SKELETON BRIDGE DIGITAL BALANCING WORKSHOP
Design Fabrication Studio workshop towards Digital Fabrication Lab Pavilion 2018
T_ADS, the University of Tokyo Obuchi Lab YUQING SHI Feburary, 2018
Digital Balancing Workshop, 2018
PART 1
// DESIGN // SKELETON BRIDGE
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Skeleton Bridge
/ TENSEGRITY STRUCTURE /
Fig. 1 R.Buckminister Fuller holds up a tensegrity sphere, April 18, 1979
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Fig. 2 Cable networks and tensegrity cables
Fig. 3 Black E.C. Tower, 1974, anodized aluminum & stainless steel, 41 x 14.5 x 12.5 inches, 104.1 x 36.8 x 31.8cm
Tensegrity, tensional integrity or floating compression is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members (usually bars or struts) do not touch each other and the prestressed tensioned members (usually cables or tendons) delineate the system spatially. Tensegrity structures are based on the combination of a few simple design patterns: - loading members only in pure compression or pure tension, meaning the structure will only fail if the cables yield or the rods buckle - preload or tensional prestress, which allows cables to be rigid in tension - mechanical stability, which allows the members to remain in tension/compression as stress on the structure increases
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Digital Balancing Workshop, 2018
/ GEOMRTRY / Fig. 4 A unit that consists of two compressive components: a triangle and a rod in the center; and tensile strings in between.
Fig. 5 A unit that consists of two triangle compressive components, and forms a triangle prism. Firm in vertical direction, but unstable in horizontal direction.
// STRUCTURE UNIT RESEARCH In tensegrity structure, the unit design is rather crucial for a feasible structure. In this process, I experimented on several unit form and found out that for a triangle based unit, the following component shown in Fig.7 has the highest structural performance.
Fig. 6 This is a unit composed of 6 compressive triangles conponents but not very applicable for further development.
The shapes of tensegrity icosahedra depends on the ratio between the lengths of the tendons and the struts. Since the tensegrity icosahedron represents an extremal point of the above relation, it has infinitesimal mobility: a small change in the length s of the tendon results in a much larger change of the distance 2d of the struts. Fig. 7 Different shapes of tensegrity icosahedra
// UNIT CONPONENTS
Top View
Side View
Top View
Side View
Parallel View
Top View
Side View
Parallel View
Parallel View
Fig. 8 This is a module of right helix tensegrity unit. It rotates to stay stable.
Fig. 9 For the general modules which are other than the base module, the compression units are connected from the middle point of bottom triangle.
Fig. 10 For the base module, the compression units are connected from the vertex of bottom triangle.
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Skeleton Bridge
// GEOMETRY SCRIPTS
Input Parameters: - Module numbers - Base curve - Triangle size - Graph mapper adjustments
Base support module
Regular support modules
Output Components: - Compressive components' position and angle - Compressive components' length - Tensile components
Fig. 11 Perspective view of skeleton bridge geometry T   ADS
Fig. 12 The initial parameter of the geometry include module number, base curve and the size of the triangle. And the curve can be of any form, which makes it possible to use the reconstructed curves for regeneration of geometry. Also, the scale of the module can be controlled by graph mapper.
Fig. 13 The base support module is the first to be constructed and differs from general modules which are costructed by connecting middle points and vertexs.
Fig. 14 The export components are piped compressive units, their length and tensive strings that connects them.
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Digital Balancing Workshop, 2018
// GEOMETRY SCRIPTS
Front view of skeleton bridge
Side view of skeleton bridge
Top view of skeleton bridge Fig. 15 Three views of skeleton bridge
Fig. 16 Due to the nature that lower a module is, more weightwould be loaded onto it, the bottomn modules should be stronger and larger than top ones. According to this feature of the structure, I used graph mapper to adjust the scale so that the geometry would have higher performance in structure.
Fig. 17 Graph mapper adjustments - pattern 1: same scale size through the curve.
Fig. 18 Graph mapper adjustments - pattern 2: wider top module scales.
Fig. 19 Graph mapper adjustments - pattern 3: wider bottom module scales.
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Fig. 20 Compressive material: wood chopsticks with PLA twined ends.
Skeleton Bridge
/ MATERIAL AND TOOLS /
Fig. 21 Tensile material PLA and 3D print pen.
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According to the nature o`f "Tension + Integrity = Tensegrity", materials for this project are chosen as wood chopsticks ad which has high compressive resisting performances and 3D printed PLA strings that has tensile features.
Fig. 22 Vive tracker for guiding and scanning system
Fig. 23 Working space with two lighthouses, guiding and scanning vive tracker tool, caliberation tool and feedback system in grasshopper. Also showing the first layer of construction.
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Digital Balancing Workshop, 2018
PART 2
// CONSTRUCTION // SKELETON BRIDGE
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Skeleton Bridge
/ WORKFLOW / // OPTIMIZATION AND FEEDBACK SYSTEM CONSTRUCTION
OPTIMIZATION
FEEDBACK
grasshopper analysis
POSITION
vive tracker guide vive tracker bake
CONSTRUCTION LAYER n 3D pen printing
gain GEOMETRY CENTER
keep the geometry center of the end of unit as close to target arc as possible
UNIT ANGLE keep if the geometry center as close to target arc as possible
grasshopper output
New position and angle of the component in LAYER n+1
CURVATURE the curvature of the line that composes of geometry centers should be continuous
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Fig. 24 This chart shows the workflow of building the tensegrity structure and presents three rules for optimization.
Geometry scanning: baking the bottom points of each layer to define its geometry center
lighthouse
geometry center vive tracker
Optimization: regenerate a new guiding geometry
grasshopper monitor
new layer
comparison of old target geometry and new target geometry after scanning
3D pen
target geometry
Construction: draw a new layer of the geometry using 3D pen
Fig. 25 The loop of actual work flow, including construction, scan, feedback and optimization.
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Digital Balancing Workshop, 2018
/ OPTIMIZATION SYSTEM / // FEEDBACK SCRIPTS
Fig. 26 The script enables vive tracker to locate a certain point in the geometry and bake it in Rhino.
Fig. 27 When the tip of scanning device gets close to target point, it gives back a feedback by making beeping sound.
// NEW GEOMETRY GENERATION Fig. 28 This script converts the baked three points into a geometry center and form a new base curve with the rest of the target modules.
Fig. 30 Layer numbers
New geometry is formed through a new base curve that is generated through the scanned geometry center and the rest of the target curve.
Fig. 29 This script is to generate new base curves through each layer of scaned points.
Fig. 31 The convert of new base curve into new geometry.
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Skeleton Bridge
/ ACTUAL CONSTRUCTION PROCESS / // CONSTRUCTION Fig. 32 The calibration base of vive tracker.
CONSTRUCTION
OPTIMIZATION
FEEDBACK
grasshopper analysis
POSITION
vive tracker guide vive tracker bake
CONSTRUCTION LAYER n 3D pen printing
gain GEOMETRY CENTER
keep the geometry center of the end of unit as close to target arc as possible
UNIT ANGLE keep if the geometry center as close to target arc as possible
grasshopper output
New position and angle of the component in LAYER n+1
CURVATURE the curvature of the line that composes of geometry centers should be continuous
Vive tracker tool guided geometry positioning and 3D pen construction.
Fig. 33 Using vive tracker tool to guide each point of the structure.
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Fig. 34 The bases are at first fixed by glue gun.
Fig. 35 Construction of the first layer.
// OPTIMIZATION Fig. 36
After first layer of construction, using vive tool for baking.
Fig. 37
Gain geometry center using the three baked points.
CONSTRUCTION
OPTIMIZATION
FEEDBACK
grasshopper analysis
POSITION
vive tracker guide vive tracker bake
CONSTRUCTION LAYER n 3D pen printing
gain GEOMETRY CENTER
keep the geometry center of the end of unit as close to target arc as possible
UNIT ANGLE keep if the geometry center as close to target arc as possible
grasshopper output
New position and angle of the component in LAYER n+1
CURVATURE the curvature of the line that composes of geometry centers should be continuous
After using the vive tracker tool to scan the new geometry, the script automatically generate its geometry center for analysis
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Digital Balancing Workshop, 2018
// OPTIMIZATION CONSTRUCTION
OPTIMIZATION
FEEDBACK
grasshopper analysis
POSITION
vive tracker guide vive tracker bake
CONSTRUCTION LAYER n 3D pen printing
gain GEOMETRY CENTER
keep the geometry center of the end of unit as close to target arc as possible
UNIT ANGLE keep if the geometry center as close to target arc as possible
grasshopper output
New position and angle of the component in LAYER n+1
CURVATURE the curvature of the line that composes of geometry centers should be continuous
Grasshopper optimization and regeneration
Fig. 38 First layer scanned points and newly generated base line.
Fig. 38 Scripts of generating new base curve. This script converts the baked three points into a geometry center and form a new base curve with the rest of the target modules.
Fig. 39 Front view and top view of the newly generated base curve.
Fig. 41 Front view and top view of the target geometry.
Fig. 40 The comparison of target geometry and newly generated geometry from scanned first layer construction.
In optimization process, I used interpolate curve to connect the geometry center of first layer scan points and the rest 9 layers' geometry center in order to generate a new base curve, then generate a new target geometry.
Fig. 42 Front view and top view of the newly generated target geometry.
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CONSTRUCTION
OPTIMIZATION
FEEDBACK
Skeleton Bridge
// FEEDBACK
grasshopper analysis
POSITION
vive tracker guide
keep the geometry center of the end of unit as close to target arc as possible
vive tracker bake
CONSTRUCTION LAYER n 3D pen printing
gain GEOMETRY CENTER
UNIT ANGLE keep if the geometry center as close to target arc as possible
grasshopper output
New position and angle of the component in LAYER n+1
CURVATURE the curvature of the line that composes of geometry centers should be continuous
After the optimization by analysing Fig. 43 Determining the new position of the new module.
new layer
3D pen
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Fig. 44 Screen monitor of positioning new layer's module.
target geometry
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Construction: draw a new layer of the geometry using 3D pen
Fig. 45 Construction process.
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Digital Balancing Workshop, 2018
// CONSTRUCTION DEVELOPMENT
Fig. 46 Second layer optimization.
Fig. 47 Third layer optimization.
Fig. 48 Fourth layer optimization.
Fig. 49 Fifth layer optimization.
Fig. 50 Sixth layer optimization.
Fig. 51 Seventh layer optimization.
Fig. 52 Eighth layer optimization.
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Skeleton Bridge
// FINAL OUTCOME AND COMPARISON
Fig. 53 Top view comparison.
Fig. 54 Side view comparison.
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Fig. 55 Perspective view comparison.
Fig. 56 Final outcome.
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Digital Balancing Workshop, 2018
/ ANALYSIS / // DEVIATION ANALYSIS The possible causes of outcome deviation are as follows: 1. The accuracy of Vive tracker tools and lighthouses are influenced by human movements and lights; 2. Human errors causes components to move slightly after positioning; 3. When constructed with 3D pen, the PLA needs to intertwine in order to stick to compressive components and also to each other, which causes the components to move and deviate； 4. The frangibility of tensile material PLA increase the difficulty to construction accuracy. // FUTURE IMPROVEMENT 1. Calibrate Vive tools more often; 2. Create a certain fixture system to avoid deviation caused by human hands movement; 3. Improve optimization script to take into account deviation factors (eg. Human errors, winds etc.) // CONCLUSION Through construction, optimization and feedback process, we can know the following things: 1. The final outcome, although deviates from original target geometry slightly, has hit the target of a self standing tensegrity arch; 2. The workflow of construction – optimization – feedback and new construction is feasible; 3. Vive tracker tools have small deviations which are around 1~5cm according to the environment condition, so there would be smaller deviation when applied to a larger scale construction.
Fig. 57 Building process.
Fig. 58 Final outcome. 16
Fig. 63 Layer 6
Skeleton Bridge
/ PHASE PHOTOS /
// FRONT VIEW Fig. 64 Layer 7
Fig. 60 Layer 2
Fig. 65 Layer 8
Fig. 61 Layer 3
Fig. 66 Layer 9
Fig. 62 Layer 5
Fig. 67 Layer 10
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Fig. 59 Layer 1
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Digital Balancing Workshop, 2018
// TOP VIEW
Fig.68 Layer 1
Fig. 73 Layer 6
Fig. 69 Layer 2
Fig. 74 Layer 7
Fig. 70 Layer 3
Fig. 75 Layer 8
Fig. 71 Layer 4
Fig. 76 Layer 9
Fig. 72 Layer 5
Fig. 77 Layer 10
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In actual construction, the geometry center shifts off the base curve a little.
// SIDE VIEW Fig. 78 Layer 3
Skeleton Bridge
// PERSPECTIVE VIEW
Fig. 79 Layer 4
Fig. 80 Layer 5
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Fig. 81 Layer 6
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Due to the nature of tensegrity structure, before the construction finishes, it can not stand by itsef and needs additional support.
Fig. 82 Layer 7
Fig. 83 Layer 8
Fig. 84 Layer 9
Fig. 85 Layer 10 The structure could not stand alone before its complition but once the last module is complete, the whole structure became very firm and stiff, which refletcts the nature of tensegrity structure. 19
Skeleton Bridge
Editor: SHI YUQING Design: SHI YUQING Book Edition Design: SHI YUQING
© 2018 Obuchi Lab, T
ADS
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Japan www.t-ads.org Printed in Tokyo 2018
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