References and Bibliography 537
subject to
3 a
d
≤ 1
Noting thatc 1 = 0. 1 563,c 2 = 0 .76,andc 3 = 3 /d, we see that Eq. (E 12 ) ivesg
v()=
(
0. 1563
− 1
)− 1 (
− 0. 76
2
) 2 (
3
d
) 1
( 1 )^1 =
2. 772
d
Noting that
0. 1563
a^2
c^2
=
(
−
2. 772
d
)
(− 1 )=
2. 772
d
− 0. 76
a
c
= −
2. 772
d
( 2 )= −
5. 544
d
and usinga=1, we find thatc∗= 0. 4 1 andd∗= 3. 0. In addition, Eqs. (E 6 ) nda
(E 4 ) ieldy
a^2 −b^2 +c^2 +d^2
= 2 cdcosφd 0 + 2 accosθ 0 cos (φd 0 −θ 0 ) − 2 adcosθ 0
orb∗= 3. 6 62. Thus the optimal link dimensions are given bya∗= , 1 b∗= 3. 6 62,
c∗= 0 .41,andd∗= 3. 0.
References and Bibliography
8.1 R. J. Duffin, E. Peterson, and C. Zener,Geometric Programming, Wiley, New York,
1967.
8.2 U. Passy and D. J. Wilde, Generalized polynomial optimization,SIAM Journal of Applied
Mathematics, Vol. 15, No. 5, pp. 1344–1356, Sept. 1967.
8.3 D. J. Wilde and C. S. Beightler,Foundations of Optimization, Prentice-Hall, Englewood
Cliffs, NJ, 1967.
8.4 M. Avriel and A. C. Williams, Complementary geometric programming,SIAM Journal
of Applied Mathematics, Vol. 19, No. 1, pp. 125–141, July 1970.
8.5 R. M. Stark and R. L. Nicholls,Mathematical Foundations for Design: Civil Engineering
Systems, McGraw-Hill, New York, 1972.
8.6 C. McMillan, Jr.,Mathematical Programming: An Introduction to the Design and Appli-
cation of Optimal Decision Machines, Wiley, New York, 1970.
8.7 C. Zener, A mathematical aid in optimizing engineering designs,Proceedings of the
National Academy of Science, Vol. 47, p. 537, 1961.
8.8 C. Zener,Engineering Design by Geometric Programming, Wiley-Interscience, New York,
1971.
8.9 D. S. Ermer, Optimization of the constrained machining economics problem by geometric
programming,Journal of Engineering for Industry, Transactions of ASME, Vol. 93, pp.
1067–1072, Nov. 1971.
8.10 S. K. Hati and S. S. Rao, Determination of optimum machining conditions: deterministic
and probabilistic approaches,Journal of Engineering for Industry, Transactions of ASME,
Vol. 98, pp. 354–359, May 1976.
