Design for Human Factors Figure 5.17 shows an airport luggage carrier and its free-body diagram when it is held in equilibrium in the tilted position. If the luggage carrier supports a weight W = 50 lb, the angle α = 30°, a = 8 in., b = 16 in., and d = 48 in., what force F must the user exert?

Question

Design for Human Factors

Figure 5.17 shows an airport luggage carrier and its free-body diagram when it is held in equilibrium in the tilted position. If the luggage carrier supports a weight W = 50 lb, the angle α = 30°, [latex]a = 8[/latex] in., b = 16 in., and d = 48 in., what force F must the user exert?

Strategy

The unknown reactions on the free-body diagram are the force F and the normal force N exerted by the floor. If we sum moments about the center of the wheel C, we obtain an equation in which F is the only unknown reaction.

Accepted Answer

Summing moments about C,

[latex]\sum{M_{(point C)} } = d (F \cos α) + a (W \sin α) - b (W \cos α) = 0 .[/latex]

and solving for F, we obtain

[latex]F = \frac{(b - a an α)W}{d}.[/latex] (5.10)

Substituting the values of [latex] W, α, a, b,[/latex] and d, the solution is F = 11.9 lb.

design Issues

Design that accounts for human physical dimensions, capabilities, and characteristics is a special challenge. This art is called design for human factors. Here we consider a simple device, the airport luggage carrier in Fig. 5.17, and show how consideration of its potential users and the constraints imposed by the equilibrium equations affect its design.

The user moves the carrier by grasping the bar at the top, tilting it, and walking while pulling the carrier. The height of the handle (the dimension h) needs to be comfortable. Since h = R + d sin α , if we choose values of h and the wheel radius R, we obtain a relation between the length of the carrier's handle d and the tilt angle α:

[latex] d = \frac{h - R }{\sin α} . [/latex] (5.11)

Substituting this expression for d into Eq. (5.10), we obtain

[latex]F = \frac{\sin α(b - a an α)W }{h - R} .[/latex] (5.12)

Suppose that based on statistical data on human dimensions, we decide to design the carrier for convenient use by persons up to 6 ft 2 in. tall, which corresponds to a dimension h of approximately 36 in. Let R = 3 in., [latex]a = 6[/latex] in., and b = 12 in. The resulting value of F/W as a function of α is shown in Fig. 5.18. At α = 63°, the force the user must exert is zero, which means the weight of the luggage acts at a point directly above the wheels. This would be the optimum solution if the user could maintain exactly that value of α. However, α inevitably varies, and the resulting changes in F make it difficult to control the carrier. In addition, the relatively steep angle would make the carrier awkward to pull. From this point of view, it is desirable to choose a design within the range of values of α in which F varies slowly, say, 30° < α < 45°. (Even though the force the user must exert is large in this range of α in comparison with larger values of α, it is only about 1 3% of the weight.) Over this range of α. the dimension d varies from 5.5 ft to 3.9 ft. A smaller carrier is desirable for lightness and ease of storage, so we choose d = 4 ft for vour preliminary design.

We have chosen the dimension d based on particular values of the dimensions R,[latex] a[/latex], and b. In an actual design study, we would carry out the analysis for expected ranges of values of these parameters. Our final design would also reflect decisions based on safety (for example, there must be adequate means to secure the luggage and no sharp projections), reliability (the frame must be sufficiently strong and the wheels must have adequate and reliable bearings), and the cost of manufacture.

Question 5.5: Design for Human Factors Figure 5.17 shows an airport luggag...

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