History and Theory of Machines and Mechanisms
http://hdl.handle.net/1813/2711
2016-05-06T07:34:12ZHistorical Mechanisms for Drawing Curves
http://hdl.handle.net/1813/2718
Historical Mechanisms for Drawing Curves
Taimina, Daina
Mechanical devices such as linkages for drawing curves are known
already from Ancient Greece. Later linkages found use in different mechanical
devices and machines like we can see it in 13th century drawings by Honnecourt
or in 16th century machine drawings by Agricola. In 17th century Descartes
accepted only those curves that had a mechanical device to draw them.
Mechanical curve drawing devices later became incorporated into different
machine design. In this paper examples from Reuleaux kinematic model collection
in Cornell University are given and some history of linkages discussed.
2004-04-21T00:00:00ZUsability, Learning, and Subjective Experience: User Evaluation of
http://hdl.handle.net/1813/2717
Usability, Learning, and Subjective Experience: User Evaluation of
Pan, Bing; Gay, Geri; Saylor, John; Hembrooke, Helene; Henderson, David
This paper describes an evaluation effort of the use of the
Kinematic Model for Design Digital Library (K-MODDL) in an undergraduate
mathematics class. Based on CIAO! framework, the research revealed usability
problems and users? subjective experience when using K-MODDL, confirmed the
usefulness of various physical and digital models in facilitating learning, and
revealed interesting relationships among usability, learning, and subjective
experience.
2004-02-27T00:00:00ZHow to Use History to Clarify Common Confusions in Geometry
http://hdl.handle.net/1813/2716
How to Use History to Clarify Common Confusions in Geometry
Taimina, Daina; Henderson, David W.
We have found that students and even mathematicians are often
confused about the history of geometry. Many expository descriptions of
geometry (especially non-Euclidean geometry) contain confusing and
sometimes-incorrect statements. Therefore, we found it very important to give
some historical perspective of the development of geometry, clearing up many
common misconceptions. In this paper we use history to clarify the following
questions, which often have confusing or misleading (or incorrect) answers: 1.
What is the first non-Euclidean geometry? 2. Does Euclid's parallel postulate
distinguish the non-Euclidean geometries from Euclidean geometry? 3. Is there a
potentially infinite surface in 3-space whose intrinsic geometry is hyperbolic?
4. In what sense are the Models of Hyperbolic Geometry 'models'? 5. What does
'straight' mean in geometry? How can we draw a straight line? We noticed that
most confusions related to the above questions come from not recognizing
certain strands in the history of geometry. The main aspects of geometry today
emerged from four strands of early human activity that seem to have occurred in
most cultures: art/patterns, building structures, motion in machines, and
navigation/stargazing. These strands developed more or less independently into
varying studies and practices that eventually from the 19th century on were
woven into what we now call geometry. In this paper we describe how these
strands can be used to clarify issues surrounding these questions.
2003-05-15T00:00:00Z3D-Printing the History of Mechanisms
http://hdl.handle.net/1813/2715
3D-Printing the History of Mechanisms
Lipson, Hod; Moon, Francis C.; Hai, Jimmy; Paventi, Carlo
Physical models of machines have played an important role in the
history of engineering for teaching, analyzing, and exploring mechanical
concepts. Many of these models have been replaced today by computational
representations, but new rapid-prototyping technology allows reintroduction of
physical models as an intuitive way to demonstrate mechanical concepts. This
paper reports on the use of computer-aided modeling tools and rapid prototyping
technology to document, preserve, and reproduce in three dimensions, historic
machines and mechanisms. We have reproduced several pre-assembled,
fully-functional historic mechanisms such as early straight line mechanisms,
ratchets, pumps, and clock escapements, including various kinematic components
such as links, joints, gears, worms, nuts, bolts, and springs. The historic
mechanisms come from the Cornell Collection of Reuleaux Kinematic Models as
well as models based on the work of Leonardo da Vinci. The models are available
as part of a new online museum of mechanism, which allows visitors not only to
read descriptions and view pictures and videos, but now also download, 3D-print
and interact with their own physical replicas. Our aim in this paper is to
demonstrate the ability of this technology to reproduce accurate historical
kinematic models and machines as a tool for both artifact conservancy as well
as for teaching, and to demonstrate this for a wide range of mechanism types.
We expect that this new form of ?physical? preservation will become prevalent
in future archives. We describe the background and history of the collection as
well as aspects of modeling and printing such functional replicas.
2003-07-31T00:00:00ZExperiencing Meanings in Geometry
http://hdl.handle.net/1813/2714
Experiencing Meanings in Geometry
Henderson, David W.; Taimina, Daina
It is deep experience of meanings in geometry (and indeed in all of
mathematics and well as art and engineering) that we believe deserve to be
called aesthetic experiences. We believe that mathematics is a natural and deep
part of human experience and that experiences of meaning in mathematics should
be accessible to everyone. Much of mathematics is not accessible through formal
approaches except to those with specialized learning. However, through the use
of non-formal experience and geometric imagery, many levels of meaning in
mathematics can be opened up in a way that most people can experience and find
intellectually challenging and stimulating. Many formal aspects of mathematics
have now been mechanized and this mechanization is widely available on personal
computers or even handheld calculators, but the experience of meaning in
mathematics is still a human enterprise. Experiencing meanings is vital for
anyone who wishes to understand mathematics, or anyone wishing to understand
something in their experience through the vehicle of mathematics. We observe in
ourselves and in our students that these are, at their core, aesthetic
experiences. In this paper we will tell some stories of our experience of
meanings in geometry and art. David's story starts with art and ends with
geometry, while Daina's story starts with geometry and ends with art. However
we both share the bulk in the middle, including experiences of non-Euclidean
geometries and kinematics models.
2003-05-15T00:00:00ZHow it was to study and to teach mathematics in Cornell at the end of
http://hdl.handle.net/1813/2713
How it was to study and to teach mathematics in Cornell at the end of
Taimina, Daina
Cornell University's Kroch Library Rare Book and Manuscript Division
has a collection called "Department of Mathematics records 1877-1976". It was
used already as case studies of the emergence of mathematical research at
Cornell University in several publications; but I will talk about my experience
going through these records and trying to imagine what mathematics students had
learned before entering Cornell University (looking at entrance exams they were
given). The earlier publications reported that mathematics entrance
requirements to Cornell "were minimal by today's standards" but I found that
this was not the case. Many of the students taking the entrance exams were
engineering students. At that time the Reuleaux kinematic models collection was
used to bring mathematical ideas into engineering curriculum. Preliminary
report partially supported by National Science Foundation's National Science,
Technology, Engineering, and Mathematics Education Digital Library (NSDL)
Program under grant DUE-0226238. (Based on a talk given at AMS- MAA Joint
Conference Special Session in History of Mathematics, January 18, 2003,
Baltimore.)
2003-05-01T00:00:00ZFranz Reuleaux: Contributions to 19th C. Kinematics and Theory of
http://hdl.handle.net/1813/2712
Franz Reuleaux: Contributions to 19th C. Kinematics and Theory of
Moon, Francis C.
This review surveys late 19th century kinematics and the theory of
machines as seen through the contributions of the German engineering scientist,
Franz Reuleaux (1829-1905), often called the "father of kinematics". Extremely
famous in his time and one of the first honorary members of ASME, Reuleaux was
largely forgotten in much of modern mechanics literature in English until the
recent rediscovery of some of his work. In addition to his contributions to
kinematics, we review Reuleaux's ideas about design synthesis, optimization and
aesthetics in design, engineering education as well as his early contributions
to biomechanics. A unique aspect of this review has been the use of Reuleaux's
kinematic models at Cornell University and in the Deutsches Museum as a tool to
rediscover lost engineering and kinematic knowledge of 19th century history of
machine.
2002-10-17T00:00:00Z