The principles of the graphic statics method have been explored in their three dimensional extent on the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams. Computational tools have been utilised to generate compression only networks through a polyhedra packing strategy; through multiple iterations, different topologies have been explored with the aim of understanding the spatial features and opportunities given by the form finding method.

Prototyping Workshop

Aim of the workshop was the application of the computational research for the materialisation of prototypes of different scales exploring the full capacities of the material and technological system in relation to the forecasted architectural applications.

Prototypes have been explored as a way to prove the theoretical principles in the physical world; small scale models have been realised first as test models which led to the fabrication of a 1:1 scale prototype.

Robotic technology has been considered as fundamental aspect of the fabrication process. The robotic arm Nachi MZ07 has been utilised as a design tool to enhance the design quality and expand the limited human capacities. The use of the latter has been exploited to spatially orient the structural members as first step of a human-robot collaborative process. An hybrid system of on site prefabrication and assembly is proposed as fabrication strategy.

DNA: DISCRETE NETWORK ASSEMBLY

Scaling up the prototyping activities were meant to explore in detail the behaviour of the material system, the logistics and timing of production, and the robot contribution in the design and assembly phase.

Tutors: Shajay Bhooshan Assistants: Alicia Nahmad, Vishu Bhooshan, David Reeves Aydinoglu Begum | Borello Federico | Siedler Philipp

Shajay Bhooshan Studio

DNA: DISCRETE NETWORK ASSEMBLY Prototyping Workshop

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Prototyping Workshop: Index _01 Introduction _01.1 Abstract _02 Computational Research _02.1 Architecture and geometry _02.2 Principles of graphic static _02.3 Principles of 3d graphic static _02.4 Topological studies _03 Manual Prototyping _03.1 Approach 1 CIDORI _03.2 Approach 2 Finger Joint Connection _04 Robotic Fabrication _04.1 Introduction _04.2 Endeffector Design _04.3 Fabrication Sequence _04.4 1:1 Large Scale Prototype

_01

Chapter 1: Introduction _01.1 Abstract

_01.1

Abstract

ABSTRACT Aim of the workshop is the application of the computational research for the materialisation of prototypes of different scales exploring the full capacities of the material and technological system in relation to the forecasted architectural applications. The principles of the graphic statics method have been explored in their three dimensional extent on the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams. Computational tools have been utilised to generate compression only networks through a polyhedra packing strategy; through multiple iterations, different topologies have been explored with the aim of understanding the spatial features and opportunities given by the form finding method.

LIGHTWEIGHT STRUCTURE (Compression Networks)

Prototypes have been explored as a way to prove the theoretical principles in the physical world; small scale models have been realised first as test models which led to the fabrication of a 1:2 scale prototype. Scaling up the prototyping activities were meant to explore in detail the behaviour of the material system, the logistics and timing of the production, and the robot contribution in the design and assembly phase. Robotic technology has been considered as fundamental aspect of the fabrication process. The robotic arm Nachi MZ07 has been utilised as a design tool to enhance the design quality and expand the limited human capacities. The use of the latter has been exploited to spatially orient the structural members1 as first step of a human-robot collaborative process. An hybrid system of on site prefabrication and assembly is proposed as fabrication strategy.

HYBRID SYSTEM (Structure + Membrane)

ROBOTIC FABRICATION (Discrete Elements Assembly)

1 Bendsoe MP, Optimal shape design as a material distribution problem. Struct Optim 1(4):193â€“202, 1989.

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Chapter 2: Computational Research _02.1 Architecture and geometry _02.2 Principles of graphic static _02.3 Principles of 3D graphic static _02.4 Topological Studies

_02.1

Architecture and Geometry

ARCHITECTURE AND GEOMETRY Core aspect of our research has been the interest in the use of geometrical principles to design complex lightweight structures1. Vaults and arches are considered great expressions of lightweight structures not because their materiality but because the geometric assembly and configuration of the material itself which leads to a reduction of its usage compared to similar structures. Axial forces play a key role in this sense; manipulating the overall geometry and the material assembly is central to control the forces flow throughout the material. Geometries are manipulated in a way to have axial forces without bending moments in order to minimize the use of material required within the structure itself.

Image 1. Apse of the Saint Chapelle du Palais, Paris 1248.

Projects from the 16th and 15th century have been considered like the Chapelle du Palais in Paris (Image 1), the central nave of the Winchester Cathedral (Image 2) as well as the Cathedral Chruch of Christ in Oxford (Image 3) as great manifestations of lightweight structures. More contemporary projects have also been explored which share the use of the geometrical principles as main parameters as solving method for complex structural problems. Felix Candela’s restaurant in Xochimilco (Mexico), Pier Luigi Nervi’s Palazzetto dello Sport in Rome and Frei Otto’s tensile structures share the focus in the tight relationship between material and geometric control as main design parameters. Structural design becomes central for the differentiation of spaces in their programatic functions, as container of social activies, enabling communication and allowing a comfortable and clear space navigation.

1

Image 2. Nave of the Winchester Cathedral, Winchester 1394-1450.

Frei Otto, Lightweight Principle, Institut für leichte Flächentragwerke (IL), 1998. Image 3. Choir of the Cathedral Church of Christ, Oxford XI Century 1478-1503.

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Architecture and Geometry

Felix Candela (1910-1997)

Pierluigi Nervi (1891-1979)

Image 4. Los Manantiales restaurant in the Xochimilco area of Mexico City (1958).

Image 5. Palzzetto dello Sport in Rome (1956).

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Image 6. German pavilion at Expo Montreal 1967 designed by Frei Otto.

_02.2

Principles of graphic statics

PRINCIPLES OF GRAPHIC STATICS Graphic statics is a method for structural form finding that originates in the pre-digital era, but continues to be used and developed even today. In graphic statics, the geometry and equilibrium of forces of a structural system are represented by two reciprocal diagrams: the form and the force diagram. Since the geometrical relationship between these diagrams provides explicit control over both form and forces of a structure simultaneously, graphic statics is considered as an intuitive technique for structural design, relevant to architects, engineers, researchers, and students1. Despite its clear strengths and advantages, existing method of graphic statics has some limitations. The most important one is that a designer can only design three dimensional structures by reducing them to a combination of two dimensional sub-systems, for example, by using projections.2

Force Diagram

Form Diagram

Image 7. “Le strutture reciproche nella statica grafica” by Luigi Cremona 1872.

Seminal projects have been explored as examples of application of the graphic static method in 19th century to solve vault structures like the St John cathedral in New York (Image 8) and St. Francis de Sales in Philadelphia (Image 9) both designed by Rafael Gustavino, as well as the Salginatobel Bridge by Robert Maillart (Image 10).

Image 8. Use of graphic static method to design the vault structure of the St John cathedral in New York by Rafael Gustavino 1888.

1 Masoud Akbarzadeh, Tom Van Mele, Philippe Block, On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams, Computer-Aided Design 63 (2015) 118–128. 2

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Luigi Cremona, Le figure reciproche nella statica grafica, 1872.

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Image 9. Tile dome of St. Francis de Sales in Philadelphia designed by Rafael Gustavino 1907.

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Image 10. Saginatobel bridge designed by Robert Maillart 1930.

_02.2

Principles of graphic statics

ROBERT MAILLART’S SALGINATOBEL BRIDGE The Salginatobel Bridge is Robert Maillart’s design for a competition held in summer 1928 to link the villages of Schuders and Schiers in the Swiss canton of Graubünden. Since its completion in 1930, the 90m-span bridge has received considerable praise: while some have celebrated its striking new art form, others have emphasized its brilliant economical and structural efficiency. It does indeed represent a great example of optimal and elegant design which did not have to undergo any repair work in its first 45 years, despite the poor quality of the concrete. There is therefore interest in the design methods employed, especially since Maillart only did handwritten workings and looked for straightforward methods to define the structure1. Built in 1929, this masterpiece has since received extensive recognition both for its structural elegance and its efficiency. However investigations into the design process enabling this degree of perfection remain incomplete. Studying Maillart’s original working drawings, this paper reviews the earliest stages chronology of the Salginatobel Bridge design process. It focuses on three methods: the use of graphically controlled parabolas, the minimization of bending moments within the bridge and the geometrical definition of the foundation block. These graphical methods reveal how Maillart simultaneously dealt with geometry and the flow of forces throughout using a straightforward, handy and efficient formfinding process which is still relevant today. Maillart used parabolas throughout the entire design process in order to define any non-straight geometry. Circles and catenaries are almost nonexistent in the first working drawings. A parabola is a regular curve frequently used for sketching arches to approximate catenary or funicular configurations under distributed loads. However, surprisingly, they are not meant to be used predominantly in that way here, but rather as a graphical convenience that is accurately reproducible and easy to handle with control points. This feature becomes essential since the geometry will be readjusted many times due to successive refining steps. The specific orientation of most parabolas and traces of their construction attest to their use as a non-structural, but purely graphical tool.

1 Corentin Fivet, Denis Zastavni, From the Salginatobel Bridge Desing Process (1928), Journal of the Internation al Association for Shell and Spatial Structures, 2012.

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Image 11. First working-drawing, Robert Maillart 1928.

Image 12. Reactions of the equilibrated half bridge in red; funicular polygon and its construction in blue; thrust line and its construction in orange.

Image 13. Line of centroids in red, thrust line in orange, eccentricities in red hatching.

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Principles of 3D graphic statics

EQUILIBRIUM OF FUNICULAR POLYHEDRAL FRAMES AND CONVEX POLYHEDRAL FORCE DIAGRAMS

F

z

Graphic statics is a method for structural form finding that originates in the pre-digital era, but continues to be used and developed even today. In graphic statics, the geometry and equilibrium of forces of a structural system are represented by two reciprocal diagrams: the form and the force diagram. Since the geometrical relationship between these diagrams provides explicit control over both form and forces of a structure simultaneously, graphic statics is considered as an intuitive technique for structural design, relevant to architects, engineers, researchers, and students1. Despite its clear strengths and advantages, existing method of graphic statics has some limitations. The most important one is that a designer can only design three dimensional structures by reducing them to a combination of two dimensional sub-systems, for example, by using projections. This paper therefore presents a three-dimensional version of graphic statics using reciprocal polyhedral form and force diagrams for the design and analysis of spatial frames with externally applied loads.

F P

z

x y

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y

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Image 1. Reciprocal relationship between the form diagram and the force diagram. Piped representation of the magnitude of the equilibrated forces. f1

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f2

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Image 2. (a) Computing normals of the faces; (b) aligning edges with their corresponding normals of the faces of the force diagram; (c) reconnecting geometry; and (d) progression and the end of the iterative process.

V2

V3

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1 Masoud Akbarzadeh, Tom Van Mele, Philippe Block, On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams, Computer-Aided Design 63 (2015) 118â€“128.

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V5

Af

Shared vertices

Shared faces

Form diagram vertices

Image 3. (a) The internal vertices and edges of the topological polyhedral frame are constructed by connecting the interior of adjacent polyhedral cells; and (b) connecting the internal vertices to the external faces completes the polyhedral frameâ€™s topology.

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_02.3

Principles of 3D graphic statics

EQUILIBRIUM OF FUNICULAR POLYHEDRAL FRAMES AND CONVEX POLYHEDRAL FORCE DIAGRAMS Subdividing the global force polygon in two-dimensional graphic statics is another technique to derive various funicular forms for given boundary conditions. In this approach, the â€œexternalâ€? polygon, representing global equilibrium, is subdivided into smaller polygons using various subdivision schemes. The result is a variety of compression-only forms with different topological properties for the same boundary condition. In threedimensional graphic statics, the force diagram of a compression-only structural form consists of a (group of) closed, convex polyhedral cell(s). Similar to 2D, the force diagram consists of external and internal components, which respectively represent the global and local (nodal) equilibrium of the spatial system of forces. Specifically, the areas of the faces of the force diagram represent the direction and the magnitude of the forces in the corresponding members in the form. The reciprocal relationship between the form and the forces in 3D, equivalent to twodimensional graphic statics, suggests that the subdivision techniques used in 2D can also be used and developed for the spatial form and force diagrams.

a

c

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b

Subdividing the global force polyhedron without changing the external faces merely changes the internal distribution of the forces and not the location, magnitude or direction of the applied loads. The result is a new compression-only funicular form with the same boundary conditions, but with a redistributed internal force flow. Various polyhedral subdivision schemes can be used to subdivide the internal space of the force polyhedrons. In general, any cell decomposition of the global force polyhedron that is closed and has planar faces, can represent the equilibrium of a spatial funicular form. Consider the funicular form and its global force tetrahedron of Figure 2. Recursive barycentric subdivision of the global force tetrahedron results in various structural forms preserving the same boundary conditions.1

1 Masoud Akbarzadeh, Tom Van Mele, Philippe Block, Three-dimensional Compression Form Finding through Subdivision, Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam.

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Image 3. A complex 3D branching structure designed using 3D form and force diagrams: (a) the force diagram consisting of 72 closed, convex cells; and (b) the reciprocal form diagram; and (c) exploded axon of the force polyhedrons representing various groups of polyhedral cells of the force diagram.

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_02.4

Topological Studies

TOPOLOGICAL STUDIES The computational research consisted in the exploration of different network topologies via algorithmic modeling. The load condition is expressed through vectors applied perpendincularly to each corresponding face of the polyhedra (force diagram). As previously mentioned the algorithm consisted into three main operations: - Definition of the force diagram via convex polyhedra aggregation sharing faces, corresponding edges and vertices. - Each polyehdra was scaled from the geometrical center to achieve the nodal center.

Polyhedra packing sharing faces, corresponding edges and vertices.

- Each of the faces were projected and extruded to the corresponding polyhedra faces to generate the dual graph of each polyhedra. - The algorithm iteratively align the polyhedra edges with the corresponding faces resulting in a form diagram with edges always perpendicular to their corresponding faces. The result of the algorithm application given the specific load condition resulted into network in a compression only state without bending moments leading to a reduction of the material need in the fabrication process. Multiple iterations have been tested differentiating the polyhedra agreggation, scale and orientation. Scaling the polyhedra from the center to achieve the central node.

Projection of the node faces to the polyhedraâ€™s corresponding faces.

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_02.4

Topological Studies

Topological studies exploring the aggregation of different convex polyhedra (force diagram) and the corresponding resulting compression networks (form diagram).

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Topological studies exploring the aggregation of different convex polyhedra (force diagram) and the corresponding resulting compression networks (form diagram).

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_02.4

Topological Studies

The algorithm explored provides another relevant advantage thanks to the geometrical costruction process of the network topology itself. All the faces of the networks mesh are planar because the perpendicularity to the corrisponding polyhedra face which makes theam suitable for multiple fabrication processes and material. Pair of faces of the mesh have one edge aligned on the same plane that makes them continuous and developable into strips with single curvature. This method allows potentially to have a structure nodes free which relies only on the faceâ€™s edges connectivity as for example a finger joints strategy. The behaviour of the membrane and the cable net have been simulated through dynamic relaxation via particle-springs system with the aim of synchronising the digital model with the real material behaviour, observed in parallel through small scale prototypes. This allowed to extend the topological research digitally without relying on physical prototyping.

Subdivision Iterations = 0

Subdivision Iterations = 1

Subdivision Iterations = 2 Developable mesh strips of a compression network structure resulting from the aggregation of one cube and four pyramids.

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Iterative subdivision of the mesh faces into continuous planar strips.

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_02.4

Topological Studies

Rigid network

Mesh membrane

compression network FORM DIAGRAM

Setup model: inner rigid network and mesh membrane.

Anchor points

Mesh converted into particle-spring system with anchored naked vertices.

tensile membrane FORCE DIAGRAM

chains of linear springs

Linear springs to simulate steel cables. Digital simulation of the membrane behaviour and the cable net through dynamic relaxation via particle-springs system .

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Dynamically relaxed model to simulate steel cables winding and membrane wrapping.

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Topological Studies

Compression network (form diagram).

Compression network (form diagram).

Membrane and cable net (force diagram)

Membrane and cable net (force diagram)

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_02.4

Topological Studies

Digital simulations with the aim to forecast the material behaviour and the global geometric output of the threading and wrapping strategy.

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Digital simulations with the aim to forecast the material behaviour and the global geometric output of the threading and wrapping strategy.

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Chapter 3: Manual Prototyping _03.1 Approach 1 CHIDORI _03.2 Approach 2 Finger Joint Connection

_03.1

Approach 1 CHIDORI

PROTOTYPE 1.0 This generation of prototype is introducing a new system which is consisting of 3 layers; skeleton, cable and wrapping. Cable(thread) system acts as a reinforcing layer for both wrapping and compression network. The prototype aims to explore variations of different qualities of surfaces by changing the parameters such as thread density, wrapping layers, threading sequences and type of geometry. All the sequences for threading and wrapping has been recorded in terms of consistency and comparability. Materials: MDF, Nylon fishing wire, LDPE Stretch Film

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Approach 1 CHIDORI

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Approach 1 CHIDORI

THREADING

10lb 4oz

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Threading is important in order to transfer the forces in all directions that are applied to compression network. After experimenting with different sequences and densities of threading, we evaluated the models in terms of strength and complexity. Using only the outline of the geometry and interpolating the naked edges, required tensile strength and equilibrium is maintained. Fishing wire has been used as a cable due to its preferable physical properties. Its high tensile strength makes the wire very hard to break and helping the system to carry maximum amount of loads. Threading also helps the system to generate wrapping paths and by that having a consistent wrapping sequence documentation has been achieved.

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Approach 1 CHIDORI

THREADING SEQUENCE

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In order to document and rebuild the threading and wrapping studies, a custom code has been generated. For this documentation system, directionality, start point, end point, knot location, type of interpolation, location of thread, snd location of stick are the parameters. This parameters has been coded for each relevant models for the prototype and set as a main documentation system for continous prototypes as well.

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PATH GENERATION LOGIC FOR WRAPPING

Threading Outline

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Threading Outline

Plane Generation 2

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Face Generation

Midpoints of Face Edges

Imaginary Plane/Plane Selection

All Reference Paths

Plane Generation 1

Path References

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Path Reference

Path Generation for Wrapping

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Approach 1 CHIDORI

APPROACH 2 CHIDORI NODE The CHIDORI system has been considered as sticks interlocking strategy which guarantees the absence of a physical node but relies only on contact faces. This method allowed a fast and intuitive fabrication of small scale prototype without any use of nails or screws.

Image 01 Robotically fabricated timber finger joint, Oliver David Krieg.

APPROACH 2 HOOK SLOTTING The sticks have been designed with regular slots on both side to accommodate different winding strategies and allowing each sequence to be encoded for further repeatability and comparison. The naked vertices of each stick have been also designed with a specific slot to allow the change of orientation in the winding process.

Image 02 Robotically fabricated timber finger joint, ICD Uni Stuttgart.

Image 03 Traditional hand made timber finger joint, David Stanton.

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Winding Iteration 01 Polyhedra type: Cube 300x300x300mm Winding strategy objective: Connecting naked vertices, creating one planar mesh of thread. B0 A1A7B1B7C1C7D1D7 B7C1C7D1D7 D1D1

A1A7B1

Winding Iteration 02 Polyhedra type: Cube 300x300x300mm Winding strategy objective: Connecting naked vertices, creating diagonal loops. B0 A4D4D4B4A4D4B4D4 A2D2D4 B4A2D2B2D2 A0D0D4B4A0D0B0D0 D1 D0A0D0A0

Winding Iteration 03 Polyhedra type: Cube 300x300x300mm Winding strategy objective: Passing through center points, triangulated pattern. A5 A4B4D4C4D4B4C4A4D4B4D4 A2B2D2C2D4B4C2A2D2B2D2 A0B0D0C0 D4B4C0A0D0B0D0 D1 C0DB0

Winding Iteration 04 Polyhedra type: Cube 300x300x300mm Winding strategy objective: Dense surface between two stick segments.

B0 A4D4D4B4A4D4B4D4 A2D2D4 B4A2D2B2D2 A0D0D4B4A0D0B0D0 D1 D0B0C0

Winding Iteration 05 Polyhedra type: Cube 300x300x300mm Winding strategy objective: Connecting naked vertices, creating two diagonal loops.

A5 AA4B4D4C4C4A4D4B4D4 A2B 2D2C2C2A2D2B2D2 A0B0D0C0C0A0D0B 0D0 Description, threading sequence code and diagram of prototypes to be modeled.

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Skeleton and wrapping prototypes.

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Winding Iteration 06 Polyhedra type: Cube 300x300x300mm Winding strategy objective: Connecting naked vertices, asymmetric density.

A5 AA4B4D4C4C4A4D4B4D4 A2B 2D2C2C2A2D2B2D2 A0B0D0C0C0A0D0B 0D0

Winding Iteration 07 Polyhedra type: Cube 300x300x300mm Winding strategy objective: Connecting naked vertices, high noise random winding for dense overall surface. 0D0

A1

A0B0D0C0C0A0D0B0D0

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Wrapping Iteration 01 Polyhedra type: Cube 300x300x300mm Wrapping strategy objective: Connecting naked vertices, wrapping tight to generate closed surface. A1

A0B0D0C0C0A0D0B0D0

Wrapping Iteration 02 Polyhedra type: Cube 300x300x300mm Wrapping strategy objective: Wrapping diagonally only. B1 A0B0D0C0C0A0D0B0D0 D7C7C7A7D7B7D7

A7B7

Wrapping Iteration 03 Polyhedra type: Cube 300x300x300mm Wrapping strategy objective: Highest possible stiffness by tight wrapping and a high count of layers of wrapped foil.

B1 A0B0D0C0C0A0D0B0D0 A7B7 D7C7C7A7D7B7D7 D8 D7A7 Description, threading sequence code and diagram of prototypes to be modeled.

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Skeleton and wrapping prototypes.

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Approach 1 CHIDORI

Winding + Wrapping Iteration 01 Polyhedra type: Double cubes 300x300x300mm Winding strategy objective: Connecting naked vertices, asymmetric density.

A5 A0B0D0C0CC0CC0DD0BB0AA0E0 A0CC0A0EE0D0CC0C0AA0E0DD0

Wrapping Iteration 01 Polyhedra type: Cube 300x300x300mm Wrapping strategy objective: Tight wrap, closed surface.

A1 A0B0D0C0CC0CC0DD0BB0AA0E0 AA0CC0AA0EE0DD0CC0CC0AA0EE0DD0 A’0C C0A’0E’0D’’0C’0C0A’0E’0D’0A’’0C’’0A’’0E’0D’0 C’’0C0A’’0E’’0D’’0

Wrapping Iteration 02 Polyhedra type: Cube 300x300x300mm Wrapping strategy objective: Wrapping diagonally only.

A1 A0B0D0C0CC0CC0DD0BB0AA0E0 AA0CC0AA0EE0DD0CC0CC0AA0EE0DD0 A’0C C0A’0E’0D’’0C’0C0A’0E’0D’0A’’0C’’0A’’0E’0D’0 C’’0C0A’’0E’’0D’’0

Wrapping Iteration 03 Polyhedra type: Cube 300x300x300mm Wrapping strategy objective: Generating most possible stiffness by tight wrap, high layer count.

A1 A0B0D0C0CC0CC0DD0BB0AA0E0A A0CC0AA0EE0DD0CC0CC0AA0EE0DD0 A’0CC 0A’0E’0D’’0C’0C0A’0E’0D’0 A’’0C’’0A’’0E’0D’0

Winding + Wrapping Iteration 05 Polyhedra type: Four cubes 600x600x600mm Winding strategy objective: Full enclosure and tight wrap. A1 A0B0D0C0CC0CC0DD0BB0AA0E0 AA0CC0AA0EE0DD0CC0CC0AA0EE0DD0A’0C C0A’0E’0D’’0C’0C0A’0E’0D’0A’’0C’’0A’’0E’0D’0 C’’0C0A’’0E’’0D’’0Aa0Bb0Dd0Cc0Dd0Bb0Aa0 Ee0a0b0d0c0d0b0a0e0 Description, threading sequence code and diagram of prototypes to be modeled.

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Skeleton and wrapping prototypes.

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Approach 2 Finger Joint Connection

APPROACH 1: NODE Two different approaches have been tested with the aim of solving the node condition of the network structure; main intention has been to design a universal node that could accommodate multiple branches independently from the cross section profile and orientation in space. The node geometry resulted from the scaling from the geometrical center of the boundary polyhedra allowing consistent corresponding faces to the outer polyhedra. Finger joints have been utilized as edge to edge connection strategy in order to maintain an hollow lightweight node.

Image 01 Robotically fabricated timber finger joint, Oliver David Krieg.

APPROACH 1: SEGMENT The entire node was developed with MDF laser cut pieces due to the planarity of the geometry itself which allowed reliability and a fast fabrication process. The second option consisted into the design of additional sockets on each planar face of the node geometry in order to be able to fix regular timber profiles independently from the face size and number of edges.

Image 02 Robotically fabricated timber finger joint, ICD Uni Stuttgart.

Image 03 Traditional hand made timber finger joint, David Stanton. Finger joint connection detail in woodwork.

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Approach 2 Finger Joint Connection

+90°

-90°

90°

Description of solving different seam angles.

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Finger joint bolder connection node.

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Approach 2 Finger Joint Connection

Tetrahedron skeleton prototype.

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Wrapped and wire-threaded tetrahedron.

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Approach 2 Finger Joint Connection

Radiolaria from 20 tetrahedral nodes. Wrapped joint detail.

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Wrapped radiolaria, 3 types of enclosure, semi-, fully-. closed and opened.

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References

Bespoke Digital Fabrication

Additive Fabrication

Carbon Fiber Wiring

Design and assembly of lightweight metal structures Gramazio Kohler Research, ETH Zurich 2014-2018

Additive Robotic Fabrication of Complex Timber Structures, Zurich, 2012-2017.

ICD/ITKE, Pavilion, Stuttgart, 2014.

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Introduction

The spread of multi-functional industrial robots has had exponential acceleration in the last decade that it has become a standard tool in many industries, where automation, efficiency and accuracy are the heart of the production process. Since the â€˜80s, with the development of information and computational technologies, the machines begin to be controlled through digital tools defining the beginning of a new paradigm in which the virtual world and the physical world come together and influence each other, drawing the foundations for the emergence of new processes and production strategies. The development of these technologies does not occur evenly in all disciplines and production companies but condenses on specific sectors, such as automotive and aerospace, going to redefine the quality standards of their respective sectors. The birth of these machines is the result of a need of greater control over the production process and greater automation, elements not necessarily connected with the world of construction and architecture. The diffusion of industrial robots in these fields occurs in manners much slower and gradual as for digitization, because of an industry in which the development timings and implementation medium assume different sizes and durations, a much more fragmented and complex industry. Very significant reason is also a limited and wellestablished design methodology and dominant constructive that has not evolved with the same speed of other disciplines; in defence of this, it is the fact that the architectural project encloses a more difficult to calculate or in some cases of not calculable variable number that can not be foreseen in advance and then inserted in a fully automated process, but they provide, at least for now, the presence of the human factor as an element of conjunction with the real world, able to use intuition and take charge of the major design decisions1. Despite a more gradual evolution of the last decade we have seen a substantial increase in the use of robot technology both within the construction process and within the design phase. The flexibility of robots such as industrial arms provides a wide spectrum of potential uses, not limiting them to unique automation tools predetermined and finite processes, but added elements able to expand the possibilities of the designer.

1 Fabio Gramazio and Matthias Kohler, The Robotic Touch: How Robots Change Architecture, Research ETH Zurich 2005-2013.

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Endeffector Design

PNEUMATIC GRIPPER The fabrication process has been exploited through the use of robotic technology in collaboration with manual operations. The robot which has been used is a Nachi MZ07 which provided the fabricaiton constraints in terms of profile lenghts. The robotic arm has been utilized in combination with a pneumatic gripper SMCHL2-20D as operating tool. The gripper has been actuated through a solenoid valve activated by the digital output signal of the robot G-Code.

G3 G4

G5

G6

Nachi MZ07

198

95.5±0.1

G2

340 440

73

50 45

190.5 160

330 410

1249 1602

4-φ 11

110.7

G1

160

95.5 ±0.1

189.5

94

345

165 495 ａ 646

618 806

228 266 723 912

7kg Payload 30kg Weigth

170°

723mm

+-170°

Axis 1

-136°

< Axis 3 <

-135°

< Axis 2 <

+-190°

Axis 4

+-360°

Axis 6

+80°

Max Reach Dust / Drip e nce am re Fr er fe int dius ra 150 R

170°

dB

Load Torque

IP67

70.2 16.6 Nm

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+-120°

Axis 5

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Endeffector Design

120mm H 102mm

1/2h

400ÂŁ

W 110mm L Approximate Dimensions

Total Man / Day to Complete

Estimated Cost

Compressed air inlet/outlet Custom Assembly Ring

Nachi MZ07

Pneumatic gripper SMCMHL2-20D

Connection plate

gripping jaws

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Fabrication Sequence

The fabrication sequence is divided into four main moments: Bespoke cut of discrete elements: the segments are pre cut with custom lengths according to the global model then positioned within the station to allow the robotic arm to record the position and automate the gripping process throughout the sequence. The longest element of each node has been positioned first in the central holder leaving to the robot the spatial orientation only. Gripping: a pneumatic gripper (SMCMHL2-20D) has been utilised. The actuation of the tool happens through the digital output of the robot; the connection end-effector / digital output allows to have the gripping process indipendent from an external controller or actuator, increasing the consistency and reliability of the whole process. Spatial positioning: the segments are gripped, positioned and oriented in place according to the network configuration. The positioning sequence has calculated in a way to avoid collision with the previously assembled elements within the node itself.

Bespoke cut of timber segments according to the global geometry

Assembly: the segments are assembled togheter with PVC plates with finger joints connection. Because the thermoformable proprieties of the material, each plate is heated and formed on the go according to the geometric conditions of the node. This method allows to not rely on any precalculation of each plate angle, increasing consequently the fabrication speed and simplifing the whole manufactoring process. Main objective has been to keep the sequence as consistent and solid as possible as well as simple, with the aim of a full automated assembly process. The sequence developed is mostly scale indipendent and could be migrated to bigger robotic arms for a 1:1 application. Three different materials have been tested for the node plates: acrylic, PVC and polyethilene. PVC turned out to be the most reliable in terms of bending capacities when heated and stiffness after drying down.

Gripping of the timber profile in station position.

Spatial orientation of the profile according to the node angle.

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Fabrication Sequence

Robot DIGITAL INPUT G-CODE Pneumatic gripper SMCMHL2-20D

Nachi MZ07

ON

OFF C-CODE

Compressed air inlet/outlet POINT COORDINATES.txt Segment

Connection plate Air compressor (2bar pressure) Solenoid valve

Fixed station as segment base

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Fabrication Sequence

First member placement

Gripping

Placement

Robot Speed

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Orienting spatially

Gripping

120s

5 s/f

Lifting

5m

1/2s

Opening/Closing Speed

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Lifting

Orienting spatially

5s

5s

2bars

Air Pressure

Global sequence speed

Global Reliability

Model stiffness

Endeffector reliability

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1:1 Large Scale Prorotype

1:1 PROTOTYPE NODE The fabrication sequence considered was meant to guarantee speed and simplify the node assembly process. Thermoformable plastics were considered because their ability to reshape when heated; plastic plates with finger joints connection were heated and formed throughout the assembly process as a way to solve complex node conditions with custom angles in space. Three different types of thermoplastics were tested: acrylic, polyethylene and PVC. Load tests have been executed on each of them before and after heating resulting in the utilization of PVC as main node material because the load bearing capacities and flexibility.

1:1 PROTOTYPE SEGMENT The segments timber profile was tested into 3, 3.5 and 5 configuration; the 3 cm profile was observed to be stiff enough and the most lightweight for the prototype purpose.

Image 01 Irregular connection node, finger jointed paper. AAG Zaha CODE

Image 02 Convex Hull node construction, CITA Rise Project. References for finger joint 3d-nodes and complex hull bolder node.

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1:1 Large Scale Prorotype

POLYMETHYL METHACRYLATE (ACRYLIC GLASS)

Version 1 Node Plate Plate: 150x35x3mm Finger: 5x3x3mm Hole: 5mm

Poly(methyl methacrylate) (PMMA), also known as acrylic or acrylic glass as well as by the trade names Plexiglas, Acrylite, Lucite, and Perspex among several others (see below), is a transparent thermoplastic often used in sheet form as a lightweight or shatter-resistant alternative to glass.

Version 2 Node Plate Plate: 150x26x3mm Finger: 5x3x3mm Hole: 5mm Version 3 Node Plate Plate: 150x41x3mm Finger: 5x3x3mm Hole: 5mm

POLYPROPYLENE (PP) Polypropylene (PP), also known as polypropene, is a thermoplastic polymer used in a wide variety of applications including packaging and labeling, textiles (e.g., ropes, thermal underwear and carpets), stationery, plastic parts and reusable containers of various types, laboratory equipment, loudspeakers, automotive components, and polymer banknotes. An addition polymer made from the monomer propylene, it is rugged and unusually resistant to many chemical solvents, bases and acids.

Version 4 Node Plate Plate: 165x38.93x3mm Finger: 5x4.46x3mm Hole: 5mm

Node Plate Plate: 155x38.93x3mm Finger: 5x4.46x3mm Hole: 5mm

Node Plate Plate: 140x38.93x3mm Finger: 5x4.46x3mm Hole: 5mm

POLYVINYL CHLORIDE (PVC) Polyvinyl chloride, more correctly but unusually poly(vinyl chloride), commonly abbreviated PVC, is the worldâ€™s third-most widely produced synthetic plastic polymer, after polyethylene and polypropylene.4 PVC comes in two basic forms: rigid (sometimes abbreviated as RPVC) and flexible. The rigid form of PVC is used in construction for pipe and in profile applications such as doors and windows.

Connector Plate Plate: 120x38.93x3mm Finger: 5x4.46x3mm Hole: 5mm

Connector Plate Plate: 80x38.93x3mm Finger: 5x4.46x3mm Hole: 5mm

Material to be tested as potential node plate.

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Connection detail node plate catalogue.

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Acryl Glass

500g

2000g

PP

500g

5000g

PVC

500g

5000g

Material load test. Top to bottom Acryl Glass, Polypropylene, Polyvinyl Chloride.

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Material post load test. Top to bottom Acryl Glass, Polypropylene, Polyvinyl Chloride.

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1:1 Large Scale Prorotype

SOFT WOOD ROFILES

Timber soft wood profiles has been used as a main structural material due to its convenience in fabrication process and physical properties. Geometrically there are 2 different types of profiles, triangulars and quads. Both quad and triangular profiles has been tested in 2cm, 3.4 cm and 3 cm sizes to evaluate the best fit for the global model. In terms of fabrication proces,as quads were more staightforward, manufacturing triangular pieces had some constraints.They were cutted from quad pieces and edges of the triangle were drawn on the face of the profile to adjust the angles of the table saw. In order to maintain the equal angle, this process continiued for each triangular members.

Profiles used in study models. Left to right 3.4cm, 3cm, 3cm, 2cm, 2cm.

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Prototype for each profile thickness. Top to bottom 3.4cm, 3cm, 3cm, 2cm, 2cm.

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Profiles and wrapping study 3.4x3.4cm node.

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Profiles and wrapping study 3x3cm node.

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Profiles and wrapping study 3x3cm node.

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Profiles and wrapping, large scale 1:1 prototype, robotically fabricated, 3x3cm node.

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TOPOLOGICAL AND GEOMETRICAL DESCRIPTION The topology of the prototype was meant to demonstrate the structural and spatial features of the system. The geometry was conceived to have a front part showing a potential facade/enclosure strategy made with cling film wrapping and an open ended part which suggested the possibility to expand the system into a full scale architectural object. Symmetry along the x-axis was considered as a way to have a global better stability and reduce the number of custom elements. Closed loops were meant on the y-direction also to improve stability and propagate deviations due to the fabrication process in a more even way.

Polyhedra packing with interpolated segment connections as regular rods.

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From polyhedra packing to center node geometry and mesh to be regularized.

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PROTOTYPE SPECIFICATIONS Bounding Box Dimensions: 307.8x125.8x223.5cm 28 x Nodes 342 x Connecting Strips 126 x Segments (12 Quad Profile, 114 Triangular Profile) 27.47 m wood (Quad 3x3cm, Regular Triangel 3cm Sides) 2052 x 6x1/2â€? Wood Screws Production Time: 18h40min Total Weight: 34 Kg

Blue is the interpolated cross section, red the original mesh output section.

Construction sequence, node 0. Longest segment as base segment perpendicular to ground.

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Prototype segments regulated by robot-reach.

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1:1 Large Scale Prorotype

Top: 1:1 Prototype connection node detail Bottom: Wired, unwrapped segment skeleton.

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1:1 Prototype wrapped front.

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Bibliography

1. Masoud Akbarzadeh, Tom Van Mele, Philippe Block, On the equilibrium of funicular polyhedral frames and convex polyhedral force diagrams, Computer-Aided Design 63 (2015) 118–128. 2. Masoud Akbarzadeh, Tom Van Mele, Philippe Block, Threedimensional Compression Form Finding through Subdivision, Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam. 3. Block P., Thrust Network Analysis: Exploring Three-dimensional Equilibrium. PhD thesis, MIT, Cambridge, MA, USA, 2009. 4.

Luigi Cremona, Le figure reciproche nella statica grafica, 1872.

5. Corentin Fivet, Denis Zastavni, From the Salginatobel Bridge Desing Process (1928), Journal of the Internation al Association for Shell and Spatial Structures, 2012. 6. Frei Otto, Lightweight Principle, Institut für leichte Flächentragwerke (IL), 1998. 7. Fabio Gramazio and Matthias Kohler, The Robotic Touch: How Robots Change Architecture, Research ETH Zurich 2005-2013.

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Image References

1. Anon, (2016). [image] Available at: https://www.locationscout.net/ public/images/2015-06/salginatobel-bridge-switzerland-switzerland_l. jpeg.

12. Parametricism.co.uk. (2016). Available at: http://www. parametricism.co.uk/blog/wp-content/uploads/2014/08/Unbenannt.png [Accessed 15 Nov. 2016].

2. Gramaziokohler.arch.ethz.ch. (2016). Gramazio Kohler Research. [online] Available at: http://gramaziokohler.arch.ethz.ch/web/e/ forschung/184.html

13. (2016): „cidori - Nick Auger“. Nauger.com. Abgerufen am 15. 11. 2016 von http://nauger.com/cidori.

3. Coray, T. (n.d.). Design and Robotic Fabrication of Complex Lightweight Structures | dfab. [online] Dfab.ch. Available at: http:// www.dfab.ch/research/design-and-robotic-fabrication-of-complexlightweight-structures/. 4. Icd.uni-stuttgart.de. (2012). researchpavilion2013-14 « Institute for Computational Design (ICD). [online] Available at: http://icd.unistuttgart.de/?tag=researchpavilion2013-14. 5. Corentin Fivet, Denis Zastavni, From the Salginatobel Bridge Desing Process (1928), Journal of the Internation al Association for Shell and Spatial Structures, 2012. 6. Anon, (2016). [image] Available at: https://www.davidstephensonart. com/vaults-2003-09/ns0azqop27odfovou76u4m2yuvbm3j 7. Images.adsttc.com. (2016). Available at: http://images. adsttc.com/media/images/5490/3cf8/e58e/cef0/e000/00fa/large_ jpg/53493e7fc07a80f351000082_ad-classics-los-manantiales-felixcandela_losmanantiales1.jpg?1418738931 [Accessed 15 Nov. 2016]. 8. 65.media.tumblr.com. (2016). Available at: http://65. media.tumblr.com/eed771d1825115ee4a49520d7bce8d78/tumblr_ mukommsKik1srv76io1_1280.jpg [Accessed 15 Nov. 2016].

13. (2016): „Head & Haft“. Headandhaft.tumblr.com. Abgerufen am 15. 11. 2016 von http://headandhaft.tumblr.com/. 14. (2016): „How To | Make Box Joints | Step By Step“. YouTube. Abgerufen am 15. 11. 2016 von https://www.youtube.com/ watch?v=1eHBwRjwLOY. 15. (2016): „Oliver David Krieg | performative architecture and digital fabrication“. Oliverdavidkrieg.com. Abgerufen am 15. 11. 2016 von http:// www.oliverdavidkrieg.com/. 16. (2016): „News « Institute for Computational Design (ICD)“. Icd. uni-stuttgart.de. Abgerufen am 15. 11. 2016 von http://icd.uni-stuttgart. de/. 17. (2016): „How To | Make Box Joints | Step By Step“. YouTube. Abgerufen am 15. 11. 2016 von https://www.youtube.com/ watch?v=1eHBwRjwLOY. 18. Tamke, Martin (2016): „The ACADIA Rise (2013) |“. Complexmodelling.dk. Abgerufen am 15. 11. 2016 von http://www. complexmodelling.dk/?p=663.

9. 66.media.tumblr.com. (2016). Available at: http://66. media.tumblr.com/b48651a631d834ec78021e354fd6dadf/tumblr_ mfvar9O4jN1r2sw03o1_1280.jpg [Accessed 15 Nov. 2016]. 10. 4dmorphology.files.wordpress.com. (2016). Available at: https://4dmorphology.files.wordpress.com/2010/04/dsc00996a1.jpg [Accessed 15 Nov. 2016]. 11. Structuremag.org. (2016). Available at: http://www.structuremag. org/wp-content/uploads/0514-f2-6.jpg [Accessed 15 Nov. 2016].

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