Optomechanics with LEGO - OSA Publishing

Optomechanics with LEGO F. Quercioli, B. Tiribilli, A. Mannoni, and S. Acciai

The basic elements of a fairly complete optomechanical kit based on the use of LEGO are presented. Taking advantage of the great variety of standard LEGO elements, and adding a few custom components made of Plexiglas, we show how most of the mechanical parts of an optical setup can be built with little effort and at an extremely reduced cost. Several systems and experiments are presented, mainly in the fields of optical filtering and interferometry, to show that the proposed mounts are excellent for didactic purposes and often perfectly suitable even in applied research. © 1998 Optical Society of America OCIS codes: 220.4880, 000.2060.

1. Introduction

Optical mounts are usually metal-made bulky, heavy structures designed to ensure the highest standards of mechanical stability against the effects induced by vibrations and thermal drifts. As a consequence, their size is often considerable, as are their weight and unavoidably their cost. Owing to their physical characteristics, they do not lend themselves to the design of compact setups, so that a typical optical experiment may be spread over a considerable area and their relative positions ~especially their heights! are sometimes quite hard to adjust, the more so if they have been purchased at different times from different manufacturers. A truly modular approach to the design of complete and compact optomechanical systems has been pursued by many firms with varying degrees of success. But again these kits are hard to integrate with more conventional mounts, and, although they are certainly attractive because they are easy to use, they pose serious limitations on the size of the optical elements that they can accommodate. Moreover they are still quite expensive. In this paper we suggest the use of LEGO for educational-grade optical mounts that will often prove good enough for more demanding applications.1,2 LEGO is a highly modular construction system in which simple pieces ~bricks, rods, beams, axles, gears, pulleys, hinges, not to mention several

The authors are with Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy. F. Quercoli’s e-mail address is [email protected] Received 16 October 1997; revised manuscript received 17 December 1997. 0003-6935y98y163408-09$15.00y0 © 1998 Optical Society of America 3408

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different sensors and actuators! can be connected by means of well-known ~and patented! stud-and-tube coupling; the bricks and other pieces are molded in ABS ~acrylonitrile butadiene styrene! and the geometrical tolerances applied in the production process are quite tight, no more than two hundreds of a millimeter from the nominal shape and size.3 As a consequence, the force needed to separate two elements reaches the remarkable figure of 1.5–3.5 N for each stud–tube unit. Considering that the weight of a single-stud LEGO element is much less than 1 g, it is evident that considerably large and complex structures can be safely assembled. The use of LEGO in scientific and technical education programs is not new. Besides a whole product line, called LEGO DACTA, specifically developed for didactic use, we mention that the research activity carried out at such prestigious scientific facilities as the Department of Electrical Engineering and Computer Science of MIT.4 With some modifications of the hundreds of standard LEGO elements, mainly of the TECHNIC series, and the introduction of a few home-made components, we have realized a great variety of basic optomechanical devices: holders, translation and rotation stages, xyz positioners, tilters, laboratory jacks, not to mention posts, bases, rails, and breadboards, that are all standard LEGO components. With these elements we have been able to build several instruments and systems, such as microscopes and interferometers, demonstrating the feasibility of using LEGO even in setups that require a high degree of stability. 2. Optical Mounts

Some basic mechanical components often used in optics experiments, such as tilters and rotators, are already included, although in a very raw version, in

Fig. 3. Tilting table realized when two LEGO bases are connected with two hinges. The tilt angle can be adjusted when the Plexiglas screw is turned. Fig. 1. LEGO frame housing a 5 cm 3 5 cm colored glass filter.

commercially available LEGO kits. These elements can be used directly without further adjustment or machining and are suitable for static mounts whose position is adjusted once and for all during the alignment phase. Figures 1 and 2 show two simple assemblies that can be used to filter a light beam, in the spatial and in the wavelength domains. The filter housing ~Fig. 1! is just a frame built with a few LEGO plates suitably connected. The iris diaphragm holder ~Fig. 2! allows for this and similar components to be positioned easily without awkward assemblies of posts and rods ~sometimes with glue or adhesive tape! as is often done. This feature is valuable if the compact size of the experimental arrangement is mandatory. Figure 3 shows a tilting table made up of two bases held together by two standard LEGO hinges. A Plexiglas screw ~one of the few nonstandard elements that we had to realize! is employed to finely adjust the tilt angle. Smaller versions of this component can be used to build coarse mirror tilters. Figure 4 shows a beam director that can be assembled straightforwardly from standard LEGO pieces and provides the means to adjust finely the direction and the height of the reflected beam. Its mechanical

Fig. 2. Iris diaphragm holder realized with standard LEGO hinges. Also the small post holder is a common LEGO element.

stability is comparable with that of a metal-made equivalent component. Lens and cube-splitter holders ~Figs. 5 and 6! have also been constructed from the small bricks, beams, axles, and other pieces of various shapes that can be found in any LEGO kit and have shown remarkable characteristics, particularly since the assembly and positioning are easy. In this respect, they are sometimes better than the usual mounts found in any optics laboratory, because the great number of different elements available in a LEGO box can be advantageously used to build custom components with little effort. The few examples of the optical mounts just shown are all characterized by an extremely simple design but can still be used to replace more professional components to perform some simple tasks with good accuracy. The realization of complex parts ~such as

Fig. 4. Beam director assembly with two tiltable mirror holders for a fine adjustment of the steering angle. 1 June 1998 y Vol. 37, No. 16 y APPLIED OPTICS

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Fig. 5. Large bar-type lens or filter holder. The component shown is a 3-in. pellicle beam splitter.

linear or rotary stages! mandates a more sophisticated approach than that when only off-the-shelf pieces are used and requires, for usable devices to be obtained, a careful design and in some cases the replacement of standard elements with custom-made ones. One of the fundamental parts that is lacking in LEGO is a long, solid, and sufficiently stiff rod. We overcame this problem by using Plexiglas rods, either threaded to obtain a precision screw ~M6 with a 0.5-mm pitch! or not, which are easy to machine and to couple to LEGO pieces. Below we briefly describe some of the optomechanical devices that have been built, emphasizing the relevant constructive details of each of them. We divide the components into five basic categories: holders and adapters, translation stages, rotators, tilters, and miscellaneous. A.

Holders and Adapters

Several different components have been realized for performing the basic task of keeping optical elements

Fig. 6. Prism holder with straight clamping arm, carrying a cube splitter. 3410


Fig. 7. Lens holder assembly made up of two 6 3 6 stud plates suitably machined to create the room necessary to sandwich a 1-in. lens between. Thicker lenses can be accommodated when one or more spacers is inserted as that shown at the center.

firmly in place. The holder shown in Fig. 5 can be used with lenses, filters, polarizers, pinholes, and other optical elements such as the 3-in. ~7.62-cm! pellicle beam splitter shown in Fig. 5. The stability provided by this simple assembly is quite good, so that it can be used to replace more conventional ~that is, metal-made! holders in a great variety of applications. Moreover its size can be scaled to accommodate components with diameters ranging from a few millimeters to several centimeters. The same features are shared by the beam-splitter table of Fig. 6 and by the filter holder of Fig. 1. One-inch ~2.54-cm! lenses can be firmly mounted in a frame like that shown in Fig. 7. The mount is composed of two 6 3 6 stud plates, pierced and machined on both sides to create the necessary room to house a typical 1-in. lens sandwiched between. Thicker lenses can be accommodated by our inserting a spacer, which is also visible in Fig. 7. Standard LEGO axles, or our longer and more robust Plexiglas rods, can be passed through the 5-mm holes pierced at the corners of the plates to assemble stand-alone systems as the microscope that will be described below, which also takes advantage of one of our custom-made components, that is, a Plexiglas adapter with a standard microscope thread. Two different designs have been devised for this component, one consisting of a Plexiglas ring with an external diameter of 1 in. that can be interfaced with the previously described mount and another employing a rectangular Plexiglas frame, which is easier to fit in more standard LEGO assemblies. Both components are visible in several pictures of experimental setups that are described below. A more refined component is the selfcentering mount shown in Fig. 8 ~holding an interference filter!, all built of standard LEGO elements, with hinges fastened to the three beams that make up the triangular frame and three spring-loaded axles pushing on the edge of the filter. The resulting structure is remarkably stable and provides an alternative to standard three-point mounts.

Fig. 8. Self-centering mount holding a 10-mm-diameter interference filter.

B.

Translation Stages

The design of a linear positioning stage can be appreciated in Fig. 9. In building this fundamental component, we used extensively a LEGO TECHNIC element that basically has the shape of a rectangular beam carrying an array of holes through which circular rods can be fitted. One of the holes must be threaded to fit the custom-made Plexiglas precision screw ~M6 3 0.5! needed to move the carriage. We have built several stages, each characterized by its own peculiar dimensions and by the different technical solutions exploited in their design: Sometimes the loading is provided by small springs, while in other cases we preferred to use rubberbands. Standard LEGO or, more often, Plexiglas rods were employed as guides. The carriage, which can be simply a single beam or more often a square frame as shown in all our figures, can be configured to function also as a lens or a filter holder ~as in the case of the component shown in Fig. 9! or to fit the rectangular microscope objective adapter described above. Two- and three-axis positioning stages ~Fig. 10 and 11! have been constructed by simply clutching together two or three linear positioners. The performance of such

Fig. 9. Linear positioning stage suitably integrated to house a small optical component ~a Glan–Thompson crystal polarizer!.

Fig. 10. Two-axis positioning stage consisting of two superimposed single-axis stages. As in Fig. 9, the upper positioner can be modified to hold several kinds of optical components.

devices, particularly as far as reproducibility is concerned, on the one hand, is not comparable with that of high-quality precision stages but, on the other hand, is not as poor as may be expected. Until now, we have used these stages in several setups, including a spatial filter and the mirror positioners employed in a Twyman–Green interferometer. We think that considerable improvement may be achieved with a more accurate design. A motorized version has also been realized by using a LEGO electric motor to turn the screw that moves the carriage. C.

Rotators

Although linear positioning stages are relatively easy to design and to build, rotary stages do not lend themselves to the same kind of approach based on the principle of making only the slightest possible modifications to existing LEGO elements. In fact, the rotators, wheels, and pulleys that can be found in the LEGO gallery are completely unsuitable for precision

Fig. 11. Three-axis stage used to adjust the position of a microscope objective finely ~to be used in a spatial filter arrangement!. The Plexiglas adapter needed to fit this component to the vertical frame of the positioner is described in the text. 1 June 1998 y Vol. 37, No. 16 y APPLIED OPTICS

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Fig. 12. Custom-built rotary stage. The structure of this component and the design concepts employed to obtain a smooth rotary motion are described in the text.

work and have to be replaced with newly designed ones. Our rotator is reproduced in Fig. 12 with the upper plate removed to show the details of the inside. The body of the component consists of a Plexiglas ring through which two collinear, off-center holes are pierced. One of the holes accommodates a hollow cylinder whose internal surface is threaded to drive a micrometric screw. A similar cylinder with a piston and a spring inside is fitted in the other hole. The top and the bottom plates are cut from standard LEGO bases: The lower plate is machined to remove the studs on a 2-mm annulus near its edge, whereas in the upper plate the tubes are removed ~still on a narrow annular region near the edge!. This removal allows for a smooth motion of the bases with respect to the Plexiglas ring. A small pin is glued to the lower plate and is pushed in opposite directions by the precision screw and the springloaded piston. Acting on the screw, the plate obtains a smooth and accurate rotary motion. The two bases are connected by another ring with a diameter of 20 mm that fits exactly the holes pierced at their centers; the lower base is free to slide, whereas the other is firmly fastened to this inner ring. One can obtain a coarse angular adjustment by rotating the upper plate with respect to the body of the device ~the outer Plexiglas ring!. Then the lower plate can be fastened to a LEGO base, and a fine rotary motion is imparted to the upper plate through the micrometric screw. The design principle just described is quite standard. A more original one was adopted for another rotator that was actually the first to be realized in practice, with threaded holes directly machined in the outer ring and a simple pulling spring to replace the quite complicated pushing system now described. Although this first version did not prove as reliable as the other one, its much simpler design is probably preferred to the complicated solution adopted in the other case. As soon as we are able to keep our mechanical tolerances small enough, we will probably stick to this less cumbersome approach, which also 3412


Fig. 13. Tilter with a 0.5-in.-diameter mirror attached. The two Plexiglas screws visible behind the L-shaped structure provide an excellent adjustment sensitivity as well as remarkably good stability.

allows replacement of the pulling spring with a rubberband. D.

Tilters

Besides using the tiltable standard elements ~basically hinged plates! described above, we have developed our own kind of high-quality, two-axis tilter, which has demonstrated very interesting performances. The mechanical assembly, shown in Fig. 13, is made up of two L-shaped structures, hinged by means of a small steel sphere and connected by Plexiglas precision screws. The loading is provided either by springs or by rubberbands as in the case of the translation stages. The mirror is glued on a tiny circular LEGO plate clutching the corner of the L, on-axis with the sphere. The assembly provides very accurate tilts because of its compact and tight design and to the considerable lever arm from the screws to the mirror. Also this component, as we show below, is accurate and stable enough to be used in a great variety of experimental setups. A slightly different version of our tilter has the studs on the horizontal arm of the L oriented vertically. When a component such as a lens or a microscope objective is inserted into a suitable LEGO frame clutching this arm, it is possible to adjust its angular position with the same degree of accuracy of the mirror shown in Fig. 13. E.

Miscellaneous Components

There are some assemblies and mounts that we have devised for specific purposes that do not belong to any of the categories described before but are nevertheless worth a few words. One of these unconventional devices is shown in Fig. 14: It is a simple assembly that was designed to house a compact CCD camera; the circuit board is fastened to the back of the plate with four screws. This component was used in several experiments and is an integral part of the microscope that is described below. Several detector modules with a similar design were also built. A more complicated object is the laboratory jack

Fig. 14. LEGO plate with a round hole in the middle to house a compact CCD camera. The circuit board is screwed to the back of the plate.

shown in Fig. 15. This familiar device was built with LEGO plates and beams together with a few Plexiglas rods and a long Plexiglas screw. The structure exhibits a remarkable mechanical strength and can easily support moderate loads. ~As will be shown below, we used it mainly as an adjustableheight platform for a low-power He–Ne laser whose weight was ; 0.5 kg.! 3. Experiments and Setups

The mechanical components that we have just described find their place in a wide variety of optical setups. Our aim in this section is to show how they can be combined to build fully functioning instruments and to realize fairly complicated experimental configurations. As we pointed out above, one cannot replace high-quality components with those made of LEGO and pretend to have the same reliability and performance, at least not with the prototypes presented here. Complete systems, especially those that include several moving parts, are even more critical.

Fig. 15. Positioning lift ~laboratory jack!, constructed with standard LEGO plates and beams together with a few Plexiglas rods. ~The longer one is threaded and acts as a screw, providing the means to raise or lower the platform.! The component can easily support a low-power He–Ne laser.

Fig. 16. Microscope realized with a few LEGO elements connected by four long Plexiglas rods. The objective is mounted on a suitable adapter, as is the CCD camera on top of the instrument. A black cardboard tube shields the path of the rays from ambient light.

Nevertheless in this section we show that with little effort some basic but instructive experiments can be performed with a LEGO-based setup, adding fun to the task of learning fundamental physical optics principles while saving a considerable amount of money. LEGO mounts are all characterized by their light weight, so that one cannot just place them on a table and hope that they will not move: Some means of firmly securing them to a sort of breadboard must be provided. Luckily, among the countless LEGO elements there are also several bases of different size, as large as 38 cm 3 38 cm ~48 3 48 studs!, that can easily accommodate even complicated systems. The remarkable strength of the stud–tube coupling ensures that, once fastened, the various components

Fig. 17. Image of a detail of a small LEGO pulley taken with the microscope of Fig. 16, working in reflection. 1 June 1998 y Vol. 37, No. 16 y APPLIED OPTICS

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Fig. 18. Dark ground image of a crosswire still taken with the same microscope ~in transmission!. The two small components on the right are, starting from the edge of the image, the source ~a LED housed in a LEGO brick! and the spatial filter that keeps the light from reaching the center of the condenser lens, thus creating the proper illumination pattern.

will not move from their desired position. Naturally, a LEGO base will never be as stable as a true breadboard, so precautions must be taken to avoid bending. The easiest way to do this is to place the LEGO base on a hard flat surface. The square pattern formed by the studs puts a serious constraint on the relative positions of the components that can be fastened to the base plate: Bricks and rods can be placed only at a right angle to the edges. One can overcome this severe limitation by using one-stud bricks as posts, that is, by raising the components slightly above the plate. In this way, several directions can be chosen at different angles with the sides of the base plate: There are some well-defined angles and distances for which the linear elements fit

Fig. 19. Experimental setup employed to perform spatial filtering experiments: Source S ~a fiber bundle! with a diaphragm to reduce the effective source size; O, object; L, lens; beam splitter that sends part of the light to the CCD camera, I, where an unfiltered image of the object is formed and part to the spatial filter assembly, F, followed by a second camera that records the filtered image, FI. 3414


Fig. 20. Schlieren image of a Fresnel cylindrical lens obtained with a setup similar to that of Fig. 19. ~The beam splitter is removed so that only the filtered image is observed.! As described in the text, the knife edge is actually the edge of a tiny LEGO plate.

perfectly in place and others that are close enough to this matching condition that an imperfect but reasonably stable fit can still be obtained. However, if maximum stability is required, right-angle positioning is preferred. Several optical instruments and systems have been mounted on our LEGO breadboard, and several experiments have been performed to show how an optics laboratory can take advantage of the proposed system. Figure 16 shows a microscope. The body of the instrument is made up of two square bases 150 mm apart connected by means of four Plexiglas rods with a black cardboard tube to shield the detector from ambient light. One of the two bases houses the objective and the other a CCD camera as described in Subsection 2.E. Figure 17 shows the microscope looking at a LEGO pulley with the image of a small detail recognizable on the monitor. The microscope was used both in transmitted and in reflected light ~in the former case the sample was illuminated by a

Fig. 21. Modern version of the Abbe–Porter experiment performed with our system. Both the filtered ~left! and unfiltered ~right! images are shown. The filter is a slit obtained when two small LEGO plates are placed close to each other.

Fig. 22. Frequency doubling in the spatial domain demonstrated with our setup. The object is a Ronchi grating whose Fourier transform has its zeroth order stopped by a thin wire glued to the xyz positioner for fine adjustment.

LED! and to demonstrate a few techniques of contrast-enhanced imaging. For example, Fig. 18 shows a dark ground image of a crosswire in which edge enhancement is apparent. The zeroth order of the transform is blocked by a tiny metal disk inserted in front of the condenser lens, held by a mount such as that shown in Fig. 2. Many more optical filtering experiments were performed with the setup illustrated in Fig. 19. The critical component here is the xyz stage made up of three linear positioners as described above, which carries the filter. In the simplest case ~schlieren filtering! the filter is just the edge of a thin LEGO plate. The result of this experiment, which we performed using as the object a Fresnel cylindrical lens, is shown in Fig. 20. Putting two of these plates close together, one obtains a slit that can be used, for example, to perform the Abbe–Porter experiment shown in Fig. 21. The object here is a square array of circular apertures. The slit is mounted on a ro-

Fig. 24. Detail of the xyz positioner with the pinhole used in the low-pass filter described in Fig. 23.

Fig. 23. Low-pass spatial filter realized with a 103 microscope objective and a 50-mm pinhole whose position can be finely adjusted with our three-axis stage. Also visible are two mirror tilters ~one realized with two small hinged LEGO plates! and the laboratory jack described in the text.

Fig. 25. Twyman–Green interferometer built with our LEGObased components. The mirror on the right is mounted on a tilter, which is in turn fastened to a linear translation stage. The source is a laser diode. The fringes are expanded by the microscope objective and can be observed on the white screen.

tary stage so that its axis can be adjusted and the desired image synthesized. A thin wire glued to the xyz stage provides an easy way to realize a high-pass filter such as that used in the well-known wire test. Figure 22 shows a frequency-doubled image of a Ronchi grating ~whose unfiltered image is also visible! obtained by stopping the zeroth diffracted order in the Fourier plane. Owing to the fair accuracy of our positioning stage, it is also relatively easy to build a beam expander with a low-pass filter assembly such as that of Fig. 23. The microscope objective has a 103 magnification, and the diameter of the pinhole is 50 mm ~Fig. 24!. The quality of the beam leaving the expander is quite good. Interferometers are undoubtedly among the most instructive optical systems. It is widely assumed

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have built thus far, and the aligning procedure was a bit more time-consuming. However, the results are remarkably good, as shown in Fig. 26, and there are no serious problems as far as the stability of the fringes is concerned. On the basis of our experience we believe that these and similar interferometers could be assembled in a reasonable time by students and teachers and prove to be a valuable didactic tool. 4. Conclusions

Fig. 26. Mach–Zehnder interferometer with a He–Ne laser source and a double output. One of the two fringe patterns can be seen on the white screen on the right, whereas the reciprocal one is projected on the rotating ground disk visible at the center of the image, just above the laser tube, and is imaged by a CCD camera whose output can be seen on the TV monitor.

that an interferometer must be built with extremely tight tolerances, which leads to rejection of the use of plastics in such an instrument as complete nonsense. We show here that, despite the relatively coarse ~if compared with those of high-quality components! positioning capabilities of our translators and tilters, several interferometric configurations can be realized when LEGO elements are used as building blocks. The most popular interferometer is probably that of Michelson, in its more modern collimated-light version proposed by Twyman and Green, and so we decided to start with it. The source was a 670-nm laser diode of poor coherence, so that to obtain the maximum fringe contrast the path difference between the two arms of the interferometer had to be kept within a few millimeters. To fulfill this condition we mounted one of the mirror tilters on top of a linear positioning stage. We emphasize that this capability of moving longitudinally one of the mirrors is very valuable for educational purposes because it provides the possibility of introducing the concept of coherence in a very straightforward way. The fringes, after passing through a magnifying objective, were projected on a screen. We found it relatively easy to adjust their spacing, acting on the Plexiglas screws of the mirror tilters. Figure 25 shows the entire setup. The straight fringes that can be seen on the white screen on the right were obtained after an alignment procedure that took ;3 min. Encouraged by our results with the Twyman–Green, we decided to also build a Mach–Zehnder. This time the source was a He–Ne laser ~as in the optical filtering experiments!, so that we were free to work with larger path differences. The laser beam was expanded before entering the interferometer, and the fringes were projected on a rotating ground glass, where they were imaged by a compact CCD camera. The reciprocal pattern could be seen, suitably magnified, on a white screen. This is probably the most complicated system that we 3416


The feasibility of using LEGO for optical mounts has been demonstrated. The versatility of the LEGO system and the ease with which complicated components and setups can be realized are sometimes almost astonishing. Components with no moving parts ~such as holders! present the fewest problems. In this respect, the objects presented here can often replace heavier, bulkier, and much more expensive professional components without seriously affecting the performance of even highly sensitive systems. Moving parts are more critical because, in spite of their remarkably small mechanical tolerances, LEGO elements are often unsuitable for precision work and the materials themselves are obviously not the optimum choice for scientific applications. Nevertheless, by carefully designing some custom elements, we have been able to build translation stages, rotators, and tilters whose accuracy and reliability are certainly adequate for didactic purposes and in many cases also for routine experimental work. We finally emphasize that the results here suggest that an integration between LEGO and conventional optomechanical elements made of metal is indeed possible and that plastic-made components often exhibit fairly good characteristics in terms of positioning accuracy and stability, to the point that they can successfully replace metallic mounts at a tiny fraction of their cost. Demanding scientific applications will always require more refined equipment than that presented here, but everyday work might benefit from careful exploitation of some of the ideas introduced. If some more research were carried out, further developing the most promising mechanical configurations and devising some new cleverly designed elements, LEGO may soon make its debut on many professional optical benches. We thank V. Guarnieri for collaboration in digitizing the images and the president of the National Institute of Optics, F. T. Arecchi, who saw us playing with LEGO and trusted us when we told him that we were actually working. References 1. F. Quercioli, A. Mannoni, B. Tiribilli, and S. Acciai, “Play optics with LEGO,” in Fifth International Meeting on Education and Training in Optics, C. H. F. Velzel, ed., Proc. SPIE 3190, 233– 242 ~1997!. 2. J. Bell, “Toy box supplies parts for teacher’s light table,” Opto Laser Eur. 44, 32–34 ~1997!. 3. See the official LEGO website: http:yywww.lego.comy professionalsyhistory.asp. 4. See the related site on MIT’s web: http:yyweb.mit.eduy6.270 and related links.