Robotic Fabrication of Stone Assembly Details

Abstract

This research follows an important body of work from
the past decade, which focuses on the design of global
surface geometries for compression-only structural
behaviour. For example, studies in thrust network
analysis have made possible the design and computation
of complex unreinforced freeform shell structures that
work purely under compressive forces once they are
completely assembled (Block, 2009). Recent built projects
have shown that while it is possible to construct these
structures with standard CNC fabrication tools and for
them to demonstrate efficient structural behaviour with
minimal bending as expected, a major challenge of
building these structures is the development of effective
assembly strategies during construction to handle
tolerance (Rippmann et al., 2016). A second key challenge
is the management of falsework, which is structurally
necessary to hold individual voussoirs, or compression
blocks, in place until the structure is stable, which is
sometimes not until the final stone is placed.

Full text

ACHIM MENGES / BOB SHEIL / RUAIRI GLYNN / MARILENA SKAVARA

FABRICATE
RETHINKING DESIGN
AND CONSTRUCTION
ACHIM MENGES / BOB SHEIL / RUAIRI GLYNN / MARILENA SKAVARA

This research follows an important body of work from
the past decade, which focuses on the design of global
surface geometries for compression-only structural
behaviour. For example, studies in thrust network
analysis have made possible the design and computation
of complex unreinforced freeform shell structures that
work purely under compressive forces once they are
completely assembled (Block, 2009). Recent built projects
have shown that while it is possible to construct these
structures with standard CNC fabrication tools and for
them to demonstrate ecient structural behaviour with
minimal bending as expected, a major challenge of
building these structures is the development of eective
assembly strategies during construction to handle
tolerance (Rippmann et al., 2016). A second key challenge
is the management of falsework, which is structurally
necessary to hold individual voussoirs, or compression
blocks, in place until the structure is stable, which is
sometimes not until the final stone is placed.
These challenges are important to address in order
for ecient, geometrically expressive masonry shell
structures to play a larger role in the contemporary
ROBOTIC FABRICATION OF
STONE ASSEMBLY DETAILS
INÉS ARIZA1, 3 / T. SHAN SUTHERLAND2 , 3 / JAMES B. DURHAM3 / CAITLIN T. MUELLER1 / WES MCGEE2, 4 / BRANDON CLIFFORD1, 4
1 Massachuset ts Institute of Technology
2 University of Michigan
3 Quarra Stone
4 Matter Design
architectural fabrication landscape alongside
conventional steel, concrete and timber structures.
In response, the research presented here oers a new
approach for the fabrication and assembly of freeform
masonry shell structures that can be built with less
error and less falsework. Made possible through a
computational workflow that simulates structural
behaviour during assembly instead of only after a
structure is completed, the approach employs cast-metal
joining details that bring ancient stonework techniques
into the digital age with customised, mechanically
responsive geometries.
New agendas for stone carving
Correlating forces (physics) and form (geometry) in
3D, thrust network analysis and accessible physics
simulation environments based on dynamic relaxation
have extended historical structural form-finding methods
into new versatile digital design workflows (Block, 2009,
Rippmann et al., 2011, Piker, 2013). One of the results of
the availability of these new geometrical exploration
approaches has been a renewed interest from designers 1
107106

in historical techniques such as stone carving (Lachauer
et al., 2011, Rippmann et al., 2016, Cliord et al., 2015,
Kaczynski et al., 2011).
Construction of discrete element structures
Most of the current research eorts in discrete
element structures have focused on the production of
geometrically challenging thin structures that perform
eciently once they are finally assembled. These eorts
have not emphasised the forces arising during assembly,
or have solved this problem through external means such
as scaolding, chains or ropes (as in Deuss et al., 2014). In
contrast, this research approaches the problem of stability
during assembly through integrated details.
Stone detail precedents and methods
Two types of detail precedent inform this research. The
first is the historic process of carving a detail geometry
into stone and direct casting metal into that geometry.
This detail is often embedded inside the thickness of
stone and is not visible. The motivation of this detail
is to resist a possible future force, such as settling or
an earthquake. These details are not constrained by
the mass of stone, but rather by the properties of metal
shaping or casting and the carving tools used (Leroy et
al., 2015). The second detail precedent is a procedural one.
For instance, Inca stonework carries vestigial details that
hint at the sequence in which a wall was constructed.
Each detail refers to a particular moment of assembly
and its relation to previously placed stones. This concept
can be seen not only in the way the stones notch into
each other, but also in the nubs used to place the stones
(Protzen, 1993). This research seeks to conflate these two
detail concepts in order to incorporate procedural and
sequential structural analysis to inform detail locations.
These locations are responsive not only to the global
conditions, but also to the discrete conditions of the
in-progress assembly (Fig. 2).
This project examines the problem of assembling
masonry structures through the integration of
computation, analysis and simulation during the
design phases. The motivation of the research is to
develop a streamlined workflow which encompasses
design, fabrication and assembly of discrete element
structures by leveraging the possibilities of digital
fabrication methods. Through a focus on historically
inspired details, this paper seeks a new approach that
can expand the possibilities for designing and building
expressive, ecient structural forms.
Physics analysis
This method proposes an alternative assembly
strategy for freeform stone shells that relies on a
local understanding of forces at each step of the
assembly sequence (Ariza, 2016). The structural
analysis includes two steps: a global analysis that
evaluates the equilibrium of the structure in its final
state and a local analysis that evaluates all intermediate
equilibrium states during assembly. The analyses are
conducted with Karamba v.1.2.1, a finite element analysis
plug-in for Grasshopper (Preisinger, 2013), and directly
contribute to the design and distribution of cast tension
details. Specifically, the analyses consider reactions
generated at boundary conditions between elements
and at the interface with the ground to determine the
types and locations of necessary details.
Global equilibrium analysis
Because the base geometry is not generated to fulfil
one single constraint (i.e. structural performance),
global stability is not guaranteed. The results of the
overall calculation of reaction forces at the base of the
eight-piece section of the structure are shown in Fig. 5.
Local equilibrium analysis
The discrete analysis step comprises assigning an
assembly sequence of voussoirs, determining the
support location and condition of each voussoir
according to the sequence and visualising the
reaction forces at each support.
Assembly sequence
The sequence of assembling voussoirs does not aect
the global stability of the final assembled structure.
However, there is a big impact on stability during the
assembly process. While this research does not rigorously
address this question, the topic has been studied in Deuss
(2014). This research establishes a reasonable assembly
sequence using rings of voussoirs, and the most stable
unit of each ring is assembled first. As each new voussoir
is added, it is not possible to assume that the previous
state of equilibrium is still valid. Ultimately, every
previous interface between voussoirs needs to
be checked, since each is aected by every new addition.
As a proxy, in this case study the stability of the global
intermediate, or the sum of all previously assembled
voussoirs, is checked at the base (Fig. 5).
1. Six-piec e mock-up,
exte rior.
2. (a) Cavities that we re
carved into s tones and
fitted with s teel joints during
the Angkorian era ( Mitch
Hendrickson, source:
Cambodia Da ily) and
(b) Inca wall assembly
detail (Brandon Clifford).
3. Sectio n of assembly
strategy.
4. A 3D diagra m showing
particles , springs and final
voussoirs.
5. A 3D diagr am showing the
variable volume eig ht-piece
mock-up and th e results
from the overall analysis
showing reacti on forces at
the base.
2 3
4
5
The assembly method in this research comprises
six steps from design to assembly: base geometry,
discretisation, physics analysis, detail design, fabrication
and assembly. The method is exemplified by an eight-
piece masonry structure case study shown in Fig. 5,
manufactured at Quarra Stone in Madison, Wisconsin.
Base geometry
This research employs a method which serves to liberate
geometry from the exclusive dedication to structural
requirements. Though essential, structural forms rarely
align with programmatic, ergonomic, thermal or formal
concerns. In order to accommodate a confluence of
diering concerns, the potentials of depth and volume
are employed, resulting in an anti-isomorphic condition,
as described previously (Cliord et al., 2015). This deep
condition produces a zone of operation that Wolfgang
Meisenheimer describes as the ‘work body’
(Meisenheimer, 1985) – a space between the visible
architectural surfaces which is dedicated to the means
and methods of making. This method begins with a
base geometry informed by the above extra-structural
concerns. This singular surface approaches a structural
logic, but does not satisfy it. Through variable depth and
detailing strategies, this non-idealised form transforms
into a proposal which satisfies a thrust network within the
middle third of the material depth (Fig. 3).
Discretisation
Next is the discretisation of the base geometry into
voussoirs. Many dierent discretisation methods are
possible – in this case, a Voronoi-based discretisation is
created using a particle-spring system, which creates a
random gradient distribution of 3D voussoirs that are
larger toward the base of the structure (Fig. 4).
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Detail design
Details can be inspired by dierent motivations. In this
project, the role of the details is to coordinate dierent
type of constraints: structural (type, direction and
magnitude of reaction forces), fabrication (properties
of the carving and casting tools and machines)
and assembly (direction and fixing steps of units).
This approach takes advantage of the ability of robots
to perform custom non-repetitive stone carving and
match it with cast metal’s ability to be formed with
geometric flexibility.
Structural constraints
The reaction forces of the discrete analysis are
interpreted one by one, matching type, direction and
magnitude with specific geometric detail strategies.
Compression forces require surface area, so the planar
edges of the voussoirs are left unmodified. Tension forces
in the plane require a locking geometry in plane and in
the direction of the tension vector to avoid units pulling
apart. Out-of-plane tension forces and bending moments
are counteracted with couples on opposing faces. In-plane
shear forces require a locking geometry perpendicular to
the plane of action of the force.
Fabrication constraints
The type of stone, the geometric properties and the
performance of tools define the carving constraints.
This paper’s case study uses Vermont Marble and a
blunt electroplated tool. The tool diameter defines the
minimum radius of possible carved curvature, and the
tool shaft height defines the maximum carving depth.
This last parameter is key to specifying possible locations
of tension details.
Casting constraints are dictated by the way in which
the metal flows through and freezes in the mould when
poured. Sharp external corners result in more rapid
cooling, leading to increased grain size and brittleness.
Sharp internal corners often result in cracking during
freezing. Drastic changes in cross-sectional area and
volume result in uneven cooling and grain structure.
Since traditional clips and butterfly joints in wood or
wrought metal do not suer from such constraints,
cross-sectional areas can be varied as much as needed.
The translation of this geometry to cast metal requires
modification to maintain a constant cross-sectional area
throughout the joint.
motion and a reduced range of joint configurations,
accuracy can be improved; in addition, the overall work
volume of the robot increases significantly. Both of these
techniques are employed in the fabrication of the case
study. In order to maximise part accuracy, individual
voussoirs are processed from a solid blank to the finished
part using a single fixturing set-up on a flat back face.
Cutting operations
The production of individual voussoirs benefits from an
automatic tool changer set-up and comprises four robotic
carving operations (Fig. 6). The majority of the stock is
removed with a thick diamond composite blade. The first
operation, a saw slab-cutting strategy, is used for cutting
the flat-bearing surfaces of the voussoir. This proved to
be the most ecient operation, with a higher material
removal rate (material removed per minute). Then the
internal face is accomplished with a parallel kerf-
roughing and a side-cutting finishing, the latter in a
motion perpendicular to the previous direction of the
blade. Finally, an electroplated diamond tool is used for a
pocketing milling operation that produces the joint voids.
Automation of geometry for toolpathing
While the implemented algorithmic design approach
generates highly unique geometries with relative ease,
it was important to identify production bottlenecks early
in the project. While fully automated design-to-machine
code strategies have been implemented in certain
projects, it was determined that a hybrid approach would
integrate better with the fabrication workflow at Quarra
Stone. This involved the automated generation and
organisation of 3D part files with the needed ‘helper’
geometry to work smoothly with the production CAM
package used by the fabrication team.
Assembly
Several challenges arise in the placement of the
individual voussoirs. First, the stones are never set
upon a level surface and the centre of mass of the
piece is often not directly over the bearing surface,
resulting in temporary instability during assembly.
Second, while the meeting faces of the voussoirs are
drafted in all directions, which facilitates positioning,
there are still several degrees of freedom in the
movement of the stones as they are individually placed.
To counteract this temporary instability, a two-step
assembly method is implemented.
Fitting and registration
Using minimal, adjustable tension and compression
falsework, each voussoir is fitted in place by hand and
registered to its correct location by a precast tapered
drift-pin applying tension normal to the adjacent faces of
the two stones. This registering operation facilitates the
minute adjustment of the voussoirs after placement and
temporarily holds them in place during the completion of
the ring. The malleable drift-pins also have the capacity
to be adjusted to fit in case of fabrication inaccuracies.
Casting and fixing
After the placement of an entire ring of voussoirs, the
pre-machined drafted voids of the shear details located
between the most vertical faces of the stones are filled
with metal in-situ, permanently fixing the ring together.
Finally, the precast adjustable pins holding the course
in place are cast over in-situ, permanently locking the
drift-pin in place. Additionally, any gaps between
voussoirs resulting from the tolerances in fabrication are
filled during the pouring of the in-situ joints. This series
of operations is then repeated for each consecutive ring.
Research evaluation
The validity of the structural analysis and assembly
method was assessed through a series of structural
tests of specific cast details and prototypes. The former
evaluated the material strength and eciency of the joint
geometry throughout a series of controlled specimens.
Dierent mock-ups explored the possibilities and
performance of the various available machining
methods, the casting and assembly processes and
the materials to be used in the precast and in-situ
details. The final eight-piece case study served as a final
evaluation of the overall detailing and assembly method.
6. Cuttin g operations: (a)
edge saw cut ting, (b) face
side- cutting and (c) detail
milling.
7. (a) Casting of specimens ,
(b) casting of join ts in-situ
and (c) sample speci men of
tension joint.
6
Assembly constraints
The assembly strategy is composed of two steps:
registration and fixing. In order to register the pieces
that are in place, a precast metal drift-pin is inserted,
followed by the cast in-situ final fixing of the unit. This
two-step assembly strategy determines the drafted
geometry and the material selection of the drift-pins.
Robot control and constraints
Industrial robots are designed to be highly flexible
manipulators, but this flexibility results in compromises
with respect to overall volumetric accuracy. One technique
for minimising positioning error is to utilise an external
synchronous positioning axis (rotary table). By allowing
the robot pose to be restricted to a smaller range of
7
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face were found to be a useful temporary falsework
method to support pieces in place until the final fixing of
the ring was achieved. Regarding structural performance,
units with larger instability were successfully supported
by drift-pins in cases of no larger than 3mm inaccuracies.
This last test proved the importance of the geometry of
the drift-pin as a tolerance-handling method.
Conclusion
This research successfully demonstrates a new method
to design, analyse and construct complex geometry shell
structures which satisfy a confluence of architectural
concerns, without the need for extensive falsework,
formwork or templating. Through computation, digital
fabrication and the adaptation of ancient detailing
strategies, this method points to a possible application
of design in synchronous feedback with the constraints
of assembly. While the potentials of such a method
accommodate an endless number of possible geometries,
the analysis points to a series of constraints. These
constraints exist primarily in the structural and material
properties of stone and metal, the geometric constraints
of fabrication and the problematics of compounding
errors during assembly.
Future research seeks to further evaluate the capabilities
of assembly simulation and sequential fixing in the
construction of a full-scale marble caldarium.
Acknowledgements
This research was co nducted as part of the 20 16 QuarraMatter Fello wship,
an industry/acade my partnership betwee n Quarra Stone (www.quarrastone.
com) and Matter D esign (www.matterdesignstudio.com). Each summer, two
fellows are embed ded in Quarra Stone to produc e a research project in
advanced fab rication techniques. Th e form generation employs T-splines
(www.tsplines.com) as an organic mod eller to inform Grasshopper (www.
grasshopper3d.com), a plug-in develop ed by David Rutten for Rhino ceros
(www.rhino3d.com), a programme develop ed by Robert McNeil . In addition,
the analysis comp utation employs Karamba (w ww.karamba3d.com) by
Clemens Preisin ger, and Kangaroo (www.g rasshopper3d.co m/group/
kangaroo), Plankton (Ibid./plankton) and MeshMachine (Ibid./meshmachine)
by Daniel Piker. The fabri cation computation utilis es a custom C# script by
Wes McGee to auto mate toolpath geometries , SUM3D (cap-us .com) for
toolpath generation and RoboM OVETM (ww w.qdrob otics.com/eng/
robomove) by QD Rob otics for robot programme s imulation. Structural
testing was provide d by Daren Kneezel and Jeff S carpelli of Wiss, Janney and
Elstner (ww w.wje .com). The project team inclu des Brian Smith and Alireza
Seyedahmadia n. The authors would like to thank Al exander Marshall, Eric
Kudrna, Ryan Askew an d Edgar Galindo for their fabric ation support.
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910
Material tests
Structural tests were performed on details with two dierent
casting alloys: pewter (AC or Brittania), an alloy of tin,
copper and antimony; and zamak 3, an industrial die-casting
alloy of mostly zinc, copper and magnesium. Despite having
a much lower ultimate tensile strength (51.7 MPa) than
zamak (284.8 MPa), pewter was selected due to its lower
melting point, shrinkage and brittleness, its resistance to
work hardening and its higher flow rate (Fig. 7).
Ten geometric variations of tension joint were tested.
Controlling variables included the length, depth and
thickness of the joint. Three specimens of each geometry
were tested to failure under tension. The most successful
specimens transferred between 9 and 12.5kN under
tension (Fig. 8).
Eight-piece case study
The eight-piece case study made from Vermont Marble
served to evaluate the various aspects of the research.
In terms of fabrication, inaccuracies (up to 3mm) related
to the location of joints were handled with the specific
assembly strategies described above. The most critical
inaccuracy location was found to be the intrados of the
voussoir, for which further fabrication and assembly
strategies need to be studied. In terms of assembly,
ratchet straps attached to the fixtures of the flat back
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