable data. Ely, Thompson and Orlansky ('63)have presented summary data on arm reaches in graphical form which are intended to aid the designer in locating controls within the workspace. Though perhaps useful as rough guides or indicators, these data are somewhat lacking in specificity and may be difficult to apply, especially since the means of determining the data and the characteristics of the population which they represent are not stated. The only other major focus of interest in arm reach studies has been the National Highway Traffic Safety Administration, Department of Transportation, and the U.S. automotive industry, who have been jointly concerned with the locations of controls that must be reached by drivers wearing lap and upper torso restraints. The culmination of rather extensive recent studies carried out within the industry has been summarized by Hammond and Roe ('72). Similar, parallel efforts have been undertaken by Woodson et al. ('71). The intent here has been to establish specific guidelines for the locations of controls in different kinds of vehicles which will be adequate for specified percentages of the driving population. METHODS In general then, the purpose of previous arm reach studies has been either to develop methodologies or techniques for obtaining the data, or to obtain specific data to answer immediate practical questions. The investigation of the interrelationships of structural and functional body dimensions has been largely ignored, though such findings should ultimately be of considerable practical interest to all concerned with equipment and workspace design. What is needed here, ideally, is some way of satisfactorily predicting functional arm reaches from a battery of easily obtained structural measurements, and a complementary set of workspace conditions, thus obviating the necessity of a special study, usually expensive and time-consuming, for each new problem area. Though the present study (Stoudt et al., '70) was primarily a n initial attempt to provide data to assist in establishing the outer permissible limits for the location of controls in motor vehicles, it was also possible to investigate certain aspects of the problem of predicting functional reaches from structural body dimensions. A small series of anatomic measurements was, therefore, obtained on each subject on whom the functional reach measurements were made. These structural dimensions were selected from those basic, commonly taken measurements that might be expect- 154 HOWARD W. STOUDT ed to affect in some way a person's ability to reach. These measurements were: height, sitting height, shoulder height, shoulder (biacromial) breadth, anterior arm length, elbow-fingertip length, and shoulder-elbow length. In addition, weight, age, and handedness of each subject were recorded a s was the preferred fore-and-aft seat adjustment. The functional reach measurements were selected primarily to define the areas in which hand controls are most likely to be located. This includes the region to the driver's front and sides, from slightly above the floor level to the top of the windshield. It was, therefore, decided to establish the lower vertical limits of the area for the measurement of arm reach at six inches above the floor and the upper limits at 42 inches. (Since the present measuring system is indexed to a reference point 9 inches above the floor, the upper and lower vertical limits are expressed as 33 inches and - 3 inches, respectively.) Within this 36 inch vertical range, measurements of functional arm reach were taken at fourinch intervals, thus making in effect a series of ten parallel horizontal planes through the driver's workspace. The selection of the four-inch vertical intervals makes possible the accurate interpolation of reach values falling between any of the measured vertical values. Once the vertical conditions of measurement were determined, the lateral constraints of the measuring system were established. Since most controls used by the driver are located in the general area to his front, it was decided to take measurements at 0" (midsagittal plane), and a t lo", 2 0 ° , 30°,40" and 50" to the right. Beyond this area reaches are apt to be less critical, though still of potential concern, so the interval of measurement was increased here to include the additional conditions of 70" and 90" to the right. All the above measurements were made with the right hand. Past studies of functional arm reach have generally assumed that left arm reaches were, for all practical purposes, a mirror image of those for the right arm, a n acceptable assumption where any constraints on movement were equal for the left and right sides of the body. However, the realities of the present situation are that the points of attachment in the vehicle of the upper torso restraint system, and its positioning on the body can differentially affect the reach capability of the right and left arms. Hence i t was necessary to make a separate series of measurements for left arm reaches to the left. The resulting system of measurement for functional arm reaches can best be visualized as ten horizontal planes intersecting with 12 vertical planes, giving a total of 120 different measuring conditions or locations. Each horizontal plane, for example, the one 33 inches above the H point, will thus have measurements taken at O " , 10" right and left, 20" right and left, etc. In practice these 120 measurements have been reduced by 3 to 117 owing to the impossibility of obtaining any reaches for many subjects at the lower level at 0" and 10" right and left. The mechanical aspects of the measuring system are shown in figures 1 and 2. The seat itself pivots about a vertical axis through the measuring reference point to attain the various reach angles to the right or left. In addition, a vertical bar rolls freely back and forth along two horizontal bars positioned directly over the seat. The bottom of this bar is vertically adjustable to each of the desired horizontal planes on which the measurements are made. After the subject was seated comfortably i n a normal position, the lap belt was tightened and the shoulder harness adjusted with exactly four inches of slack. The measuring chair was then positioned for the 0" measurements, and the adjustable vertical bar placed for the highest, or 33 inch, level. The subject was then told that the white button at the base of this bar would be pushed toward him until he could easily reach it with the thumb-tip of his outstretched hand and arm, with his back against the backrest. He was then asked to push the button as far away as he comfortably could, leaning forward until restrained by the shoulder harness. The vertical bar was then lowered to the next level at 29 inches, the bar brought forward to the subject, and this arm reach made a s above. This was repeated until all of the ten vertical levels were completed for the 0" reach angle. The chair was then rotated 10" to the left. The button ARM LENGTHS AND ARM REACHES Fig. 1 155 Arm reach at 0 degrees, 33 inches above reference point. to which the subject was reaching was now located 10" to the right of his 0" center line. The vertical bar was raised to the 33 inch level, the arm reach measurement taken and the bar dropped to the 29 inch level. This same procedure was followed until all reach angles were measured. The thumb-tip reach utilized here is admittedly one rather specialized reach condition, but it is a basic, easily defined one, and more importantly, one for which it is possible to derive a standard series of correction factors to obtain any other desired kind of reach, i.e., thumb-forefinger grasp, full-hand grasp, etc. In figure 1, the reach is being made a t 0 " in the midsagittal plane to the 33 inch level above the reference point, the latter indicated by the small white ball on the vertical rod in front of the hip. In figure 2, the subject is reaching 40" to the right of the midsagittal plane to a vertical level nine inches above the reference point. This reference, or H, point is intended to correspond to the hinge point of the hip and thigh. Anatomically it approximates the palpable maximum lateral protrusion of the greater trochanter. In practice, however, it is very precisely defined and located by a three-dimensional manikin constructed for the Society of Automotive Engineers ('70), and widely used by the automotive industry a s a n initial design point in vehicle seating and control placement. This H point, which defines one end of our functional arm reach dimensions, was established by placing the threedimensional manikin in the measuring 156 HOWARD W. STOUDT Fig. 2 Arm reach at 40 degrees right, 9 inches above reference point. seat used in these studies. Most importantly, however, it is a precisely fixed point which can be easily located and measured with accuracy and reliability. Other such points might serve as well. (For more precise details of the construction and operation of the measuring apparatus, as well as the rationale for the inclusion of its various aspects, see Stoudt et al., '70). Each of the reaches attained by the subjects was recorded photographically with a 35 mm camera equipped with a 250 exposure power-operated film transport. All photographs were taken under identical conditions of alignment of measuring seat, reach target and camera. Every subject thus had a single 35 mm frame taken a t the farthest reach point attainable at each of 117 different positions. To extract the reach measurements from each of these photographs, a Grafacon Model lOlOA was used, which was interfaced with a small PDP-8/S computer. The Grafacon is, briefly, a n electronic tablet ten and onequarter inches square containing a grid of 100 lines to the inch i n both the axes. Any point on this tablet when touched by the tip of a n electronic stylus can be defined in terms of the values of the coordinates of that point. Thus the computation of the distance between any two points on the tablet surface is a matter of simple trigonometry. To determine the arm reach measurements, the first slide in the film strip was projected onto the Grafacon tablet. The two reference points in this film, the H point and the fingertip reach point, were ARM LENGTHS AND ARM REACHES then touched in turn by the electronic stylus, the coordinates were processed through the computer, and recorded both on paper punch tape and on teletype printout. The next photograph was then automatically displayed by means of a stepping motor on the slide projector. The projector-to-tablet distance was set to permit the largest projection of that area of the slides needed for data analysis. For ease in computation and in running standardization checks of the system, the ratio of Grafacon to “real world’ distances was set at precisely 1:8, i.e., any eight inch dimension will, when photographed under standardized conditions and projected from a slide onto the Grafacon surface, measure exactly one inch. The accuracy with which repeated measurements of the coordinates of the same point on a projected slide could be made was commonly of the order of one coordinate line, or less. Rarely was the difference as great as two lines. Since there are 100 lines to an inch, a reliability factor for repeated measurements on the tablet is about f 0.01 inch. Applying the 1:8 conversion to obtain real world measurement our factor increases to about t 0.08 inch, or still less than k 0.1 inch for the determination of most coordinates. RESULTS Data were obtained in this study on 100 subjects, 50 males and 50 females, who were selected to approximate the distribution of the general adult driving population in height and weight as determined by the National Health Examination Survey (Stoudt et al., ’65). On each subject the eight structural measurements previously noted, plus age and weight, were obtained, as were the 117 functional reach measurements. The correlations between these two classes of measurements show some interesting associations, especially in view of a statement from the earliest study of arm reaches by King, Morrow and Vollmer (‘47), that “. . . no one anthropometric measurement is a satisfactory predictor for effective reach. Prediction on the basis of a combination of anthropometric measurements, although theoretically possible, cannot be considered practicable.” Such a position is no longer tenable in view of the 157 findings from this study, as well as those of Kennedy (‘64). Table 1 presents correlation coefficients for the 9 structural anthropometric variables plus age, and a selected group of 24 (of 117) of the more critical, or useful, functional reach dimensions. In summarizing these findings we note that age is very poorly if at all related to reach capability. In the series of 117 correlation coefficients, almost all ranged between 0.0 and 0.1. Of these extremely low correlations, 49 were negative, the rest positive (only with age did any negative correlations with reach measurements appear - all others were positive). Correlations between weight and the 117 reach measurements were only moderate, ranging between about 0.2 and 0.5 and averaging around 0.4. Height was substantially better, varying generally between 0.5 and 0.7, and averaging over 0.6. Here, as elsewhere, the location of the reach area affected the correlations. The highest single correlation with height, 0.820, was found at the highest reach level, 90” to the right. The lowest correlations, on the other hand, generally in the 0.400s and the very lowest at 0.378, were almost always reaches to the very lowest level. Anterior arm length also showed uniformly high correlations with functional reach, though often not quite so high as stature. The values here also ranged between 0.5 and 0.7, averaging over 0.6. Though it may seem unusual that arm length, seemingly more closely related to arm reach than stature, should not be more closely correlated, the answer probably lies in the greater lack of reliability of this measurement, being partly influenced by the extent to which the subject presses his shoulder back against the wall when the measurement is being taken. Elbow-fingertip length suffers from no such problems. It is an easy measurement to take accurately, has high reliability, and is clearly one of the major components of arm reach. It shows, overall, probably the highest general correlation with the 117 functional reaches. The intercorrelations are for the most part around 0.6 and 0.7. Shoulder-elbow height, another component of overall arm length, rather closely parallels the pattern of elbow-fingertip 0.028 0.029 0.033 -0.034 0.050 0.031 0.052 0.012 0.071 0.050 0.069 0.048 17 13 9 5 17 13 9 5 17 13 9 5 30 40 50 0.007 - 0.053 - 0.069 0.413 0.396 0.364 0.344 0.439 0.392 0.409 0.351 0.470 0.445 0.438 0.386 0.425 0.406 0.363 0.314 - 0.008 17 13 9 5 0.583 0.540 0.495 0.470 0.600 0.567 0.573 0.540 0.601 0.601 0.580 0.573 0.625 0.592 0.588 0.587 0.645 0.613 0.623 0.600 0.607 0.562 0.554 0.523 0.633 0.603 0.602 0.569 0.620 0.564 0.556 0.519 0.581 0.527 0.541 0.475 0.563 0.533 0.455 0.431 0.521 0.466 0.458 0.438 0.478 0.460 0.426 0.384 0.632 0.623 0.618 0.586 0.585 0.539 0.539 0.499 0.620 0.585 0.602 0.588 0.558 0.535 0.506 0.506 0.489 0.484 0.475 0.613 0.439 0.439 0.443 0.419 0.426 0.406 0.404 0.331 0.397 0.344 0.323 0.314 0.513 0.482 0.445 0.424 0.522 0.461 0.471 0.388 0.498 0.464 0.405 0.382 0.439 0.436 0.412 0.335 0.516 0.478 0.450 0.387 0.588 0.551 0.536 0.502 0.496 0.450 0.461 0.482 0.603 0.588 0.571 0.591 0.633 0.613 0.610 0.627 0.619 0.624 0.608 0.625 0.415 0.389 0.359 0.333 0.496 0.463 0.409 0.363 0.359 0.334 0.403 0.363 0.581 0.543 0.510 0.483 0.401 0.445 0.446 0.452 0.421 0.438 0.445 0.521 0.616 0.598 0.577 0.596 Heel pointH point Shoulder height 0.633 0.621 0.609 0.630 0.614 0.612 0.583 0.589 0.611 0.600 0.567 0.588 0.617 0.590 0.560 0.571 20 -0.147 - 0.109 0.631 0.607 0.585 0.597 0.396 0.363 0.304 0.222 - 0.043 - 0.066 17 13 9 5 10 0.593 0.546 0.576 0.197 -0.165 5 0.497 0.466 0.443 0.389 0.604 0.567 0.603 0.581 0.580 0.281 -0.110 9 0.506 0.467 0.598 0.599 13 0.583 0.501 0.629 0.634 0.585 0.594 0.354 -0.107 0.629 0.643 0.437 -0.056 17 0 Sitting height erect Biacromial breadth Sboulderelbow length Elbowfingertip length Anterior arm length Height Weight Height (inches) Angle (degrees) Age Functional arm reach (from “H” point) Correlation coefficients f o r selected f u n c t i o n a l a r m reaches a n d s h u c t u r a l body d i m e n s i o n s , age, w e i g h t a n d seat a d j u s t m e n t TABLE 1 v) U c3 3c ARM LENGTHS AND ARM REACHES length in its correlation with the various functional arm reaches though the values are usually slightly lower. It is possibly a slightly less reliable measure than elbowfingertip length and is in terms of gross size a somewhat smaller dimension. Sitting height erect also correlates reasonably well with functional arm reach, though not quite so well as stature or the various segments of arm length. The range is generally between 0.4 and 0.7. The pattern of the correlation of shoulder height with functional arm reach is, not surprisingly, similar to that of sitting height. The values of the correlations are, however, somewhat lower, ranging generally between 0.4 and 0.6, averaging perhaps 0.4 plus. Shoulder breadth, or biacromial diameter, demonstrates the lowest intercorrelations of any of the anthropometric variables except weight. It varies usually between 0.3 and 0.5. The H point to heel point distance as measured horizontally on the floor plane from a vertical line dropped from the H point is not a n anatomical dimension, but rather an indicator of fore-and-aft seat adjustment. As such, it is determined primarily by leg length and hence general body size, and also by personal preferences in seating comfort. The correlations are moderately high, mostly around 0.4 and 0.5. Obviously longer reaches are indeed positively associated with more rearward seat adjustments. To determine to what extent it is possible to predict dynamic measurements from traditional anthropometric measurements, the eight static dimensions taken in this phase of the study were included in a regression analysis with a selected group of functional arm reach measurements. The functional measurements selected were those which defined the most commonly used area for the location of controls in a vehicle, the region around the instrument panel to the front and sides of the driver. Four levels were selected for each of six angles for a total of 24 functional reach points to be predicted. The levels were 17, 13, 9 and 5 inches above the H point, and the angles were O " , and lo", 2 0 " , 30°, 40°, and 50" to the right. The method employed was that of stepwise regression, in which one attempts 159 to obtain the best linear prediction of a variable Y (in this case, functional arm reach) from a series of X variables (structural measurements). It is important to include only those independent variables which are likely to contribute to the effectiveness of the linear relationship. Secondly, only those structural measurenients should be utilized that are either commonly available, or can be relatively easily obtained, Obscure measurements, or those difficult to take, are less useful. The eight measurements included here meet the above two criteria. In addition, in developing the equations the number of structural measurements should be kept as small as possible. Too many variables are undesirable, not only because of possible difficulties in obtaining the data, but more importantly because a smaller number of variables, perhaps two or three, can often serve just as effectively as predictors. Theoretically only those structural measurements should be included which show a high correlation with the dependent variable and a low correlation with each other. If two independent variables have a fairly high correlation with the dependent variable and a low correlation with each other, both measure different aspects of the dependent variable and both will contribute substantially to prediction. In anthropometry, however, body heights and lengths, which might be supposed to be the best predictors of functional reaches, are within themselves, fairly highly correlated. The basic data employed here consist of values from 100 subjects for each of the 24 different functional reach positions and the eight independent variables. Each of these reach positions were run in turn against the structural variables, and in each case, those variables which contributed least to prediction were eliminated step by step. In all of the 24 reach positions, the results were similar, Two measurements consistently emerged at the end of each calculation that were clearly superior for predictive purposes. With these two static dimensions in the equations, none of the remaining six improved the accuracy of prediction in any substantial way. These two measurements are: elbow-fingertip length, and shoulder-elbow length, both components of arm length 160 HOWARD W. STOUDT and reach. In spite of the relatively high intercorrelation of these two measures, they nevertheless proved to be the best two predictors when coupled together. The resulting prediction equations are presented in table 2. Here the arm reach (in inches, the unit presently preferred by designers) is computed from a constant followed by weightings for variables X (elbow-fingertip length) and Y (shoulder-elbow length). The latter measurements are retained in millimeters since these are the units in which they are normally obtained from the anthropometer. The values that result from the application of these equations are the average, or roughly fiftieth percentile, reaches as measured from H point to the thumb tip of the outstretched hand. However, these equations predict less accurately at the extremes of the reach distributions. For this reason the appropriate standard deviations obtained in the analysis of the original reach data have been included for each prediction equation. With these standard deviations it is possible to estimate given percentiles from the predicted mean values as follows: for the fifth and ninety-fifth percentiles, 1.645 X S.D. is subtracted or added, respectively to the mean; for the 1st and ninety-ninth percentiles, 2.326 X S.D. (see Damon, Stoudt, and McFarland, '66). TABLE 2 Formulae f o r predicting functional a r m reaches f r o m structural body m e a s u r e m e n t s u n d e r certain specified conditions" Arm reach location Angle Height Prediction formulae S.D. 10 10 10 10 17 13 9 5 20 20 20 20 17 13 9 5 30 30 30 30 17 13 9 5 + 0 . 0 2 3 +~ 0 . 0 2 9 ~ + 0 . 0 2 2 ~+ 0.032; + 0 . 0 2 2 ~+ 0 . 0 3 3 ~ + 0 . 0 2 8 ~+ 0 . 0 2 4 ~ 0.94 + 0 . 0 2 5 ~ +0.028~ 8.24 + 0 . 0 2 8 ~+ 0 . 0 2 6 ~ 6.17 + 0 . 0 3 0 ~ +0.024~ 2.99 + 0 . 0 3 2 ~+ 0 . 0 2 5 ~ 1.21 + 0 . 0 3 0 ~ +0.023~ 8.88 + 0.028x + 0 . 0 2 7 ~ 7.87+ 0 . 0 3 1 + ~ 0.021~ 3.21 + 0 . 0 3 3 + ~ 0.026~ +0.034~ 10.77 + 0 . 0 2 4 ~ +0.035~ 8.67 + 0 . 0 2 4 ~ 7.45 + 0 . 0 2 8 ~+ 0 . 0 2 8 ~ 2.98 + 0 . 0 3 1 f~0 . 0 3 2 ~ 40 40 40 40 17 13 9 5 11.05+0.027x+O.O32y 8.16 0 . 0 2 2 ~ 0.042~ 5.67 0 . 0 2 8 ~ 0 . 0 3 6 ~ 5.57 0 . 0 2 7 ~ 0 . 0 3 2 ~ 2.28 2.46 2.53 2.50 50 50 50 50 17 12.38f 0 . 0 2 8 +O.O29y ~ 11.82 0 . 0 2 3 ~ 0 . 0 3 2 ~ 9.02 0 . 0 2 6 ~ 0 . 0 3 1 ~ 7.31 0.029~ 0.027~ 2.41 2.59 2.61 2.81 0 0 0 0 17 13 9 5 13 9 5 10.37 8.31 5.55 3.86 + + + + + + + + + + + + 2.11 2.21 2.26 2.33 2.13 2.29 2.36 2.41 2.21 2.30 2.29 2.47 2.30 2.31 2.37 2.57 Arm reaches in inches from reference H point Angles in degrees right from reference H point Heights in inches above reference H point x = elbow-fingertip length i n mm y = shoulder-elbow length in mm * The specific conditions for which the measurement predictions are valid are: (1) a hard, non-deformable seat with a seat surface angle 17.5O from the horizontal, and a backrest angle 25O from the vertical; (2) a n H point 9.0" above the floor, 3.8" from the seat surface, and 5.3" from the backrest (see text and Stoudt et al., '70 for more specific details). ARM LENGTHS AND ARM REACHES Details of the specific stepwise regression analysis utilized here are available in Neff ('69). CONCLUSIONS Functional arm reaches can be predicted from as few as two structural body measurements with a degree of accuracy that should be satisfactory for most design problems involving control location and workspace layout. At present such predictions can only be made within the context of a fixed workspace configuration; that is, for each anthropometrically distinct population, we can accurately predict the changes in functional arm reaches that can be attained in that workspace. However, prediction formulae determined under one set of workspace conditions will not necessarily still be valid if one or more of those conditions are significantly changed. What is needed now is a mathematical model of human reaching behavior which will take into account the effects of changes in any relevant workspace variable and, in conjunction with limited structural anthropometric data, generate the desired functional reach dimensions. LITERATURE CITED Clauser, C. E., P. E. Tucker, J. T. McConville, E. Churchill, L. L. Laubach and J . A. Reardon 1972 Anthropometry of air force women. AMRL-TR-70-5, Wright-Patterson Air Force Base, Ohio, pp. 1-1 157. Damon, A., H. W. Stoudt and R. A. McFarland 1966 The H u m a n Body i n Equipment Design. Harvard University Press, Cambridge, pp. 1-355. Dempsey, C. A. 1953 Development of a workspace measuring device. WADC Tech. Rept. 55-53, Wright-Patterson Air Force Base, Ohio, pp. 1-12. Dempster, W. T. 1955 Space requirements of the seated operator: geometrical, kinematic, and mechanical aspects of the body with special reference to the limbs. WADC Tech. Rept. 55-159, Wright-Patterson Air Force Base, Ohio, pp. 1-254. 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