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  • DrD

    #20 -- A Question of Stability (Revised)

    By DrD

        Mechanics Corner
        A Journal of Applied Mechanics and Mathematics by DrD, #20
        © Machinery Dynamics Research, 2015
    A Question of Stability Introduction     The word stability in its several forms is widely used in nontechnical communication. A person whose life it highly consistent from day to day is said to have a stable life. When the political situation in a particular area appears to be unlikely to change, it is said to be stable. A person who is well balanced and unlikely to be easily provoked to anger is said to be a stable person. When the medical condition of a sick or injured person ceases to get worse, the person is said to be stabilized. A company on the verge of bankruptcy is said to be an unstable company. But what does the word stability mean in a technical context? Each of the foregoing examples hints at the technical meaning without really being explicit about it.   A factor g = accel of gravity was missing in the potential energy expression. That is now corrected.
        
     
        Stability.pdf
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  • DrD

    A Question for Readers

    By DrD

    Many of you have asked me various questions, so now it is my turn. Let me lay a bit of background first, and then the questions.   I have had some conversations recently with JAG (one of the other writers here at ME Forums) regarding the choice of software for 3D modeling and analysis. JAG has made some excellent suggestions, specifically a cloud based program called Onshape. Unfortunately, for reasons that are unclear, my computer cannot run Onshape; I have worked with their help people for several hours, all to no avail. JAG recommends this in part because there is a "free version for the hobbyist" and a relatively inexpensive "full version for the professional." That is pretty attractive, but since I can't run it, I'm stuck.   I gather that virtually all engineering colleges these days are teaching some sort of 3D modeling and analysis software, but that raises a few questions in my mind. 1. If your college teaches brandX 3D software, what will you do when you go to work for a small company that cannot afford anything more than 2D drafting (simple CAD), with no analysis capability at all? How will you do your job then? You probably have your own pocket calculator, but will you have your own copy of ANSYS or Pro-E? 2. What software does your school teach (every students should have an answer to this question, so I expect lots of replies on this one!)? 3. If you have used software extensively for analysis of engineering problems (beam deflections, stress analysis, fluid flow, heat transfer, etc), are you confident  that you will be able to work all of those problems if there is no such software available to you on the job?   I might add, as sort of a postscript, most of you know that I am older than dirt (I just had another birthday, so the situation is even worse!), so I tend to look at things from an elderly perspective. One of my great fears as a working engineer was "What will happen when I'm ask to do something that I don't know how to do?" It happened more than once, and it usually resulted in a flurry of intense research to come up to speed on whatever topic was involved. I could usually do that because I have a pretty good library, and I knew how to use a university library as well. But in terms of software, I was always concerned that I had no FEA program, so how could I do problems that others were doing by FEA? I have come up with some interesting work-arounds, including writing my own FEA for some problems, but I never wanted to be dependent on software that I could not afford to own. So, back to my questions about: How are you going to buy your own copy of ANSYS? DrD
    • 28 comments
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  • saurabhjain

    Calling Mechanical Engineers to collaborate on Twitter

    By saurabhjain

    If you are a mechanical engineering professional and have a twitter account .. we invite you in our mechanical engineering  campaign to collaborate on twitter.. Retweet the following status on https://twitter.com/mechportal/status/646544243649961985 Look forward for your presence. Regards Mechanical Engineeirng forum
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Our community blogs

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    Hi

    We are using planetary gear box to reduce the speed of ouput shaft. We are using Rack and pinion arrangement. Pinion is mounted on output shaft of the motor.

    The ouptut shaft is not rotating untill the last ring gear is stationary. To lock the last gear we have introduced the pin.

    But due to high Torque, pin is getting locked in the ring gear. it is not comming out even the Soenoid is discharged.

    So guys, need help in this to avoid locking of Pin in Ring gear.

    Regards,

    Amol Mane

  1. Welcome to Krish Piping Systems, we provide PIPING SOFTWARE TRAINING AND SOFTWARE INSTALLATION with quality and affordable price.

    Piping Software Training and Installations for PDS, PDMS, SP3D, SPPID,SPI,IN-TOOLS, SPEL, SPM, SPF, SPR,SPRD, SMART SKETCH, MICRO STATION, AUTO CAD, PLANT 3D, AUTO PLANT 3D, AVEVA PID, AVEVA INST, TEKLA STRUCTURES, SMART PLANT PUBLISHER, NAVIS REVIEW, PDMS REVIEW, CAT VIEW, SP MATERIAL.

    By Krish Piping Systems, Kukatpally, Hyderabad, Andhra Pradesh, India

    Knowledge Through Quality,

    Engineer Innovates New World.

    Contact Us: Krish Murali: 8686857553, Chakri: 9700275867

    e-mail: krishpsystems@gmail.com .

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    sable
    Latest Entry
    blog-0068202001369455131.jpg

    i am from china ,jiashan county ,it is not big ,but beautiful ,there is one small old town which is called xitang ,. It dates back to the Spring and

    Autumn Period (770 BC-476 BC) and the Warring States Period (476 BC-221 BC). The town was a place of strategic importance on the boundary

    of the Wu and Yue states. Its flat terrain is marked by a quiet, natural environment with rivers running through it. From a bird's-eye view of the

    whole town, one sees blue water sparkling almost in every point the eyes touch and reflections of the houses in the water. The quiet water,

    handsome bridges, and the reflections in the early morning and the rosy sunset, fishing boats and the glistening lights in the evening, form an

    amazing picture full of a sense of poetry which can only be seen in the south lower reaches of the Yangtze River. People there, whether local

    residents or visitors, feel that this is fairyland. They even have no idea as to whether people are wandering in the picture or the picture is moving

    in their hearts.

    my factory is only 15 minutes by car to xitang .....

    welcome

    www.ksobearings.com sablyoung@hotmail.com sales@ksobearings.com

    devoted to self-lubricating industry

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    Dear Construction Industry Professionals,

    It would be much appreciated if you would take two minutes to follow the below link and contribute to the results of my Undergraduate Research Project on Industry attitudes towards BIM. As ever, all information and data collected will be treated with the strictest of confidence

    https://www.surveymonkey.com/s/BIMIndustryAttitudes

    I am hoping to compare and analyse the results of my survey against the NBS Building Information Modelling Reports 2011 and 2013 results.

    Please bear in mind that to not have heard of BIM as a construction professional is a valid response in itself and offers interesting results analysing against previous data given so please be honest with your responses. I appreciate your time.

    My Kindest Regards

    Andrew R Turvey ICIOB

    Undergrad Student - University of Northampton (Bsc Construction Management)

  2. blog-0058824001362248818.gif

    All we are talking about here, is the flow simulation on a project car to analyze almost all necessary experiments before the car is on the track.

    Solidworks is the software that is used with the flow simulation add ins for this purpose. All aerodynamic experiments are thoroughly checked here on different perspectives although the real world experiences deflect from above one very slightly. But these studies are too much important.

  3. As we know designing is all about experience with knowledge, how u utilize it depends on you,,

    software are only tools to do all these in short time, with shortcuts

    but my suggestion is to learn things and not the software if u learn all the basics these software are only tools,u can learn them easily

    as we know piping is of three major branch layout, materials & stress . however some firms consider layout and materials as a same entity,

    for layout : taking MTO, developing layout, plot plan, isometrics, GAD are the basic functions.

    MTO: material take off: it is the list of items or materials required for the fabrication on site,or items required by piping.

    layout: layout is the arrangement of equipment, vessels, and all other required machines in plant.

    plot plan : plot plan is overall plan of a plant, including its road connectivity, nearby terrain , available facility etc.

    isometrics: isometrics is the piping drawing drawn in 3d view ( isometric view)

    GAD : GAD is general arrangement drawing arrangement of equipment on single sheet

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    Hi, I want to design a sensor who can mesure a force in direction x and a force in direction and moment Mx. I have to use strain gague in my sensor. I found some article about strain gauge and if we have some a force in one direction but my problem is that i cant find any ressource about combination of 2 force and a moment.does some one have an idea?i put article here.

    of course i can put 2 sensors in a orthogonal but I should have a balanced forces like this:

    Rc=fx.h/l-fy/2+Mx/l

    Rb=-fy/2-fx.h/l-Mx/l

    of course we have Rb and Rc, and we want to mesure fx,fy,Mx.

    if i put 2 sensors like orthogonal, i have Mx=fy.l+fx.l and i dont want it,

    is there any one who have idea for mesuring 3 value with strain gauge??

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    blog-0385823001358696318.jpg

    What is CATIA?? And why choose?

    ,if you are thinking,what is Catia,then i thinks you're at right place.

    Here are Top ten reason why to choose Catia?

    if you think i missed some,please share your knowledge with us.

    CATIA Stands for Computer Aided Three-dimensional Interactive Application

    1.CATIA is a designing software to design most complex mechanical components within their material selection.

    2.Almost every design can made in CATIA.

    3.Aerospace industry almost depend on it.

    4.Most Accurate.

    5.Its a P.L.M. (Product life-cycle management)

    what is PLM?

    refer this link =http://en.wikipedia.org/wiki/Product_lifecycle_management

    6.A variety of tools.

    7.Famous worldwide.

    8.Interesting software(Addicted)

    9.Easily manage all parameters for less material loss.

    10. it can learn from only few authorized centers,not everyone can manage its license,due to its high accuracy and cost(12 lacks approx)

    (in English usually pronounced /kəˈtiə/) is a multi-platform CAD/CAM/CAE commercial software suite developed by the French company Dassault Systemes.since 1981. Written in the C++ programming language,CATIA competes in the high-end CAD/CAM/CAE market with Siemes NX.

  4. Dear All

    I want to design a crank shaft for single cylinder, single stage compressor. I am not that much aware of the forces and stress acting on it and what are the things to consider. Is there any standard available for this. If so, kindly advice.

    Thanks & regards

    Satheesh

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    Asim Sarwar
    Latest Entry

    It’s fun,

    It’s entertaining,

    & It’s back!!!

    That’s right…..

    ASME GIKI Chapter (Pakistan) is organizing one of the most anticipated events of the year the 2nd International Mechanical Engineering Convention from 19th - 21st April, 2013. IMEC 2013 includes modules that have been designed to give you the true essence of Mechanical Engineering. This mega event brings you all the awesome and the most overwhelming activities all in one single event. It is going to be one of the biggest and most exciting conventions all over the world. Most of the modules are open to everyone. Hobbyists are especially encouraged to participate from all over the world. It doesn’t matter whether you are a mechanical engineer or not. You only need to have the will to participate and a creative mind in order to win the modules.

    IMEC 2013 includes:

    Human Powered Vehicle Contest

    Climate Control Challenge

    Rapid Design Competition

    Mind Crunch

    Xploneering Pakistan

    MENSA IQ Test

    Team Activities

    And much more.

    The details regarding all the modules will be available shortly. Stay Tuned for a lifetime experience!

    For Info please contact us at asme@giki.edu.pk

    Or log onto www.giki-asme.com

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    The Gryroscopic Couple which acts on a particular body like an Aircraft,ship,automobiles etc;It has been proved through observations which take place in the body or there is a real cause which has a force which causes the body to raise the nose or tail?

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    Hello friends,

    as we know about six stroke engine in which 5th & 6th strokes are only different.

    As our conventional four strokes get completed fifth strokes will take place in which water is sucked from third valve. As working tempurature of engine around 100 c so it will immediately converted to steam and volume will expand to about 1400 times so it will make power stroke. Than in 6th stroke that steam will get exhausted and normal first stroke will take place.

    So on this pls answer my few questions....

    1) What is the power generated when water turns to steam in fifth

    stroke? And how much water is taken?

    2) How much temperature goes down when water absorb energy

    form engine to get converted to steam?

    3) Is there any disadvantage of six stroke engine?

    4) Where do we find application of six stroke engine currently

    going on?

  5. Wish & Win! Did you ever experience sealing issues with your equipment? Or, when working on new machine design?

    Trelleborg Sealing Solutions wants you to share these issues you'd like to see solved! Enter your wishes, ideas, issues, and just plain how we can help you solve your sealing problem.

    Please submit your case on www.forum.seals-innovation.com .

    Should your thoughts be chosen, there's 5,000 € prize waiting for you.

    To start your brainstorming, here are some ideas...

    Ideas for Today

    - General sealing issues that people would finally like to see solved

    - Challenges resulting from current or upcoming design projects

    - Ideas on how sealing technology could add more value to equipment

    - Ways of adding sustainable value to sealing solutions

    - Improvement of processes in cooperation with customers

    - Innovative developments for services

    - Recommendations for digital engineering tools

    Ideas for Tomorrow

    - Suggestions on which direction sealing technology should take in the future

    - Ideas for future focus areas for Trelleborg Sealing Solutions R&D

    - Predictions of future trends and changes to machine design which would affect sealing technology – and thoughts on how to deal with these challenges

    - Visions on future processes and cooperation between equipment manufacturers and suppliers

    - Proposals on services to be offered by suppliers in the future

    The final deadline for idea submission has been extended to February 28, 2013.

    Please submit your case on www.forum.seals-innovation.com .

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    Hey engineers, I have a design project as a course of my study but don't know how to start and doing stuff like parts calculations and the required equation so if anybody can help me to do this project i'll be so thankful..

    The project says that: Design a drum dumper. The machine is to raise a 55-gal dmm of bulk material from floor

    level to a height of 60.0 in and dump the contents of the drum into a hopper.

  6. Randstad USA is currently looking for a Mechanical Engineer Manager in the East Volusia county area. Our client is specifically looking for someone who has at least fifteen years of experience including six years specialized in medical devices. Please feel free to contact me via email at ginny.farrens@randstadusa.com or by phone 386-615-1388.

  7. What input an design engineer gets from a company? I am doing drafting from 6 months in a company . what role does a design engineer do in a company with 1 year experience ?

  8. cam-follower-mechanism.gif

    I have added this gif file so that you can instantly get idea of my cam follower prototype for clean energy.

    You can see cam follower mechanism for clean energy cheaper than coal. My cam follower mechanism is different than today’s cam follower. In general cam follower system,

    cam shaft is rotated and follower move up and down according to cam profile.

    In my cam follower system,

    1. Follower is offset.

    2. Force is applied from follower to cam and by using this force cam is rotated.

    3. We can decide how much follower come down for helping cam to rotate particular circumference length.

    4. Follower down 6 cm with 100 kg and rotate cam of 27 cm at 70 kg.

    5. Input energy we use to move follower is =0.06*100 =6 N-Meter

    6 Out put energy we get on cam = 0.27*70 = 18.9 N-Meter

    You can find prototype at http://mechanicalresearch.info/

    http://www.youtube.com/user/MyJigarpatel/featured

  9. For details, click: http://www.suvidhajobs.com/online_training.php

    Are you working in Design engineering, construction, EPC, Petroleum, Automotive and Aerospace Industry?

    If yes, we offer short term training courses to enhance your skills. We are connected though a network of Engineering Training Institutes across the globe. Just fill in the form given on the right side and send your training requirements, we will soon revert back to you. We offer personal as well as corporate training solutions in engineering domain. At present we offer courses in the following domains.

    PDMS – piping

    Basic Piping Design

    Smart Plant Instrumentation – Corporate Training Only

    Basic process design for Chemical engineers

    Structural design

    HSE/NEBOSH

    PMP Certification

    Caesar – II – Stress Analysys course for mechanical engineers

    CAD/CAM/CAE – Hypermesh/LS Dyna/Abaques – For Automotive and Aerospace domain

    SAP – IS – Oil and Gas

    Basic Petroleum Engineering Practices

    NDT – Training, ASNT Level II, Level III

    If interested to undergo training in any of the above courses,

    email us at: sales@suvidhajobs.com,

    Contact Persons: Gijo.Vijayan/Sumit Kumar

    Mobile: 0091-7250288088, 7739307360

    For details, click: http://www.suvidhajobs.com/online_training.php

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    Ashraf_9326
    Latest Entry

    Nano Technology is one of the best emerging and innovative technology Today... Here is Some Link from where You Can some more information.

    NANOTECHNOLOGY

    NANO – INTERNAL COMBUSTION ENGINE

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    Cheryl Chapman
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    hi

    can you tell me

    any device that one

    sound energy convert into electrical energy??

    but that device should be a miniature/not big more then 15 cm sq!!!!!!!!!

  10. [This blog is a repost from my other blog site, thought would be useful to Mechanical Engineering readers]

    Now every mechanical engineer uses CAD softwares. Weather software is SolidWorks, SolidEdge, Inventor or CATIA, Creo or UG-NX it has same theory of CAGD and Computational Geometry. Unforuntaly we in Mechanical Engineering does not have subjects to taught this in detailed. I hope this blog series helps you to understand What Lies Benith Your CAD Software !!! biggrin.png

    Mechanical CAD solid models are consisting of geometry and topology. Geometry by virtue of its visualization capability is easy to understand and comprehend. Topology is on the other hand, more of pure virtual concept hence many find it difficult to understand. In this article brief introduction to manifold topology is illustrated. Intended audience is new CAD developers or students of computational geometry.

    Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Many scientists have made contribution to its theory and lot has changed since Euler first laid foundation stone of Geometry. Following is brief review of the development.

    Euclid 300 BC, also known as Euclid of Alexandria, was a Greek mathematician and is often referred to as the Father of Geometry. His work “Elements” is the most successful textbook in the history of mathematics. In “Elements”, the principles of what is now called Euclidean geometry were deduced from a small set of axioms. The geometrical system described in the “Elements” was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the 19th century.

    Euclid undertook a study of relationships among distances and angles, first in a plane (an idealized flat surface) and then in space. An example of such a relationship is that the sum of the angles in a triangle is always 180 degrees. Today these relationships are known as two- and three-dimensional Euclidean geometry. An essential property of a Euclidean space is its flatness. Important point to note is other spaces exist in geometry that are not Euclidean. For example, the surface of a sphere is not; a triangle on a sphere (suitably defined) will have angles that sum to something greater than 180 degrees.image002.jpg

    Next major contribution in Geometry came after around 2000 year by Leonhard Paul Euler (15 April 1707 – 18 September 1783). In 1736, Euler solved the problem known as the Seven Bridges of Königsberg. The city of Königsberg, Prussia was set on the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point. It is not: there is no Eulerian circuit. This solution is considered to be the first theorem of graph theory, specifically of planar graph theory.

    image003.jpg

    In the processEuler also discovered the formula V − E + F = 2 relating the number of vertices, edges, and faces of a convex polyhedron, and hence of a planar graph. The constant in this formula is now known as the Euler characteristic for the graph (or other mathematical object), and is related to the genus of the object. The study and generalization of this formula, specifically by Cauchy and L'Huillier, is at the origin of topology.

    Next path breaking contribution was from Georg Friedrich Bernhard Riemann (September 17, 1826 – image009.jpgJuly 20, 1866) an extremely influential German mathematician who made important Non-Euclidean geometries. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory. Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean. The subject founded by his work is Riemannian geometry. Riemann found the correct way to extend into n dimensions the differential geometry of surfaces. The fundamental object is called the Riemann curvature tensor. For the surface case, this can be reduced to a number (scalar), positive, negative or zero; the non-zero and constant cases being models of the known non-Euclidean geometries. contributions to analysis and differential geometry. He was first one to discover

    Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives in particular local notions of angle, length of curves, surface area, and volume. From those some other global quantities can be derived by integrating local contributions. Riemannian geometry deals with a broad range of geometries categorized into two standard types of Non-Euclidean geometry,spherical geometry and hyperbolic geometry, as well as Euclidean geometry itself.

    Non-Euclidean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, while in elliptic geometry, any line through A intersects l.

    400px-Noneuclid.svg.png

    Another way to describe the differences between these geometries is as follows: Consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line. In Euclidean geometry the lines remain at a constant distance from each other, and are known as parallels. In hyperbolic geometry they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultra parallels. In elliptic geometry the lines "curve toward" each other and eventually intersect.

    We started discussing how we end up in geometry discussion? I felt it was necessary to create basic understanding of historical development of Euclidean Geometry and Non-Euclidian geometry to understand next topics.

    image011.jpg

    As we saw earlier Euler was first one publish paper on topology in seven bridge problem demonstrating that it was impossible to find a route through the town of Königsberg that would cross each of its seven bridges exactly once. This result did not depend on the lengths of the bridges, nor on their distance from one another, but only on connectivity properties: which bridges are connected to which islands or riverbanks. In other words to solve many of geometric problems we do not need to know spatial information but what is requiring to be known is neighborhood or connectivity information termed as topology.

    Problems like a Möbius strip, an object with only one surface and one edge; such shapes are alos an object of study in topology.

    image012.jpgJules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician and theoretical physicist, and a philosopher of science.

    As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory.

    He was a founder of topology, also known as “rubber-sheet geometry,” for its focus on the intrinsic properties of spaces.

    From a topologist’s perspective, there is no difference between a bagel (shape like torus or from Indian menu medu wada J ) and a coffee cup with a handle. Each has a single hole and can be manipulated to resemble the other without being torn or cut. Poincaré used the term “manifold” to describe such an abstract topological space.

    Mug_and_Torus_morph.gif

    The simplest possible two-dimensional manifold is the surface of a soccer ball, which, to a topologist, is a sphere—even when it is stomped on, stretched, or crumpled. The proof that an object is a so-called two-sphere, since it can take on any number of shapes, is that it is “simply connected,” meaning that no holes puncture it. Unlike a soccer ball, a bagel is not a true sphere. If you tie a slipknot around a soccer ball, you can easily pull the slipknot closed by sliding it along the surface of the ball. But if you tie a slipknot around a bagel through the hole in its middle you cannot pull the slipknot closed without tearing the bagel.

    image013.jpg

    Euler- Poincaré equation

    Euler’s polyhedron formula was applicable to only simple polyhedron. This new equation from Poincaré provides relationship between topological elements for any single two-manifold body.

    V -E + F - Li = 2(1 - G)

    where,

    V : Number of vertices.

    E: Number of edges.

    F: Number of faces.

    Li: Number of interior loops.

    G: Genus, the number of closed paths on a surface which do not separate the surface into more than one region. Or, genus is the number of handles to be added to a sphere to make it homeomorphic to the object.

    Classification of manifolds

    · 0-manifold is just a discrete space. Eg Point in Cartesian space corresponds to vertex in topological space. Point or set of points are zero dimensional manifolds

    · 1-manifold is curve in Cartesian space. Eg circle, line, parabole b-spline curve (non intersecting)

    · 2-manfold is surface Cartesian space. Sphere (empty inside), torus, plane, cylinder, b-spline surface (if closed empty inside, orientable and non self-intersecting ) , circular disc

    · 3-manfold is 3 dimensional manifold. Eg Solid Objects, Solid Sphere, Solid Cylinder, Our universe J

    Two-dimensional manifolds were well understood by the mid-nineteenth century. But it remained unclear whether what was true for two dimensions was also true for three. Poincaré proposed that all closed, simply connected, three-dimensional manifolds—those which lack holes and are of finite extent—were spheres. The conjecture was potentially important for scientists studying the largest known three-dimensional manifold: the universe. Proving it mathematically, however, was far from easy. Most attempts were merely embarrassing, but some led to important mathematical discoveries, including proofs of Dehn’s Lemma, the Sphere Theorem, and the Loop Theorem, which are now fundamental concepts in topology.

    By the nineteen-sixties, topology had become one of the most productive areas of mathematics, and young topologists were launching regular attacks on the Poincaré. To the astonishment of most mathematicians, it turned out that manifolds of the fourth, fifth, and higher dimensions were more tractable than those of the third dimension. By 1982, Poincaré’s conjecture had been proved in all dimensions except the third. In 2000, the Clay Mathematics Institute, a private foundation that promotes mathematical research, named the Poincaré one of the seven most important outstanding problems in mathematics and offered a million dollars to anyone who could prove it.

    image014.jpg

    After nearly a century of effort by mathematicians, Grigori Perelman sketched a proof of the conjecture in a series of papers made available in 2002 and 2003. The proof followed the program of Richard Hamilton. Several high-profile teams of mathematicians have since verified the correctness of Perelman's proof.

    The Poincaré conjecture was, before being proven, one of the most important open questions in topology. It is one of the seven Millennium Prize Problems, for which the Clay Mathematics Institute offered a $1,000,000 prize for the first correct solution. Perelman's work survived review and was confirmed in 2006, leading to him being offered a Fields Medal, which he declined. The Poincaré conjecture remains the only solved Millennium problem.

    This article was written with the help of various sources of web sources, mainly Wikipedia. Intention is to explain interesting subject such as manifold which carries paramount importance in CAD development in less mathematical and elaborative manner. Research in Manifolds is as recent as 2006 and is one of the most studied area in mathematics.

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    Hi friends,

    We are pleased to inform you that our team has created a website "techno-zeal" (forwarding url: www.pjbindass.com) with a purpose to share the knowledge among students & working professionals from Engineering background specially for Mechanical design. This website contains projects ideas, interview experience of many PSUs and other relevant content. We are also dedicated to provide free online assistance for learning and projects execution. Although we did our best to keep the content simple and easy to understand. We are also planning for the content of other branches of engineering as well as the content from medical domain. There are still pages like PSUs Guide and B.Tech project ideas, that is common to all engineering branches.

    We need your cooperation to make our service better and having a quality content to help students achieving their goals.

    Please visit the website and provide your valuable suggestions.

    We thank you for your time and consideration.

    Regards,,

    Admin-techno-zeal

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    Recent Entries

    abhisonu.ranjan
    Latest Entry

    Hii every one, I am a 3rd year mechanical student from New Delhi, INDIA, i and my some freinds want to make a F1 car, very much intrested and want to participate in SAE BAJA and Supra, Can any one tell me what is the procedure of making it and executing a best project, or post me some helpful links.

    Thank You

    Abhijeet Ranjan

    (a.ranjan.gbu@gmail.com)

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