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A novel method of recording motion

Amir Ben-Shalom, Bloomfield Science Museum, Jerusalem, Israel
Paul Gluck, Jerusalem College of Engineering, Israel

Demonstrating various motions important in science and engineering is a favourite topic in science museums the world over, as well as in the classroom when teaching introductory mechanics and the laws of motion.

Take for example the problem of exhibiting the simple harmonic motion associated with the swings of a mathematical pendulum. Apart from filming and analyzing the motion, or recording it with a motion sensor, both of which are indirect and nontangible 'black-box' methods, there are various direct ways of doing this. One is to attach a felt pen to the bob and use as the time base a sheet of paper moved at constant speed. There are several problems with this, especially in an exhibit to be used thousands of times. First, friction between the pen and the paper produces a heavily damped harmonic motion curve. Secondly, the maintenance of the exhibit would be difficult, quite apart from the fact that young visitors would be tempted to use the pen for graffiti purposes. An alternative might be  a magnetic pen above a thin surface containing black iron oxide in a white fluid (like drawing boards for children), but the surface would quickly deteriorate due to constant contact with the pen. Some museums resort to a device comprising a funnel from which sand, poured in by visitors, trickles onto a 'writing board' of black rubber which they move by activating a lever. We do not envy the task of a crew maintaining such an exhibit.

By combining the chemistry of the 1960's for photochromatic materials and the development in the last decade of easily available highly focusable tiny LEDs and laser diodes, together with some simple engineering construction, we have found an elegant and novel way of exhibiting various motions in our museum, and based a comprehensive interactive exhibition on our method.

In the following we give a brief discussion of the principles behind these components, and then describe some novel exhibits based on them.

Photochromatic materials change their colour when exposed to light. In the natural state they do not absorb light in the visible spectrum, but when exposed to photons of sufficient energy (e.g. in the UV region) they undergo structural changes, breaking of molecular bonds, and are in effect turned into a dye. These changes are usually nonreversible. This effect has been known since the 19th century. Our interest is in a subgroup of such materials which were investigated in the 1950s and 1960s. They are special in that the change is reversible: when the UV radiation is removed they return to their original state. They have found application in sunglasses, windows which darken when exposed to light, security inks for marking documents, etc. Photochromatic materials in such commercial applications were developed to react to the UV in sunlight rather than to the visible spectrum.  In addition, efforts focused on reducing the recovery time to transparence (the 'fading phase') as much as possible.

On the contrary, for display purposes we were interested in prolonging the time before fading. We also looked for materials that would darken when exposed to light in the 400-405 nanometer range. These materials remain almost completely white when exposed to the strong artificial light in the museum. The only restriction is that they shall not be exposed to sunlight. After considerable search and effort we located three suitable materials: one becomes red when bathed in UV, the other two turn blue and violet. We do not know the exact chemical formulas, since we bought them from commercial suppliers and these are not fond of revealing trade secrets. We surmise that they are probably based either on the naphtopyran molecule, or the spiroindolinobenzopyran molecule. We mix these and dissolve them in transparent dye solvents such as acrylic or epoxy, so as to able to brush or spray them on surfaces. The solvents strongly influence the sensitivity to UV, the fading time and the resulting hue of the paint. By trial and error we found that for best results in terms of sharpness of the trace, the photochromic material should not exceed 3-10% of the final mixture, which we applied in multilayers to the surface of interest. The fading time of several seconds allows the visitor to get a good idea of the tracks we want to demonstrate.

Light sources 
We use LEDs or lasers of wavelengths 400-405nm to excite the photochromic materials. These satisfy safety requirements, have very fast switching times, and can be focused with lenses packaged with them to a small spot on the surface. Such properties are results of intensive developments of the past decade or so, directed in no small measure to finding efficient alternatives to incandescent filament bulbs. Our LEDs have diameters of 1.8 or 3mm.

Blue-Ray DVD used in game consoles and HD movie players employ recently developed short wavelength lasers, enabling one to increase dramatically the density of information on the disc. We chose such lasers, drastically reduced in price to a few tens of dollars due to mass production in DVD, because they increase the energy density of photons hitting the photochromic material, 'coloring' the material faster, and  creating a narrower line than is possible with a LED. Lasers allow one to project their beam further and so one can record the tracks they create on a distant screen. With them one is able detect changes in motion of only a few degrees when projected to a distance of a few meters.

In applications we need to attach the LED or the laser diode to a point on the mechanism whose motion we wish to monitor, paint the recording surface opposite that point with photochromic material, and finally build the exhibits themselves. The light sources are mounted so that the visitor never looks into them directly.

Our exhibition
In addition to building exhibits based on the above-described principles for purely 'fun', containing little educational message, we describe here devices we constructed which will be of interest to readers of this journal.

1. Exhibits devoted to pendulums

a) Three 'mathematical' pendulums of different lengths holding lasers in their bobs, are swung by the visitor. During their swings sinusoidal tracks of different periods are drawn on a drum coated with photochromic material rotating at constant speed, as shown in Figure 1.



Figure 1. a. Display apparatus with three pendulums constrained to move in a plane, and the rotating drum covered with photochromic layers. b. Tracks of different periods described by pendulums of different lengths on the rotating drum. Note the laser 'writers' in the bobs, a few centimeters above the drum.

b) Another pendulum is suspended from two knife edges in two planes, thus executing two perpendicular SHM's and creating the well-known Lissajous figures, as illustrated in Figure 2.

Figure 2. Examples of Lissajous figures created by two harmonic motions at right angles to each other.

The two periods are slightly different due to the fact that the rotation axes in the X and Y directions are not at the exactly the point, resulting in different effective lengths and therefore periods. This difference is not more than one or two percent. Ignoring this difference, the resulting track will thus depend only the phase difference, and can vary from a degenerate straight line through a circle to an ellipse. The small difference in periods itself can generate phase differences which may add up in the course of many swings (say 25) to a significant track change. The visitor can follow these changes on the light sensitive surface below the pendulum.

c) We built a chaotic pendulum in which a magnet housed in the bob is repulsed by an electromagnet under the recording surface. The repulsive force pushes the pendulum in a random manner, the bob comes to a halt at different unpredictable positions, and visitors observe that the resulting track bears no resemblance to anything harmonic, as shown in Figure 3. They can alter the polarity of the magnet,  thereby switching to attraction instead of repulsion, leading to immediate moving towards and stoppage at the center. Alternatively, they may synchronize this changeover with the pendulum swings and thereby ensure that the oscillations will not decay.

Figure 3. Path described by the bob of a chaotic pendulum.

2. Utilizing the fast switching of the light source
We give a couple of examples using this property of LEDS and lasers.

a) The visitor may grasp the principle of creating a monitor picture by sweeping across it, in the exhibit we call the 'light brush'. Here a row of LED's is activated by a tiny control module turning them on and off, so that as the row is passed above the recording surface one creates a complete picture. Each LED creates a line of the picture, and the visitor thus learns the principle of scanning in display units and cameras. The resolution is not high (only a few tens of pixels per LED), but the learner may vary the scanning speed and thereby narrow or broaden the picture, or distort the result when moving the 'brush' slightly diagonally.

b) In another exhibit based on the same principle visitors sit on a bicycle. By pedaling they rotate a pair of large disks opposite covered by photochromatic materials, as shown in Figure 4. A row of LED's positioned opposite each disk draws a brief story of comics, which appears and disappears with periodic regularity.

Figure 4. Device for comics 'drawn' by rows of  lasers
(photo by of Tomer Appelbaum)

3. Mechanical devices
A series of exhibits illustrate the geometry of various mechanical devices. Among these there is a pantograph which enlarges pictures, a pair of compasses, and a pair of arms which demonstrate both polar and Cartesian coordinates.

4. Convection
A tall and narrow jar contains a transparent liquid in which we dissolved a photochromatic dye. A laser situated at the bottom of the container illuminates the solution and warms it. The heating causes convection currents to form which can be seen very clearly and beautifully by this simple means, as shown in Figure 5.

Figure 5. Convection currents in a column of liquid containing photochromic dyes, illuminated from below by a laser.

We hope to have shown that a combination of recent technologies enables one to add to the repertoire of useful demonstrations in the teaching of science and the education of the general public. We think that with suitable scaling down and a dedicated laboratory staff with access to a mechanical workshop our approach could also be used to build demonstrations in a classroom.


Amir Ben-Shalom

Amir Ben-Shalom has a PhD in electrical engineering. He is chief designer of exhibits in the Jerusalem Science museum, Israel, and is a consultant to industry.

Paul Gluck

Paul Gluck has held positions at various universities in the UK, US and Israel, doing research in theoretical solid state physics, has taught for 20 years at a high school for gifted children, has been involved in physics teacher training, and is currently teaching physics to undergraduate engineering students.

This is an author-created, un-copyedited version of an article accepted for publication in Physics Education. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Date Created: 23/04/13
Date Updated: 23/04/13