Lattice Hinged Booklets

A Set of Hinged Covers
A Set of Hinged Covers

I’m pleased to have created a first product using the lattice hinges: a laser engraved, hand printed A5 sketchbook for Red-Violet Made.

They use a pair of lattice hinges gives a double fold that operates like a normal hard back book, with a flat spine instead of curved like other booklets. Using such a small radius corner with the lattice hinges means only having a small number of torsional links, so there must be more clearance than a single laser cut between each link so the hinge doesn’t bind at maximum bending deflection.

To lower the stiffness of the hinge and make it soft enough to open and close, this booklet uses long, thin torsional links. However, the increased link gap with the lower stiffness links means the hinge needs to be supported on the inside to stop any extension and perform normally.

The inner liner is screen-printed by hand, as well as a pocket on each side that holds the card cover of the sketchbook. The sketchbook inside is held by the pocket, so it can be replaced to refill the wooden cover. A ribbon on each side can be used to tie the book closed, though the softness of the hinge means it will stay closed without it.

The front covers are engraved by laser with original hand-drawn artwork from Jennifer Fenner (under the studio name Red-Violet Made) that are scanned and resized to cover the whole area. Using laser etching gives a consistent depth of etch and allows very fine detail in the wood, while also picking up some of the grain detail and a fine striated pattern where material is removed, caused by the repeated close scanning of the laser beam.

This first run of booklets were presented for sale at the Bluecoat Artist’s Book Fair. Of the seven manufactured, only three remain unsold, and we’ve been asked to present the remainder for sale in our online shop — with only a short time before the last posting dates for Christmas!

More detail of the manufacturing procedure is shown below. Continue reading Lattice Hinged Booklets

Lattice Hinge Design — Choosing Torsional Stress

The first set of lattice hinge tests I generated were a little fragile, with the maximum stress in the torsional links set to be 60MPa (the yield stress of the acrylic) it’s not very surprising that, with acrylic being a very brittle material (where the ultimate/breaking stress is very close to the yield stress) that the samples were very easy to break.

For a 90 degree bend in a 3mm thick sheet of acrylic with 3mm wide links, 23 torsional links are needed if the laser kerf is 0.2mm. This will form a bend with a 44mm internal radius. The minimum length of link (rounded up to the nearest mm for simplicity) is dependant on maximum allowed torsional stress:

14mm long, 23 Link Hinge around 44mm Radius
14mm long, 23 Link Hinge around 44mm Radius
  • For \( \tau_{allowed} = 36 \)MPa, \( l = 8 \)mm;
  • For \( \tau_{allowed} = 20 \)MPa, \( l = 14 \)mm;
  • For \( \tau_{allowed} = 10 \)MPa, \( l = 28 \)mm.

To test this, I’ve produced a cut file for the hinges with the three sizes of link. Included is a arc of 44mm radius to act as a guide for the calculated internal radius of each lattice hinge bend.

The SVG file is linked below if you’d like to cut your own. Or if you’d like these samples but you don’t have access to a laser cutter at the moment, or you normally send away for samples, Lattice Hinge Test 2 is also available to purchase from Ponoko. Continue reading Lattice Hinge Design — Choosing Torsional Stress

Lattice Hinge Design — Minimum Bend Radius

The last set of hinge tests that I showed used a cut out a rectangle of material to form the links. By re-arranging a formula that calculates the required inter-link clearance, it’s possible to find the minimum number of links to make a bend using only a single cut with the laser if the width of the cut (laser kerf) is known. Its then also possible to calculate what the radius of that minimum bend is from the length of the lattice cut area.

For a 90 degree bend in a 3mm thick sheet and 3mm wide links, 23 torsional links are needed if the laser kerf is 0.2mm. This will form a bend with a 44mm internal radius.

Lattice Hinges

Lattice hinges are formed when a set of parallel, overlapping cuts divide a flat sheet into thinner, linked sections that can deform more easily than the solid sheet. By dividing the sheet into an array of parallel columns, each column can twist along its own length to let the sheet form a bend by twisting around the axis of these torsional links. Flexibility of the joint is determined by the material properties of the plate and the geometry (length of the overlapping cuts and cross sectional area) of the torsional links. For simplicity I’m only considering links where the width of the link is equal to the plate thickness.

Lattice Hinge Torsional Links
Lattice Hinge Torsional Links

Continue reading Lattice Hinge Design — Minimum Bend Radius

Seat Reclining Bar

When I originally posted about the seat structure, I left the seat adjustment separate from the main seat structure design. I had the ideas about how to implement the adjuster, but it needed some time to let them mature into a practical design.

The idea is to use the simplest adjustment mechanism possible. It needs to be set-and-forget, so the seat height doesn’t change when you lift it up, but also be easy to adjust, so that means no fiddly mechanism and adjusting it shouldn’t need tools. Low parts count and low weight is important too and there shouldn’t be any extra hardware/fastenings if possible (i.e. I don’t want to use car seat style lever and slide mechanism).

The seat adjuster uses the sloped back of the side support as the control surface for the seat back so, because it is to all be operated by hand, any pinch points needs to be removed or protected. There needs to be no sharp/pointed/serrated edges that could catch loose clothing or skin — especially because opening and closing the seat is to be a normal process for using the luggage space.

The end of the adjuster beam is rounded, as it is a moving structure that sticks out. The radius on the beam where the support locates to minimise the risk of pinching anything when the seat settles back. The horizontal gap between the seat and support means it shouldn’t be able to trap anything between the two.

The adjuster bar clips/unclips to the seat back which holds it in place, while allowing easy adjustment (the removable bar is simpler than having a captive, sliding motion).

Like with the previous lattice hinges work, I’ve been doing some calculations for integrated elastic clips for laser cutting — I’ll be publishing more details on these soon.

Having a long distance between the support positions, which means they are only supporting point loads (and no bending moments), this length allows for a natural shock adsorption as part of the seat design. One downside of this layout however, is that it’s not possible to adjust the seat with anyone sitting in it, you’d have to get out to readjust.

add_rel_lightbox version 0.4.1

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When I moved add-rel-lightbox across to using Simple DOM Parser in place of the regex controlled for version 0.4, I had a little problem with the pre-release code stripping line breaks from every post that, although it didn’t cause a display problem by it’s self, caused another regex based plugin to bork the page at the point of render. While this was sorted for the version 0.4 release, there was still some quieter newline-stripping that was still going on that version 0.4.1 now resolves.

As with the previous problem, this again came from the default settings of the Simple HTML DOM Parser. By default, the parser will try to close any un-closed html tags in the input that it’s given; to try and allow for malformed html with the minimum of fuss, and allow the PHP that’s using the parser to call any tag in the content. However, one of the results of this behaviour is that it will concatenate all the lines of a multi-line tag — such as <code> or <pre> — by removing all the newlines.

To stop this happening, I’ve set $forceTagsClosed = false for the the parser. While this option true by default to allow for less trusted html, this shouldn’t be an issue for parsing WordPress post content as this is inherently trusted content and because only a small subset of tag information is used, it should have little effect on the actual output.

If you’ve seen multi-line <code> or <pre> elements reduced to one line after installing version 0.4, an update to version 0.4.1 should fix that for you.

Completed Laser Cut Brackets

You might remember from the other week that I had designed and cut some perspex brackets as an mounting for a piece of art for an exhibition. The show is now up and open as one of the independent exhibitions that are part of the Liverpool Biennial. If you were wondering how the parts I showed looked like, here’s a few images of it mounted:

In addition to the brackets, a central bridge supports the hanging parts of the artwork and the laser-cut perspex and print is held in place by gravity.

The artwork, titled “Xenia” is based upon the story of “”, part of the Re-view Textile group‘s exhibition around the theme of Hospitality.

The exhibition is open until 12th October 2012, Monday to Saturday, 10am-4pm,

Baltic Creative,
Creative Campus,
46D Jamacia Street

Rear Hanger Shear Strap

Using adhesive as the main joining method for the Atomic Duck requires careful design of the part interfaces. Where welding is equally as strong in all directions, adhesive performs well in compression and shear, but badly when there is tension across the joint.

This is not a problem of the type of adhesive, this is a characteristic of all adhesives and can be demonstrated with any type of adhesive tape. Take a piece of sellotape and stick it to a table-top — feel free to use tape-of- and a table-top-of-the-mind, I don’t want you taking the varnish off!

Done? OK. Now you have made an (imaginary) adhesive joint between the plastic tape and the table surface, where the adhesive on the tape sticks to both surfaces.

Tape-Table Diagram
Tape-Table Diagram

If you press down onto the tape, straight down against the table surface, that loads the junction in compression — the force between the tape and table compresses the glue. I will be very surprised if you do this and get the tape to come off the table (joint failure) before the table gives way. [No points if you just imagine something else happening; we’re modelling our universe’s physics here]


If you are very strong, the piece of tape is small, or the tape glue is dry, you might just be able to get the tape to move across the surface of table. If you are pulling the tape exactly parallel with the table: no pressure on the table, and not pulling the tape away from the table; then the glue is being loaded in shear. The top surface of the glue is being forced one way by the tape and is being resisted in the parallel plane by the table-top.


Compare this performance to what happens when you try and pull the tape off the table. With very little force, all of the tape can be removed. When the tape is pulled upwards, the glue is placed in tension and the force applied soon overcomes the adhesive capability of the glue with the surface. [Strictly, this is the peel-off force.]


In the Atomic Duck chassis, most of the joints are arranged to be in shear and compression, but at the bottom of the rear hanger arrangement it’s only possible to put these joints in tension. To stop these joints from falling apart as soon as the any weight gets put in the chassis, there needs to be a shear strap — a thin plate that is connected in shear — to transfer the load across them.

Shear Strap Position
Shear Strap Position

A001_P018_R001 Chain Cover

As the chain has been rerouted for this design revision, and now goes through the cab and luggage area, that area needs to be covered.

While this could be covered with 3 interlocking panels, I don’t want to leave sharp corners in the luggage area. Instead, a single piece that uses lattice hinges to create large radius bends will curve over the chainline.

A001_P018_R001 Chain Cover
A001_P018_R001 Chain Cover

Using lattice hinges is only available to me as a result of my decision to design parts for their industrial manufacture, even if that meant made them more difficult to make by hand. This part is particularly designed for manufacture by laser cutting and the thinness of the laser’s kerf means it would be difficult to make by any other method. However, the single piece part could be replaced by a three-pieces that would be easier to make by hand, could be bent without lattice cuts or the number and size of the cuts could be changed for a wider kerf.

Two sets of cuts make the lattice hinge, one offset from the other so when they overlap, the material zig-zags to provide the living hinge mechanism. The thin, long sections of the zig-zag will twist along the axis of the bend, so the flexibility of the material allows the sheet to be curved, without breaking or permanent deforming the material.

Lattice Hinge Diagram
Lattice Hinge Diagram

As the bend will be supported on all sides, there’s no need to have the overlapping lattice extending the full length of the bend so, to reduce the length (and time) of the cuts, there are 5 hinge areas along each bend line.

A001_P018_R001 Net
A001_P018_R001 Net

A003_R002 Seat Design

The seat structure seems to have taken the most time of all the assemblies to re-design, though it was interrupted by some thesis redrafts. It’s perhaps a measure of the amount of how much work was needed on the previous revision (A003_R001).

One crucial task in the redesign was changing the cross beams from aluminium bars that needed manual machining to laser cut parts that can be produced automatically along with most of the other parts in the chassis. Having parts that can be created and finished in a single manufacturing step helps keep the manufacturing costs down.

Not using bars means the beam also doesn’t have to be the same size all along it’s length, the ends can flare out to better resist the bending moments generated when the seat is used.

Where the previous Cross Beam (A003_P003_R001) was a threaded bar that bolted to the Seat Side (A003_P001_R001), it has now been replaced by a two-part laser cut beam (A003_P003_R002 & A003_P004_R001) where the Cross Beam slots into the Seat Side. To prevent movement of the cross beam structure once it is in place, a “biscuit” insert (A003_P005_R001) is glued to the beam, through the Seat Side.

Also important is the hinge area. The Seat Side (A003_P001_R002) and the Hinge Plate (A003_P002_R002) rotate compared to each other around the pivot, so the Seat Side is radiused about that point. This means that, as the seat moves, there is no change in the position where the edges of each part meet. If this wasn’t the case, the movement of the two plates would make a scissoring action; but centering the arc of the Seat Side with the pivot will mean there are no pinch points.

These parts are still subject to some revisions to connect them properly to the rest of the chassis.

add-rel-lightbox Version 0.4 Released

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Version 0.4 switches from identifing the link-wrapped images in a page with hacked-together regexes that just about work, to properly parsed HTML structure using PHP Simple HTML DOM Parser.

When I initially tried to release version 0.4 and installed the updated plugin on this site, suddenly the content for half the posts stopped being displayed. After retracting the update, having a small panic, and reviewing the code that had been working without error in testing, I eventually found the culprit of the missing content: a regex in another plugin!

It turns out that the Simple HTML DOM Parser is set to strip linebreaks from the HTML input as standard. It was this operation, on content that otherwise was not altered by add-rel-lightbox that was breaking a (.*?) heavy regex. See also: Death to Dot-Star!

I’ve now changed add-rel-lightbox to leave the linebreaks in the content, so it will return content completely untouched if there are no link-wrapped images in the post. This means that it will play nicely with with other plugins but, if nothing else, this is a good example of why HTML should be parsed properly instead of using regular expressions for all but the most predictable content.

The couple of questions on the plugin’s support forum suggests that add-rel-lightbox is being used with less lightbox-compatible image handlers, so it’s probably a good time to add some configuration options for the plugin. Nothing too complex; just some variables that can be stored so they don’t get overwritten by a plugin update.