references - springer978-0-387-74244-1/1.pdf · 978 references chapter 4 cossalter, v., 2002,...

References

Chapter 1American Association of State Highway Officials, AASHO, Highway De-

finitions, June 1968.American National Standard, Manual on Classification of Motor Vehicle

Traffic Accidents, Sixth Edition, National Safety Council, Itasca, Illinois,1996.Cossalter, V., 2002, Motorcycle Dynamics, Race Dynamic Publishing,

Greendale, WI.National Committee on Uniform Traffic Laws and Ordinances, Uniform

Vehicle Code and Model Traffic Ordinance, 1992.United States Code, Title 23. Highways. Washington: U.S. Government

Printing Office.

Chapter 2Cossalter, V., 2002, Motorcycle Dynamics, Race Dynamic Publishing,

Greendale, WI.Genta, G., 2007, Motor Vehicle Dynamics, Modeling and Simulation,

World Scientific, Singapore.Norbe, J. P., 1980, The Car and its Weels, A Guide to Modern Suspen-

sion Systems, TAB Books Inc.Wong, J. Y., 2001, Theory of Ground Vehicles, John Wiley & Sons, New

York.

Chapter 3Andrzejewski, R., and Awrejcewicz, J., 2005, Nonlinear Dynamics of a

Wheeled Vehicle, Springer-Verlag, New York.Cossalter, V., 2002, Motorcycle Dynamics, Race Dynamic Publishing,

Greendale, WI.Ellis, J. R., 1994, Vehicle Handling Kinematics, Mechanical Engineering

Publications Limited, London.Genta, G., 2007, Motor Vehicle Dynamics, Modeling and Simulation,

World Scientific, Singapore.Haney, P., 2003, The Racing and High—Performance Tire, SAE Inc.Milliken, W. F., and Milliken, D. L., 2002, Chassis Design, SAE Inc.Milliken, W. F., and Milliken, D. L., 1995, Race Car Vehicle Dynamics,

SAE Inc.Norbe, J. P., 1980, The Car and its Wheels, A Guide to Modern Suspen-

sion Systems, TAB Books Inc.Wong, J. Y., 2001, Theory of Ground Vehicles, John Wiley & Sons, New

York.

References978


Greendale, WI.Genta, G., 2007, Motor Vehicle Dynamics, Modeling and Simulation,

World Scientific, Singapore.Milliken, W. F., and Milliken, D. L., 1995, Race Car Vehicle Dynamics,

SAE Inc.Wong, J. Y., 2001, Theory of Ground Vehicles, John Wiley & Sons, New

York.

Chapter 5Asada, H., and Slotine, J. J. E., 1986, Robot Analysis and Control, John

Wiley & Son, New York.Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland

Publication, Amsterdam, The Netherlands.Goldstein, H., Poole, C., and Safko, J., 2002, Classical Mechanics, 3rd

ed., Addison Wesley, New York.Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford Univer-

sity Press, London.Kane, T. R., Likins, P. W., and Levinson, D. A., 1983, Spacecraft Dy-

namics, McGraw-Hill, New York.MacMillan, W. D., 1936, Dynamics of Rigid Bodies, McGraw-Hill, New

York.Mason, M. T., 2001, Mechanics of Robotic Manipulation, MIT Press,

Cambridge, Massachusetts.Murray, R. M., Li, Z., and Sastry, S. S. S., 1994, A Mathematical Intro-

duction to Robotic Manipulation, CRC Press, Boca Raton, Florida.Nikravesh, P., 1988, Computer-Aided Analysis of Mechanical Systems,

Prentice Hall, New Jersey.Paul, R. P., 1981, Robot Manipulators: Mathematics, Programming, and

Control, MIT Press, Cambridge, Massachusetts.Rosenberg, R. M., 1977,Analytical Dynamics of Discrete Systems, Plenum

Publishing Co., New York.Tsai, L. W., 1999, Robot Analysis, John Wiley & Sons, New York.Schaub, H., and Junkins, J. L., 2003, Analytical Mechanics of Space Sys-

tems, AIAA Educational Series, American Institute of Aeronautics andAstronautics, Inc., Reston, Virginia.Spong, M. W., Hutchinson, S., and Vidyasagar, M., 2006, Robot Modeling

and Control, John Wiley & Sons, New York.

Chapter 6Beatty, M. F., 1986, Principles of Engineering Mechanics, Vol. 1, Kinematics-

The Geometry of Motion, Plenum Press, New York.Jazar, R. N., 2007, Applied Robotics: Kinematics, Dynamics, and Con-

trol, Springer, New York.

References 979

Hartenberg, R. S., and Denavit, J., 1964, Kinematic Synthesis of Link-ages, McGraw-Hill Book Co.Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford Univer-

sity Press, London.Nikravesh, P., 1988, Computer-Aided Analysis of Mechanical Systems,

Prentice Hall, New Jersey.Soni, A. H., 1974,Mechanism Synthesis and Analysis, McGraw-Hill Book

Co.







sion Systems, TAB Books Inc.Rajamani, R., 2006, Vehicle Dynamics and Control, Springer-Verlag,

New York.Wong, J. Y., 2001, Theory of Ground Vehicles, John Wiley & Sons, New

York.



Greendale, WI.Dixon, J. C., 1996, Tire, Suspension and Handling, SAE Inc.Ellis, J. R., 1994, Vehicle Handling Kinematics, Mechanical Engineering




sion Systems, TAB Books Inc.

980

Chapter 9Goldstein, H., Poole, C., and Safko, J., 2002, Classical Mechanics, 3rd

ed., Addison Wesley, New York.Jazar, R. N., 2007, Applied Robotics: Kinematics, Dynamics, and Con-

trol, Springer, New York.Mason, M. T., 2001, Mechanics of Robotic Manipulation, MIT Press,

Cambridge, Massachusetts.Rosenberg, R. M., 1977,Analytical Dynamics of Discrete Systems, Plenum

Publishing Co., New York.MacMillan, W. D., 1936, Dynamics of Rigid Bodies, McGraw-Hill, New

York.Schaub, H., and Junkins, J. L., 2003, Analytical Mechanics of Space Sys-

tems, AIAA Educational Series, American Institute of Aeronautics andAstronautics, Inc., Reston, Virginia.Skalmierski, B., 1991, Mechanics, Elsevier, Poland.Wittacker, E. T., 1947, A Treatise on the Analytical Dynamics of Parti-

cles and Rigid Bodies, 4th ed., Cambridge University Press, New York.





SAE Inc.Rajamani, R., 2006, Vehicle Dynamics and Control, Springer-Verlag,

New York.Wong, J. Y., 2001, Theory of Ground Vehicles, John Wiley & Sons, New

York.




World Scientific, Singapore.Milliken, W. F., and Milliken, D. L., 1995, Race Car Vehicle Dynamics,

SAE Inc.Rajamani, R., 2006, Vehicle Dynamics and Control, Springer-Verlag,

New York.

References

References 981

Chapter 12Balachandran, B., Magrab, E. B., 2003, Vibrations, Brooks/Cole, Pacific

Grove, CA.Benaroya, H., 2004,Mechaniscal Vibration: Analysis, Uncertainities, and

Control, Marcel Dekker, New York.Del Pedro, M., and Pahud, P., 1991, Vibration Mechanics, Kluwer Aca-

demic Publishers, The Netherland.Den Hartog, J. P., 1934,Mechanical Vibrations, McGraw-Hill, New York.Harris, C. M., and Piersol, A. G., 2002, Harris’ Shock and Vibration

Handbook, McGraw-Hill, New York.Inman, D., 2007, Engineering Vibrations, Prentice Hall, New York.Meirovitch, L., 2002, Fundamentals of Vibrations, McGraw-Hill, New

York.Meirovitch, L., 1967, Analytical Methods in Vibrations, Macmillan, New

York.Jazar, R. N., Kazemi, M., and Borhani, S., 1992, Mechanical Vibrations,

Ettehad Publications, Tehran. (in Persian).Rao, S. S., 2003, Mechanical Vibrations, Prentice Hall, New York.Roseau, M., 1987, Vibrations in Mechanical Systems, Springer-Verlag,

Berlin.Shabana, A. A., 1997, Vibration of Discrete and Continuous Systems,

Springer-Verlag, New York.

Chapter 13Balachandran, B., Magrab, E. B., 2003, Vibrations, Brooks/Cole, Pacific

Grove, CA.Benaroya, H., 2004,Mechaniscal Vibration: Analysis, Uncertainities, and

Control, Marcel Dekker, New York.Del Pedro, M., and Pahud, P., 1991, Vibration Mechanics, Kluwer Aca-

demic Publishers, Netherland.Den Hartog, J. P., 1934,Mechanical Vibrations, McGraw-Hill, New York.Harris, C. M., and Piersol, A. G., 2002, Harris’ Shock and Vibration

Handbook, McGraw-Hill, New York.Inman, D., 2007, Engineering Vibrations, Prentice Hall, New York.Jazar, R. N., Kazemi, M., and Borhani, S., 1992, Mechanical Vibrations,

Ettehad Publications, Tehran. (in Persian).Meirovitch, L., 2002, Fundamentals of Vibrations, McGraw-Hill, New

York.Meirovitch, L., 1967, Analytical Methods in Vibrations, Macmillan, New

York.Rao, S. S., 2003, Mechanical Vibrations, Prentice Hall, New York.Roseau, M., 1987, Vibrations in Mechanical Systems, Springer-Verlag,

Berlin.

982

Shabana, A. A., 1997, Vibration of Discrete and Continuous Systems,Springer-Verlag, New York.

Chapter 14Alkhatib, R., Jazar, R. N., and Golnaraghi, M. F., Optimal Design of

Passive Linear Mounts with Genetic Algorithm Method, Journal of Soundand Vibration, 275(3-5), 665-691, 2004.Asada, H., and Slotine, J. J. E., 1986, Robot Analysis and Control, John

Wiley & Sons, New York.Murray, R. M., Li, Z., and Sastry, S. S. S., 1994, A Mathematical Intro-

duction to Robotic Manipulation, CRC Press, Boca Raton, Florida.Jazar, R. N., Alkhatib, R., and Golnaraghi, M. F., Root Mean Square

Optimization Criterion for Vibration Behavior of Linear Quarter Car UsingAnalytical Methods, Journal of Vehicle System Dynamics, 44(6), 477—512,2006.Jazar, R. N., and Golnaraghi, M. F., Engine Mounts for Automotive

Applications: A Survey, The Shock and Vibration Digest, 34(5), 363-379,2002.Jazar, R. N., Narimani, A., Golnaraghi, M. F., and Swanson, D. A.,

Practical Frequency and Time Optimal Design of Passive Linear VibrationIsolation Mounts, Journal of Vehicle System Dynamics, 39(6), 437-466,2003.Roseau, M., 1987, Vibrations in Mechanical Systems, Springer-Verlag,

Berlin.Snowdon, J. C., 1968,Vibration and shock in damped mechanical systems,

John Wiley, New York.

Chapter 15Esmailzadeh, E., 1978, Design Synthesis of a Vehicle Suspension System

Using Multi-Parameter Optimization, Vehicle System Dynamics, 7, 83-96.Jazar, R. N., Alkhatib, R., and Golnaraghi, M. F., Root Mean Square

Optimization Criterion for Vibration Behavior of Linear Quarter Car UsingAnalytical Methods, Journal of Vehicle System Dynamics, 44(6), 477—512,2006.Jazar, R. N., Narimani, A., Golnaraghi, M. F., and Swanson, D. A., Prac-

tical Frequency and Time Optimal Design of Passive Linear V ibrationIsolation Mounts, Journal of Vehicle System Dynamics, 39(6), 437-466,2003.Roseau, M., 1987, Vibrations in Mechanical Systems, Springer-Verlag,

Berlin.

References

Appendix A

Frequency Response CurvesThere are four types of one-DOF harmonically excited systems as shownin Figure 12.14:

1− base excitation,2− eccentric excitation,3− eccentric base excitation,4− forced excitation.The frequency responses of the four systemscan be summarized, labeled

and shown as follows:

S0 =XF

F/k(A.1)

=1q

(1− r2)2 + (2ξr)2(A.2)

S1 =XF

F/√km

(A.3)

=rq

(1− r2)2 + (2ξr)2(A.4)

S2 =XF

F/m=

ZBY=

XE

eεE=

ZReεR

(A.5)

=r2q

(1− r2)2+ (2ξr)

2(A.6)

S3 =ZBωnY

=XE

eεEωn=

ZReεRωn

(A.7)

=r3q

(1− r2)2+ (2ξr)

2(A.8)

S4 =ZBω2nY

=XE

eεEω2n=

ZReεRω2n

(A.9)

=r4q

(1− r2)2+ (2ξr)

2(A.10)

984 Appendix A. Frequency Response Curves

r

0S

0ξ =

0.1

0.2

0.3

0.4

0.50.6

0.81.0

/F

0XS

F k=

FIGURE A.1. Frequency response for S0.

G0 =FTFF

=XB

Y(A.11)

=

q1 + (2ξr)2q

(1− r2)2 + (2ξr)2(A.12)

G1 =XB

ωnY(A.13)

=r

q1 + (2ξr)2q

(1− r2)2 + (2ξr)2(A.14)

G2 =XB

ω2nY=

FTBkY

=FTE

eω2nme=

FTReω2nme

³1 +

mb

m

´(A.15)

=r2q1 + (2ξr)

2q(1− r2)

2+ (2ξr)

2(A.16)

Appendix A. Frequency Response Curves 985

r

1S

0ξ =

0.1

0.2

0.3

0.4

0.50.6

0.81.0

/F

1XS

F km=

&


r

2S

0ξ =

0.2

0.1

0.3

0.40.5

0.6

0.81.0

/F B E R

2E R

X Z X ZSF m Y e e

= = = =ε ε

&&



r

3S

0ξ =0.1

0.3

0.4

0.5

0.6

0.81.0

0.2

B E R3

n E n R n

Z X ZSY e e

= = =ω ε ω ε ω

& & &


r

4S

0ξ =

0.1

0.3

0.4

0.5

0.60.8

1.0

0.2

B E R4 2 2 2

n E n R n

Z X ZSY e e

= = =ω ε ω ε ω

&& && &&


Appendix A. Frequency Response Curves 987

r

0G

0ξ =0.1

0.3

0.50.60.8

1.0

0.2

0.4

FT B0

F XGF Y

= =

FIGURE A.6. Frequency response for G0.

r

1G

0ξ =

0.1

0.3

0.50.6

0.81.0

0.2

0.4

B1

n

XGY

=ω

&



r

2G

0ξ =

0.1

0.3

0.50.60.81.0

0.2

0.4

E E RT T TB a2 2 2 2

n n e n e

F F FX mG 1kY mY e m e m

⎛ ⎞= = = = +⎜ ⎟⎝ ⎠ω ω ω

&&


Appendix B

Trigonometric FormulasDefinitions in Terms of Exponentials

cos z =eiz + e−iz

2(B.1)

sin z =eiz − e−iz

2i(B.2)

tan z =eiz − e−iz

i (eiz + e−iz)(B.3)

eiz = cos z + i sin z (B.4)

e−iz = cos z − i sin z (B.5)

Angle Sum and Difference

sin(α± β) = sinα cosβ ± cosα sinβ (B.6)

cos(α± β) = cosα cosβ ∓ sinα sinβ (B.7)

tan(α± β) =tanα± tanβ1∓ tanα tanβ (B.8)

cot(α± β) =cotα cotβ ∓ 1cotβ ± cotα (B.9)

Symmetry

sin(−α) = − sinα (B.10)

cos(−α) = cosα (B.11)

tan(−α) = − tanα (B.12)

Multiple Angles

sin(2α) = 2 sinα cosα =2 tanα

1 + tan2 α(B.13)

cos(2α) = 2 cos2 α− 1 = 1− 2 sin2 α = cos2 α− sin2 α (B.14)

tan(2α) =2 tanα

1− tan2 α (B.15)

cot(2α) =cot2 α− 12 cotα

(B.16)

990 Appendix B. Trigonometric Formulas

sin(3α) = −4 sin3 α+ 3 sinα (B.17)

cos(3α) = 4 cos3 α− 3 cosα (B.18)

tan(3α) =− tan3 α+ 3 tanα−3 tan2 α+ 1 (B.19)

sin(4α) = −8 sin3 α cosα+ 4 sinα cosα (B.20)

cos(4α) = 8 cos4 α− 8 cos2 α+ 1 (B.21)

tan(4α) =−4 tan3 α+ 4 tanαtan4 α− 6 tan2 α+ 1 (B.22)

sin(5α) = 16 sin5 α− 20 sin3 α+ 5 sinα (B.23)

cos(5α) = 16 cos5 α− 20 cos3 α+ 5 cosα (B.24)

sin(nα) = 2 sin((n− 1)α) cosα− sin((n− 2)α) (B.25)

cos(nα) = 2 cos((n− 1)α) cosα− cos((n− 2)α) (B.26)

tan(nα) =tan((n− 1)α) + tanα1− tan((n− 1)α) tanα (B.27)

Half Angle

cos³α2

´= ±

r1 + cosα

2(B.28)

sin³α2

´= ±

r1− cosα

2(B.29)

tan³α2

´=1− cosαsinα

=sinα

1 + cosα= ±

r1− cosα1 + cosα

(B.30)

sinα =2 tan α

2

1 + tan2 α2

(B.31)

cosα =1− tan2 α

2

1 + tan2 α2

(B.32)

Powers of Functions

sin2 α =1

2(1− cos(2α)) (B.33)

sinα cosα =1

2sin(2α) (B.34)

cos2 α =1

2(1 + cos(2α)) (B.35)

sin3 α =1

4(3 sin(α)− sin(3α)) (B.36)

Appendix B. Trigonometric Formulas 991

sin2 α cosα =1

4(cosα− 3 cos(3α)) (B.37)

sinα cos2 α =1

4(sinα+ sin(3α)) (B.38)

cos3 α =1

4(cos(3α) + 3 cosα)) (B.39)

sin4 α =1

8(3− 4 cos(2α) + cos(4α)) (B.40)

sin3 α cosα =1

8(2 sin(2α)− sin(4α)) (B.41)

sin2 α cos2 α =1

8(1− cos(4α)) (B.42)

sinα cos3 α =1

8(2 sin(2α) + sin(4α)) (B.43)

cos4 α =1

8(3 + 4 cos(2α) + cos(4α)) (B.44)

sin5 α =1

16(10 sinα− 5 sin(3α) + sin(5α)) (B.45)

sin4 α cosα =1

16(2 cosα− 3 cos(3α) + cos(5α)) (B.46)

sin3 α cos2 α =1

16(2 sinα+ sin(3α)− sin(5α)) (B.47)

sin2 α cos3 α =1

16(2 cosα− 3 cos(3α)− 5 cos(5α)) (B.48)

sinα cos4 α =1

16(2 sinα+ 3 sin(3α) + sin(5α)) (B.49)

cos5 α =1

16(10 cosα+ 5 cos(3α) + cos(5α)) (B.50)

tan2 α =1− cos(2α)1 + cos(2α)

(B.51)

Products of sin and cos

cosα cosβ =1

2cos(α− β) +

1

2cos(α+ β) (B.52)

sinα sinβ =1

2cos(α− β)− 1

2cos(α+ β) (B.53)

sinα cosβ =1

2sin(α− β) +

1

2sin(α+ β) (B.54)

cosα sinβ =1

2sin(α+ β)− 1

2sin(α− β) (B.55)

992 Appendix B. Trigonometric Formulas

sin(α+ β) sin(α− β) = cos2 β − cos2 α = sin2 α− sin2 β (B.56)

cos(α+ β) cos(α− β) = cos2 β + sin2 α (B.57)

Sum of Functions

sinα± sinβ = 2 sin α± β

2cos

α± β

2(B.58)

cosα+ cosβ = 2 cosα+ β

2cos

α− β

2(B.59)

cosα− cosβ = −2 sin α+ β

2sin

α− β

2(B.60)

tanα± tanβ = sin(α± β)

cosα cosβ(B.61)

cotα± cotβ = sin(β ± α)

sinα sinβ(B.62)

sinα+ sinβ

sinα− sinβ =tan α+β

2

tan α−+β2

(B.63)

sinα+ sinβ

cosα− cosβ = cot−α+ β

2(B.64)

sinα+ sinβ

cosα+ cosβ= tan

α+ β

2(B.65)

sinα− sinβcosα+ cosβ

= tanα− β

2(B.66)

Trigonometric Relations

sin2 α− sin2 β = sin(α+ β) sin(α− β) (B.67)

cos2 α− cos2 β = − sin(α+ β) sin(α− β) (B.68)

Appendix C

Unit ConversionsGeneral Conversion Formulas

Namb sc ≈ 4.448a × 0.3048b × lba ftb sc

≈ 4.448a × 0.0254b × lba inb sc

lba ftb sc ≈ 0.2248a × 3.2808b × Namb sc

lba inb sc ≈ 0.2248a × 39.37b × Namb sc

Conversion FactorsAcceleration

1 ft/ s2 ≈ 0.3048m/ s2 1m/ s2 ≈ 3.2808 ft/ s2

Angle

1 deg ≈ 0.01745 rad 1 rad ≈ 57.307 degArea

1 in2 ≈ 6.4516 cm2 1 cm2 ≈ 0.155 in21 ft2 ≈ 0.09290304m2 1m2 ≈ 10.764 ft21 acre ≈ 4046.86m2 1m2 ≈ 2.471× 10−4 acre1 acre ≈ 0.4047 hectare 1 hectare ≈ 2.471 acre

Damping

1N s/m ≈ 6.85218× 10−2 lb s/ ft 1 lb s/ ft ≈ 14.594N s/m1N s/m ≈ 5.71015× 10−3 lb s/ in 1 lb s/ in ≈ 175.13N s/m

Energy and Heat

1Btu ≈ 1055.056 J 1 J ≈ 9.4782× 10−4 Btu1 cal ≈ 4.1868 J 1 J ≈ 0.23885 cal1 kWh ≈ 3600 kJ 1MJ ≈ 0.27778 kWh

Force

1 lb ≈ 4.448222N 1N ≈ 0.22481 lb

994 Appendix C. Unit Conversions

Length

1 in ≈ 25.4mm 1 cm ≈ 0.3937 in1 ft ≈ 30.48 cm 1m ≈ 3.28084 ft1mi ≈ 1.609347 km 1km ≈ 0.62137mi

Mass.

1 lb ≈ 0.45359 kg 1 kg ≈ 2.204623 lb1 slug ≈ 14.5939 kg 1 kg ≈ 0.068522 slug1 slug ≈ 32.174 lb 1 lb ≈ 0.03.1081 slug

Moment and Torque

1 lb ft ≈ 1.35582Nm 1Nm ≈ 0.73746 lb ft1 lb in ≈ 8.85075Nm 1Nm ≈ 0.11298 lb in

Moment of Inertia

1 lb ft2 ≈ 0.04214 kgm2 1 kgm2 ≈ 23.73 lb ft2

Power

1Btu/h ≈ 0.2930711W 1W ≈ 3.4121Btu/h1 hp ≈ 745.6999W 1kW ≈ 1.341 hp1 hp ≈ 550 lb ft/ s 1 lb ft/ s ≈ 1.8182× 10−3 hp1 lb ft/h ≈ 3.76616× 10−4W 1W ≈ 2655.2 lb ft/h1 lb ft/min ≈ 2.2597× 10−2W 1W ≈ 44.254 lb ft/min

Pressure and Stress

1 lb/ in2 ≈ 6894.757Pa 1MPa ≈ 145.04 lb/ in21 lb/ ft2 ≈ 47.88Pa 1Pa ≈ 2.0886× 10−2 lb/ ft2

Stiffness

1N/m ≈ 6.85218× 10−2 lb/ ft 1 lb/ ft ≈ 14.594N/m1N/m ≈ 5.71015× 10−3 lb/ in 1 lb/ in ≈ 175.13N/m

Temperature

◦C = ( ◦F− 32)/1.8◦F = 1.8 ◦C+ 32

Velocity

1mi/h ≈ 1.60934 km/h 1 km/h ≈ 0.62137mi/h1mi/h ≈ 0.44704m/ s 1m/ s ≈ 2.2369mi/h1 ft/ s ≈ 0.3048m/ s 1m/ s ≈ 3.2808 ft/ s1 ft/min ≈ 5.08× 10−3m/ s 1m/ s ≈ 196.85 ft/min

Appendix C. Unit Conversions 995

Volume

1 in3 ≈ 16.39 cm3 1 cm3 ≈ 0.0061013 in31 ft3 ≈ 0.02831685m3 1m3 ≈ 35.315 ft31 gal ≈ 3.785 l 1 l ≈ 0.2642 gal1 gal ≈ 3785.41 cm3 1 l ≈ 1000 cm3

Index2R planar manipulator

dynamics, 561equations of motion, 564ideal, 561joint 2 acceleration, 280kinetic energy, 562Lagrangean, 563potential energy, 563

4-bar linkages, 309—311, 325, 326,330, 356

acceleration analysis, 317, 318concave, 315convex, 315coupler angle, 310coupler link, 310coupler point, 356—358coupler point curve, 356—358,

360—362crank-crank, 319crank-rocker, 319crossed, 315dead positions, 320designing, 321elbow-down, 315elbow-up, 315Grashoff criterion, 319input angle, 310input link, 310input variable, 310limit positions, 319non-crossed, 315output angle, 310output link, 310position analysis, 310possible configurations, 314rocker-rocker, 319spatial, 363sweep angles, 325

velocity analysis, 315, 316

Acceleration, 184angular, 272, 277, 278, 280,

281body point, 263, 280, 281, 523capacity, 183centripetal, 280Coriolis, 525matrix, 273tangential, 280

Accelerationpower-limited, 184traction-limited, 184

Acceleration capacity, 183Ackerman

condition, 377history, 392mechanism, 424

Ackermangeometry, 379mechanism, 379steering, 377, 379

Ackerman condition, 377Angle

attitude, 230bank, 230camber, 96heading, 230inclination, 46, 62pitch, 230roll, 230sideslip, 96spin, 230steering, 378tilting, 46tire contact, 111tireprint, 111

998

yaw, 230Angular acceleration, 272, 273, 279,

281combination, 277in terms of Euler parameters,

278matrix, 273relative, 278vector, 273

Angular momentum, 528, 530—532,537, 538

2 link manipulator, 535Angular velocity, 236, 238, 239,

248, 254alternative definition, 264, 265alternative proof, 265combination, 253, 254, 277coordinate transformation, 256decomposition, 253elements of matrix, 257Euler frequency, 236instantaneous, 250instantaneous axis, 251matrix, 249, 255principal matrix, 252transformation, 254vector, 236, 239, 248

Atan2 function, 64Attitude angle, 583, 586Axis-angle rotation, 282—287

B-derivative, 257Based excitation, 755

acceleration, 761, 764frequency response, 755transmitted force, 764velocity, 761, 764

Bicycle carmode shape, 854—856Natural frequency, 854—856vibration, 851—854

Bicycle model, 599, 607, 615, 618,629, 682

body force components, 599camber trust, 690

characteristic equation, 640coefficient matrix, 634, 683constant lateral force, 628control variables, 610, 614, 683,

685coordinate frame, 581, 582critical speed, 626curvature response, 619, 632,

686eigenvalue, 640equations of motion, 682, 684force system coefficients, 604,

620, 681free dynamics, 692free response, 636, 643, 692global sideslip angle, 602hatchback, notchback, station,

699input vector, 610, 614, 685kinematic steering, 605lateral acceleration response,

619, 632, 687linearized model, 629neutral distance, 628neutral steer, 625neutral steer point, 628Newton-Euler equations, 608oversteer, 625passing maneuver, 696, 699roll angle response, 687roll damping, 679roll steer, 690roll stiffness, 679rotation center, 649sideslip coefficient, 600, 677sideslip response, 619slip response, 686stability factor, 625steady state conditions, 632steady-state motion, 686steady-state response, 622, 628,

686step input, 635, 644, 647, 693time response, 633, 691time series, 643

Index

999

torque coefficient, 679transient response, 634understeer, 625vehicle velocity vector, 601yaw rate response, 619, 687zero steer angle, 636

Bump steering, 405

Camber, 481angle, 96, 145, 148line, 505moment, 148stiffness, 145theory, 505torque, 147trail, 147

Camber angle, 476Camber theory, 505Car

classifications, 25flying, 81

Cartesianangular velocity, 238

Caster, 480negative, 480positive, 480theory, 495

Caster theory, 495Catapults, 569Centrifugal moments, 540Characteristic equation, 786Chasles theorem, 288, 300Christoffel operator, 558Clutch, 182

dynamics, 178Foettinger, 182, 183hydrodynamic, 182

Coordinate framebody, 583global, 583rim, 491tire, 485vehicle, 485, 581, 583, 663wheel, 485wheel , 596

wheel-body, 485, 597Coriolis

acceleration, 277, 281effect, 525force, 524

Couple, 520, 521Critical speed, 626Critically-damped

vibration, 789, 790Crouse angle, 583, 586Curvature response, 619, 632, 686Cycloid, 490, 491

curtate, 491prolate, 491

Damper, 727linear, 728parallel, 730, 731serial, 729viscous, 728

Damping ratio, 745determination, 797

Deviation moments, 540Differentiating, 257

B-derivative, 257, 260G-derivative, 257, 263second, 266transformation formula, 262,

263Directions

cosine, 222principal, 544

Dissipation function, 825, 826Driveline, 165, 173, 175

clutch, 173differential, 173drive shafts, 173drive wheels, 174engine, 173gearbox, 173propeller shaft, 173

Dynamicsdirect, 525forward, 525

Index

1000

Eartheffect of rotation, 524kinetic energy, 557revolution, 557rotation, 557rotation effect, 277

Eccentric base excitation, 773, 830frequency response, 773, 778mass ratio, 776

Eccentric excitation, 767, 829acceleration, 772eccentric mass, 767eccentricity, 767frequency response, 767mass ratio, 768transmitted force, 773velocity, 772

Eccentricity, 768Efficiency, 173

convertor, 174differential, 179driveline, 175engine, 168mechanical, 177, 178overall, 174thermal, 177, 178transmission, 174volumetric, 177, 178

Eigenvalue, 786Eigenvalue problem, 845

characteristic equation, 845Eigenvector

first-unit, 846high-unit, 846last-unit, 846normal form, 846normalization, 846

Eigenvector problem, 845Ellipsoid

energy, 537momentum, 537

Energyconservation , 565, 567Earth kinetic, 557ellipsoid, 537

kinetic, 521, 522, 525, 529,533, 537, 554, 727, 826

mechanical, 564, 565potential, 559, 727, 826

Engine, 165Diesel, 166dynamics, 165efficiency, 168front, 176gasoline, 166ideal, 171injection Diesel, 166maximum speed, 184performance, 165rear, 176spark ignition, 166speed, 179torque, 178, 179working range, 187, 200

Envelope, 181Euler

-Lexell-Rodriguez formula, 285angles, 231, 233—240coordinate frame, 238equation of motion, 528, 532—

534, 538, 540frequencies, 236, 238, 254global rotation matrix, 233inverse matrix, 246local rotation matrix, 233rotation matrix, 231, 233, 234,

246Euler equation

body frame, 532, 533, 540Eulerian

viewpoint, 271Excitation

base, 742, 744, 755, 981eccentric, 742, 744, 981eccentric base, 742, 744, 981forced, 742, 744, 981harmonically, 742, 981

Force, 519, 520, 523body, 519

Index

1001

centrifugal, 524conservative, 559contact, 519Coriolis, 524, 525effective, 524external, 519generalized, 552, 555, 559, 826internal, 519moment of, 520potential, 559resultant, 520rotating, 533time varying, 525total, 520

Force system, 520, 523equivalent, 520, 523

Forced excitation, 744acceleration, 749fequency response, 744transmitted force, 751velocity, 749

FormulaEuler-Lexell-Rodriguez, 285Rodriguez, 285

Four wheel steering, 407Frame

central, 527principal, 529, 533, 541, 544

Free dynamics, 692Free response, 636, 643, 692Free system, 843Frequency

angular, 728cyclic, 728damped natural, 788natural , 787nodal, 807ratio, 745response, 742, 745

Frequency ratio, 745Frequency response, 742Freudenstein’s equation, 312, 321Friction ellipse, 155, 156Friction mechanisms, 132Front-engined, 176

Front-wheel-drive, 176Front-wheel-steering, 377Fuel

consumption, 170Full car

mode shape, 868natural frequency, 868vibration, 862—865, 868

Functiondissipation, 826Rayleigh, 826

G-derivative, 257Gear ratio, 179Gear reduction ratio, 174Gearbox, 178, 180, 184, 185, 187,

188, 190, 191, 193, 196,200, 202

design, 187, 188, 190, 191, 193,196, 200, 202

dynamics, 178geometric, 188, 191, 193, 196,

200, 202progressive, 190, 191stability condition, 184, 185step jump, 188

Gearbox ratio, 174Generalized

coordinate, 552, 555, 556, 559,560

force, 552, 554, 555, 557, 559,561, 564

Global sideslip angle, 598, 602Gough diagram, 141Grashoff criterion, 319

Half carantiroll bar, 858, 861mode shape, 859—861natural frequency, 859—861vibration, 857, 858

Heading angle, 583, 586Helix, 288Hermitian form, 837Homogeneous matrix, 289

Index

1002

Hook joint, 363Hydroplaning, 18

dynamic, 19rubber, 19speed, 19viscous, 19

Instant center, 346application, 350number of, 349of acceleration, 355

Inverted slider-crank mechanism,339

acceleration analysis, 345application, 346coupler point curve, 361input-output, 339possible configurations, 342velocity analysis, 343, 344

Jackknifing, 398Joint, 309

coordinate, 309prismatic, 309revolute, 309universal, 363

Kennedy theorem, 347Kinematics

acceleration, 272Kinetic energy, 521, 522, 537, 554

Earth, 557rigid body, 533rotational body, 529

Kronecker’s delta, 243, 257, 528,551

Lagrangeequation, 825, 827equation of motion, 552—557,

559mechanics, 559method, 825

Lagrange equationexplicit form, 558

Lagrangean, 559, 825, 827viewpoint, 271

Lateral acceleration response, 619,632, 687

Lawof motion, 521second of motion, 521, 526third of motion, 521

Linearized model, 629oversteer, 633understeer, 633

Link, 309ground, 310

Linkage, 3094-bar, 309coupler link, 310dyad, 322, 329four-bar, 310ground link, 310input angle, 310output link, 310two-link, 322, 329

Location vector, 290, 292, 496

Manipulator2R planar, 561one-link, 560

Manjaniq, 569Mass center, 521, 522, 526, 527Matrix

angular velocity, 249Euler rotation, 233global rotation, 220local rotation, 226skew symmetric, 245, 246, 249,

283McPherson suspension

equivalent vibrating model, 886kinematic model, 463

Mechanism, 310closed loop, 310instant center, 346inversion, 339inverted slider-crank, 339open loop, 310

Index

1003

parallel, 310pole, 346serial, 310slider-crank, 332steering, 383, 401suspension, 346trapezoidal steering, 383

Mode shape, 843Moment, 519, 520, 523

external, 532resultant, 520, 532total, 520

Moment of inertia, 540about a line, 551about a plane, 551about a point, 551about the origin, 552characteristic equation, 549diagonal elements, 540, 548eigenvalues, 543, 548eigenvectors, 548elements, 540frame-dependent, 541Huygens-Steiner theorem, 543matrix, 540off-diagonal elements, 540parallel-axes theorem, 541—543polar, 540principal, 541, 542, 544, 550principal axes, 529principal invariants, 549product, 540rigid body, 528, 531, 532rotated-axes theorem, 541—543

Moment of momentum, 520Moments of inertia

determination, 799Momentum, 520

angular, 520, 521, 528, 530—532, 537

angular , 538ellipsoid, 537linear, 520translational, 520

Natural frequency, 745, 787, 843determination, 799

Neutral distance, 628Neutral steer, 625, 626Neutral steer point, 628Newton

equation in body frame, 527equation of motion, 521, 526,

528, 534, 552equations of motion, 554Lagrange form, 554rotating frame, 524

Onager, 569One-eighth car model, 881, 886

absolute acceleration, 888absolute displacement, 888, 890,

891damping ratio, 882design curve, 919equation of motion, 882excitation frequency, 887frequency response, 888, 892hard suspension, 898, 901model, 737natural frequency, 882optimal characteristics, 902optimal damping, 902optimal design chart, 904optimal design curve, 892, 904,

906optimal stiffness, 902optimal suspension, 901optimization, 892optimization strategy, 894relative displacement, 888, 890,

891soft suspensions, 898, 901step input, 916suspension clearance, 898suspension room, 898suspension travel, 898time response, 916, 919trade-off, 909wheel travel , 898

Index

1004

working frequency range, 894Optimization

alternative method, 912cost function, 915design curve, 951one-eighth car, 881, 892quarter car, 951RMS, 892, 951time response, 916, 919transient response, 916, 919trivial, 909vehicle suspension, 902vibration, 802—810wheel travel, 962

Orthogonality condition, 242Over-damped

vibration, 789, 790Oversteer, 625, 626, 647

Passing maneuver, 696, 699Pendulum

chain, 833double, 832inverted, 740oscillating, 556simple, 274, 555spherical, 560

Permutation symbol, 257Pitch moment, 582Planar dynamics, 607, 615

attitude angle, 586body force components, 599characteristic equation, 640coefficient matrix, 634constant lateral force, 628control variables, 610, 614coordinate frame, 581, 582critical speed, 626crouse angle, 586curvature response, 619, 632eigenvalue, 640force system coefficients, 604,

620free response, 636, 643global sideslip angle, 602

heading angle, 586input vector, 610, 614kinematic steering, 605lateral acceleration response,

619, 632linearized model, 629neutral distance, 628neutral steer, 625neutral steer point, 628Newton-Euler, 587Newton-Euler equations, 608oversteer, 625rotation center, 649sideslip coefficient, 600sideslip response, 619stability factor, 625steady state conditions, 632steady-state response, 622, 628steady-state turning, 618step input, 635, 644, 647time response, 633time series, 643transient response, 634understeer, 625vehicle velocity vector, 601wheel number, 584yaw rate response, 619zero steer angle, 636

Plotgear-speed, 194, 196, 202power, 191, 202progressive, 190working range, 191

Poinsot’s construction, 537Pole, 297Potential

energy, 559force, 559kinetic, 559

Powerat wheel, 175constant, 171driveline, 175engine, 175equation, 166

Index

1005

friction, 178ideal, 171law, 176maximum, 172peak, 171performance, 165, 166, 168,

170, 171units, 169

Power steering, 405

Quadrature, 836, 837asymmetric, 837

Quarter car, 840model, 737natural frequency, 849sprung mass, 849unsprung mass, 849

Quarter car model, 9293-D frequency response, 936body bounce frequency, 944coefficient matrix, 933dimensionless characteristics,

931equations of motion, 930frequency response, 931—934,

942, 944history, 931invariant amplitude, 939invariant frequency, 936, 939,

944main suspension, 929mathematical model, 929natural frequency, 936, 939,

943nodal amplitude, 941nodal frequency, 939—941optimal characteristics, 962optimal design curve, 951, 956optimization, 951optimization strategy, 952principal natural frequency,

944resonant frequency, 939sprung mass, 929street cars, 934

tire damping, 930unsprung mass, 929wheel hop frequency, 944wheel travel, 962working frequency range, 953

Rear wheel steering, 387Rear-engined, 176Rear-wheel drive, 176Resonance, 848Resonance zone, 748Ride, 825Ride comfort, 825Rigid body

acceleration, 279angular momentum, 530—532centroid, 271Euler equation, 532, 533Euler equation of motion, 538kinetic energy, 533moment of inertia, 528, 531,

532moment-free motion, 537principal rotation matrix, 548rotational kinetics, 528steady rotation, 534translational, 526velocity, 267, 269

Rim, 1, 3, 21—23alloy, 23diameter, 3flange, 21hub, 21spider, 21width, 5

Road pavement, 121Rodriguez

rotation formula, 285, 286, 291,295

Roll angle, 582, 664Roll angle response, 687Roll axis, 468Roll center, 350, 468, 470Roll dynamics, 663

bicycle model, 675

Index

1006

camber trust, 690coefficient matrix, 683control variables, 683, 685curvature response, 686equations of motion, 682, 684force system, 669force system coefficients, 681free dynamics, 692free response, 692hatchback, notchback, station,

699input vector, 685lateral acceleration response,

687lateral force, 672Newton-Euler equations, 664,

667, 668passing maneuver, 696, 699roll angle response, 687roll damping, 679roll steer, 690roll stiffness, 679roll-steering angle, 672sideslip angle, 672sideslip coefficient, 677slip response, 686steady-state motion, 686steady-state response, 686step input, 693time response, 691tire slip coefficient, 673torque coefficient, 679two-wheel model, 675vehicle slip coefficient, 674wheel force system, 669yaw rate response, 687

Roll moment, 582Roll-pitch-yaw

frequency, 239global angles, 225, 230global rotation matrix, 225,

230Rolling disc, 831Rolling friction, 115, 117, 119, 122

Rolling resistance, 114, 117, 119,121, 122, 124, 126, 127

Rotation, 285about global axis, 219, 223about local axis, 226, 229axis-angle, 282, 285—287direction cosines, 222, 227general matrix, 241global Euler matrix, 247global matrices, 222instantaneous axis, 251instantaneous center, 271local Euler matrix, 247local matrix, 230matrix, 224nutation, 231off-center axis, 299order of, 224orthogonal, 224orthogonality condition, 242pitch, 225pole, 271precession, 231radius of, 378, 381roll, 225roll-pitch-yaw matrix, 230spin, 231successive, 223, 229X-matrix, 220x-matrix, 226Y-matrix, 220y-matrix, 226yaw, 225Z-matrix, 220z-matrix, 226

Rotation matrixelement of, 242

SAE steering definition, 629Screw, 290, 300

axis, 288central, 289, 290, 292, 294coordinate, 288general, 290left-handed, 288

Index

1007

location vector, 288, 290motion, 288parameters, 288, 297pitch, 288principal, 299right-handed, 288rotation, 288special case, 296transformation, 292, 294, 296,

299translation, 288twist, 288

Second derivative, 266Sideslip angle, 96, 583, 598Sideslip coefficient, 599, 600Sideslip response, 619Slider-crank mechanism, 332

acceleration analysis, 337, 338coupler point curve, 360input angle, 332input-output, 332limit positions, 338possible configurations, 334quick return, 339slider position, 332velocity analysis, 335, 336

Slip response, 686Speed equation, 178, 180, 181Speed ratio, 174Speed span, 189Spring, 727

linear, 728massive, 734parallel, 730, 731serial, 729stiffness, 728

Stability factor, 622, 625Steering, 377, 378, 408

4WS factor, 417Ackerman, 423Ackerman condition, 377Ackerman mechanism, 424active steer, 419autodriver, 420bicycle model, 378, 379, 418

command, 402comparison, 418counter steer, 413error, 385, 423, 430, 432four wheel, 407—417, 419, 420front wheel, 377independent rear wheel drive,

390inner steer angle, 377, 378,

408inner wheel, 377, 378, 387,

389, 408inner-outer relationship, 378,

383jackknifing, 398, 433kinematic, 377, 381, 387kinematic condition, 377, 379,

418locked rear axle, 385—387maximum radius, 381mechanism, 383, 401—403midline, 394more than two axles, 393, 394multi-link, 425offset, 405optimization, 423, 425, 427,

429, 430, 432outer steer angle, 377, 378,

408outer wheel, 377, 378, 387,

389, 408passive steer, 419Pitman arm, 401racecars, 390radius of curvature, 416rear wheel, 387reverse efficiency, 403same steer, 413self-steering wheels, 396sign convection, 413, 417sign convention, 408six-wheel vehicle, 394smart steer, 419space requirement, 381, 399speed dependent, 392

Index

1008

steer angle, 378steering length, 417trapezoidal, 407, 423, 424trapezoidal mechanism, 383,

385, 423turning center, 407, 413—415turning radius, 378, 379, 381,

412, 413, 417unequal tracks, 389with trailer, 396, 398, 433—

440, 442—445Steering axis

caster angle, 496caster plane, 497forward location, 497lateral location, 497lean angle, 496lean plane, 497

Steering mechanismsdrag link, 402lever arm, 402multi-link, 403optimization, 423, 425, 427,

429, 430, 432parallelogram, 401Pitman arm, 401rack-and-pinion, 401steering wheel, 401tie rod, 402trapezoidal, 423

Steering ratio, 401Step input, 635, 647, 794Step jump, 188Step response, 794

overshoot, 796peak time, 796peak value, 796rise time, 796settling time, 796steady-state, 796

Step steer input, 644, 649Suspension

anti-tramp bar, 455antiroll bar, 467camber, 481

camber angle, 476caster, 480caster angle, 496caster plane, 497Chebyshev linkage, 457De Dion, 462dead axle, 462dependent, 453double A-arm, 463double triangle, 457double wishbone, 463equilibrium position, 473Evance linkage, 457forward location, 497four-bar linkage, 473Hotchkiss, 454independent, 463, 466, 467lateral location, 497lean angle, 496lean plane, 497live axle, 462location vector, 497McPherson, 463, 886multi-link, 463optimization, 881Panhard arm, 457rest position, 473Robert linkage, 457roll axis, 468roll center, 350, 468, 470S shape problem, 454semi-trailing arm, 467short/long arm, 463solid axle, 453—455, 457, 460,

462spung mass, 454stabilizer, 468steering axis, 496, 497straight line linkages, 457swing arm, 466swing axle, 466toe, 477trailing arm, 466triangulated linkage, 457trust angle, 481

Index

1009

twisting problem, 455unsprung mass, 454unsprung mass problem, 460vibration, 881Watt, 457with coil spring, 462

Suspension mechanism, 330, 346,453

Chapman, 346double A arm, 330double wishbone, 330dynamic requirement, 484kinematic requirement, 483,

484McPherson, 346

Symbols, xv

TheoremChasles, 300, 523Chasles , 288Huygens-Steiner, 543Kennedy, 347, 470parallel-axes, 541, 543Poinsot, 523rotated-axes, 541

Time derivative, 257Time response, 785

free dynamics, 692free response, 692hatchback, notchback, station,

699homogeneous, 785homogeneous solution, 785initial condition, 791—793initial-value problem, 785non-homogeneous, 785particular solution, 785passing maneuver, 696, 699step input, 693vehicle dynamics, 633, 634,

691Time series, 636, 643Tire, 1, 95

adhesion friction, 132

aligning moment, 98, 136, 138,139, 150

American, 6aspect ratio, 3, 6bank moment, 96bead, 11, 13belt, 12bias ply, 3bias-ply, 15blocks, 17bore torque, 98camber angle, 127, 148, 150camber arm, 148camber force, 145, 148camber moment, 148camber stiffness, 145, 152camber torque, 147camber trail, 147camber trust, 145Canadian, 7carcass, 12circumferential slip, 129cold welding friction, 132combined force, 152combined slip, 155, 156components, 11contact angle, 111coordinate frame, 95, 98, 485cords, 13cornering force, 139cornering stiffness, 136, 139critical speed, 119damping structure, 117deflection, 101deformation friction, 133diameter, 5dissipated power, 123DOT index, 6drag force, 139E-Mark, 7effective radius, 109, 111, 112equivalent radius, 130equivalent speed, 128European, 7, 8force system, 96, 151

Index

1010

forces model, 157forward force, 96forward velocity, 110friction, 131, 132friction coefficient, 127friction ellipse, 155friction stress, 108function, 17geometric radius, 109, 112grip, 139groove, 12, 17, 19height, 1, 4hydroplaning, 18hysteresis, 103inflation, 10inflation pressure, 112, 124,

125inner liner, 11lateral force, 96, 136, 138, 141,

143—146, 148lateral load, 108lateral ratio, 135lateral stiffness, 136lateral stress, 144light truck, 8load, 111load index, 3, 4loaded height, 109longitudinal force, 96, 127longitudinal friction, 131longitudinal ratio, 135longitudinal slip, 127, 128, 152lugs, 17M&S, 6motorcycles, 123non-radial, 15, 16, 117non-radiale, 150normal force, 96normal load, 104, 106, 107normal stress, 104, 106, 107,

115, 117overturning moment, 96pitch moment, 98plane, 95plus one, 10

pneumatic trail, 138racecar, 122radial, 3, 15, 16, 117radial displacement, 113radiale, 150radius, 5roll moment, 96rolling friction, 115, 117, 119,

122rolling radius, 109rolling resistance, 114, 117,

119, 121, 122, 124, 126,127

rolling resistance torque, 98rubber, 12—14SAE coordinate frame, 98section height, 1section width, 1self aligning moment, 98shallow, 16shear stress, 108side force, 139sideslip angle, 126, 136, 148,

152sidewall, 1, 9, 10, 12size, 1, 2, 5slick, 122sliding line, 137slip coefficient, 128slip models, 133, 134slip moment, 138slip ratio, 127—131, 133, 134,

152slots, 17spare, 24speed index, 3, 5, 6spring structure, 117stiffness, 98, 101—103, 136stress, 104, 106—108tangential slip, 129tangential stress, 108, 109tilting torque, 96tireprint, 20tireprint angle, 111tireprint model, 151

Index

1011

tread, 12, 13, 17, 18, 114tread travel, 114tread wear index, 9tube-type, 16tubeless, 16type index, 2UTQG index, 9vertical force, 96voids, 17wear, 20wear friction, 133weight, 6wheel load, 96width, 1, 2, 5yaw moment, 98

Tireprint, 20, 96, 104, 106, 151angle, 111

Toe, 477Toe-in, 477Toe-out, 477Torque, 520

at wheel, 176, 179equation, 166maximum, 172peak, 171performance, 166, 168, 179

Track, 378Traction

force, 178Traction equation, 178, 180, 181Trailer, 59, 65Transformation

general, 241tire to vehicle frame, 493tire to wheel frame, 488tire to wheel-body frame, 489,

490wheel to tire frame, 486, 488wheel to wheel-body frame,

491wheel-body to vehicle frame,

495Transformation matrix

elements, 243Transient response

free dynamics, 692free response, 692hatchback, notchback, station,

699passing maneuver, 696, 699step input, 693vehicle dynamics, 634, 691

Transmission ratio, 174, 175, 179Transmission ratios, 185Trapezoidal steering, 383, 385Tread, 17, 18

grooves, 17lugs, 17slots, 17voids, 17

Trebuchet, 567Trigonometric equation, 64Trochoid, 491Trust angle, 481Turning center, 407, 413—415Two-wheel vehicle, 599, 605, 607,

615, 618, 629, 682body force components, 599camber trust, 690characteristic equation, 640coefficient matrix, 634, 683constant lateral force, 628control variables, 610, 614, 683,

685coordinate frame, 581, 582critical speed, 626curvature response, 619, 632,

686eigenvalue, 640equations of motion, 682, 684force system coefficients, 604,

620, 681free dynamics, 692free response, 636, 643, 692global sideslip angle, 602hatchback, notchback, station,

699input vector, 610, 614, 685kinematic steering, 605

Index

1012

lateral acceleration response,619, 632, 687

linearized model, 629neutral distance, 628neutral steer, 625neutral steer point, 628Newton-Euler equations, 608oversteer, 625passing maneuver, 696, 699roll angle response, 687roll damping, 679roll steer, 690roll stiffness, 679rotation center, 649sideslip coefficient, 600, 677sideslip response, 619slip response, 686stability factor, 625steady state conditions, 632steady-state motion, 686steady-state response, 622, 628,

686step input, 635, 644, 647, 693time response, 633, 691time series, 643torque coefficient, 679transient response, 634understeer, 625vehicle velocity vector, 601yaw rate response, 619, 687zero steer angle, 636

Under-dampedvibration, 789, 790

Understeer, 625, 626, 644Unit system, xvUniversal joint, 363, 365—367, 369—

371history, 369, 371speed ratio, 366, 367

Vectorbounded, 521line, 521line of action, 521

sliding, 521Vehicle, 25

accelerating, 50, 52, 54, 55,57, 58

classifications, 25FHWA classifications, 25ISO classifications, 25longitudinal dynamics, 39, 41,

42, 44, 46—48, 50, 52, 54,55, 57, 58, 65, 67, 68, 71—74, 76, 78, 80—82, 86

mass center, 72mass center position, 41, 42,

44maximum acceleration, 52, 54,

57, 58more than two axles, 74, 76on a banked road, 65, 67on a crest, 78, 80—82on a dip, 82, 86on a level pavement, 39on an inclined pavement, 44,

48optimal brake force, 68, 71optimal drive force, 68, 71,

72passenger car classifications,

28, 30wheel loads, 40wheel locking, 73with a trailer, 59, 65

Vehicle dynamics180 deg quick turn, 616aligning moment, 582attitude angle, 583, 586bank moment, 582bicycle model, 599, 601, 607,

615, 618, 629, 675body force components, 599body force system, 595camber trust, 690characteristic equation, 640coefficient matrix, 634, 683coefficients matrix, 610, 615constant lateral force, 628

Index

1013

control variables, 610, 614, 615,683, 685

critical speed, 626crouse angle, 583, 586curvature response, 619, 632,

686direct, 635eigenvalue, 640equations of motion, 601, 682,

684force system, 582, 669force system coefficients, 604,

620, 681forward, 635forward force, 582four-wheel-steering, 611free dynamics, 692free response, 636, 643, 692front-wheel-steering, 631general motion, 668hatchback, notchback, station,

699heading angle, 583, 586indirect, 635input vector, 610, 614, 685inputs vector, 615inverse, 635Lagrange method, 590lateral acceleration response,

619, 632, 687lateral force, 582, 598, 603,

672lateral moment, 582linearized model, 629, 632longitudinal force, 582neutral, 625, 626neutral distance, 628neutral steer, 625neutral steer point, 628Newton-Euler, 587Newton-Euler equations, 608,

664normal force, 582oversteer, 625, 626overturning moment, 582

passing maneuver, 696, 699path of motion, 592pitch angle, 582, 664pitch moment, 582pitch rate, 582, 664planar, 581principal method, 592rear-wheel-steering, 615rigid vehicle, 581, 663roll angle, 582, 664roll angle response, 687roll damping, 679roll dynamics, 663, 664, 668roll moment, 582roll rate, 582, 664roll rigid vehicle, 668roll steer, 690roll stiffness, 679roll-steering angle, 672rotation center, 649SAE steering definition, 629second-order equations, 652sideslip angle, 583, 672sideslip coefficient, 600, 677sideslip coefficients , 599sideslip response, 619six DOF, 667slip response, 686stability factor, 622, 625steady state conditions, 632steady-state motion, 686steady-state response, 622, 628,

686steady-state turning, 618steer angle, 600step input, 635, 644, 647, 693step steer input, 649tilting torque, 582time response, 633, 644, 647,

691time series, 636, 643tire force system, 595tire lateral force, 597tire slip coefficient, 673torque coefficient, 679

Index

1014

traction force, 582transient response, 634, 691two-wheel model, 599, 601, 607,

615, 618, 629, 675understeer, 625, 626vehicle load, 582vehicle slip coefficient, 674vehicle velocity vector, 601vertical force, 582wheel force system, 669wheel frame, 596wheel number, 584yaw angle, 582, 664yaw moment, 582yaw rate, 582, 664yaw rate response, 619, 687zero steer angle, 636

Vehicle vibration, 825alternative optimization, 912antiroll bar, 858, 861base excited model, 881bicycle car, 851, 854—856body pitch, 851body roll, 857, 858bounce, roll, and pitch, 862dissipation function, 826driver, 840excitation frequency, 887frequency response, 888full car, 862—865half car, 857, 858Lagrange equation, 826Lagrange method, 826McPherson suspension, 886mode shape, 843, 859—861, 868natural frequenc, 868natural frequency, 843, 859—

861one-eighth model, 881optimal design curve, 892optimization, 881optimization strategy, 894quadrature, 836quarter car, 840, 929sprung mass, 881

time response, 916, 919wheel travel , 898working frequency range, 894

Velocitybody point, 523

Vibration1/8 car model, 737absorber, 802amplitude, 744angular frequency, 728angular lag, 745application, 797base excitation, 742, 755, 981beating, 753characteristic equation, 845cyclic frequency, 728damping ratio, 745discrete model, 736displacedspring, 885, 886dynamic amplitude, 748eccentric base excitation, 742,

981eccentric excitation, 742, 981eigenvalue problem, 845eigenvector problem, 845equilibrium position, 736Equivalent system, 738excitation, 729forced, 729, 748forced excitation, 742, 981Frahm absorber, 803—810Frahm damper, 803—810free, 791—793free system, 843frequency ratio, 745frequency response, 742, 745,

749harmonic, 729initial condition, 791—793isolator, 802lumped model, 736measurement, 797mechanical, 727natural frequency, 745Newton’s method, 736

Index

1015

nontrivial solution, 845optimization theory, 802—810orthogonality functions, 752periodic, 729phase, 745quarter car model, 737random, 729resonance zone, 748rest position, 845ride comfort, 825stable, 736static amplitude, 748steady-state solution, 742step input, 794tilted spring, 883, 885, 886transient, 729transmitted force, 751, 764trivial solution, 845two-DOF base excited, 739unstable, 737vehicle, 825work of a harmonic force, 793

Virationcharacteristic equation, 786characteristic parameters, 786critically-damped, 789damped natural frequency, 788eigenvalues, 786forced, 785forced classification, 780free, 785initial-value problem, 785natural frequency, 787, 788over-damped, 789time response, 785, 786transient response, 786under-damped, 789

Virtualdisplacement, 555work, 555

Wheel, 21, 22angular velocity, 109camber angle, 483coordinate frame, 483, 485

degrees-of-freedom, 483forward velocity, 110history, 25non-steerable, 484spin, 483steer angle, 483steerable, 484wire spoke, 23

Wheel number, 584Wheel travel, 898

lower, 898upper, 898

Wheel-bodycoordinate frame, 485

Wheelbase, 378Windshield wiper, 322

double-arm opposing, 322double-arm parallel , 322sweep angles, 325

Work, 522, 525virtual, 555

Work-energy principle, 522Wrench, 523

Yaw moment, 582Yaw rate response, 619, 687Yaw velocity, 386Yoke joint, 363

Zero steer input, 636Zero velocity point, 271

Index

references - springer978-0-387-74244-1/1.pdf · 978 references chapter 4 cossalter, v., 2002,...

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