POSTURAL CONSIDERATIONS 137
In the general case of exertion in any direction, the man in Fig. 3 is exerting a force which has components of LIFT and PUSH
(PRESS & PULL if negative), and also a torque TWIST. The torque may be important if the hands are separated in the sagittal plane, but were negligible in the experiments for which results are presented. The experimental rig incorporates a bar handle, fitted with force transducers to measure the manual forces. The LIFT and
138
S.,IIe, lO' e.
T_c s.,s-" c.oo
D. W. GRIEVE AND S. T. PHEASANT
Fig. 4. Left: Experimental PSD record (hand height 1m, toes O.Sm to rear. Right: Means ~ 1 sd, 10 males, same conditions.
The envelope is based on a periodic cubic spline function.
If we consider the static balance of the man in Fig. 5, by taking moments about the centre of foot pressure, we obtain the Equation of Static Exertion (ESE):
LIFT/W = (h/b).PUSH/W -(a/b) -(TWIST/b.W)
This simple equation is given a special name because it links some important quantities, namely the LIFT and PUSH components of force at the hands, the weight of the body, the centre of pressure at the feet and the position of the centre of gravity. The ESE can be represented as a line on the PSD (see Fig.S). The slope of the line is the slope of the Live axis. The intercept on the base of the PSD (LIFT/W= -1) equals the horizontal distance of the centre of gravity from the handle as a fraction of handle height. The perpendicular distance of the line from the origin represents the Dead-weight force. The Jack-in-a-Box effect is to generate forces whose vector heads are varying distances along the line. At any instant, static exertion is made according to a particular ESE. If a required force is not on the line, the slope and/or the intercept must be altered to accommodate the vector. The slope is altered by changing the centre of pressure within the foot base. The intercept is altered by moving the centre of gravity of the body. The ESE states what
combinations of LIFT and PUSH are possible in a given posture and manner of support. It does not, of course, say what actual force can be generated, because that is a matter of choice if it is sub- maximal, and subject to physiological constraints, not merely the laws of statics when maximal.
POSTURAL CONSIDERATIONS
-500N
Stu· lit. /OOc.m Toes 50. SDc",
o ~ o 10 I
(a-bl/h
PUSH SOoN
Fig. 5. Top left: Diagram illustrating the quantities which appear in the Equation of Static Exertion.
139
Top Right: The ESE plotted as line EE' on the PSD.
Vectors OD and DP may be recognised as the dead-weight and Jack-in-a-Box components of the manual force vector.
Bottom: ESEs observed experimentally with a subject standing on his metatarsal heads. Lines obtained in two postures which differed by virtue of a shift of the subject's centre of gravity (a-b), but the hand and foot centroids (h/b) did not alter.
140 D. W. GRIEVE AND S. T. PHEASANT
The experimental record in Fig. 5 shows that the ESE is operative. The subject maintained a fixed posture and stood on the heads of his metatarsals, while trying to exert forces in as many directions as possible. He then shifted his weight and repeated the exercise. The Live axis was the same for both postures so that the records obtained both had the same slope. The effect of shift- ing the centre of gravity was to change the intercept of the line which contained the heads of the vectors.
Studies of manual exertion have been mainly devoted to lifting tasks, although horizontal pushing and pulling have also received some attention. In contrast, very little data is available concern- ing the general case of exertion in any direction. If they were, the information could be used in the design and analysis of tasks.
A framework for the application of PSDs to task design was outlined by Grieve (1979 a, b). Consideration has so far been given to analysis in the sagittal plane. Our experiments are designed to provide an appropriate data base in PSD form. The merit of the dia- gram is that other statements besides strength can be made on it.
These include task demands and environmental constraints such as floor friction; superposition of the statements allows the task designer or safety engineer to consider how satisfactory a match exists between the operator and the environment.
Fig. 6 contains 12 PSDs which show the mean forces that can be exerted relative to body weight, in a variety of foot and hand placements. The columns, left to right, refer to hand placements of head, waist and shin height. The rows, top to bottom, refer to feet together with shoe-toes under the bar, with one foot 50cm to the rear, both feet together 50cm behind the bar, and finally with one foot at 50cm and the other 100cm behind the bar. The force in any particular direction is systematically affected by both foot and hand placement; this fact suggests why the information is relevant to task design. For example, we see in Manoeuvre 2 (hands at head height, toes 50 cm behind the bar) that subjects have an ability to exert themselves in the Live axis and also to press downwards, but they are otherwise quite weak. In contrast, the subjects in Manoeuvre 5 (hands at shin height, toes beneath the bar) have considerable strength in all directions in which a LIFT component is involved.
By means of a large balance board, the limiting anterior and posterior locations of the centre of gravity were determined for each combination of foot and hand placement. Limiting ESEs apply when the centre of pressure at the feet is at the anterior limit of the foot base while the centre of gravity is at its posterior limit, and vice versa. The extreme lines (average slopes and intercepts) are drawn on the PSDs in Fig. 6. The limiting lines come close to, or touch, the force vector envelopes in many cases.
It is concluded that the limiting combination of anterior foot
POSTURAL CONSIDERATIONS