Interlocking Folded Plate – Integral Mechanical Attachment for Structural Wood Panels

Article (PDF Available)inInternational Journal of Space Structures 30(2):111-122 · June 2015with 7,696 Reads
DOI: 10.1260/0266-3511.30.2.111
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Abstract
Automatic joinery has become a common technique for the jointing of beams in timber framing and roofing. It has revived traditional, integral joints such as mortise and tenon connections. Similarly, but only recently, the automatic fabrication of traditional cabinetmaking joints has been introduced for the assembly of timber panel shell structures. First prototypes have used such integrated joints for the alignment and assembly of components, while additional adhesive bonding was used for the load-bearing connection. However, glued joints cannot be assembled on site, which results in several design constraints. In this paper, we propose the use of dovetail joints without adhesive bonding, on the case study of a timber folded plate structure. Through their single-degree-of-freedom (1DOF) geometry, these joints block the relative movement of two parts in all but one direction. This presents the opportunity for an interlocking connection of plates, as well as a challenge for the assembly of folded plate shells, where multiple non-parallel edges per plate must be jointed simultaneously.
Interlocking Folded Plate - Integral Mechanical Attachment for
Structural Wood Panels
Christopher Robeller 1and Yves Weinand 1
1Timber Construction Laboratory IBOIS, EPFL
June 20, 2015
Abstract
Automatic joinery has become a common technique for the jointing of beams in timber framing and
roofing. It has revived traditional, integral joints such as mortise and tenon connections. Similarly,
but only recently, the automatic fabrication of traditional cabinetmaking joints has been introduced
for the assembly of timber panel shell structures. First prototypes have used such integrated joints
for the alignment and assembly of components, while additional adhesive bonding was used for the
load-bearing connection. However, glued joints cannot be assembled on site, which results in several
design constraints.
In this paper, we propose the use of dovetail joints without adhesive bonding, on the case study
of a timber folded plate structure. Through their single-degree-of-freedom (1DOF) geometry, these
joints block the relative movement of two parts in all but one direction. This presents the opportunity
for an interlocking connection of plates, as well as a challenge for the assembly of folded plate shells,
where multiple non-parallel edges per plate must be jointed simultaneously.
1 Introduction
Architectural designs have often been inspired by
folded shapes such as Origami, however the fold-
ing principle can rarely be applied to building
structures directly. Instead, many folded plates
have been cast as concrete thin-shells in the 1960s.
These constructions were labour-intensive and re-
quired elaborate formwork for the in-situ casting.
Prefabricated constructions with discrete ele-
ments made from fiber-reinforced plastics have
been researched in the 1960s. [1]
Folded plates built from laminated timber pan-
els have been presented by C. Schineis [19] (Glu-
lam) and H. Buri [2] (Cross-laminated Timber).
These designs combine the elegant and efficient
shape of folded plate shells with the advantages of
structural timber panels, such as CO2 storage and
a favorable weight-to-strength ratio. However, a
major challenge in the design of a timber folded
plate is presented by the joints: Since timber pan-
els cannot be folded, a large amount of edgewise
joints has to provide two main functions. One
of these functions is the load-bearing behaviour,
where connector features of the joints must pro-
vide a sufficient stiffness and rigidity. The second
main function of the joints is the assembly of the
parts, where locator features of the joints are es-
sential for a precise and fast positioning and align-
ment of the parts.
B. Hahn [5] examined the structural behaviour
of a first timber folded plate shell which was built
from plywood and assembled with screwed miter
joints, concluding that the load-bearing perfor-
mance could be improved significantly with more
resistant connections.
Inspiration for such improvements may be found
in integral mechanical attachment techniques, the
oldest known technique for the jointing of parts,
where the geometry of the parts themselves blocks
their relative movements [13]. Such integrated
joints have recently been re-discovered by the tim-
ber construction industry. Beginning in 1985,
mortise-and tenon joints have been repatriated in
timberframe and roof constructions [7]. Only very
recently, integrated joints have also been proposed
for the edgewise jointing of timber panels. In
the ICD/ITKE Reserach Pavilions 2011 [12] and
1
2013 [11], fingerjoints have been applied to ply-
wood panels and an application of dovetail joints
for cross-laminated timber panels (CLT) was pre-
sented in the IBOIS Curved Folded Wood Pavil-
ion 2013 [18]. In these prototype structures, the
integrated joints have played an important role
for the assembly of the components. They have
also participated in the load-bearing connection
of the parts, but additional adhesive bonding was
needed. With few exceptions [6], such glued joints
cannot be assembled on site, because they require
a curing period with a specific constant tempera-
ture and humidity [15]. Therefore, their applica-
tion is limited to off-site assembly of larger compo-
nents, which complicates both transport and han-
dling while still requiring additional connectors for
the final assembly.
In this paper, we propose the use of dovetail
joints without additional adhesive bonding, on the
case study of a timber folded plate shell. (Figure
1).
Through their single-degree-of-freedom (1DOF)
geometry, these joints block the relative movement
of two parts in all but one direction. This presents
the opportunity for an interlocking connection of
plates, as well as a challenge for the assembly
of folded plate shells, where multiple non-parallel
edges per plate must be jointed simultaneously.
1.1 Dovetail joint geometry and me-
chanical performance
Using polygon mesh processing, we describe an
edgewise joint based on its edge E. From the
mesh connectivity, we obtain the edge vertices p
and qand the adjacent faces F0and F1with their
face normals n0, n1. We use the polygon mesh
to represent the mid-layer of timber panels with
a thickness tand offset F1and F2at ±t
2to ob-
tain the lines L(Figure 2a). From a division of
E, we obtain the points Xjfor a set of refer-
ence frames {u1, u2, u3}, where u1k~pq and u2kn0
(Figure 2b). A finger joint geometry is obtained
from an intersection of planes located at Xj, nor-
mal to u1, with the four lines L.
Without additional connectors, finger joints are
a kinematic pair with three degrees of freedom
(3DOF), also called planar joints. They can re-
sist shear forces parallel to the edge and in-plane
compressive forces. However depending on the
plate geometry, thickness and most of all rota-
tional stiffness of the connection detail, bending
moments are also transferred between the plates.
Also, due to the rotation of the plate edge caused
Figure 3: FEM analysis (top view) of a 3x3m,
21mm Kerto-Q folded plate thin shell assuming
fully stiff joints. Distribution of traction (red)
and compression (blue) stresses in the y direction.
Top: gravity load case. Bottom: asymmetric snow
load.
by bending, in-plane traction forces perpendicu-
lar to the edge line appear and their magnitude
increases under asymmetrical loads. Such forces,
which occur as a result of out-of-plane loading,
cannot be supported only by shear and in-plane
compression resistant joints.
On a dovetail joint (Figure 2d,e), the intersec-
tion planes on the points Xjare normal to a ro-
tated vector w1. It is obtained from a rotation
of the reference frame {u1, u2, u3}about u3at an
alternating angle ±θ3. The resulting rotated side
faces reduce the dovetail joints degrees of freedom
to one translation ~w3(1DOF). Simek and Sebera
[20] have suggested θ3= 15for spruce plywood
panels. Such prismatic joints can only be assem-
bled or disassembled along one assembly direction
~v =~w3. In addition to the finger joints resistance
to shear and compressive forces, dovetail joints
can, without adhesive bonding, also resist bend-
ing moments and traction forces which are not
2
Figure 1: Folded thin shell prototype built from 21mm LVL panels, assembled with single-degree-of-
freedom dovetail joints without adhesive bonding. Components interlock with one another
p
q
p
q
p
q
n0n1
w3
F0
F0
F+
F0
F-F1
F1
F+
F1
F-
a. b. c. d. e.
u2u3
u1
Ei
L1
L
L3
LL2
L
L0
L
Xj
j+1
j+2
j+3
j+1
j+2
j+3
j+1
j+2
j+3
v
w1
w2
Figure 2: Joint geometry. a: Basic parameters, b: Intersection planes (grey) normal to ~pq, c: 3DOF
joint, d: Rotated intersection planes (grey) normal to ~wj, e: 1DOF joint
parallel to ~v. Due to the inclination of the side
faces of the joint, resistance to these forces can be
improved significantly. In that way the inclined
faces take over the role that the glue would have
in a finger joint. (Figure4)
1.2 Fabrication Constraints
One of the main reasons for the resurgence of fin-
ger and dovetail joints is the possibility of auto-
matic fabrication. However, the mechanical per-
formance of the joints depends on fabrication pre-
cision. At the same time, fast machine feed rates
are important for a time-efficient production. We
have fabricated such joints with a robot router and
a gantry router, achieving higher precision with
the gantry machine, which is more stiff and pro-
vides a higher repeat accuracy.
The variability of the machine-fabricated joints
is enabled by the 5-axis capability of modern
routers: Although traditional edgewise joints in
cabinetmaking were used for orthogonal assem-
blies, both the finger and dovetail joint can also
be applied for non-orthogonal fold angles, which
was essential for the reference projects mentioned
before. However, there are certain fabrication-
related constraints for machine-fabricated dovetail
joints. In order to integrate the joint fabrication
directly with the panel formatting, we use a side-
cutting technique [8], which is limited to a tool
inclination βmax. We obtain this limit from the
specific geometry of the tool, tool-holder and spin-
dle used for the joint fabrication. (Figure 5)
The parts can be assembled in two ways, as
shown in figure 5, which allows to address a larger
range of dihedral angles ϕ. From this we ob-
tain the fabrication-constrained most acute fold
ϕmin = 90βmax and most obtuse fold ϕmax =
90+βmax. With standard cutting tools, this tech-
nique allows for the jointing of acute folds up to
3
Figure 4: FEM simulation of bending on a dovetail joint connecting two Kerto-Q 21mm LVL panels.
The bending moment applied is transformed into compression, normal and shear forces parallel to the
inclined contact faces.
βmax
φmax
φmin
βmax
βmax
TCP
TCP
TCP
TCP
TCP
TCP
TCP
TCP
TCP
TCP
TCP
TCP
Figure 5: Fabrication Constraints. Side-cutting technique used for the automated fabrication of 1DOF
edgewise joints with common 5-axis CNC routers. The maximum tool inclination βmax results from
the tool and the tool holder geometry. From this we obtain the range of possible dihedral angles ±ϕ
between panels.
ϕ= 50, which is ideal for folded plate structures.
Very obtuse fold angles ϕ140, which might be
required for smooth segmented plate shells, can-
not be fabricated with this method.
1.3 Simultaneous Assembly of Multiple
Edges
The assembly of doubly-corrugated folded plates
requires the simultaneous joining of multiple edges
per component (Figure 1), which has implications
on both the shell and the joint geometry.
For multiple 1DOF-jointed edges, simultaneous
assembly is only possible if the individual assem-
bly directions ~v are parallel. With a normal dove-
tail joint geometry (Figure 7a), this is not the case:
A simultaneous assembly is only possible for par-
allel edges, which allows only for rectangular as-
semblies, such as drawers or a cabinets.
In order to simultaneously join non-parallel
edges, we must rotate the assembly direction vof
the joints to make them parallel. This possibility
is known from Japanese cabinetmaking [9], where
certain joints, like the Nejiri Arigata Joint (Figure
7b), are assembled diagonally, along a vector that
does not lie on either one of the two planes. While
European dovetail form a prism with a single tab,
e1
e2
e1
e0
e2e1
e0
x3
x2
Figure 6: The assembly of a folded plate from dis-
crete elements (left side) requires the simultaneous
assembly of non-parallel edges. (right side) We
rotate the insertion direction of our 1DOF joints,
to make the insertion vectors of simultaneously
jointed edges parallel. We chose a hexagon re-
verse fold pattern which requires only moderate
rotations.
4
vv
a. b.
faces across
edge only faces
across edge
faces along
edge +
Figure 7: a. Dovetail Joint, b. Nejiri Arigata Joint
using faces both acrioss and along the edge, the
Nejiri Arigata joints form a prism using multiple,
differently shaped tabs.
We extend this Japanese technique to a vector
subset of possible assembly directions. Figure 8
shows that the rotation about the edge line is con-
strained to 180ϕi. The vector subset is large for
acute and small for obtuse fold angles. This is par-
ticularly important when joining multiple edges
simultaneously, because an intersection must be
found between multiple vector subsets (Fig. 9).
If there is an intersection, the parts can be joined
simultaneously along any direction within the in-
tersection of the subsets.
Finally we extend this concept to a 3-
dimensional rotation (Fig. 10). This is possible
through a second rotation θ2, which is constrained
to a maximum value of ±θ2,max. The limitation
results from multiple other corelated parameters,
such as θ1and βmax. We call the resulting 3D
vector subset rotation window.
With this method, we can search for a joining
solution for the prototype in figure 6. We compute
rotation windows S1,S2,S3for the edges E1,E2,
E3and overlay them at their center point. Fig-
ure 11 shows that there is a common vector sub-
set S1TS2TS3between these three edges, we can
choose our assembly direction within it.
As a result of these limited rotations, the an-
gle between neighbouring, simultaneously joined
edges cannot be very acute. Folded plate pat-
terns like the Herringbone, the Diamond, or the
Hexagon pattern, which we chose for our proto-
types, (Figure 6) work well for our joining tech-
90° 130°50°
"
#
!
!
E34 68344
a.
Figure 8: 2D vector subset
3"3$
3"
3$
E1E2
E1
E2
b.
Figure 9: 2D simultaneous assembly
2, max
1
Figure 10: 3D vector subset
5
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