Posture prediction for static sagittal-plane lifting

Pergamon

PII: SOO2L9290(96)00028-O

TECHNICAL

POSTURE

PREDICTION

J. Biomechanics, Vol. 29, No. 10, pp. 1393-1397, 1996 Copyright 0 1996 Elsevier Science Ltd. All rights reserved Printed in Great Britain OOZI-9290/96 $15.00 + .M)

NOTE

FOR STATIC

SAGITTAL-PLANE

LIFTING

Marc J. Dysart* and Jeffrey C. Woldstadt * Virginia Polytechnic Institute and State University, Blacksburg, Virginia; and t Texas Tech University, Lubbock, Texas, U.S.A. Abstract-Three separate models are presented to predict the postures of humans performing static sagittal lifting tasks. The models use a common inverse-kinematics characterization to represent mathematically feasible postures, but explore different criteria functions for selecting a final posture. The first criterion assumes that subjects minimize the overall effort associated with a posture. The second criterion expresses effort locally as opposed to globally, and minimizes this value. The third criterion maximizes body stability. The postures predicted by these three models were compared to the postures assumed by 16 subjects performing 4 static sagittal lifting tasks. The results showed that all of the prediction errors were significantly greater than zero, but that the first objective function (minimum total torque) was more accurate than the other two criteria. The models were in general less accurate for postures that had lower hand positions than for those with higher hand positions. Copyright 6 1996 Elsevier Science Ltd. Keywords: Posture prediction; Nonlinear programming; Inverse kinematics; Lifting.

INTRODUCTION

Most analysis procedures currently used to evaluate the musculoskeletal demands of working tasks rely upon an accurate depiction of the posture of the worker. Unfortunately, measuring human posture has proven to be a difficult, time consuming, and expensive process. This paper explores a method to predict human body posture as an alternative to measurement. The algorithms use the position of the hands, the position of the feet, and anthropometric information about the subject to predict the position of four other joints of the body (knee, hip, shoulder, and elbow) in the sag&al plane. For most postures, the joints and connecting segments of the human body define a redundant linkage system, with many different postures possible for a given hand and foot position. To deal with this redundancy, our posture prediction algorithms consist of two distinct components or steps. The first step uses the hand and foot position and the subject anthropometry to generate all of the possible or feasible postures for the situation. Given these feasible postures, the second step is to select the one posture that the subject is most likely to select. This paper investigates three different behavioral criteria or objective functions proposed in the biomechanics literature. The first criterion assumes that subjects choose a posture which requires the minimum overall effort (Byun, 1991). For this criterion, effort is defined as the total external torque (summed over all the joints) created by the posture. This criterion assumes that when a large amount of torque is exerted, a human perceives that a large amount of effort is required. The second criterion assumes that subjects minimize local effort or fatigue (Bean et al., 1988; Park, 1973). Local effort is defined for each joint as the torque exerted relative to the strength of the joint. The criterion selects the posture with the minimum maximum local effort. The final criterion assumes that subjects choose the

posture with the greatest stability. Stability is defined as the subject’s ability to resist falling forwards or backwards (Kerk, 1992). The need for general computational techniques to predict human posture and motion has become acute with the increasing use of computer-based design methods in engineering. The models presented in this paper represent an approach to developing these algorithms distinctly different from the empirically based linear and nonlinear regression approach often used to predict human posture (Beck, 1992; Kilpatrick 1970; Snyder et al., 1972). The proposed models specifically assume an underlying theory as to the mechanisms used by people to select posture. While three specific criteria are explored in this paper, the modeling framework can easily be extended to consider other criteria or objective functions. Fully developed models of this type should be much less situation specific than currently available methods, as well as providing greater insight into the mechanisms behind human motor behavior.

POSTURE

MODELS

The posture prediction models described in this paper were developed and written in Mathematics. Each model employs a whole-body sagittal plane representation of the worker with five links corresponding to the forearm, upper arm, torso, thigh, and calf. Inputs are required which specify the horizontal and vertical distances between the hand and ankle, the link lengths, the link weights, the link center-of-mass locations, the whole body weight, and the magnitude and direction of the force applied to the hands. The resulting kinematic model has three degrees-of-freedom that are specified as the hip position (x,,+ y& and the forearm angle 4 relative to horizontal. Determining

Received in final form 30 October 1995. Address correspondence to: Jeffrey C. Woldstad, Ph.D., Department of Industrial Engineering, P.O. Box 43061. Texas Tech University, Lubbock, TX 79409-3061, U.S.A.

PREDICTION

the feasible

postures

Forward and inverse kinematic procedures (Byun, 1991; Fu et al., 1987; Jung et al., 1992) were used to specify each joint angle in terms of the unknown variables (xhipr Ybip) and I#. A complete description of this derivation and the resulting

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Technical Note

equations is quite lengthy and can be found in Dysart (1994). Postures were further restricted using the following constraints: (1) The joints could not be dislocated. As shown in Fig. 1, the hip joint (xhip. yhip) had to be inside the feasible solution defined by the link constraints. (2) The joint angles for a posture had to be within the defined range-of-motion (Webb Associates, 1978). (3) The posture had to be a stable static posture as defined by the balance constraints (see Fig. 1). Tipping over backwards was assumed to occur if the torque at the heel of the foot was greater than zero (thee,> 0), and tipping over frontwards was assumed to occur if the torque at ball of the foot was greater than zero (tbal, > 0) (Kerk, 1992). Figure 1 demonstrates how these constraints limit the possible positions for the hip joint. Selecting

an optimal

posture

Given a feasible set of postures described in terms of the three unknown variables (xhipr yhip) and 4, a best or optimal posture was selected using three different criteria. The first criterion, labeled Total Torque, assumes that subjects choose a posture which requires the minimum total effort. Effort is defined as the torque summed over all joints. The objective function is shown in Equation (1) where tjoint is the torque at each of the 5 joints:

Chaffin and Andersson (1991): Minimize

Max

TantIe, [ hkle

i

Tknee Sknee

, Tkip

, %ou~der

Ship

, Te~bow

&houlder

&lbow

II

(2)

The third criterion, labeled Balance, assumes that subjects choose a posture which produces the greatest body stability. Stability in this case is defined as the ability to resist falling forwards or backwards which can be investigated by looking at the torques at the heel and ball of the foot (Kerk, 1992). Minimize { I ~~~~~ -

~~~~~~

}

(3)

Optimal postures were calculated using a nonlinear search method based on the Nelder-Mead search method (Bazaraa et al., 1993). This method was selected because it is known to be computationally efficient for multidimensional problems of the type described above.

COMPARISONS

Material

TO ACTUAL

POSTURES

and methods

Eight male and eight female subjects recruited from the student body at Virginia Tech participated in the experiment. The average age of the subjects was 22.3 yr (SD = 4.9). Male subjects Mi~mize{ITank~,I + ITkneel + bhipl + l~shou~derl + ITanklel}. (1) averaged 181.2 cm (SD = 6.6) in stature and 77.5 kg (SD = 6.8) in mass; female subjects averaged 165.4 cm (SD = 5.0) in The second criterion, labeled Percent Strength, is similar to stature and 56.6 kg (SD = 6.8) in mass. All participants were in good health and reported no history of back pain and no injuries the first except that effort is defined as the amount of torque exerted at each joint relative to the strength of the joint. This in the past year. The protocol and informed consent procedures represents the posture which distributes the torque across all used in the experiment were reviewed and approved by the joints in proportion to each joint’s ability to overcome that Institutional Review Board of Virginia Polytechnic Institute and State University. torque. The objective function is shown in Equation (2), where Each subject performed eight isometric sagittal lifts at each of Sjoint is the estimated strength moment of that joint based on four designated hand positions. Hand positions were selected based on model simulations to maximize the difference between the postures predicted for each of the three posture prediction models. Hand positions were specified in terms of the horizontal and vertical distance from the ankle. The four hand positions used were: (0.3 m, 0.5 m), (0.3 m, 1.2 m), (Max, 0.5 m), (Max, 1.2 m), where ‘Max’ represents each subjects maximum reach distance. During each trial, subjects held a 4 kg weight attached to a wooden dowel (total weight of 4.6 kg). The weight was held with two hands and both the dowel and the subjects heels were aligned with markers. Subjects were given no instruction on what posture to assume for a given condition, other than the specification of hand and foot position. Sagittal plane body postures were measured using a Watsmart three-dimensional motion analysis system at a sample rate of 20 Hz. Data for each trial were collected for 4 s; with a minimum of 2 min of seated rest provided for the subject between each trial. Markers were attached at the hand, at the elbow, along the upper arm, along the thigh, at the knee, and at the ankle. Using these markers, the shoulder joint was located by estimating the length of the upper arm link segment from measurements between external landmarks (Webb Associates, 1978) and projecting a vector of this magnitude from the elbow through the marker along the upper arm. Hip position was estimated in a similar manner using the knee and thigh marker. Joint center-of-rotations and associate link lengths were calculated for each joint following the procedures in Webb Associates (1978). Link mass values and center-of-mass locations were approximated as a percentage of total body weight estimated link length, respectively (Webb Associates, 1978). Prediction error for each model was defined as the Euclidean distance between the predicted and observed postures in the three-dimensional space defined by the unknown parameters of Fig. 1. Feasible solutions for the hip position based on the link the model: length and balance constraints. Link length constraints define the elliptical area and balance constraints define the crosshatched area. Given this feasible set, one of the three criteria was used to select a single solution.

Technical Note where (x,,,~(~,,~), yhipCbs),&J are the x and y hip position and the forearm orientation that define the observed posture and are the same three variables that de(Xbip(pred), Ybip(pred)r &red)) fine the predicted posture. Predicted postures were estimated using each subjects individual anthropometry and the actual hand and foot positions measured during each experimental

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trial (1536 cases).Prediction error was analyzed using a repeated measures analysis of variance (ANOVA). Probability values in this analysis were corrected for violaiions of the-sphericity assumption using the Geisser-Greenhouse correction (Winer et al., 1991).

pp r hf i‘ (Ma 0.5)(M= (0.3, 1.2)

(0.3,0.5)

1.2)

Fig. 2. Representative postures chosen by subjects for the four hand positions. These postures were derived by superimposing the postures for all subjects and visually selecting a posture most representative of the group. For postures at the lower hand position, two representative postures were identified, one for stoop type postures, and one for squat type postures. None of the three models tested were able to predict disparate postures of this type.

CRITERION +

Total

"4

Percent

-&

- Balance

torque Strength

0

1.8

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 (0.3,

1.2)

(0.3,

0.5)

(Max,

1.2)

(Max,

0.5)

HAND POSITION Fig. 3. The effect of hand position and model criterion on the average model prediction error as defined equation (5). The total torque criterion predicted postures with much lower error than the other criteria at the (0.3, OS) and (Max. 1.2) conditions and with only slightly higher error than the percent strength criterion at the other two conditions.

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Techni cal Note RESULTS

The body postures selected by different subjects were notably consistent for the higher hand positions, but could be separated into categories representing stoop postures and squat postures for the lower hand positions (see Fig. 2). For Hand Position (0.3 m, 0.5 m), three subjects chose a squat posture compared to the 13 other subjects who assumed a stooped posture. Similarly, for (Max, 0.5 m), 4 subjects chose a squat posture compared to the other 12 subjects who assumed a stooped posture. The ANOVA showed significant main effects for gender (F(1, 14) = 12.43, p = 0.003), hand position (F(3,42) = 78.51, p < O.OOl),and criterion (F(2, 28) = 18.63, p < O.OOl),and a significant Hand Position x Criterion interaction (F(6, 84) = 5.93, p < 0.001). The significant gender effect was a result of all three models predicting male postures more accurately than female postures (males s = 0.89; females E = 1.09). The Hand Position x Criterion interaction (see Fig. 3) demonstrates that the Total Torque criterion was as good or better than the other criteria, especially at the hand positions of (0.3 m, 0.5 m) and (Max, 1.2 m). DISCUSSION

Among the three criteria evaluated, the total torque criterion was, on the average, the most accurate. However, the accuracy of this model was highIy dependent on the experimental condition, and based on visual inspections of the data, was not within an acceptable margin of error for most conditions (see Fig. 4). The total torque criterion represents a general measure of overall effort or energy expenditure. In principle, it is very similar to the minimum energy criterion found by Park (1973) to be most effective in predicting sagittal plane postures. All three of the models had difficulty predicting the forearm angle accurately. This may be due in part to the absence of constraints on the head orientation. In evaluating the postures selected by the subjects, it appeared as if they may be attempting to minimize the moment created by the head about the neck, while also always maintaining sight of the load. Neither of these factors was considered in any of the current model formulations or in any previous posture prediction models we were able find

in the literature. To include these factors, we are currently working on a model which uses a separate link for the head and neck. In addition, a line-of-sight constraint has been placed on the orientation of the head to make sure that subjects are in a position to view the load at all times. In addition to accounting for head and neck position. it is clear from our results that future models will need to account for individual differences in posture selection. As shown in Fig. 2, subjects chose either a stooped or a squat posture for the lower hand positions. Possible reasons why subjects may choose one of these posture over the other include: past injuries at either of these joints. flexibility, relative strength, and fatigue. All of these factors have been noted by Haslegrave and her colleagues (Haslegrave, 1990, 1991; Haslegrave and Corlett, 1988; Haslegrave et al., 1988) as affecting posture, but again are not captured by this or other biomechanical models of posture. Passive tissue effects also need to be evaluated further. Both the Total Torque and the Percent Strength criteria assume that more effort is perceived when more torque is applied at the joint. This assumption does not consider the forces applied by passive tissues. For example, the squat posture selected by several subjects allowed the passive tissues at the knee and thigh to produce a large portion of the static torque required. Quantifying passive tissue effectsand including them in a model may produce more accurate estimates at the lower hand positions. Finally, the accuracy of the models presented in this paper may have been adversely affected by some of the computational procedures used and some of the approximations used in estimating anthropometric values. The solution space defining the feasible postures for each condition was nonconvex with multiple local optima. While the Nelder and Mead search procedure is known to be both an accurate and efficient method, identification of the global optima is not guaranteed. In addition, the use of other methods to estimate anthropometric and strength parameters may improve the models predictions. In conclusion, the models presented in this paper can claim only moderate success in predicting actual human posture. Among the three criterion evaluated, the total torque criterion seems to be the most promising. Future models will further evaluate this criterion while incorporating several of the modifications discussed above.

Fig. 4. A representative comparison of the observed postures (thin lines) with the predicted postures (thick lines) for the three criteria: total torque (TT), percent strength (PS), and balance (B). The comparisons represent a single experimental trial (selected from the eight repetitions) for a single subject at each posture condition. Note that the predictions of all three models are relatively inaccurate, especially for the shoulder and elbow joints.

Technical Note AcknowledgementtiFunds for the support of this research have been provided by the Association of American Railroads, Washington, D.C.. We would also like to thank Carolvn Bussi. Suzanne Lee, Mark McMulkin, and Jose Pesante-Saitana fo; their help in preparing this paper. REFERENCES

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