Second Lattice Hinge Samples

As part of my first week as the new Technician-in-Residence at DoES Liverpool I’ve found time to photograph the acrylic test samples.

From the earlier posts, this second set of samples is sized to have the minimum possible bend radius for single laser cut to create the torsional links, and has three torsional stress levels; each with a different amount of robustness.

  • 36MPa — While this is a low enough stress for normal, gentle handling and can bend to 90 degrees; this is likely to break if mistreated, and does not bend much beyond 90 degrees before breaking.
  • 20MPa — Better than the 36MPa sample, this one can easily bend to 90 degrees, but may break if the sample is bent as far as 180 degrees, especially if the sample is cool.
  • 10MPa — More robust again, this can bend comfortably to touch both ends of the sample together, but is noticably less stiff than the 20MPa sample.

The minimum internal bend radius for 3mm panels with square cross-section links so the inner links do not bind was shown to be 44mm, so the test samples includes a 44mm radius corner.

The samples have 3 different sized hinges, where the torsional link length varies to affect the maximum stress that those links experience in a 90 degree bend (the design specification). The different lengths also affect the stiffness of the hinge too, so the longest (28mm) sample is much more flexible, and allows the hinge to twist slightly when handled as well as bend, though the lower stress give a much more robust hinge that can deal with rougher handling without breaking. By comparison, the stiffest hinge (8mm links) may break if moved too quickly or at too low a temperature; though it may be suitable for permanent or pre-assembled structures and the reduced length may be an advantage for use in shallow structures.

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

Lattice Hinge Test Results

Sine last week’s post about modelling Lattice Hinges, I’ve received the test pieces I ordered and also some very kindly cut by .:oomlout:. (the MDF set gave me some good insight into the hinge performance). I’ve had time to bend some, break some (and figure out why) and take some pictures.

Probably worth a look at last week’s post for details on the parts of the hinge structure (junctions and spring links).

In short: I’m quite happy that the torsion based formula I calculated gave me some hinges that worked, but it looks like the hinge design needs some more parameters.

For defining hinges I’d currently recommend:

  • Calculate the minimum number of links for the material, sheet thickness and link length.
    \[ n \geq 0.676125 \times \frac{\Theta G t}{\tau_{yield} l} \]
  • Calculate the minimum clearance gap for the links to twist freely — if this is less than the width of the kerf of the laser then only one cut is required.
    \[ k = -t + 2 \sqrt{ \frac{t^2}{2} } \times \cos \left( \frac{\pi}{4} – \frac{\Theta}{n} \right) \]
  • Decide the link length from the total hinge width (or the centreline radius of the curve)
    \[ W = tn + k(n+1) \]
  • To keep twisting of the bend joint, limit the spring length to less than four times the sheet thickness.
    \[ l \leq 4t \]

Symbol meanings at the bottom of the page.

Obviously, this is not very intuitive as a set of formulas, so I’ll have to generate some graphs/tables that give more succinct design guidance. And some more test pieces to validate them.

Test Results

Of all the test cuts in acrylic, I was able to bend all 4 samples to 90⁰, which suggests that the formula for calculating the number of spring links for the hinge is successful in limiting the material stress. However, the longer the spring connection samples were not very robust. Continue reading Lattice Hinge Test Results

Laser-cut Lattice Living Hinges

AKA: Snijlab-style living hinges, Sninges, Laser cut hinges, or my prefered title: Lattice Hinges

Flexi-Acrylic Test by Solarbotics, on Flickr
Flexi-Acrylic Test by Solarbotics, on Flickr

After this style of hinge popped up again, this time on Makezine, I was having a look at the linked project guide and at how they worked and I realised that a bit of mathematical modelling could lead to better designed hinges. This could mean fewer rounds of trial-and-error prototype tests, which would reduce the cost of using lattice hinges in a project, and better fatigue resistance, meaning the hinges could be used for moving parts instead of just for static bends.

Download links for the test specimen files are included at the end of this post.

This style of hinge appeared recently in the work of Snijlab, a Dutch laser cutting workshop when they showcased a folding notebook cover mode from a flat sheet of laser cut plywood. They apparently took some inspiration from MEMS hinges; and work by other designers has used some similar principles.

Others soon started to see the usefulness of a hinge that can be cut into flat sheet materials, .:oomlout:. released a plywood arduino box that can be made from only 3 pieces. Solarbotics and @kngunn showed that the lattice cuts also make acrylic, a notoriously brittle material, flexible enough to bend cold.

How do they work?

In addition to giving a hinge, a set of lattice cuts also allow for in-plane expansion and compression prependicular to the line of the cuts.

Basic Lattice Hinge Shape
Basic Lattice Hinge Shape
Lattice Hinge in Compression
Lattice Hinge in Compression
Lattice Hinge in Tension
Lattice Hinge in Tension

In tension and compression, there are three repeated parts that allow the distortion to take place: two “Junctions” that do not deform connected by a thin piece that deflects along its length that I’ve dubbed the “Spring Connection”. It’s the elasticity (springiness) of the connection that allows the two ends to move relative to each other, and its this action gives a clue to how the connected system might work as a hinge. Continue reading Laser-cut Lattice Living Hinges