Abstract. The classical Heron problem states: on a given straight line in the plane, find a
point C such that the sum of the distances from C to the given points A and B is minimal. This
problem can be solved using standard geometry or differential calculus. In the light of modern
convex analysis, we are able to investigate more general versions of this problem. In this paper
we propose and solve the following problem: on a given nonempty closed convex subset of
Rs , find a point such that the sum of the distances from that point to n given nonempty closed
convex subsets of...
Dedicated to the memory of V. I. Gurarii Abstract We prove that if X is a separable inﬁnite dimensional Banach space then its isomorphism class has inﬁnite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of c0 .
A allow b B c C d dhole drod D e E fom f(x) F FI Fs Range number Spring wire strength constant, cross-sectional area, Jacobian matrix Diametral allowance Range number Bushing diameter Distance to outer fiber, radial clearance Spring index Did Wire diameter Hole diameter Rod diameter Helix diameter, journal diameter Eccentricity Young's modulus Figure of merit Function Spring force, cumulative distribution function, function Spring working load Spring load at closure (soliding)...
C H A P T E R
1. Introduction. 2. Advantages and Disadvantages of Chain Drive over Belt or Rope Drive. 3. Terms Used in Chain Drive. 4. Relation Between Pitch and Pitch Circle Diameter. 5. Velocity Ratio of Chain Drives. 6. Length of Chain and Centre Distance. 7. Classification of Chains. 8. Hoisting and Hauling Chains. 9. Conveyor Chains. 10. Power Transmitting Chains. 11. Characteristics of Roller Chains. 12. Factor of Safety for Chain Drives. 13. Per missible Speed of Smaller Sprocket. 14. Power Transmitted by Chains. 15.
NOTATION BD C CD CCD D Dp G H HP Kf Kr L MHD MUTS n N TV1 TV2 Bottom diameter, in Center distance, in chain pitches Caliper diameter, in Chain clearance diameter, in Roller outside diameter, in Gauge pin diameter, in Maximum guide groove diameter, in Maximum chain height, in Horsepower Constant for link plate fatigue Constant for roller and bushing impact Chain length
Fractional area reduction Area Critical hardness for carbon content and tempering temperature, Rockwell C scale Diameter Tempering decrement, Rockwell C scale; carbon ideal diameter, in Ideal critical diameter, in Distant hardness, Rockwell C scale Equivalent Jominy distance, sixteenths of inch Tempering
Measurement of macro-geometric characteristic variables involves the acquisition of features of geometric elements that are defined in design by dimensions and tolerances for dimensional, form, and positional deviations (Figure 3.1-1). The term ‘dimension’ refers both to the diameter of rotationally symmetrical workpieces and to distances and angles between planes and straight lines and to cone angles. The sensors used for measurement can be classified according to the method used to acquire the measured value into mechanical, electrical, and optoelectronic sensors....
GLOSSARY OF SYMBOLS bG C d d0 dR D Db D0 D1 / hk ht L mG m0 mp nw nG Dedendum of gear teeth Center distance Worm pitch diameter Outside diameter of worm Root diameter of worm Pitch diameter of gear in central plane Base circle diameter Outside diameter of gear Throat diameter of gear Length of flat on outside diameter of worm Working depth of tooth Whole depth of tooth Lead of worm Gear ratio = NGINW Module, millimeters of pitch diameter per tooth (SI use) Number of teeth in contact Rotational speed of worm, r/min Rotational speed...
NOMENCLATURE a A b C0 C1, C2 d di E F g / 7 / k K Kf € Distance Area Distance Constant Constants Outside diameter of shaft Inside diameter of hollow shaft Modulus of elasticity Load Gravitation constant index Second moment of area Polar second area moment Torsional spring rate Transverse shear stress magnification factor Fatigue stress concentration factor Span
NOMENCLATURE a A b B bhn BHN c C Cp d de D D1 E / fi Distance, exponent, constant Area, addition factor, IiNt Distance, width, exponent "Li2N1 Brinell hardness, roller or pinion Brinell hardness, cam or gear Exponent Coefficient of variation Materials constant in rolling contact Difference in stress level, diameter Equivalent diameter Damage per cycle or block of cycles Ideal critical diameter Young's modulus Fraction of mean ultimate tensile
NOMENCLATURE A b Cp C8 di d2 e E F fb / M n P q r s t v z Cross section Width Angular factor Service factor Diameter of driving pulley Diameter of driven pulley Center distance Modulus of elasticity Force Bending frequency Datum length of flexible connector Torque Speed Power Mass per length Radius Belt thickness Pitch Velocity Number
GLOSSARY OF SYMBOLS A b d D e E F g h / / Ka KL K5 L € m Area or parallel misalignment Bearing spacing Diameter Diameter or distance between equipment Eccentricity Young's modulus or shape factor for maximum allowable stress, psi Force Acceleration due to gravity Height of keyway Second moment of area Polar second moment of area U-joint angle correction factor U-joint life correction factor U-joint speed correction factor Life or length of engagement Length Mass
K. S. Edwards, Ph.D. Professor of Mechanical Engineering University of Texas at El Paso El Paso, Texas
36.1 INTRODUCTION / 36.2 36.2 KINEMATICS / 36.3 36.3 VELOCITY AND FRICTION / 36.5 36.4 FORCE ANALYSIS / 36.5 36.5 STRENGTH AND POWER RATING / 36.9 36.6 HEAT DISSIPATION / 36.12 36.7 DESIGN STANDARDS / 36.13 36.8 DOUBLE-ENVELOPING GEAR SETS /36.18 REFERENCES / 36.22 ADDITIONAL REFERENCE / 36.22
GLOSSARY OF SYMBOLS bG C d d0 dR D Db D0 D1 / hk ht L mG m0 mp nw nG Dedendum of gear teeth Center distance Worm pitch diameter Outside diameter of worm Root...
1. Introduction. 2. Advantages and Disadvantages of Chain Drive over Belt or Rope Drive. 3. Terms Used in Chain Drive. 4. Relation Between Pitch and Pitch Circle Diameter. 5. Velocity Ratio of Chain Drives. 6. Length of Chain and Centre Distance. 7. Classification of Chains. 8. Hoisting and Hauling Chains. 9. Conveyor Chains. 10. Power Transmitting Chains. 11. Characteristics of Roller Chains. 12. Factor of Safety for Chain Drives. 13. Per missible Speed of Smaller Sprocket. 14. Power Transmitted by Chains. 15. Number of Teeth on the Smaller or Driving Sprocket or Pinion. 16.
Distance, range number, bilaterial tolerance Width, range number Constant Helix diameter Dimensional operator Young's modulus Error using n applications of Simpson's rule The /th exponent Function The /th derivative of function / Fundamental dimension of force, fractional reduction of interval of uncertainty Function Function, ordinate spacing Index Second area moment, value of integral Approximate value of integral using i applications of Simpson's rule Spring rate
MINIMIZING ENGINEERING EFFORT
Charles R. Mischke, Ph.D., P.E. Professor Emeritus of Mechanical Engineering Iowa State University Ames, Iowa
11.1 INTRODUCTION/11.2 11.2 REDUCING THE NUMBER OF EXPERIMENTS /11.3 11.3 SIMILITUDE/11.7 11.4 OPTIMALITY/11.9 11.5 QUADRATURE/11.13 11.6 CHECKING/11.15 REFERENCES/11.