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Introduction to Mechanical Engineering Design 23
numbers with three significant figures. For trailing zeros, a little more clarification is nec-
essary. To display 706 to four significant figures insert a trailing zero and display either
3
2
706.0, 7.060 × 10 , or 0.7060 × 10 . Also, consider a number such as 91 600. Scientific
notation should be used to clarify the accuracy. For three significant figures express the
3
3
number as 91.6 × 10 . For four significant figures express it as 91.60 × 10 .
Computers and calculators display calculations to many significant figures. However,
you should never report a number of significant figures of a calculation any greater than
the smallest number of significant figures of the numbers used for the calculation. Of
course, you should use the greatest accuracy possible when performing a calculation. For
example, determine the circumference of a solid shaft with a diameter of d = 0.40 in. The
circumference is given by C = πd. Since d is given with two significant figures, C should
be reported with only two significant figures. Now if we used only two significant figures
for π our calculator would give C = 3.1 (0.40) = 1.24 in. This rounds off to two signif-
icant figures as C = 1.2 in. However, using π = 3.141 592 654 as programmed in the
calculator, C = 3.141 592 654 (0.40) = 1.256 637 061 in. This rounds off to C = 1.3
in, which is 8.3 percent higher than the first calculation. Note, however, since d is given
with two significant figures, it is implied that the range of d is 0.40 ± 0.005. This means
that the calculation of C is only accurate to within ±0.005/0.40 =±0.0125 =±1.25%.
The calculation could also be one in a series of calculations, and rounding each calcula-
tion separately may lead to an accumulation of greater inaccuracy. Thus, it is considered
good engineering practice to make all calculations to the greatest accuracy possible and
report the results within the accuracy of the given input.

1–16 Design Topic Interdependencies
One of the characteristics of machine design problems is the interdependencies of the
various elements of a given mechanical system. For example, a change from a spur gear
to a helical gear on a drive shaft would add axial components of force, which would
have implications on the layout and size of the shaft, and the type and size of the bear-
ings. Further, even within a single component, it is necessary to consider many differ-
ent facets of mechanics and failure modes, such as excessive deflection, static yielding,
fatigue failure, contact stress, and material characteristics. However, in order to provide
significant attention to the details of each topic, most machine design textbooks focus
on these topics separately and give end-of-chapter problems that relate only to that
specific topic.
To help the reader see the interdependence between the various design topics, this
textbook presents many ongoing and interdependent problems in the end-of-chapter
problem sections. Each row of Table 1–1 shows the problem numbers that apply to the
same mechanical system that is being analyzed according to the topics being presented
in that particular chapter. For example, in the second row, Probs. 3–40, 5-65, and 5–66
correspond to a pin in a knuckle joint that is to be analyzed for stresses in Chap. 3 and
then for static failure in Chap. 5. This is a simple example of interdependencies, but as
can be seen in the table, other systems are analyzed with as many as 10 separate prob-
lems. It may be beneficial to work through some of these continuing sequences as the
topics are covered to increase your awareness of the various interdependencies.
In addition to the problems given in Table 1–1, Sec. 1–17 describes a power trans-
mission case study where various interdependent analyses are performed throughout
the book, when appropriate in the presentation of the topics. The final results of the case
study are then presented in Chap. 18.