3-D Printing the History of Mechanisms
Hod Lipson
e-mail:hod.lipson@cornell.edu
Francis C.Moon口译资料
Jimmy Hai
Carlo Paventi
School of Mechanical and Aerospace Engineering, Cornell University,Ithaca,NY,14853,USA
Physical models of machines have played an important role in the history of engineering for teaching,analyzing,and exploring me-chanical concepts.Many of the models have been replaced to-day by computational reprentations,but new rapid-prototyping (RP)technologies are now allowing reintroduction of physical models as an intuitive way to demonstrate mechanical concepts. This paper reports on the u of RP to document,prerve,repro-duce,and share in three dimensions,historic machines,and mechanisms.We have reproduced veral preasmbled,fully functional historic mecha
nisms from the Cornell Collection of Reuleaux Kinematic Models,and made the available as part of a new online muum of mechanism:Not only can visitors read descriptions,view pictures and videos,and interact with simula-tions of machines,but they can now also download and3D-print their own physical functional replicas.We expect that this new form of“physical”prervation will become prevalent in future archives.͓DOI:10.1115/1.1902999͔
1Introduction
The u of physical models in engineering has had,until the last
quarter century,a long and uful history.This is especially true in
machine design and engineering.Filippo Brunelleschi͑1377–
1436͒,the architect and engineer of the Duomo in Florence is
known to have created construction models,including machines.
In later centuries Christopher Polhem͑1661–1751͒in Sweden cre-
ated a“mechanical alphabet”of models for machines.Robert Wil-
lis͑1800–1875͒of Cambridge was also known for his kinematic
teaching models though few have survived.Franz Reuleaux ͑1829–1905͒of Berlin created the world’s largest collection of kinematic models at the Technical University of Berlin with over
800models.Most of this collection was destroyed in the cond
world war,though there are60models in the Deutsches Muum
in Munich.However,Reuleaux authorized and supervid the re-
production of approximately360mechanisms by the model maker
husterthe time of my lifeV oigt͓1͔.Another model maker,J.Schroeder of Darmstadt,also
created kinematic models bad on the books of Reuleaux and
Redtenbacher,which were later produced by the model works of
Peter Koch.Some of the models of Schröder and V oigt are in
collections in Europe,North America,and Japan.A recent confer-
ence on the history of machines and mechanisms contains veral
papers related to Reuleaux͓2͔.We have published two reviews of
Reuleaux’s ideas and u of kinematic models͓3,4͔.Descriptions
of some of the models may be found in Reuleaux’s books,pub-
lished in English translation͓5͔and The Constructor͓6͔.The earlier kinematic models of Willis also show the u of kinematic models͓7͔.
Cornell University was fortunate to have purchad a substan-tial part of the V oigt–Reuleaux models in1882.A history of this collection͓3͔shows that the models were ud for teaching machine design up until the1970’s.A new generation of academ-ics has again found the models uful for teaching and rearch. Also a number of scholars,engineers,and artists have begun to travel to Ithaca to e the Reuleaux Collection.As a result,Cor-nell University has decided to document and make the collection available on the World Wide Web as part of the U.S.National Science Digital Library͑NSDL͒.The kinematic collection com-pris230models from the V oigt catalog,a dozen models from the Schroeder works and a Robert Willis model made in Paris͓4͔, as well as various other instru
永远相伴ments.Cornell also has models and artifacts from Robert Thurston,who was an expert and historian on the steam engine.The University Library has a substantial collection of original19th century machine design books of Wil-lis,Laboulaye,Reuleaux,Rankine,Redtenbacher,Burmester, Kennedy,Thurston,and others along with earlier so-called“the-atre of machines”books by Besson͓8͔,Ramelli͓9͔,Bockler͓10͔, and Leupold͓11͔,as well as facsimiles of the notebooks of Le-onardo da Vinci.The combined collections of both physical kine-matic models and rare books on the history of machines at Cornell is a unique combination of resources matched only by larger in-stitutions such as the Deutsches Muum in Munich and the Smithsonian Institution in Washington,D.C.
To share this collection,Cornell has recently created an online muum that contains most of the Reuleaux models with math-ematical and historic annotation,pictures,movies,animations, and simulations͓12͔.Many of the above-cited historic books are digitized and referenced in the relevant web portal page of each of the kinematic models.Each of the models contains descriptive and historical text.To e the models in action,we also created ani-mations of many of the models.A special goal was to create the opportunity for the web site ur to interact with the models through simulations,such as offered by the Kyoto University Mu-um collection of19V oigt–Reuleaux models,which were mod-eled in a CAD program and animated with the multibody dynam-ics code͓13͔.
What cannot be experienced with a web collection,however,is the physical handling of the models.Although physical models of machines were prevalent in early exhibitions and universities, their u has been largely replaced today by CAD models and simulations.The computational models are more versatile and of lower cost,but they lo the physical embodiment that is es-ntial for an intuitive appreciation of many critical concepts of motion and force,such as friction,damping,backlash,compli-ance,geometric tolerances,surfacefinish,and dynamics.How-ever,new rapid-prototyping technology allows reintroduction of physical models as an intuitive and simple way to demonstrate the fundamental mechanical concepts.We now u the web to integrate both the textual and artifact collections on the history of machines and mechanisms.Besides reading textual descrip-tions,viewing pictures and videos,and interacting with simula-tions,visitors may now also download,3D-print,and interact with their own fully functional physical replicas.We expect that as rapid-prototyping becomes more commonly available,such forms of documentation will become increasingly prevalent.
23D Printing of Kinematic Models
To document the Reuleaux models,CAD models of veral mechanisms were made.The models were constructed as asm-blies of parts constrained by kinematic and geometric interfer-ence.Besi
des exporting the models as drawings,rendered3D images and animations,they may be exported for printing on rapid-prototyping fabricator as afile in STL format.Thisfile de-scribes the surfaces of the object as a tesllation of triangles.
Contributed by the Mechanisms and Robotics Committee for publication in the
J OURNAL OF M ECHANICAL D ESIGN.Manuscript received:June23,2004;revid
October17,2004.Associate Editor:Gordon R.Pennock.
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Copyright©2005by ASME
ping是什么意思
There are veral rapid prototyping technologies,including laminated object manufacturing ͑LOM ͒,lective lar sintering ͑SLS ͒,photopolymerization ͑stereolithography,SLA ͒,and fud deposition modeling ͑FDM ͒.The FDM process was ud in this study to reproduce veral Reuleaux–V oigt kinematic models.The process creates a quence of thermoplastic layers from a filament wound coil that is heated and extruded through a nozzle.The trajectory of the nozzle is derived from the triangle mesh,so as to raster scan and fill solid volumes.In order to create functioning mechanisms,a
cond,soluble relea material is placed in the gaps between the movable parts.The basic material ud was acrylonitrile-butadiene-styrene ͑ABS ͒.Information on the mate-rials can be obtained from Montero as well as from the manufac-turer ͓14͔.
Various kinematic components have been created before and even featured on some manufacturers’web sites.Similarly,simple joints and preasmbled robot morphologies have been printed ͓15–19͔.Our aim in this paper is to demonstrate the ability of this technology to reproduce complete,functional,preasmbled,and accurate historical kinematic models and machines as a tool for both artifact conrvancy and for teaching,as well as to demon-strate the applicability to a wider variety of mechanisms.We have reproduced veral preasmbled,fully functional historic mecha-nisms 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.
Some models are shown in Fig.1:A slider crank allowing multiple inversions,a double slider crank,a ratchet mechanism with three spring-loaded stoppers,a worm-gear transmission,a double-chamber leaf pump,and a clock escapement.
Other models are available online at the Kinematic Machines for Design Digital Library ͓12͔.
3Reproduction Challenges and Model Authenticity
It is clear from viewing and handling the Reuleaux models that they were carefully designed to follow his ideas of kinematics theory.Reuleaux’s major contributions to kinematics includes the notion of lower and higher kinematic pairs,kinematic chains,in-version of mechanisms,rolling centrode curves,aesthetics in ma-chine design and kinematic synthesis and invention.The models made by Gustav V oigt were inscribed with letters and numbers of the links and the joints corresponding to the diagrams in Reu-leaux’s classic text on the Kinematics of Machinery in 1875/1876.Many of the models were designed such that one could fix different links in the kinematic chain and obtain three or
four
Fig.1Sample printed models.…a …Original models …left …and printed reproduction …right ….Top:slider crank;Middle:Scotch–Yoke mechanism;Bottom:A ratchet mechanism with three spring-loaded pawls.…b …Original models …left …and printed reproduction …right ….Top:Worm gear mechanism;Middle:A double-chamber leaf pump;Bottom:A clock escapement mechanism
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kinematic inversions.In some models,such as the curves of con-stant width or the positive return cams,the centrode pairs are inscribed on glass platesfixed to the mechanisms.Reuleaux de-signed the pedestal of each model according to aesthetic prin-ciples outlined in his other classic text on machine design,The Constructor͑1854–1893͒.In this work he advid the designer that the choice of smooth aesthetic curves will likely bring the machine element clor to an optimum constant stress design. Thus the pedestals in the Reuleaux models exhibit beautifulflow-ing curves.Finally,Reuleaux cho materials of brass and cast iron that have stood the test of time with very little wear and rust. He boasted in his letter to the President of Cornell University of 1882that he had a special heat treat
ment method that would pro-tect the iron from the perspiration of many students hands. The qualities of the models in this collection guarantee that their reproduction in today’s market would be very expensive͑the Cornell t of approximately250models cost$8000in1882 American dollars͒.Providing a less expensive reproduction method in cheaper materials,such as thermoplastics,is afine goal. However basic limitations of the rapid prototyping process leads to certain necessary compromis.Specifically,we strived to make every model printable as a single,preasmbled unit,so that it is fully functional right out of the printer.This necessitates careful consideration and,in some cas,redesign of some fea-tures of the model.We thus sacrifice some dimensional authentic-ity for functional authenticity.
3.1Clearance between Moving Surfaces.One of the major differences between the preasmbled printed copies and the originals is the clearance between moving parts.The printing pro-cess cannot directly leave the tight mating between parts.Instead the process either leaves an air gap,if possible,or puts in waste support material:This material is later dissolved,melted,etched, or blown away.The clearance between parts is on the order of 0.4mm in our ca,a rather large gap—an order of magnitude greater than the originals.The large gaps affect the rigidity of the mechanism,add backlash effects,and become detrimental when
tight surfaces are critical for functionality,such as in pumps.This necessity for large gaps originates in veral reasons: Relea:Ensuring the surfaces do not fu together while printing.
Friction:Printed models do not have any lubrication,so a large gap helps reduce friction.This is especially true for process that have low surfacefinish quality.
Etching pathways.Most rapid prototyping process require a condary process for removing support material,by dissolving, melting,blowing,or etching or by manual removal.If gaps are too tight,the solvents cannot reach the material to be removed and/or the dissolved material cannotflow out.Conquently,the design is typically modified to allow easy pathways for removal of relea materials.
Large gaps typically result in loofits among parts.In some precision instruments,the gaps will make a mechanism inoper-able and must be compensated for.For example,Fig.2shows a horizontal shaft under load.If the shaft is printed horizontally with gapsfilled with support material͓Fig.2͑a͔͒,then the shaft will lo its alignment once the support material is removed͓Fig. 2͑b͔͒.To ensure that the shaft remains horizontally aligned after support materials are removed,the geometry must be compen-sated in advance,for example as shown in Fig.2͑c͒.Similar but more complex compensations need to be carried out for more elaborate mechanisms.
3.2Strength and Compliance.Another issue is the strength of the rapid prototyping material itlf.For example,Reuleaux’s brass handles on his models have a beautiful shape that is fragile in the ABS plastic.Several aspects affect the strength of the printed mechanism:
Material:Various materials can be ud,affecting the durabil-ity of the resulting mechanism.A typical ABS product is far weaker than the original.Weak points and stress concentration points may need to be reinforced.
Warping:Thermoelastic warping may occur during cooling of the material after deposition,leading to warping and misalignment that is especially noticeable on planar surfaces.Reinforcement brackets,fillets,and ribs are often needed to be inrted to coun-teract the effects.
Deposition pattern.Becau the deposition process is lay-ered and,with some process alsofibered,the material’s me-chanical behavior approximates laminated material͑e.g.,compos-ites͒orfibrous material͑e.g.,hardwood͒more than it does a solid material.Thus the material properties end up being largely depen-dent on the orientation of the part and exact deposition pattern.It is therefore desirable to t the mechanism at a state such that it may be printed withfibers along the length of load gradients.New materials and deposition process may alleviate this problem in the future.
Compliance.The elasticity of the material may be uful when printing compliant mechanisms such as springs.However,in such components the geometry interacts with the material properties,so that the geometry must be changed to achieve certain kinematic behavior.This is demonstrated in the printing of the spring loaded-ratchet mechanism,in which leaf-springs length and width needed to be adjusted to produce the proper functionality͓Fig. 3͑b͔͒.
Weight:In some models the difference in weight between the original model and the printed replica may cau functional dis-crepancies,especially when dynamic behavior is involved.For example,the pendulum of the clock in Fig.1is too light,as printed,to sustain momentum;it must be enlarged͑or printed with other materials͒to be functional.
3.3Preasmbled Fasteners and Markings.From a
blundering
peda-Fig.2Misalignment caud by large gap requirements:…a…A loaded shaft printed with gapsfilled with support material;…b…will misalign when support material is removed;…c…shaft mis-alignment is precompensated so that…d…final functioning model will perform properly.More complex compensations need to be carried out for more elaborate mechanisms
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gogical point of view,many of the Reuleaux models can be de-mounted so they can be remounted with another fixed link to form an inversion.The V oigt models have fine screws for demounting the mechanism from the pedestal,which are difficult to replicate in the plastic with their original diameter and pitch,again becau of the large gaps necessary between movable parts.To replicate the fasteners and inversion capabilities,we modeled fasteners with an enlarged diameter and pitch ͓Fig.3͑a ͔͒.
Many of the models have links and bearings inscribed with numbers and letters.This is difficult to replicate becau of the digital nature of the layering process which sometimes produces a fine stepped finish;however,depending on the orientation,suffi-ciently large fonts have been reproduced.
Putting the caveats aside however,the FDM produced copies of the Reuleaux models are remarka
bly visually true to the origi-nals as shown in a comparison in Fig.1.The models are fairly robust to u and move.The cost and time to produce one is a fraction of that necessary to manufacture a traditional copy in iron and brass,but require veral days to model and adjust for print-ing.A half scale model of the slider crank took approximately 10h in the FDM machine ͑Stratasys FDM 3000͒.A full scale model took substantially more time,over 40h.Some time and material can be saved,however,if one designs in some cavities in some of the parts such as the ba and the pedestal.We expect many of the caveats to largely disappear in the future as the printing technology improves.
3.4Model Sharing Challenges.The current market of rapid prototyping equipment has not yet reached the level of maturity that would enable a single file to be made suitable for all varieties of rapid prototyping process.The current de facto industry stan-dard for exchange of rapid prototyping data is the STL file format,which is a relatively information-poor reprentation of the target model,omitting many important functional and material aspects of the target object.We have found that the greatest varying factor among current machines,relevant to our application,is the mini-mal allowable gap size,and so we typically provide veral model files with varying gap widths among moving surfaces.We expect that future file rapid prototyping formats and automated process
planning will allow for specifying much of this information in a technology-independent way,and have the rapid prototyping equipment itlf adjust the model and process automatically ͓20,21͔.
4Conclusions
Physical models of machines have played an important role in the history of engineering for teaching,modeling,and exploring mechanical concepts.Many of the models have been replaced by computational reprentations,but new rapid-prototyping tech-nology allows reintroduction of physical models as an intuitive way to demonstrate mechanical concepts.This paper reports on the u of computer-aided modeling tools and rapid prototyping technology to document,prerve,and reproduce in three dimen-sions,historic machines,and mechanisms.We have reproduced veral preasmbled,fully functional historic mechanisms such as early straight line mechanisms,ratchets,pumps,clock escape-ments and counting devices,including various kinematic compo-nents such as links,joints,gears,worms,nuts,bolts,and springs.In an online muum of mechanism,not only can visitors read descriptions,e pictures and watch movies of mechanisms,but they may now also download,3D-print and interact with their own physical replicas.
Our aim in this paper is to demonstrate the ability of this tech-nology to reproduce accurate historical
kinematic models and ma-chines as a tool for both artifact conrvancy as well as for teach-ing,and to demonstrate is applicability to a wide range of mechanism types.Though the objects demonstrated in this paper were replicas of existing Reuleaux models,the potential scope is clearly much broader:One can realize many historical
concepts
Fig.4Leonardo da Vinci’s version of a slider crank and end-less screw:…a …Original drawing;…b …rapid prototype
妈妈英文model
Fig.3Cloup of components:…a …screw with thread and nut in prismatic joint;…b …three loaded ratchet springs.All parts printed preasmbled in one pass.
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实习推荐信that exist only on paper,such as Leonardo da Vinci’s slider crank mechanism͑Fig.4͓͒24–26͔,as well as other models that exhibit more contemporary concepts from aerodynamics to molecular bi-ology.Independent of the specificfields of applications,the in-cread accessibility of the models through electronic sharing, dismination,and rapid prototyping greatly increas the incen-tive for designing them.
We expect that this new form of physical prervation will be-come prevalent in future archives.As rearch in rapid prototyp-ing advances to allow for more durable materials and more accu-rate,faster and cheaper production,more elaborate machines may be printable by a growing community around the world.More-over,as new rearch leads to multimaterial functional freeform fa
brication,we expect that incorporation of elastomers,lubricants, actuators,and nsors,electronics and power devices͓22,23͔will allow faithful replication and electronic sharing of an ever-increasing scope of physical models and artifacts. Acknowledgments
This work has been supported in part by the U.S.Institute of Muums and Library Services͑IMLS͒Grant No.LG-30-04-0204-04.The and other models are available online at the Ki-nematic Machines for Design Digital Library at ll.edu which was created as part of the U.S. National Science Foundation’s National Science Digital Library ͑NSDL͒Program.CAD/STL Model contributions are welcome. References
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