Marble Run Construction Set

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The marble run construction set is a user project.


Marble Run Construction Set
Benutzerprojekt
Projekt: Marble Run Construction Set
Benutzer: Christian Walther
Bereich: Wooden Toys
Technologie: Laser Cutting
Figure 1: Marble Run

This kit allows building a great variety of marble runs out of three kinds of simple laser-cut wooden parts. The parts are easily assembled and disassembled with no permanent connections, only held together by interlocking slits and gravity, and can be stowed away in a box when not in use.

  • The track elements are all the same shape. Having only one kind of track element makes for an elegant design with several advantages for the builder:
    • Fewer parts to distinguish, you can’t pick the wrong one.
    • Your creativity is not limited by having too few of one part and too many of others.
    • If you break one, there are still plenty left.
  • The stilts are all different, staggered by height in multiples of the board thickness. I tried to come up with a design that has only one stilt shape as well, or at least fewer, but without success. This means that the stilts lack the above advantages, although the second one is not as important because you never need two stilts of the same height in a single-track marble run.
  • Clamps are used to connect two track elements in place of a stilt where no stilt can be placed because there are other parts of the track below that would get in its way. They snap in place by a spring mechanism using the elasticity of a thin strip of the wood.


Design

The important feature of the track element is the shape of the inner edges of the jaws, on which the marble rolls. The goal is to have the marble follow a smooth trajectory from one element to the next, rather than make steps as if rolling down stairs. This is achieved by starting with a desired trajectory, sweeping a sphere of the size of the marble along it, and intersecting the surface of the resulting shape with the top surface of the board.

This is simple enough for a straight run: The desired trajectory is a straight line with a downward slope given by the length and thickness of the track element, sweeping a sphere along it produces a cylinder, and intersecting the cylinder with a horizontal plane results in a (very elongated) ellipse. Obviously only a part of the ellipse would be used, as we only want to make a groove for the marble, not a full tube. In fact, my earliest sketches had straight track elements, in addition to curved ones, until I realized that I could get by with only curved ones.

But how about the curved track elements? For a circular arc, the ideal trajectory is a helix, and the intersection of a helical tube with a plane is a somewhat complex to describe banana shape. How to construct that? Fortunately, it turns out that Onshape is very adept at performing the mentioned geometrical operations, even with arbitrary shapes. It can make helices, sweep arbitrary 2D shapes along them (the sphere can be replaced by a circle in a perpendicular plane to the trajectory, or by a groove cross-section with a circular bottom to make a groove rather than a tube), intersect the resulting 3D surfaces with planes, and even use the resulting curves as a basis for further 2D constructions such as drawing tangent lines and circles to them. This made it quite easy to design a visually pleasing part with smooth transitions between the groove edges, constructed as described, and the outer edges, consisting mainly of circular and elliptic arcs.

The smoothness of the marble trajectory is very sensitive to the marble size: A smaller marble than designed for touches the bottom element too early and gets a horizontal piece in its trajectory where it rolls on the plane surface of the bottom element before reaching the beginning of the groove of the bottom element and descending into it. If sufficiently too small, it may even fall down vertically between the jaws, at which point it is very prone to getting jammed between them, as detailed in the next paragraph. On the horizontal part it may come to a halt if it is traveling too slowly and the floor is not perfectly level so that it has to roll upward. A larger marble than designed for will stay on the top element for too long and then fall down into the groove of the bottom element after it has already started, making for a stair-step trajectory. It is not however in danger of getting stuck, so erring on the side of designing for too small marbles is preferable. The marbles I bought had a diameter of 15 to 17 mm, so I made a groove cross-section with a bottom curvature diameter of 15 mm and straight sides sloped such that a 17 mm marble would roll 1/3 of the board thickness above the bottom.

Figure 4: Track thickness considerations

An important point to realize is that the thickness of the track element must be less that half the marble diameter, as illustrated in figure 4. If it is more, there is no smooth trajectory, because the marble falls down vertically by a nonzero distance between the point where it stops being supported by the top edges of the track and the point where it touches the bottom element. Furthermore, at this point it is located between the jaws and easily gets jammed between them. After that point, it continues rolling horizontally on the plane surface of the bottom element until it returns to the intended trajectory at the point where it reaches the beginning of the bottom groove. In addition, the thinner the track element, the better, because the closer the element thickness gets to the marble radius, the smaller the rotation radius between the point where the marble touches the track and its horizontal axis of rotation. The smaller that radius, the faster the marble needs to spin for a given forward velocity, and accelerating to that rotation speed slows down the forward movement.

For my 15 mm marbles, a thickness of 6.4 mm proved just about sufficient. Going thinner, while preferable according to the foregoing argument, would have reduced the slope of the track, making it harder to keep the marbles in motion, unless the length of the elements were also reduced. Reducing the length in turn would require either reducing the radius of the curves in the track, which (especially together with the shallower groove made by thinner elements) increases the chance of a marble escaping in a fast curve, or reducing the angle by which a single element curves, requiring more elements for a full circle. So in the end the dimensions are a compromise between conflicting requirements.

6.4 mm in addition has the advantage of being one third of the height of a Duplo brick – early sketches included provisions for supporting the track on Duplo structures rather than the stilts of the final design.

Figure 5: Possible track shapes

The curve angle of one track element was chosen as 30°, 1/12 of a full circle. This allows for 90° turns (3 elements) to make structures that fall on a square grid of circles, for 60° turns (2 elements) to make structures that fall on a hexagonal grid of circles (in particular a track that loops back under itself), and for sufficiently approximate straight segments by alternating left- and right-turning elements. Given a necessary minimum slope of the track, it also results in a nice large enough curve radius. It is worth noting that all possible track shapes made from 30° elements do not lie on a regular grid, as shown in figure 5. The only angles that achieve regular grids are 60° and 90°, which are too large for our purposes.

Making a full circle from 12 30° elements means that the beginning of the circle lies exactly above the end of the circle, so that the stilts at those two points get in the way of each other. I first tried to avoid that by making the curve angle slightly larger or smaller than 30°, but found that this would just cause the same kind of collisions in other places on practical track shapes. In the end, the angle was left at exactly 30° and these collisions are now resolved by the natural flexibility of the whole track that arises from the loose fit between all parts – two strictly colliding stilts can in practice be placed adjacent to each other without any resistance. Even other collisions like a stilt intruding on a track part or another stilt from outside, which in a perfectly rigid system would require the use of a clamp instead of a stilt, can often be resolved in this way. I also thought about making multi-story stilts, where two overlapping track parts are supported by rungs on different heights of one and the same stilt. The problem with that is that there is no set difference in height between two overlapping track parts. Varying track shapes can have sufficiently varying height differences that the resulting large number of rungs would be too close to each other for a marble to pass between.


Production

Figure 6: Laser cutting material tests

I had some leftover 6.5 mm birch plywood from a previous project that I considered potentially suitable. A test using the power/speed test pattern however confirmed its reputation of not laser-cutting easily: while it would engrave nicely on the low-energy end, high power and low speeds would just set the material on fire, but still not cut through (figure 6 top).

Next, I visited Wiederverwerkle to see if they had anything suitable, especially any nice-looking massive wood. I found some board from dismantled wine chests (unknown variety of wood) that looked vaguely promising. The laser test concluded successfuly (figure 6 center), on par with the standard laser-cutting material, poplar plywood (figure 6 bottom). In the end however I still decided against it, for the following reasons:

  • Being massive wood, not plywood, the wine-chest board was not plane, but noticeably bent.
  • It was embossed and painted in places, and placing my parts between these areas would be a challenge.
  • At about 7.4 mm, it was a little too thick (although sanding or planing that down would also have reduced the previous disadvantages).

6 mm poplar plywood, which turned out to have an actual thickness of about 6.4 mm, fit the requirements perfectly, except for maybe not looking quite as nice along the laser-cut edges, and was therefore chosen for the final product.

I also considered CNC machining the parts instead of laser-cutting, but shied away from it because it seemed like more effort:

  • They have many inward corners that would require finishing with a very small milling bit – doable, but more work to set up and takes longer.
  • Sanding the rough edges is a lot of manual work (in retrospect, the work on the laser-cut parts probably wasn’t less).
  • It requires traveling to Zürich for the CNC router, while laser-cutting can be done in my home town Winterthur.

In an effort to reduce the unsightly stains left on the wood surface by residues from the laser-cutting fumes, I tried covering the surface with paper. 60 g/m² A4 typewriter paper (that I had lying around with not much use for) was glued to the top and bottom surface with spray glue. Using only removable glue (3M Re Mount) proved to provide a little too weak adhesion, so I used a mixture of the removable glue and a bit of permanent glue (3M Spray Mount) sprayed on in quick succession, which worked better. Results were good, the sandwich was cut easily and the paper could easily be removed afterwards, leaving a pristine wood surface in most places. In particular, the ugly imprints of the honeycomb structure on the bottom were all gone. Only in a few places, the paper had peeled up ever so slightly along the cut edge, resulting in all the stronger brown stains on the wood that had to be sanded off. In conclusion however, even though it had worked for the most part, I probably would not do this again, as sanding the surfaces was required anyway for reasons mentioned next, and it uses large amounts of the expensive spray glue.

I tried several techniques of cleaning the charred edges to stop them from leaving marks. What worked best was to brush them under warm water with dishwashing detergent, submerging the entire part, then rub them with a damp cloth until they stop giving off color. The wood does not seem to mind the watering, it does not bend or delaminate. It expands slightly in thickness and the surface gets a bit rougher – both, along with the mentioned remaining stains, reasons for sanding it smooth and clean again.


Box

Figure 7: Box

A box (figure 7) with compartments for the different parts stores the finished kit in a compact way. The bottoms of the compartments follow the shapes of the parts to hold them firmly in place together with the lid of the box. The box was made from 2.5 mm gray cardboad (for the frame and the ribs that shape the curved compartments) and 0.3 mm Bristol board (for the compartments and the lid). Apart from one small job on the Curio cutting plotter, marking the ribs, it was all made by hand, with no digital tools. Even that could just as well have been done by printing the shapes out on paper and cutting by hand – the cutting had to be finished by hand anyway because the Curio cannot cut through the whole 2.5 mm.


Conclusions

I am pretty proud of how the finished kit turned out. The marble runs work well for the most part, although the smaller and rougher marbles occasionally get stuck when slowed down by touching. That larger marbles run faster than smaller ones (due to the higher required rotation speed of the latter) encourages running races. It is fun to construct different marble runs, which turns out to take a bit of planning, because the run has to be built strictly from bottom to top, as inserting track elements at the bottom or in the middle is not possible without taking everything apart to adjust to the changed heights. This makes it interesting for an adult – how frustrating it will turn out for the two-year-old for whom it was built remains to be seen.

The fit between the parts is very loose, much more so than required to separate colliding stilts as detailed above. The gap of 0.1 mm that was inserted in some places, in addition to the cut width of the laser cutter that was not corrected for, can probably be reduced. The looseness makes it easier to put the parts together, but it also makes the structures somewhat fragile – they fall apart easily, especially when trying to slide them around on the floor. Moving a large construction when you are running out of space in one direction is virtually impossible. The most common mode of falling apart is that a combination of a track element and its upper stilt will lift out of the lower stilt and fall over backward, in the ascending direction of the track. This is helped by the fact that the center of gravity of a track element is very close to the upper stilt. One stilt/track combination falling over then often causes a chain reaction of its neighbors falling over as well.

Ideas to remedy this include:

  • Reduce the gaps for a tighter fit to make friction keep things in place. Probably friction needs to increase gradually as two parts are put together, in order not to lose the ease of starting a joint even when the two parts are not aligned perfectly yet.
  • Use the spring snapping mechanism of the clamps not only on the clamps but also on the stilts to prevent the track element from lifting out. This too bears the risk of making it harder to put parts together.


Version 2

Version 2 addresses the stability issue by adding a snapping mechanism to the stilts and was exhibited at Zürich Mini Make Faire 2017. In addition, a base plate with holes for the stilts was produced for the exibition that provides additional stability, at the expense of only supporting one particular construction. The Onshape document below is up to date, for SVG files check back here later!


Files

Main design in Onshape – adjust parameters, then either right-click on the appropriate faces of the 3D parts and export as DWG, or export individual sketches as DXF.

Lasersaur-ready SVGs, version 1 (arranged for my particular material sizes): Track elements, Stilts, Clamp.

Sketches for the box (SVG).

© 2017 Christian Walther ‹cwalther gmx ch›, licensed CC BY-SA 4.0.