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ME 562 Simulation of Mechanical SystemsH.J. Sommer III

Professor of Mechanical EngineeringThe Pennsylvania State University

337 Leonhard Building, University Park, PA 16802(814)863-8997 ... FAX (814)865-9693

hjs1@psu.edu ... http://www.mne.psu.edu/sommer/

Student Biographies of Famous Kinematicians andDynamicists

Spring 2006

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Sir Robert Ball(1840-1913)

Biography by: Dustin Dienno

Robert Ball was born in Dublin in 1840. He also had the good fortune of having parents thatwere wealthy enough to send him to boarding school in Turvin England. At boarding schoolRobert received excellent grades, but most importantly he excelled mathematics which wouldlater help him in his studies of astronomy and kinematics.

His thirst for knowledge at a young age was insatiable, and it often landed him in trouble. Whileattending school in Turvin, he almost had to have his hand amputated after a homemadefireworks experiment went horribly wrong. The scars that remained on his hand for the rest ofhis life reminded him every day how dangerous knowledge could be if it was not properlyrespected.

Soon after his father died, Robert went to the prestigious Trinity College in Dublin where hecontinued his academic excellence. He was awarded with three Fellowshipman prize honorsalong with numerous scholarships. Robert became interested in astronomy while attendingCollege and put these skills to use teaching astronomy to three young boys at the Birr household.

Teaching astronomy was not his main motivation for accepting the position. Robert secretly justwanted to gain access to the most massive reflective telescope know to man at the time called theLeviathan, which just happened to reside at the Birr Estate. Using this telescope he catalogedmassive quantities of astronomical data and made many observations which helped him to beelected Fellow of Royal Society in 1873. Even though he was extremely unsuccessful atproviding hard evidence of the stellar parallax which he studied for over 15 years, he gained the

title Astronomer Royal.

Robert then decided that lecturing to the general public about astrology and mathematics wouldbe the best way to utilize his knowledge, so he set out on a lecturing rampage. He gave over 700lectures in from 1874 to 1884, and for his valiant effort he was knighted in 1886.

Despite losing his site in his right eye, Robert was appointed as the Scientific Advisor to Irishlights where he enjoyed the pursuit of improving lighthouses.

Unfortunately, the lighthouses could not hold his attention for long. Robert returned to the onesubject that was continuously haunting his every thought, the infamous screw theory.

Cambridge University Press published Robert Steward Balls Treatise on Theory of Screws in1900. This remains on of the most influential pieces of literature on screw theory to this day.

In 1892 he accepted the Lowndean Chair of Astronomy and Geometry at Cambridge University,where he remained until his death in 1913.

References:

http://www.geocities.com/ziksby2/Sir_Robert_Ball.html

http://www.freewebs.com/ziksby/index.htm http://www.geocities.com/ziksby/SRB05.html

http://www.geocities.com/ziksby2/Sir_Robert_Ball.htmlhttp://www.freewebs.com/ziksby/index.htmhttp://www.geocities.com/ziksby/SRB05.htmlhttp://www.geocities.com/ziksby/SRB05.htmlhttp://www.freewebs.com/ziksby/index.htmhttp://www.geocities.com/ziksby2/Sir_Robert_Ball.htmlhttp://www.freewebs.com/ziksby/index.htm

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Joseph Stiles Beggs (10.23.1905 9.6.1991)

by James Allen II

In his early twenties, Joseph Stiles Beggs was anapprentice Western Electric where he studied machinedesign. Also in his early twenties, he worked for Goodyearmanufacturing tire tread molds. Joseph Beggs earned hisB.A. in Physics in 1931 and his M.S. in Spectroscopy in1934 at the University of Alberta at Edmonton, Canada. In1934 he worked for Eastman Kodak where he was a cameradesigner. He designed a photo finish system that wasinstalled at Santa Anita racetrack.

During World War II, Joseph Beggs designed remote control gun turret system on the Boeing B-29 Super Fortress. Furthermore, he designed the periscope gun aiming system for the Douglas A-26 andB-26 bombers. After WWII, Joseph Beggs moved to Pasadena, California with his wife and kids, andworked on developing cameras for Hollywood movie production.

In 1947 Joseph Beggs began his teaching career at University of California at Los Angeles (UCLA) at therequest of the late Dean of Engineering, L.M.K. Boelter. He would remain a professor at UCLA for over 25 years.

He would eventually earn the prestigious title of Professor Emeritus of the School of Engineering and AppliedScience at UCLA. His teachings were in the areas of machine design, kinematics and mechanisms. In 1959, Beggsearned his Doctor Ingenieur in Kinamatics at the Technical University of Hanover, Germany.

His book entitled Kinematics, written in 1983, covers the following topics: coordinatetransformations, attitude (direction cosine matrix), displacement, motion, quaternions in kinematics, non-Cartesian coordinate systems, and applications of previous topics. It was intended to be a reference bookfor everyone who had a need for kinematics. Beggs emphasized the importance of the use of matrices intheir application to moving mirrors and space mechanisms. He also encouraged students to write theirown computer code to manipulate matrices and display the results on a screen or plotter. At a timebefore MATLAB was the common everyday matrix manipulator, Beggs saw the importance of suchsoftware development for the study of kinematics. One mechanism that fascinated Beggs was the BennettMechanism, which he had analyzed in Kinematics.

The Joseph Beggs Foundation for Kinematics provides scholarships for students studyingengineering at the following universities: UCLA, UC-Davis, and University of Alberta, Canada. Thefoundation also donates funds to UC-Davis Mechanical Engineering Department for the development ofan inertia measurement device for medium to heavy-duty vehicles.

Books:Beggs, J.S. Mechanisms. New York: McGraw-Hill. 1955Beggs, J.S. Advanced Mechanisms: Consultant: Douglas Aircraft Co New York: Mcmillan. 1966Beggs, J.S. Kinematics. Washington: Hemisphere Publishing Co. 1983

Selected Papers:Beggs, J.S. Torque transmission through Bennett mechanism.American Society of Mechanical Engineers

Papers, 1968,8pBeggs, J.S. Gimbals, mirrors and matrices. American Society of Mechanical Engineers - Papers, 1964, 5pBeggs, J.S. Mirror-image kinematics. Optical Society of America Journal, v 50, n 4, Apr, 1960, p 388-93

Beggs, J.S. Planeten-Jurven-Getriebe (Planetary cam gears). Verein Deutscher Ingenieure VDIZeitschrift, v 99, n 19, July 1, 1957, p 839-840Beggs, J.S. Cams and gears Join to stop shock loads. Product Engineering, v 28, n10, Sept 16, 1957, p84-

5Beggs, J.S. Synthesis of surface of friction skew gears.American Society of Mechanical Engineers

Papers, 1954, 2pBeggs, J.S. Time required for the action of a spring.Machinery, v 36, n 5, Jan, 1930, p 781Beggs, J.S. Variable rotary motion.Machinery, v 36, n 10, June, 1930, p760-1

Additional sources:http://anmarti.bol.ucla.edu/L2aboutUsL1.htm

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Michel Chasles

Born: November 15, 1793Died: December 18, 1880

Report by: Steve Meyers

Michel Chasles started out his career in education at the Lycee Imperial, and then movedon the Ecole Polytechnique in 1812. This education was quickly halted by his involvement inthe War of the Sixth Coalition. He was drafted by Napoleon to defend Paris in 1814. Soon afterthis war was over, he was offered a job in the engineering corps, but later refused and returnedback to school.

The next step in Chasles life was becoming a stockbroker in Paris. While this pleased hisfather very much, his true interests, history and mathematics, were not being fully developed, atleast not until 1837. In this year, he published his famous workHistorical view of the origin anddevelopment of methods in geometry. This paper, which was written in response to an 1829

question noted by the Royal Academy in Brussels, explores the method of reciprocal polars as anapplication of the principle of duality in projective geometry. This basically shows geometers toproduce new figures from old ones.

From his fame, he was offered a position at the Ecole Polytechnique in 1841. He taughtideas in geodesy, mechanics, and astronomy. Five year later, in 1846, he moved on to Sorbonne,heading the department for higher geometry. This position was specially created for him. Laterthat year, he solved a problem determining the gravitational attraction of an ellipsoidal mass toan external point.

Chasles was also quite famous for his enumeration of conics. Steiner posted a problemcalled Problem of Five Conics, in 1848. The goal was to determine the number of conicstangent to five given conics. Steiner erroneously predicted there would be 7776 different

possible solutions. Chasles later solved this problem correctly with an answer of 3264.From these advances in mathematics, he earned many honors which were certainly welldeserved. He was elected a member of the Academy of Science in 1839. Chasles also was aFellow of the Royal Society of London, and won its Copley Medal in 1865. Chasles also brokeinternational boundaries, becoming the first foreigner to gain acceptance into the LondonMathematical Society.

Sadly, the final years of Michel Chasles ended in great distress and embarrassment.Chasles was a great fan of autographs and manuscripts from famous historical figures, such asJulius Caesar, Newton, and Cleopatra. He spent nearly 200,000 francs for his collection.Unfortunately, these documents turned out to be forgeries, done by a man named Denis Vrain-Lucas. This man was put on trial to stand for his crimes, and Chasles had to appear as a witness.

To his dismay, he had to admit that he bought all these forged manuscripts. The embarrassingpart was for him was that most of the documents were written in French, not an appropriatelanguage for Newton, Caesar, and others.

Sources:www.en.wikipedia.org/Michel_Chasleswww.britannica.com/eb/article-9022666www.groups.dcs.st-and.ac.uk/~history/mathematicians/Chasles.html

http://www.en.wikipedia.org/Michel_Chasleshttp://www.britannica.com/eb/article-9022666http://www.groups.dcs.st-and.ac.uk/~history/mathematicians/Chasles.htmlhttp://www.groups.dcs.st-and.ac.uk/~history/mathematicians/Chasles.htmlhttp://www.britannica.com/eb/article-9022666http://www.en.wikipedia.org/Michel_Chasles

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ME 562 - Spring 2006 H3 Name : Zihni B. Saribay

Gaspard-Gustave de CoriolisMathematician, mechanical engineer and scientist

May 21, 1792 September 19, 1843

Gaspard-Gustave de Coriolis's father was Jean-Baptiste-Elzar Coriolis became an officer withLouis XVI in 1790 but this put him in difficulties when the monarchy was in trouble. Gaspard-Gustave Coriolis was born in June 1792 and on 21 September of that year the monarchy wasabolished. Coriolis's father fled to Nancy where he became an industrialist. Coriolis was broughtup in Nancy and attended school there. He sat the entrance examination for the colePolytechnique in 1808 and he was placed second of all the students entering that year. Aftergraduation he served for several years in the corps of engineers (of the Ponts et Chausees). In1816 he started his teaching career. He was recommended for this position by Cauchy.

Coriolis became professor of mechanics at the cole Centrale des Artes et Manufactures in 1829.

In July 1830 there was a revolution and, following this Cauchy left Paris in September 1830.Coriolis was offered Cauchy's position at the cole Polytechnique but by this time he was highlyinvolved in his research and decided not to take on any further teaching duties. Despite notaccepting further duties at the cole Polytechnique, Coriolis did take on a position at the coledes Ponts and Chausses in 1832. There he teamed up with Navier teaching applied mechanics.Navier died in 1836 and Coriolis was appointed to his chair at the cole des Ponts andChausses. He was also elected to replace Navier in the mechanics section of the Acadmie desSciences. Coriolis continued teaching at the cole Polytechnique until 1838 when he decided toend teaching and take on the role of director of studies.

As a result of studying formulations of dynamical problems in rotating machinery he was led to

consider the effect of changes of coordinate systems in analytical mechanics. The result of thesestudies was presented to the Academie des Sciences on June 6, 1831. .In 1835 he published apaper, On the Equations of Relative Motion of Systems of Bodies, in which heshowed that on a rotating surface, in addition to the ordinary effects of motion of abody, there is inertial force acting on the body at right angles to its direction ofmotion. Also, he introduced the terms work and kinetic energy in their modernscientific meanings in his first major book, On the Calculation of MechanicalAction, in which he attempted to adapt theoretical principles to applied mechanics.

Coriolis proposed a unit of work, namely the 'dynamode'. The unit represents 1000 kilogram-metres and was proposed by Coriolis as a measure which could provide a sensible unit withwhich to measure the work which a person might do, a horse, or a steam engine. However,

although his term 'work' has become standard, the dynamode did not prove popular as the unit ofwork. His other works include Treatise on the Mechanics of Solid Bodies andMathematical Theory of the Game of Billiards. His work has been used in mechanics,dynamics, hydraulics, atmospheric sciences, and oceanography by scientists. Coriolis's ownpapers do not deal with the atmosphere or even the rotation of the earth. Coriolis's name began toappear in the meteorological literature at the end of the nineteenth century, although the term"Coriolis force" was not used until the beginning of the twentieth century.

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http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Coriolis.html

http://www.britannica.com/eb/article-9026304

http://faculty.rmwc.edu/tmichalik/coriolis.htm

http://www.answers.com/topic/gaspard-gustave-coriolis

www.reference.com/browse/wiki/Gaspard-Gustave_Coriolis

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Coriolis.htmlhttp://www.britannica.com/eb/article-9026304http://faculty.rmwc.edu/tmichalik/coriolis.htmhttp://www.answers.com/topic/gaspard-gustave-coriolishttp://www.reference.com/browse/wiki/Gaspard-Gustave_Coriolishttp://www.reference.com/browse/wiki/Gaspard-Gustave_Coriolishttp://www.answers.com/topic/gaspard-gustave-coriolishttp://faculty.rmwc.edu/tmichalik/coriolis.htmhttp://www.britannica.com/eb/article-9026304http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Coriolis.html

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Jean Le Rond dAlembert by Milton Aguirre(1717-1783)

Jean dAlembert was a mathematician, mechanician, physicist,philosopher and was one of the editors of the early French encyclopedia,Encyclopedie. Born in Paris, dAlembert was the illegitimate son of writerClaudine Guerin de Tencin and artillery officer Louis-Camus Destouches.His father was out of the country at the time of his birth; this forced hismother to abandon him on the steps of Saint-Jean-le-Rond de Paris church.The child was quickly discovered and taken to a home for homeless children. The child was soonbaptized Jean Le Rond, named after the church on whose steps he had been found [2].

When his father returned to Paris he arranged for Jean to be cared for by MadamRousseau, whom Jean later considered his mother. After the death of his father the Destouchesfamily oversaw Jeans education and would later help him graduate from the Jansenist Collegedes Quatre Nations. He enrolled into the college under the name Jean-Baptiste Daremberg butsoon after changed his name to Jean dAlembert. For many years he would change his academiccareer path by studying theology, law, art, and medicine but his true passion was mathematicsand spent most of his spare time on the subject. After submitting work on the mechanics of fluidsand several papers on the integral of calculus dAlembert was admitted to the Paris Academy ofScience [2].

DAlembert is credited for several mathematical accomplishments in his career. Hehelped resolve the controversy over the conservation of kinetic energy in his published workTraite de dynamique by improving Newtons definition of force, which contains dAlembertsprinciple of mechanics, stating Newtons third law of motion applies to bodies free to move aswell as stationary bodies [2] [5].

DAlemberts Principle:

Where - mi d2 ( ri )/dt

2 is the inertia forces and Fi, fiare the applied and constraint forces.

Fi + fi mi d2 ( ri ) = 0

dt2

In another of his scientific worksMemoire sur le refraction des corps solides, in the fieldof fluid mechanics, dAlembert theoretically explained refraction and also wrote what is nowknown as the dAlemberts paradox. DAlemberts paradox makes the assessment that drag on abody immersed in an inviscid incompressible fluid is zero [4].

In his latter years, dAlembert suffered from bad health and died in October 29, 1783 dueto a bladder illness [1].

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[1] D.R. Wilkins. School of Mathematics Trinity College, Dublin.Jean-le-Rond DAlembert.http://www.maths.tcd.ie/pub/HistMath/People/DAlembert/RouseBall/RB_DAlembert.html.

Jan. 30 2006.

[2] J.J. OConnor and E.F. Robertson.Jean le Rond dAlembert, http://www-history.mcs.st-andrews.ac.uk/~history/Mathematicians/D'Alembert.html. Jan. 30 2006.

[3] Karl-Erik Tallmo,Jean le Rond dAlembert. http://art-bin.com/art/oalembert3e.html. Jan. 282006.

[4] Ronald Grimsley.Jean dAlembert. http://en.wikipedia.org/wiki/Jean_le_Rond_d'Alembert.Jan. 30 2006.

[5] The Columbia Electronic Encyclopedia.DAlemberts Principle.

http://www.infoplease.com/ce6/sci/A0814519.html.Jan. 30 2006.

http://www.maths.tcd.ie/pub/HistMath/People/DAlembert/RouseBall/RB_DAlembert.htmlhttp://www-history.mcs.st-andrews.ac.uk/~history/Mathematicians/D'Alembert.htmlhttp://www-history.mcs.st-andrews.ac.uk/~history/Mathematicians/D'Alembert.htmlhttp://art-bin.com/art/oalembert3e.htmlhttp://en.wikipedia.org/wiki/Jean_le_Rond_d'Alemberthttp://www.infoplease.com/ce6/sci/A0814519.htmlhttp://www.infoplease.com/ce6/sci/A0814519.htmlhttp://en.wikipedia.org/wiki/Jean_le_Rond_d'Alemberthttp://art-bin.com/art/oalembert3e.htmlhttp://www-history.mcs.st-andrews.ac.uk/~history/Mathematicians/D'Alembert.htmlhttp://www-history.mcs.st-andrews.ac.uk/~history/Mathematicians/D'Alembert.htmlhttp://www.maths.tcd.ie/pub/HistMath/People/DAlembert/RouseBall/RB_DAlembert.html

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Jacques Denavit and Richard Scheunemann Hartenberg by Bryan Markovich

Jacques Denavit was born on October 1, 1930 in Paris, France. He attended theUniversity of Paris and obtained his baccalaureate in 1949. He moved to America and obtainedAmerican citizenship. He then attended Northwestern University where he received his M.S in

1953 and his Ph.D. in 1956, both in mechanical engineering. Following completion of hisdegrees, Denavit became an assistant professor in the mechanical engineering department ofNorthwestern in 1958. He retired from Northwestern as a full professor in 1982. He alsoworked as resident physicist for the Naval Research Lab from 1969-1971. Following hisretirement from Northwestern, Denavit worked as a physicist at the Lawrence LivermoreNational Laboratory from 1982 1993. Much of his later work dealt with plasma physics andsolid state devices1.

Richard S. Hartenberg was born on February 27, 1907 in Chicago, Illinois. He attendedthe University of Wisconsin where he received his B.S in 1928, his M.S. in 1933, and his Ph.D.of engineering mechanics in 1941. Following completion of his Ph.D. he became an assistantprofessor at Northwestern University. He spent 34 years at Northwestern before retiring in 1975.

Hartenberg was a member of ASME (American Society of Mechanical Engineers) and Sigma Xi(the Scientific Research Society). He was awarded the mechanism award from ASME in 1974.His research interests included kinematics, machine design, and the history of technology1. Dr.Hartenberg passed away on December 24, 1997.

Denavit and Hartenbergs 1964 text, Kinematic Synthesis of Linkages, described the pre-1900s developments on kinematics, and helped to develop a notation for synthesis that wasstandardized3. Their work, while not earth shattering, has been vital to 20th century kinematics,dynamics, and robotics. The major contribution comes from their approach of unambiguouslydefining the position of spatial mechanisms. Many previous scholars had spent time workingwith planar mechanisms and had not derived a standardized way of describing the more complexspatial mechanisms.

Denavit Hartenberg Notation on an arbitrary linkage.4

1O'Donnell, Owen, ed. American Men and Women of Science. 20th ed. New York: R.R. Bowker, 1999.

2http://www.wilmettehistory.org/vri/obitH.html3Denavit, Jacques, and R.S. Hartenberg. Kinematic Synthesis of Linkages. New York: McGraw-Hill, 1964.

4Craig, John J. Introduction to Robotics. 3rd ed. Upper Saddle River: Pearson, 2005.

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Robert Fulton(November 14, 1765 February 24, 1815)

Vipul V. Mehta

Robert Fulton was an engineer and inventor who developed the first steam-

powered ship. He was born in Little Britain in Lancaster County, Pennsylvania.His father died when he was just three years of age. So he grew up under thecover of his mother. He was a very quick learner and had exceptional talent indrawing. But unfortunately he could not fare well in his school. While he wasgreatly admired for his talent in mechanisms and drawings by the employers inthe machine shops he used to visit in his leisure time, his teachers andcompanions used to consider him as a dull boy. When one of his teachers

complained his mother about his negligence towards the studies, he told them that his brain is sofull of original ideas he dont have vacant chamber to store away contents of the dusty books. Hewas just 10 years of age at that time. In 1778, he designed a sky-rocket to illuminate sky on theeve of Independence Day. Until summer of 1779, he used to visit gun-smith shops and

endeavored to manufacture a small air-gun.

When he was 16 years old, he worked for one his friends father to help him in pushing thefishing boats in the water. It was a rather menial task so he decided to devise a mechanism tolighten the labor. He then designed a paddle operated fishing boat. It consists of a two timbersheets attached at right angles to each other and they were connected to a crank. The crank wasdriven by the paddles. It was his first successful experiment in navigation.

He chose the profession of painting and went Philadelphia and stayed there for four years. Thenhe went to England for the purpose of completing his studies in profession. While traveling therehe got acquainted with the Duke of Bridgewater. The Duke convinced Fulton to abandon the

profession of an artist and become an engineer. He took a number of patents in England and wentto France to implement a new design. He commenced the first practical submarine, calledNautilus,in Paris which was commissioned by Napoleon.

Around this time he designed a huge steamboat. He wrote to James Watt and ordered an engineto be built to his plans and had it shipped to New York where he sailed separately and was goingto build the first successful paddle steamer. His first steamboat was called as North RiverSteamboat or Clermont. This ship sailed from New York City to Albany, NY. Further Fultondesigned steam powered warship called Fulton the First. After this wonderful success New YorkLegislation provided him full rights to provide all steamboat traffic for thirty years.Unfortunately in the later he could not keep with the competition in the steamboat traffic and

resulted in his bankruptcy. Few days later he had to retire to bed because of inclemency of theweather and rapidly his indisposition prostrated him again, growing worse. He died at the age offifty years.

References:

1. http://en.wikipedia.org/wiki/Robert_Fulton2. http://www.gutenberg.org/files/15161/15161-h/15161-h.htm#CHAPTER_XIII3. http://www.geocities.com/Heartland/4547/fulton.html

http://en.wikipedia.org/wiki/Robert_Fultonhttp://www.gutenberg.org/files/15161/15161-h/15161-h.htm#CHAPTER_XIIIhttp://www.geocities.com/Heartland/4547/fulton.htmlhttp://www.geocities.com/Heartland/4547/fulton.htmlhttp://www.gutenberg.org/files/15161/15161-h/15161-h.htm#CHAPTER_XIIIhttp://en.wikipedia.org/wiki/Robert_Fulton

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Leonhard Euler (1707-1783)(pronounced lay-own-hard oiler)

Compiled by -- Ryan Landon

Considered one of the greatest mathematicians of all time, LeonhardEuler provided much of the mathematical foundation forelectromagnetism, acoustics, fluid mechanics, mechanics, andcartography. His contributions also influenced the standardization oscientific notation. For example, after the divisive dispute over theinvention of calculus between Leibniz and Newton, it was Euler whoadopted Leibnizs compact notation and allowed for a reunifof thought and mathematics in the early nineteenth century. Eulecredited with the term "function" to describe an expression involvi

various arguments; i.e., y = F(x). And much of his notation for imaginary numbers, pi, naturallogarithms, and common geometric functions such as sine, cosine, and tangent is still used to

(1) His discoveries and proofs are too many to list in this short biography. Regarding mecEulersMechanica provided a solid foundation of thought and method. Significantly, it was hisclarification of the principle of least action that laid the foundation for the calculus ofvariations; the mathematics of variational dynamics. (4) Yushkevich, in the Dictionary ofScientific Biography (2) wrote,

f

icationr isng

day.

hanics,

Euler, Leonhard: Struik,D. J.A Concise History ofMathematics. p. 132f. (5)

The distinguishing feature of Euler's investigations in mechanics as compared to

those of his predecessors is the systematic and successful application of analysis.

Previously the methods of mechanics had been mostly synthetic and geometrical;

they demanded too individual an approach to separate problems. Euler was the

first to appreciate the importance of introducing uniform analytic methods into

mechanics, thus enabling its problems to be solved in a clear and direct way. Euler was born on 15 April, 1707 in Basel Switzerland (within miles of the south-western cornerof Germany). Raised in a devout Protestant family, he and his family were deeply religious.Leonhards father, Paul, studied theology at the University of Basel, where he attended thelectures of Jacob Bernoulli and became friends with another famous scientist/mathematicianJohann Bernoulli. Although Paul Euler wanted his son to follow his example and join theministry, it was his introducing Leonhard to scientific ideas that likely sparked the insatiable butdisciplined curiosity which remained strong in him until his dying day 18 September, 1783 in St.Petersburg, Russia. (3)

Leonhard was extremely ambitious and resourceful as he funded his self study of JacobBernoulli, Varignon, Descartes, Newton, Galileo, van Schoten, Hermann, Taylor, and Wallis.He received numerous honors, and held prominent positions from a young age. However, in1735 his career experienced a hiccough when he had such a sever fever that he almost lost hislife. Then eyestrain in 1738 and a series of events led to complete blindness at age 59. Even so,almost half of his 886 (6) compiled works--filling over 70 volumes--were completed after thistime. It has been estimated that it would take eight-hours work per day for 50 years to copy allhis works by hand. (1)

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(1) http://en.wikipedia.org/wiki/Euler(2) Biography inDictionary of Scientific Biography (New York 1970-1990). cited in (3)(3) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html(4) In Fundamentals of Applied Dynamics Williams, James H., John Wiley and Sons, 1996

(5) http://scienceworld.wolfram.com/biography/Euler.html(6) http://www.usna.edu/Users/math/meh/euler.html

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Franz Grashof: 1826 1893by Mike Hast

Franz Grashof was born on July 11th 1826 in the town of Dusseldorf, Germany. As ayoung man, Franz had an undeniable interest in the study of mechanicsby the age of fifteen,Grashof had quit traditional schooling in order to attend trade school, with mechanicsspecifically in mind. Three years later, Grashof enrolled at the Berlin Royal Technical Institute.There, he studied mathematics, physics, and machine design. Upon graduation, Grashoftemporarily sacrificed his career in mechanics in favor of traveling the world. In 1849, Grashofset sail on a two and a half year voyage that would take him through India, the Dutch Indies,Australia, and parts of Africa. He would not return to Europe until 1851.

Upon his return to Germany, Grashof began his career as a professor of appliedmathematics at the Berlin Royal Technical Institute. During the nascent stages of his career, theeager young professor played an integral role in the creation of the Society of German Engineers.His work with the Society would not go unnoted: the Karlsruhe Polytechnical Institute namedhim department head of Applied Mechanics and Mechanical Engineering in 1863. During histenure at Karlsruhe Polytechnical Institute, Grashof taught a wide variety of subjects including

Strength of Materials, Hydraulics, Theory of Heat, and General Engineering.During his 30 year tenure as a professor, Grashof demanded a great deal from his

students. He preferred to work from the most general form of an equation to a specific case,instead of vice-versa. This proved to be a difficult method for some students, especially becauseGrashof preferred to use mathematical methods instead of diagrams to explain theories. Hispresentations were notably impersonal, but the content of the lectures was always presentedclearly and confidently.

In 1866, Grashof published Theorie der Elasticitt und Festigkeit. Not only does this textintroduce fundamental equations of the theory of elasticity, but it also further develops severaltheories proposed by various scholars of the era. Through his meticulous work, Grashof gained agreat deal of respect within the worldwide scientific community. Indeed, his status became so

great that the superior reputation of Karlsruhe Polytechnical Institute was largely due toGrashofs presence there as superintendent.

Upon his death on October 26th, 1893, the Society of German Engineers created theGrashof Commemorative Medal. This medal is considered to be the ultimate honor the Societycan award to scholars of engineering.

Even after his death, Grashof continued to make marks on the field of engineering. In1921, fluid dynamicist H. Groeber defined the Grashof number as the following:

Despite the fact that there was a Grashof number in fluid dynamics, Grashof was honoredagain in the field of mass transfer with a second Grashof number. It has the following form:

Finally, Grashof also has his name tied to four bar kinematics. Specifically, the linkage isconsidered to be Grashof if the sum of the lengths of the shortest and longest links is less thanor equal to the sum of the lengths of the two remaining links.

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Bibliography

http://www.dekker.com/sdek/abstract~db=enc~content=a713499277http://en.wikipedia.org/wiki/Grashof_number

http://www.ichmt.org/dimensionless/dimensionless.htmlNorton, Robert L. Design of Machinery: Second Edition. New York: McGraw-Hill BookCompany, Inc., 1992.

http://www.personal.psu.edu/faculty/g/a/gal4/AcademicLineage/AcademicLineage.html#anchorGrashofhttp://www.seas.ucla.edu/jht/pioneers/pioneers.html

http://www.dekker.com/sdek/abstract~db=enc~content=a713499277http://en.wikipedia.org/wiki/Grashof_numberhttp://www.ichmt.org/dimensionless/dimensionless.htmlhttp://www.personal.psu.edu/faculty/g/a/gal4/AcademicLineage/AcademicLineage.html#anchorGrashofhttp://www.personal.psu.edu/faculty/g/a/gal4/AcademicLineage/AcademicLineage.html#anchorGrashofhttp://www.seas.ucla.edu/jht/pioneers/pioneers.htmlhttp://www.seas.ucla.edu/jht/pioneers/pioneers.htmlhttp://www.personal.psu.edu/faculty/g/a/gal4/AcademicLineage/AcademicLineage.html#anchorGrashofhttp://www.personal.psu.edu/faculty/g/a/gal4/AcademicLineage/AcademicLineage.html#anchorGrashofhttp://www.ichmt.org/dimensionless/dimensionless.htmlhttp://en.wikipedia.org/wiki/Grashof_numberhttp://www.dekker.com/sdek/abstract~db=enc~content=a713499277

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Jason Hines ME-562 Spring 2006

Sir William Rowan Hamilton

(August 4, 1805 September 2, 1865)

Sir William Rowan Hamilton was born in Dublin Ireland in 1865, and within a few years,would be recognized as an extraordinarily gifted child. Educated by his uncle, an Anglican

priest, William mastered not only the contemporary european languages, but also Latin, Greek,Hebrew, Persian, Arabic, Hindustani, Sanskrit, and Malay. His introduction to mathematicsoccurred as early as age 12 after reading works by Euclid and Newton. He became immediatelyfascinated, and began studying the mathematical works of Lagrange and Laplace. Hamiltonwould develope an uncanny ability to perform mathematical calculations to a high number ofdecimal places without any pen or paper. He would go on to study at the Trinity College, inDublin, where he later became Professor of Astronomy, remarkably before he even graduated.The post provided Hamilton with the freedom to pursue his various scientific interests withoutbeing restricted to one specific branch of study (due to the circumstances surrounding theposition). Hamilton would spend his life at Trinity College as a mathematician, physicist, andastronomer. He worked feverishly on his scientific pursuits, frequently overworking, missing

meals, even to the point of illness. In his later years, Hamilton developed a dependancy onalcohol and died in 1865 at the age of 60, the father of two sons.One of Hamiltons most significant contributions was his introduction of quaternions in

1843. In his attempt to extend complex numbers from planar geometry to higher dimensionalspaces, he discovered a way to apply them to 4-dimensional space. The discovery came toHamilton as he strolled with his wife along the Royal Canal in Dublin on 16 October 1843,where he carved the fundamental equation of quaternions onto the Broome Bridge. While thecarving is no longer visible, a plaque remains to commemorate the location of Hamiltonsscientific epiphany. As a by-product of this work, Hamilton also laid out the groundwork for thecross and dot products of vector algebra. HamiltonsLectures on Quaternions (Dublin, 1852), asignificant contribution to the mathematical sciences, introduced quaternions as an analyticalmethod. Vector notation used in algebra and calculus eventually displaced quaternions as thepreeminent mathematical theory of its time, but for a portion of the 1800s quaternions were theprimary (and in some cases, the only) advanced mathematical theory taught in universities. Thelimitation of quaternions to 4-dimensional space was the primary reason for their eventualdecline in popularity. Quaternions are fundamental to the study of orbital mechanics to this day,and are also applied in computer graphics, signal processing and control theory. Hamilton alsodeveloped an analytical method to describe the motion of discrete systems, which became analternative to Lagranges method. In addition, he studied optical systems, where his researchincluded the development of conical refraction theory. His published results supported the wavetheory of light, which at his time had not been fully accepted by the academic community.However, much of his work on the subject of optics was much too abstract to generateimmediate acclaim, but has since become useful in the production of optical devices.References:

http://en.wikipedia.org/wiki/William_Rowan_Hamiltonhttp://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.htmlhttp://physicsweb.org/articles/world/18/8/7

http://en.wikipedia.org/wiki/William_Rowan_Hamiltonhttp://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.htmlhttp://physicsweb.org/articles/world/18/8/7http://physicsweb.org/articles/world/18/8/7http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.htmlhttp://en.wikipedia.org/wiki/William_Rowan_Hamilton

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John HarrisonMarch 24, 1693 March 24, 1776

By Alex Moerlein

John Harrison, inventor of the first clocks accurate enough for maritime longitudecalculations, was born in Foulby, England on March 24, 1693. The son of a carpenter and theeldest of five children, Harrison initially followed his father into the trade. He soon becameinterested in the design of clocks, and created his first at the age of twenty. It was constructedentirely of wood, not unusual given his experience with it, and the relative cost of metal parts.

Even before he tackled the challenge of longitude calculation, Harrison revolutionized theconstruction of clocks. He solved two serious issues through novel approaches: the slowing ofpendulum clocks during warm weather, and the breakdown of clock internals due to poor-qualitylubricants. The first problem was caused by the expansion of the steel comprising the pendulumshaft, increasing its effective length. He remedied this by using alternating strands of brass andsteel, whose contraction and expansion rates would cancel each other out. This allowed him toattain an accuracy of one second per month, far better than any competitors devices. For thelubrication issue, Harrison designed a nearly-frictionless system called the grasshopperescapement, a ratcheting device that used a pendulum attached to a lever to limit the motion offlywheel attached to a rotational spring. It allowed the controlled release of the energy stored inthe spring, with the rate determined by the period of the pendulum.

The determination of latitude is simple, and can be obtained using the position of the starsin the night sky. Longitude, however, requires knowledge about the location of the sun (orequivalently, the time of day) in some reference location. While pendulum-driven clocks ofHarrisons day were more than accurate enough to make longitude calculations, the moisture and

rocking motion found on ships rendered them useless. Longitude calculation was considered soimportant that the Board of Longitude was created, with a 20,000 prize offered to the individualwho could devise a reliable shipboard method. Harrison ultimately designed five prototypesbefore receiving the prize.

The first three were essentially pendulum-based, with complicated balancing mechanismswhich would isolate them from the motion of the ship. These designs he deemed unsatisfactory,and created a fourth which resembled a large pocket watch. The design was proven highlyaccurate to within five seconds over six weeks, and though it was subjected to repeated andrigorous testing, the Board dragged its feet in paying out the reward. Harrison finally receivedthe 20,000 in 1773 (at the age of 79) after enlisting the help of King George III and designing afifth prototype.

Thought Harrison is best known for his work on the longitude problem, he was also veryinterested in instrument tuning, and developed a meantune system based off of pi. He arguedthat all integer-based tuning systems produce low-frequency beating due to their slightinaccuracy. Harrisons remarkable achievements have earned him a place among the greatnames of ocean explorers and inventors.References:

Wikipedia: http://en.wikipedia.org/wiki/John_Harrison

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National Maritime Museum: http://www.nmm.ac.uk/server/show/conWebDoc.355/viewPage/1

BBC News: http://news.bbc.co.uk/1/hi/sci/tech/1864737.stm

Longitude: The true story of a lone genius who solved the greatest scientific problem of his time.

Dave Sobel, 1995.

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Thomas. R. Kane (1924 - )Biography by: Rajiv Ranganathan

Professor Thomas R. Kane was born in Austria in 1924. After emigrating to the United

States in 1938, he attended Columbia University in the city of New York. While at ColumbiaUniversity, he earned four degrees a B.S. in Mathematics, a B.S. and an M.S. in CivilEngineering and a Ph.D. in Applied Mechanics. After graduating, Dr. Kane spent the next 45years teaching at the University of Pennsylvania and Stanford University. Currently, Dr. Kane isa Professor Emeritus of Mechanical Engineering at Stanford University.

Dr. Kanes research interests lie in the areas of multibody dynamics, dynamics of humanmotion, spacecraft dynamics and computerized symbol manipulation. In particular, he isrenowned for his work on developing a new method for formulating equations of motion basedon the concept of partial velocities. Using this method, one has the advantage of being able towrite the equations of motion in terms of independent variables without using Lagrange

multipliers, thereby reducing computational complexity1. These have been referred to in theliterature as Kanes method and have found widespread applications in the fields of roboticsand computer graphics.

He was also instrumental in developingAutolev an advanced symbol manipulationsoftware for engineering and mathematical analysis that is particularly well suited to motionanalysis. He currently heads a consultation company, Kane Dynamics Inc., that specializes inproviding kinematic and dynamic analyses of mechanical systems to industries.

Dr. Kane has authored 10 textbooks and more than 150 technical papers. Some of hisrecent textbooks that he has co-authored with David Levinson include Dynamics Online

(1996),Engineering Mechanics Online: Statics (1998), andEngineering Mechanics Online:Dynamics (1998). He has been the recipient of a number of prestigious awards for hiscontributions to the field of mechanics, including the 2005 DAlembert award of the AmericanSociety of Mechanical Engineers.

References:1. Nukulwuthiopas, W., Laowattana, S, & Maneewarn, T. (2002). Dynamic modeling of a one-

wheel robot by using Kane's method. IEEE International Conference on IndustrialTechnology.Vol. 1, 524 - 529

2. OnLine Dynamics, Inc., Autolev: a symbolic manipulator for statics, dynamics, andmathematical analysis. http://www.autolev.com/

3. Stanford University : Mechanical Engineering : Faculty Directory Webpage.http://me.stanford.edu/faculty/facultydir/kane.html

4. Stanford University: Honors and Awards Webpage.http://news-service.stanford.edu/news/2005/november2/ppl-110205.html

5. University of Florida: EML 5215: Analytical Dynamics Course Webpage.

http://www.autolev.com/http://me.stanford.edu/faculty/facultydir/kane.htmlhttp://news-service.stanford.edu/news/2005/november2/ppl-110205.htmlhttp://news-service.stanford.edu/news/2005/november2/ppl-110205.htmlhttp://me.stanford.edu/faculty/facultydir/kane.htmlhttp://www.autolev.com/

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Cyrus Hall McCormick was born in RockBridge County, Virginia. His father, Robert,was a wealthy landowner who had patentedseveral farming implements. At age 15, Cyrusbegan to take after his father by inventing a

cradle to carry grain. Cyrus also observed hisfathers attempts to create a mechanical reaper.His father was never quite able to perfect thedevice. After fifteen years of hard work, Robertdecided to pass the project on to his son.

Cyrus Hall McCormick

Father of Modern Agriculture

15 February 1809 13 May 1884

by Janine Kowalczyk

Cyrus took on the challenge and began to modify his fathers design. He spent late nightsstudying the machine to determine exactly when and where faults occurred. He made new plans,built a reaper, tested his contraption, and remodeled his design all within six weeks. Cyrusmanaged to create a reaper he was confident with before the end of the same harvesting season.He first publicly demonstrated his reaper in July of 1831 in a field near Steeles Tavern, Virginia.

It consisted of a sickle which was used to cut grain that fell on a platform. The original designrequired the grain to be raked off by hand, but the reaper itself only needed a horse to pull it inorder to function.

Farmers were not originally willing to trust his design, but Cyrus continued to makeimprovements. By 1832, he managed to use his reaper to successfully harvest 50 acres of hisfathers land. In 1834, he applied for his first patent. The reaper was capable of increasingharvesting by at least tenfold. Farmers, however, were still hesitant to purchase one.

Cyrus then proved his talent as a businessman. He began to manufacture reapers on hisfamilys estate in 1837. By 1843, he provided licenses to manufacturers in other parts of thecountry. To increase sales he utilized door to door canvassing, written money-back guarantees,and replacement parts. He began to provide credit to farmers promising they could pay him backwith their increase in harvest. By making his invention known to the public, Cyrus earned thetrust of farmers and helped make the transition to more productive farming methods byconvincing the world mechanical machines really did work.

Cyrus opened a factory in Chicago in 1847 to keep up with his sales. It became one of thegreatest industrial establishments in America. He continued to make improvements on his reapermaking models that could rake themselves and eventually bind the grain autonomously.

In 1851, Cyrus was awarded the Gold Medal at the London Crystal Palace Exhibition. Hetoured Europe with his impressive innovation. In 1879, he became a member of the FrenchAcademy of Sciences as having done more for agriculture than any other living man.

Unfortunately, Cyrus also faced some hardships. He spent many years defending his patentsin court. His factory was even destroyed by the Chicago Fire of 1871. Furthermore, strikes athis factories helped lead to the infamous Haymarket Square riot in 1886.

Nonetheless, Cyrus acquired a great fortune. He invested his money in railroad and miningenterprises. He also edited the Chicago Times until he sold it in 1861.

Cyrus McCormick passed away in 1884. He will always be remembered for hisinnovations that encouraged westward expansion and forever changed the farming industry. Hisson took over the company which became part of the International Harvester Corporation in1902.

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References:

http://www.invent.org/hall_of_fame/101.html http://en.wikipedia.org/wiki/Cyrus_McCormickhttp://web.mit.edu/invent/iow/mccormick.html http://www.vaes.vt.edu/steeles/mccormick/bio.htmlhttp://www.wisconsinhistory.org/wlhba/articleView.asp?pg=1&id=13857&hdl=&np=&adv=yes&ln=McCormick&fn=Cyrus&q=Mr%2E&y1=&y2=&ci=&co=&mhd=&shd=

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Thomas Newcomen (1663-1729) by Rob Wilson

Thomas Newcomen was an English inventor responsible for developing asuccessful steam pumping engine. His innovations would later be improved by

James Watt and the resulting technology would power the industrial revolution.

There are noknown images ofNewcomen [3]

Newcomen was born in Dartmouth, Devon in 1663. His old English family hadlost its estates during an uprising against King Henry VII in 1536 and hadrelocated to Devon as merchants and traders. Thomas became a dealer ofiron hardware (or an ironmonger), a blacksmith, and a Baptist preacher [1].Many of his customers were from mines in nearby Cornwall, and it isthrough these contacts that Thomas became aware of the problem of mine flooding and waterremoval [2].

Around 1702 Newcomen began experimenting with the dousing of steam in a cylinder to create avacuum. These experiments led to the development of an atmospheric engine, consisting of apivoting beam connected on one end to a vacuum driven piston-cylinder and on the other to a

pump. As the piston cylinder filled with steam, gravity wouldpull the pump piston down; after the steam was doused, theresulting vacuum would pull the pump back up, drawing waterout of the mine [4]. Automatic valves were implemented tomanage water flow. This system was called an atmosphericengine because the maximum pressure was ~1 atm, an importantfactor considering reliable pressure vessel technology was notdeveloped at this time [3].

Around the same time, another inventor from Devonshire,

Thomas Savery, designed and patented a steam pump. Saverysdesign involved the condensation of steam in a vessel to create avacuum that directly sucked up water. This pump did notfeature the Newcomen engines transmission of power, was not

automatic, and could not effectively pump water without unreasonably high pressures. Additionally,the Savery pump doused the steam by pouring water on the outside of the vessel, whileNewcomens operated by squirting water into the cylinder. Despite the dissimilarities, Savery andhis investors successfully claimed Newcomens engine was covered by their patent and forced himto work with them, preventing Thomas from becoming wealthy off his invention [1]. The firstengine was constructed near Dudley Castle in 1712. It operated at 12 cycles per minute and lifted 10gallons of water per stroke [3].

When Newcomen died in 1729, roughly one hundred steam engines had been built. They continuedto be constructed until the early 1800s, and one in Barnsley remained in operation until 1934 [2].Watt later improved the steam engine by adding a separate condenser, allowing condensation ofsteam without cooling the cylinder [4].

Resources:

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Isaac Newton by Sanjeevakumar Redlapalli

Sir Isaac Newton (1642-1727), was an English physicist, mathematician, astronomer, alchemist,inventor and natural philosopher who is regarded by many as the most influential scientist inhistory. He was born in Woolsthorpe, near Grantham in Lincolnshire. He was a sober, silent,

thinking lad, and mostly remembered for his strange inventions and extraordinary inclination formechanical works in school. His uncle noticed Newtons interest and strongly recommendedNewton's mother to send him for the university. Newton set out for Cambridge early in June1661, matriculating to Trinity College. He entered Trinity as a subsizar, a poor student whoearned his keep by performing menial tasks for the fellows. At Cambridge he was exposed tomany philosophical texts and ideas, especially those of the French philosopher Ren Descartes,who was very highly regarded at the time. After studying the work of Descartes, Newton wasattracted to mechanical philosophy, and began to question the environment around him,including the nature of matter, cosmic order, light, colors and sensations. Newton was at theheight of his creative power but he was forced to leave (1665-1666) the University which wasclosed as a precaution against the Great Plague. For the next two years Newton worked at home

on calculus, optics and law of gravitation.Working on mathematics, Newton applied himself to drawing tangents beneath curves(differentiation) and finding areas under curves (integration). Newton began to treat the areasunder curves kinetically, as areas swept out by a moving line. From the idea of motion, hederived the term 'fluxional', to describe his method, which is now called as calculus. Newtonthen moved to the science of mechanics and started analyzing the circular motion. Newtonwondered if he couldn't think of a way to join the ideas of Johannes Kepler's work on howplanets circle the sun and, in the book, Galileo was talking about how things fell to the earth.Newton made the link, and called his findings Universal Law of Gravitation. The idea did notcome to Newton in a flash of inspiration, but was developed over time. Newton then startedexperimenting with the 'celebrated phenomenon of colors'. He proved that white light was madeup of colors mixed together, and the prism merely separated them. It is believed that he is thefirst to explain precisely the formation of the rainbow from water droplets dispersed in theatmosphere in a rain shower. In October 1669, Newton became the second ever Lucasianprofessor of mathematics. For the first year of his tenure, he devoted much of his time tocontinuing his optics research. It was Newton's reflecting telescope, made in 1668, that finallybrought him into full view of the scientific community. The Royal Society got wind of theinvention, and sent an invitation to display it. Newton was ecstatic and also sent them his theoryof colors in a letter. Robert Hooke, a leading power at the Royal Society, however, refuted muchof what Newton said. Infact, Newton was criticized and was accused of plagiarism. Newton thenmoved to chemistry, and more specifically alchemy. He labored day and night in his chemicallaboratory and immersed himself in mathematical and mystical calculations. He also developed alaw of cooling, describing the rate of cooling of objects when exposed to air. In the late 1670stheological studies occupied most of his time. He began a history of the church, starting in thefourth and fifth centuries. In 1686 he presented his single greatest work, the PhilosophiaeNaturalis Principia Mathematica ('Mathematical Principles of Natural Philosophy'). In it,Newton revealed his laws of motion, and the Universal Law of Gravitation. He enunciated theprinciples of conservation of momentum and angular momentum. Finally, he studied the speedof sound in air, and voiced a theory of the origin of stars. The Royal Society were going topublish Newton's book, but withdrew due to lack of funds. The astronomer Edmund Halley, who

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was wealthy and thought highly of Newton, eventually paid for its publication. The Principiaredirected Newton's intellectual life, away from theology and alchemy and back into 'real'science.

After the Principia appeared, Newton became somewhat bored with Cambridge. In 1689, he was

elected a Member of Parliament for the University, and he moved to London. In 1696 Newtonwas appointed Warden of the London Mint, becoming Master in 1699. He took these duties veryseriously, revising the British coinage and taking severe measures against forgers. He waselected President of the Royal Society in 1703, but only just - very few members seemed to wantthis cantankerous genius as their president. However, he held this office until his death. In 1709,Newton began work on a second edition ofPrincipia, and he also published a second edition ofOpticks, however after he moved to London, he did nothing but reshuffle ideas that he had had inCambridge. As he became older, he seemed concerned with leaving his image behind - he hadmany portraits painted. As his health began to deteriorate he began to distribute his wealthamongst his family. After a series of debilitating illnesses he died on 31 March 1727.

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Sittikorn LapapongME 562 Spring 2006 Homework 3

Joseph Louis Lagrange

Born: January 25, 1736 in Turin, Sardinia-Piedmont (now Italy)Died: April 10, 1813 in Paris, France

Joseph Louis Lagrange is usually considered to be a Frenchmathematician, but the Italian encyclopedia refers to him as an Italianmathematician since he was born in Turin and baptized in the name ofGiuseppe Lodovico Lagrangia (he moved to Paris in 1787 and becameFrench citizen, adopting the French translation of his name, Joseph LouisLagrange). Lagrange was a son of Giuseppe Francesco LodovicoLagrangia, Treasurer of the Office of Public Works and Fortifications inTurin, and Teresa Grosso who was the only daughter of a medical

doctor. Despite the fact that Lagrange's father held a position of someimportance in the service of the king of Sardinia, the family was not wealthy because Lagrange'sfather had lost large sums of money in unsuccessful financial speculation. He studied in LawSchool at the College of Turin as his father planned. At first he had no great enthusiasm formathematics. Lagrange's interest in mathematics emerged when he read a copy of Halleys book1693 work on the use of algebra in optics. He was also attracted to physics by the excellentteaching of Beccaria at the College of Turin and later decided to make a career as amathematician. He certainly did devote himself to mathematics, but largely he was self taughtand did not have the benefit of studying with leading mathematicians. At the age of 19, Lagrangewas appointed professor of mathematics at the Royal Artillery School in. Besides, he helped tofound a scientific society in Turin, which later became the Royal Academy of Sciences of Turin.By November 1766, Lagrange accepted a position in Berlin as Director of Mathematics at theBerlin Academy by persuasion of dAlembert and Frederick II. After the death of his wife,Vittoria Conti who was his cousin, and Frederick II, he again moved to Paris to be a member ofthe Academic des Sciences in Paris in 1787 and spent the rest of his life there. He survived theFrench Revolution. During 1970s, he worked on the metric system and advocated a decimalbase. In addition, Lagrange served as a professor at Ecole Polytechnique where he was afounding member in 1797. During his life, not only did he invent and bring to maturity thecalculus of variations and later applied the new discipline to celestial mechanics but he alsocontributed significantly to the numerical and algebraic solution of equation, to theory ofdifferential equations, and to number theory. His greatest treatise, Mecanique Analytique(Analytical Mechanics) that was written in Berlin and published in 1788, was a mathematicalmasterpiece and the basis of all later work in this field. In this he transformed mechanics in to abranch of mathematical analysis and laid down the law of virtual work that simplifies manyphysical problems, and from that one fundamental principle, by the aid of the calculus ofvariations, deduced the whole of mechanics, both of solids and fluids. The method of generalizedco-ordinates by which he obtained this result is perhaps the most brilliant result of his analysis.

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Under Napolean, Lagrange was named to the Legion of Honor and Count of the Empire in 1803.On April 3, 1813, he was awarded the Grand Croix of the Ordre Imperial de la Reunion. He dieda week later. He is buried in the Pantheon.References

1. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Lagrange.html

2. http://en.wikipedia.org/wiki/Joseph_Louis_Lagrange3. http://www.answers.com/topic/lagrange-s-equation4. http://euler.ciens.ucv.ve/English/mathematics/lagrange.html

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FRANZ REULEAUX (18921905) Herman van Werkhoven

The father of kinematics, as Franz Reuleaux is sometimes referred to, was born in to anengineering family, with his father and grandfather being machine builders in Belguim. He wasborn in Eschweiler, a German speaking area of Belgium, on 30 September in 1829 (died April25, 1905). He received his technical training at the Polytechnic School at Karlsruhe from 1850

to 1852. Reuleaux then went on to universities in Berlin and Bonn to study philosophy, logic,natural sciences and other liberal arts.In 1856, at the age of 27, he received an invitation to become a professor of mechanical

engineering in Zurich and after eight years he was called to Berlin to develop a new program inmechanical engineering at the Royal Industrial Academy where he also served as Director from1868 to 1879. Many original ideas about kinematics of mechanisms and multi-body systems wasdiscussed in Reuleauxs two major books, The Kinematics of Machinery and The Constructor, amachine design book which was published in four languages. He attempted to use amathematical and more scientific basis in the areas of invention, kinematic synthesis and designof the machine as a whole. His main contributions lie in the area of using constraints andgeometric topology to provide tools for kinematic synthesis.

Reuleaux also took an interest into biomechanics after the first ASME president, RobertThurston, sent him a copy of a monograph that he wrote on The Animal as Machine and PrimeMoverin which he discussed the limits of force and power of humans and animals, comparingtheir capabilities with machines such as the steam engine. Reuleaux translated this book intoGerman in 1895 and in a latter book of Reuleauxs on kinematics, he devoted a chapter on thesubject of the skeletal system and its analogy with kinematic chains in machines.

Another important contribution to kinematics was his design and construction of 800models of mechanisms to help illustrate his symbol machine theory. Cornell University has thelargest remaining collection of these Reuleaux models, some examples of which are shownbelow.

Four bar linkage Slider crank mechanism Belt drive mechanismReuleauxs name now lives on in the Reuleuax triangle (shown below), which he

designed. This is an equilateral triangle, but each side is an arc of a circle whose centre is at theopposite corner. This design is used in the Wankel rotary internal combustion engine.

References:1. Moon, F.C. Franz Reuleaux: Contributions to 19th C.

Kinematics and Theory of Machines. Applied MechanicsReview, Vol 56, Nr2. ASME. 20032. Cornell University Library Kinematic Models For Design.

http://kmoddl.library.cornell.edu3. Wikipedia, the free encyclopedia.

http://en.wikipedia.org/wiki/Franz_ReuleauxReuleuax triangle 4. The Seiflow archives

http://www.seiflow.co.uk/Franz%20Reuleaux.htm

http://kmoddl.library.cornell.edu/http://en.wikipedia.org/wiki/Franz_Reuleauxhttp://www.seiflow.co.uk/Franz%20Reuleaux.htmhttp://www.seiflow.co.uk/Franz%20Reuleaux.htmhttp://en.wikipedia.org/wiki/Franz_Reuleauxhttp://kmoddl.library.cornell.edu/

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James Watt (1736-1819) by Dave Kraige

Renowned inventor, mechanical engineer, and civil engineer James Watt was born in Greenock,Scotland on January 19th, 1736. Early in his professional career, he took an interest in improvingthe steam engine, which at the time was used to pump water out of mines. Because of his manycontributions to the development of the steam engine, there is a misconception that he inventedit. However, the steam engine had been developed earlier by English engineers Thomas Saveryand Thomas Newcomen. Watts first work on improving steam engines involved characterizingthe properties of steam, particularly the relationship between temperature, pressure, and density.As a result of this work, he developed a steam condensing chamber which improved theefficiency of steam engines. Other early changes which improved the efficiency of the engineincluded cylinder insulation to reduce heat loss and oil lubrication to reduce frictional losses.These improvements were covered by Watts first patent, which he obtained in 1769.

James Watt is often referred to as the first kinematician, based on his invention of a straight-linelinkage used to control the long-stroke pistons used in his steam engine design. Because therewere no planes or other metal-cutting machines at that time which would create a long straightguide for the piston, Watt was forced to devise a mechanism that could create straight-linemotion. In the pursuit of such a mechanism, Watt was the first to record a study of the motion ofthe coupler in a fourbar linkage. This study led him to develop several mechanisms whichutilized the couplers motion to generate useful straight-line motion. Watts straight-linemechanism was patented in 1784, and continues to be used in many modern devices, includingsome automobile suspensions which constrain axle motion to a straight line.

Another of Watts important inventions was the planetary gear set. Because James Pickard hadalready patented the crankshaft and connecting rod in 1780, Watt took an alternative approachand developed a sun and planet gear set to drive his straight-line mechanism. Watt was also theinventor of the flyball governor, invented in 1788. Also known as a centrifugal governor, thisdevice maintained the speed of an engine automatically, and was one of the first automaticcontrol systems.

Along with being an outstanding mechanical engineer, Watt also made contributions to civilengineering. His invention of an attachment which allowed a telescope to be used to measuredistance aided his efforts in surveying canal routes. Because of Watts excellent and varied workon all things mechanical, a standard unit of power was named the Watt in his honor. Watt diedin Heathfield, England on August 19, 1819.

References:

Norton, Robert L. Design of Machinery, 3rd Edition. Boston: McGraw Hill, 2004.

"James Watt" Microsoft Encarta Online Encyclopedia. 2005. 2 February 2006< http://encarta.msn.com/encyclopedia_761564086/Watt_James.html>

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Eli Whitney

(12/8/1765 1/8/1825)By: Shamus Cronin

Born in Westboro, MA in 1765, Eli Whitney became famous for inventing the cotton gin;although he was never able to profit from the invention. His patent appeared in 1794, one yearafter the cotton gin was born, but was not legally upheld by the courts until 1807. For thisreason, Whitney and a business partner, Phineas Miller, struggled to win any cases againstfarmers who were making their own gins. Since the cotton gin was a simple design, it was easyfor farmers to duplicate the machine and use it without paying Whitney and Miller a huge fee.About 60 lawsuits were filed by Whitney and Miller and it was not until 1800 that they finallywon a case.

In 1798, Whitney, frustrated with the legal proceedings of his cotton gin, started delving

into the manufacturing of firearms business through his shops in Whitneyville, MA. Althoughstandardization (or interchangeable parts) was invented previously in England and France, nosignificant results were every produced; thus the honors of bringing standardization to the worldgo to Whitney in his firearm production line. Today this is the standard for every modern, large-scale assembly plant but at the time critics were skeptical as to whether Whitney could take theart out of manufacturing. It was not until Whitney built ten muskets from indiscernible partsfrom his assembly line for the Secretary of War that the critics were silenced. This also gaveWhitney a contract from the US government for 10,000 military muskets.

Whitneys goal, after observing clock makers using gears interchangeably, was to haveeach one of his unskilled workers build one type of part each day and as long as that workermade each part the same the assembly of the final product would be easy. Prior to Whitney ittook a skilled gunsmith to produce a firearm and many of his first workers were these sameskilled gunsmith; however, many of them became bored after making only one part day after dayand quit. A breakout of scarlet and yellow fever in 1794, reducing the number of eligibleworkers, and a fire that burned down all but one of his buildings a year later set Whitney back inhis quest for the ideal factory.

Eventually Whitney was able to bring standardization to the world in a viable manner.Contrary to popular belief, muskets, not the cotton gin, brought wealth to Whitney and this wasbecause his muskets could be repaired faster on the battlefield to be used again the next dayduring battle. Whitneys factory would eventually be leased to Oliver Winchester, the founder ofthe Winchester Repeating Arms Company by Whitneys grandson. Whitneys methods formanufacturing were mimicked in the production of carriages, clocks, springs, rubber products,and much more as the industrial revolution swept through America and Europe.

Whitney was also held in the highest regard by everyone that knew him and it has beensaid that, he was on intimate terms with every President of the United States from GeorgeWashington to John Quincy Adams. With so many achievements and class, it is no wonder thatEli has gone down in history as one of Americas greatest inventors.

Sources:- http://inventors.about.com/od/cstartinventions/a/cotton_gin.htm

http://inventors.about.com/od/cstartinventions/a/cotton_gin.htmhttp://inventors.about.com/od/cstartinventions/a/cotton_gin.htm

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- http://www.u-s-history.com/pages/h287.html- http://www.yale.edu/ynhti/curriculum/units/1979/3/79.03.03.x.html

http://www.u-s-history.com/pages/h287.htmlhttp://www.yale.edu/ynhti/curriculum/units/1979/3/79.03.03.x.htmlhttp://www.yale.edu/ynhti/curriculum/units/1979/3/79.03.03.x.htmlhttp://www.u-s-history.com/pages/h287.html