Optimum design of containers for manual material handling tasks

Applied Ergonomics 1977, 8.2, 67-72

Optimum design of containers for manual material handling tasks M.A. Ayoub North Carolina State University The container in manual material handling represents the point of interface between the worker and his task as well as with the surrounding environment. It is at this point that many of the well known handling hazards occur which manifest themselves in stresses and strains that are transmitted to the body via the musculo-skeletal system. If a substantial number of handling hazards is to be controlled or eliminated at the source, containers designed in accordance with principles of biomechanics and related recommendations provide a logical starting point. The container characteristics to be considered in the design process are weight (and its distribution), shape, stiffness, and availabili~ty of coupling devices. This paper presents several examples which outline and detail a number of problems associated with the design of containers involved in manual tasks. Application of basic mechanics, coupled with the use of optimization techniques, is presented as the approach for dealing with the hazards and problems of containers.

Introduction

Example 1 In the manufacturing area of a large textile plant, operators are required to lift and transport product units weighing either 11 or 14 lb (5-6.5 kg). The manufacturing area contains machines for producing the products, a conveyor system for transporting the products to other areas

in the plant, and carts which are used for storage of tools and as a place for in-process inventory of the product. Operators work under a noise level of 103-110 dBA for 450 rain per work shift. This requires all operators to wear ear plugs. Levels of illumination, temperature, and humidity are controlled and meet existing safety and health standards. Fumes are occasionally noticed in the manufacturing area, but there are no airborne particles present. The floor is concrete and has no 'fatigue reducing' mats because buggies and carts must be rolled through the area. Almost all operators are males in good health with an average age of 23 years. Each operator works between the machines and the outgoing product conveyor (Fig.l). The cart is usually placed to the operator's left as he faces the machines. Approximately 16 steps and 16 body turns occur during each work cycle (loading and unloading the products). The product is removed from the machine at two different heights and then is placed on the top surface of the cart. A tool is used to remove two product units from the machine at a time (Fig. 2). The product units are lifted slightly to a support on the cart for checking, and are then lowered and transported to the conveyor. The geometry of the workplace makes it possible for operators to use proper lifting and lowering techniques. As a general rule, however, operators have a tendency to twist the body rather than turn with the feet. Total cycle time per machine (multiple machines are served by each operator) is 8 min. Operators remain standing for the larger part of the work shift, ie, they sit only during rest periods.

Preparation of this paperwas supported in part by the National ScienceFoundationunder Grant GK-43386.

The workplace, as presented above, depicts many obvious handling problems which warrant further analysis and assessment. However, discussion will be limited to the

Containers (the objects to be handled: lifted, pushed, pulled, etc) can be characterized in terms of the following: (1)

Weight of the container and its contents.

(2)

Distribution of the weight inside the container; eg, uniform density versus uneven distribution of the load within the container.

(3)

Geometry (shape and bulk) of the container.

(4)

Stiffness of the load and/or of the container itself.

(5)

Possible modes of interface between the container and the man performing the task. The interface can be facilitated through the use of handles and similar coupling devices.

Herrin, et al (1974) give a detailed review of the literature on container characteristics as related to manual materials handling. Several design problems associated with containers which are typically used in manual tasks are presented and discussed via several examples in the following section.

Examples

Applied Ergonomics June 1977

67

Cort

2

The new design brings the weight and the reactive tbrce (muscular effort) together in such a way that their lines of action coincide;thus, the net force required for performing the task is kept to just the magnitude of the external load. 28 lb (125 N).

[ rC veY°'

This example shows how the use of simple mechanics (see Fig.3) can be used effectively to design and evaluate lifting tasks, especially the design of containers.

Floor plon

Fig. 1

Example 2

Side view

Work place layout

F I 16in(406rnm)_,_

1-

-

!

~

"t

z:=0 Right bond

a

1 5 i n _,_W 13in

(330r,~lq33Omm[

F2

22 (28) tb (9e-125 N)

A biomechanical reference load for manual lifting tasks can be defined as one that induces a torque Tat the Ls/S t spinal joint. The load is assumed to be highly concentrated, and, as such, its size - for all practical purposes - can be assumed to be negligible. The distance between the load and the Ls/S 1 disc is L. If the resultant lifting torque is to be kept constant (ie, equal to T), what is the maximum weight that can be placed in a container of size s? It is assumed that the mode of holding would result in having the container oriented in such a way that the dimension s appears in the sagittal plane. The question posed above is one that has received considerable attention (directly or indirectly) from many researchers in the field (eg, McConville and Hertzberg, 1966; Tichauer, 1971).There is a general concensus in the literature that as container size (its dimension in the sagittal plane) increases, the permissible weight to be handled should decrease proportionately.

Current design F

This relationship between the load and its size can be derived as follows: Let

W = weight of the reference load, and L = distance between the load (centre of mass and point of holding) and Ls/S 1 disc.

b Fig. 2

Proposed design

The reference torque is given by

W 22 (28) I,b (98 - 125 N)

T=WxL

Product removal tool

design of the product removal tool - the container in this case. As shown in Fig. 2(a), in handling the tool, the operator performs two functions: (i) provides a reactive torque at point A, and (ii) balances the tool and the product units over point B - the right hand. The torque and the resultant reactive force can be computed by considering the equilibrium of the tool-load aggregate.

W×L

= ~ [ L +s/2]

...(3)

The hands are assumed to at a distance L + s/2 from Ls/S 1 disc. From Equation (3), it follows that -- w [

c ] LL +.~I~s/2

...(4)

Equation (4) depicts a linear relationship between the

Let

/'1

= force applied by the left hand at point A,

load and its size. This relationship is in agreement with the

and

F2

= force maintained by the right hand at point B.

lifting literature; eg, see Fig. 4, Equation (4) can be modified to account for the effects of having handles (coupling devices) placed on the container.

For equilibrium, we write (see Fig. 2(a)) /'1

m 18-23 lb (80-102 N) . . . .

(1)

F2

- 4 5 - 5 2 lb (200-231 N) . . . .

(2)

From Equations (1) and (2), it is clear that because of the current tool design, the operator is required to apply a substantially larger force (perhaps twice as much) than is actually necessary. The operator's effort in handling the tool with the product units can be reduced significantly if a design similar to the one shown in Fig. 2(b) is adopted.

68

Now, consider the container of size s. We define W as the maximum weight to be placed in the container. For maintaining constant torque, T, the following condition should be satisfied:

Applied Ergonomics June 1977

Example 3 A computer manufacturing firm packages small electronic components in cardboard containers that measure s X h X l. Based on an economic study of several modes of transportation, W is selected as an acceptable minimum weight for each container. The delicate nature of the electronic components necessitates that all handing be performed manually. What are the optimum dimensions

()

()

~W2 / / ~ 1t //I 1~ WI

a

Fig. 3

b

Reactive forces and torques as a function of mode of holding and dimensions of container Case A: Uniform loading of the container

Case B: Uneven loading of the container

2s 2

4~ +~f 2]

F1 =

W[1

F2 =

2s 2 W [ 4s 2 + ~ 2 ]

FI =

2 te2 - s 2 1212 +3s 2 [3wt +W2] 6W 1 [s 2 + t 2 ] + 2 W 2 [5/p2 + 2 s 2]

F2 =

12/'2 + 3s 2

$2 Tt =

WX[1 -

-

2s 2 + 0 . 5 1 2

3WIX[612 - 3 s 2] + W 2 X [ 2 t 2 - s 2]

]

T1 =

36~ 2 + 9s 2

$ T2 =

W X [ 2 s 2 + 0"5t'2]

T2=

where s4

x

=

+

0.25s 2 ~ 2

[

18W1X[s 2 + { 2 ] + 2 W 2 X [ 5 ~ 2 + 2s2 ] 36 tQ2 + 9s 2

where

_ t4

] 4s 2 + t 2

x =

+ , 2 / 4 - i$ 2 + ,212 }/14,e2 + , 2

for the containers? Assume a uniform average density of p for the components.

subject to the minimum weight constraint, would yield an optimum design for the container.

Lifting literature supports the premise that the bulk and weight of containers are the primary contributor to the total torque induced at the Ls/S 1 disc - the critical joint of the spine. As is always the case, the weight of the object (and consequently the container) is fixed. In this case, the designer is left with the task of defining an optimal shape for the container. It is proposed here to accomplish this by formulating the problem as a non-linear optimization model, then proceeding to solve it by using the Lagrange multiplier technique. For the model, the obvious objective function would be one that is written in terms of the bulk (or surface area) of the container. Minimizing this function,

Mathematically, the optimization model can be stated as follows: Minimize: Z

...(5)

= sxh+sxt+hx~

Subject to: sxhxIxP

= W

...

(6)

Using the Lagrange multiplier technique, we write W L

= sxh+sxf+hxf+X[sxhx¢-

-~]

By differentiating L with respect to s,/, h, and X; and then

Applied Ergonomics June 1977

69

optimum solution

I00

1/3

= 0.5 (_w)

90

P Weight = 5 5 . 5 2 - 0 . 1 6 9 width

80

(W) t/3

SE estimate = 10.37

#*=

7O ~, 6 0

1"1 P

h *= 1"8 (-W) 1/s P

50

'S

~ 4o 30;

00

I

I

|

I0

20

30

/

I

[

[

40

50 60 70 Width of the object,cm

I

[

80

90

I00

Lifting capacity as a function of the container size (Based on data from MeConville and Hertzberg, 1966)

Fig. 4

proceed by setting the derivatives equal to zero, we obtain ~SL_ = h + ~ ' + h x ~ ' 8s ~L -

5h ~L 51 8L 8~

s +~'+s×f

= 0

= 0

- s+h+sxh

=

_ sxhxt~ -

_I¢= 0 p

0

Solving the above simultaneous equations, we fred the optimal dimensions for the container.

h*

s*=

=

t*=

(W-) 1~ P

and =

_21W v3

The model objective function attaches equal weights to all the container dimensions (s, h, and/'). Howver, an increase in s would have a pronounced effect on the torque produced at Ls/$1, more so than any comparable increase in for h. To account for this, the objective functions should be changed to read Z

=

el X s x t ' + P 2 x s x h + P 3

xhx'f

where PI' P2 and Pz = relative costs (penalty) associated with per unit area increase in the container panels. To illustrate the effects of including these differential costs on the optimum solution, the model was solved once more with P1 = 3, P2 = 2, and Ps = 1. This resulted in the following

70

Applied Ergonomics June 1977

The use of the Lagrange multipLier technique was not a prerequisite for solving the simple model of this example. Indeed the same answer could have been obtained if the model was solved via the use of differential calculus directly after utilizing the constraint equation to eliminate one of the variables in the objective function. On the other hand, techniques of non-linear programming should be used for solving the model if problem formulation or conditions call for the use of inequality constraints (for an introduction to these and similar techniques, see Wilde and Beightler, 1967).

Example 4

A machine part consists of two components that weigh W1 and W2 , respectively. The possible weights for each part can vary from 10 to 60 lb (4.5-27 kg). Because of engineering and production requirements, the minimum acceptable Linear dimensions for the two parts are 20 and 10 in (508 and 254 mm), respectively. A container is to be designed for shipping the machine part as well as similar ones. The part components can be shipped together or separately. All containers will be shipped to plants where most of the handling tasks are performed manually. If it is desired to limit the handling effort to approximately 30 lb (133 N) per hand (reactive force), what is the optimum weight for each container? In the course of handling, the forces acting on the handle will be a function of the posture assumed as well as the dynamic characteristics of the motion executed (eg, velocity and acceleration profiles). For many cases, these forces would range from four to eight times the hand reactive forces due to the static weight of the container. For the purpose of this example, it is assumed that the speed of movement (Lifting) will be of such a low magnitude that contribution of the motion to the hand-reactive forces can be safely neglected. However, for the general case when this cannot be assumed, the solution procedure outlined for this example can still be applied provided that the static forces are adjusted by using a certain multiplier; eg, multiply the hand forces (F 1 and F 2 in Fig. 5) by six, say, and then proceed with analysis as given. The problem here is to determine the maximum possible values for W1 and W2 while maintaining the resultant hand force less than or equal to 60 lb (267 N). This is a case that has all the characteristics typical of Linear programming models. First, the objective is to maximize the sum of W1 and W2. Second, the objective function is maximized sul~ject to a set of linear constraints; two of these are on reactive forces at both hands. The linear programming model can, therefore, be stated as follows (refer to Fig. 5). Maximize: Z = WI+W 2

This solution signifies that the weight per container should not exceed 60 lb (27 kg). The components of any part should be shipped separately if their combined weight exceeds the optimal weight as determined by the model.

180 WlX3~+W2x ~0 =30 160 =

1,40

Example 5 A group of men perform a lifting task for 6 h every working day. The task consists of picking boxed machine parts from a floor and positioning them on shelves approximately 30 in (762 mm) high. The weight of the boxes is normally distributed with mean SD and standard deviation oSD. Strength capability of the men is__assumed to be also normally distributed with mean s c and standard deviation aSc . What is the probability that one of the men will attempt to handle a load which exceeds his strength capability?

120 I00

8O 6\:\\\ 6O 40 2O

W2= I0

,\

i 20

, \,

40

60

80

I00

120

Wr

a

20 in (508ram)

bL I0 in (254mm)

1r

IOin(254mm)

15in (381ram)

WI

b

~

5in 4

~F2

W2

Optimum loading for a container of given dimensions. (a) Graphical solution of the model (b) Loading diagram for the container

Fig. 5

Subject to: W I + W 2 <~

120

10 < W I <

60

lo

60 20

Constraint on total weight of each container. Constraints on individual loads. 5

Wl x -~- + w2 x - ~ < 3o 10

25

W~xy6+ w2xy6<3o

Constraints on hand forces; obtained by taking movements about both ends of the simple beam representing the loading condition for the container.

The problem at hand addresses the very subject of how much safety factor is adequate or acceptable for developing a standard for manual handling tasks. Assuming that the weight (or its biomechanical equivalent, see Example 2) of the object will form the basis for such standard, the question becomes: what is the maximum permissible weight that an individual should be asked to handle? Traditionally, this question has been answered by (1) determining the maximum weight an individual (usually defined in terms of some basic characteristic such as age, weight, etc) can lift without incurring any physiological or anatomical damages, and (2) adjusting this maximum weight by using a safety factor to yield a permissible work load; ie, a concensus standard. However, in many instances the inclusion of safety factors in determining the weight limits is achieved indirectly via extensive experimentation as typified by the work of Snook and his co-workers (see Snook et al, 1970). Insofar as lifting is concerned, a variety of recommended maximum limits exist which in many instances are inconsistent (Herrin et al, 1974). We do not, however, wish to launch an inquiry to determine which ones are justified or applicable and which are not. Indeed our primary purpose here is to underscore the fact that using a safety factor (regardless of how it is incorporated) in setting performance standards can, for the most part, be misleading. The following cases will illustrate this point. As stated in the problem, consider the two variables: strength demand ($D) and strength capability (SC); both are normally distributed (see Fig. 6). For other than normal distribution, a similar procedure can be used. The basic idea would remain intact. The only change would be the outcome of the integration. The area of overlap in Fig. 6 determines the probability that the demand will exceed the available strength, ie, probability of failure PF. This probability can be given as

I4/1 , W 2 < 0 The above model is very. basic and can be solved graphically or by using the simplex method. When the number of variables (loads), however, exceeds two, the simplex method is the algorithm to be used for solving the linear programming model (Hillier and Lieberman, 1974). The optimum solution of the given model yields: W,

=

40 lb (18 ks)

W2 = 201b(9kg)

For two normally distributed random variables, PF is given by

Z PF = 1 - f

-Z2/2 e

dZ

...(7)

where Z = the normalized random variable

Applied Ergonomics June 1977

71

I

I

~g

In other words, a safety factor of 9 would be sufficient if we desire to have practically 100% of the work force succeed in performing their tasks.

I

~(s°~//'~~

Strength demond

~

I

~(sc)

Strength copability

Fig. 6 Distributionof strengthdemandandstrength capability

=

To illustrate the use of Equation (7), consider the following three cases.

Case 1

L tgc _-%= o.2gc %--

o.3

Conclusions

In the preceding examples, an attempt was made to emphasize that the design of containers is basically a problem of mechanics. The use of optimization techniques was also presented as a viable approach for dealing with specific container design problems. Furthermore, the application of a probabilistic approach to the definition of permissible weights for manual tasks seems feasible and thus warrants further consideration. If safety standards for manual tasks are to be practical and meaningful, there is no other alternative than the development of standards which account for the uncertainties associated with man and his performance. Although a challenge in itself, the design of a container should not, in and of itself, mask the need for using a total approach to the design and evaluation of manual tasks; ie, consideration of man, task, equipment, environment, and management practices. To this end, the modelling approach inbiomechanics stands to contribute the most, since modelling offers the flexibility of stud~ng and analysing problem variables in integrated and complete fashion (Ayoub, 1975). In addition, modelling confers the potential of bypassing the limitation and difficulties which are typical of many other approaches, eg, experimentation.

For the given data, we compute Z = 3.33. Using table of normal distribution, the probability of failure is given as

PF

=

0"001

References

Ayoub, M.A.

Case 2 Let SC

=

3-0 ffD

%--

o-2 c

%--

1.o -D

1975 'Occupational Biomechanics and Human Motion Analysis'. International Conference on Voluntary Human Movement, NSF Workshop at the University of Florida, Gainesville, Florida.

Similar to case 1, the given data yields a probability of failure

PF

=

0.058.

Notice that the two cases possess the same safety factor (je, S c / S D = 3.0) ; however, they are far from having the same renability or probability of failure - a result that substantiates the case against the blind use of safety factors in design.

Herrin, G.D., Chaffin, D.B., and Mach, R.S. 1974 'Criteria for Research on the Hazards of Manual Material Handling'. Workshop Proceedings, Contract No CDC-00-74-118, National Institute for Occupational Safety and Health, US Department of Health, Education and Welfare.

Hilfier, F.S., and Lieberman, G.J. 1974 'Introduction to Operations Research'. 2nd Edition. Holden-Day, Inc, San Francisco, California.

McConvige, J.T., and Hertzberg, H.T.E. 1966 'A Study of One-handed Lifting'. AMRL-TR-66-17, Aerospace Medical Research Laboratories, WrightPatterson Air Force Base, Ohio.

Snook, S.H., Irvine, C.H., and Bass, S.R. 1970 American Industrial Hygiene Association Journal,

Case 3 Compute the mean strength capability if the probability of failure is to be limited to 0.01%. Assume

OSc = 1.5ffC andoSD = 1-5ffD. From normal distribution tables, for a P~, = 0.0001, we obtain Z = 3.72. Substituting Z into E~uation (7) and solving for SC' we obtain

SC

=

Tichauer, E.R. 1971 Journal of Safety Research, 3.3, 98-115. A pilot study of the biomechanics of lifting in simulated industrial work situations.

Wade, D.J., and Beightler, C.S. 1967 'Foundations of Optimization'. Prentice-Hall, Inc, Englewood Cliffs, New Jersey.

8-89 S-D

72 Allied ErgonomicsJune

31.5,579-586. Maximum weights and work loads acceptable to male industrial workers.

1977