DESIGN AND FABRICATION OF 3D RECIPROCAL FRAME

S. Chien, S. Choo, M. A. Schnabel, W. Nakapan, M. J. Kim, S. Roudavski (eds.), Living Systems and Micro-Utopias: Towards Continuous Designing, Proceedings of the 21st International Conference of the Association for Computer-Aided Architectural Design Research in Asia CAADRIA 2016, 725–734. © 2016, The Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong.

DESIGN AND FABRICATION OF 3D RECIPROCAL FRAME STRUCTURE

ZIYU TONG and RONGLOU ZHOU Nanjing University, Nanjing, China {tzy, mf1336032}@nju.edu.cn

Abstract. Reciprocal frame structure is a special type of spatial struc-ture, which consist of elongated elements. The elements support each other along their span, compose a stable geometrical configuration without any clear structural hierarchy. Based on the morphology, the reciprocal frame could be categorized to 1D, 2D, and 3D. Compared to 1D and 2D, 3D reciprocal frame presents some novel features. It shows a growing pattern with some simple rules. Even with the same rule, 3D reciprocal frame could grow up to different form. It’s a typi-cal process of bottom-up which implies a considerable wealth of pos-sibilities. Study on the 3D reciprocal frame gives the potential for achieving novel and complex forms. With the restriction of the cate-gory of 3D reciprocal frame, the paper summarized the characteristics of the frame as growth, regularity, and spatiality. And the structure should be repeated, simulated, and constructed. The paper also ex-tracted three basic factors - growth rule, initial form, and bar size. Through the simulation experiments with different factors, the rela-tionships between the frame shape and the factors were established. At the end, a full-scale model validates the feasibility of the growth result of 3D reciprocal frame.

Keywords. Reciprocal frame structure; spatial structure; 3-dimension; fabrication; rule-based.

1. Introduction

Reciprocal frame structure is a special type of spatial structure, which con-sist of elongated elements. The elements support each other along their span, compose a stable geometrical configuration without any clear structural hier-archy (Baverel and Larsen, 2011; Larsen, 2014). The structure is most com-monly used for roof structures because the span distance could be much longer than the length of the element. Reciprocal frame structure can be

726 Z. TONG AND R. ZHOU

found in ancient China and Japan, also in sketch script of Leonardo (Parigi and Pugnale, 2014).

Based on the topological form, the reciprocal frame could be categorized to 1D (Leonardo da Vinci’s bridge), 2D (Leonardo da Vinci’s grid), and 3D. Most researches were focused on the form of 2D (Parigi and Pugnale, 2014). The 2D reciprocal frame usually is a topological planar surface, composed with some regular or irregular units. It shows a sprawling tiled pattern. And the design process is top-down. The reciprocal frame is applied to fit the predefined form. The key problem of such application is how to optimize the model to ensure collinear contacts while preserving the geometric from (Douthe and Baverel, 2009; Song et al, 2014; Thonnissen, 2014). Compared to 2D, 3D reciprocal frame presents some novel features. It shows a growing pattern with some simple basic rules. Even with the same rules, 3D recipro-cal frame could grow up to very different result. It’s a typical process of bot-tom-up which implies a considerable wealth of possibilities. Therefore, study on the 3D reciprocal frame gives the potential for achieving novel and com-plex forms (Parigi and Pugnale, 2014).

The complexity is the characteristic of 3D reciprocal frame, it’s also the obstacle to study it directly. In this paper, we defined the researchable cate-gory of 3D reciprocal frame, summarized the characteristics of the frame, and extracted basic factors to generate the structure. With the simulation and fabrication of the parametric 3D reciprocal frame, we explore the potential morphology and design opportunity.

2. Definition of 3D reciprocal frame

Compared to 1D or 2D reciprocal frame, 3D one presents more abundant possibilities and complexity. In general, the structure composed by inter-laced elements could be regarded as 3D reciprocal frame. However, there are huge differences among such structures. Interlaced elements could be com-posed as an ordered bird nest, or as an unordered haystack (Figure 1). Alt-hough the latter is also complex, it is very difficult to study since its absence of regularity. So we have to define the 3D reciprocal frame at the viewpoint of research.

Figure 1. Different organized forms of interlaced elements.

DESIGN AND FABRICATION OF 3D RF STRUCTURE 727

A researchable 3D reciprocal frame should possess the characteristics of growth, regularity, and spatiality. Moreover, the structure should be repeat-ed, simulated, and constructed.

2.1. THE GROWTH OF 3D RECIPROCAL FRAME

The typical 3D reciprocal frame could be grown gradually. Just like a bird nest, it is generated piece by piece. We can restore a 3D reciprocal frame to its original state and observe the growth process to understand dynamic morphology. Also, we can rebuild it.

On the other hand, the growth of 3D reciprocal frame means that the final form is indeterminate. The form will be affected by many factors during its growing process.

The 3D reciprocal frame is grown from a simple unit. The unit is also the basis of the final frame. The bars of the unit compose a pool of components which provide structural support for the subsequent bars. Based on the exist-ing pool of components, any two bars could be selected to add the third bar which ensures the three bars construct a new basic reciprocal frame unit. Meanwhile, the new bar is added to the pool to generate the next bar. With the continued growth, the pool becomes larger, and thus the possibility of the next growth becomes larger, the potential of the final form becomes more. Such growth characteristics, making 3D reciprocal frame difficult to predict the final form, while also showing the richer possibility and complexity.

2.2. THE REGULARITY OF 3D RECIPROCAL FRAME

Without limitation, the growth of the 3D reciprocal frame could be out of control, and the result is not only difficult to predict, but also difficult to cognized. Therefore, the application of the rules has a profound significance for the study of 3D reciprocal frame.

In the description of the growth, any two bars of the pool could be used to generate the third one. However, in practice, limited by the length and diam-eter of the bar and the distance between the bars, only a few bars could be used. The new added bar also causes different results. Some are beneficial to the next growth of the frame, some are not. Therefore, the regularity of 3D reciprocal frame includes two parts, one is the rule of selection from the ex-isting bars pool, and another is the rule of growth of the new bar. The com-bination of these tow rules makes the 3D reciprocal frame with distinct growth logic, and makes the final form recognizable.


2.3. THE SPATIALITY OF 3D RECIPROCAL FRAME

Finally, the research of 3D reciprocal frame is used for exploring the novel enclosed structure. Therefore, the spatiality of the form is an important crite-rion to evaluate the research. The different initial form, bar size, and growth rules may result in a completely different spatial form. From a practical sense, the study of the spatiality of these elements is valuable.

In summary, the growth and regularity characteristics make the 3D recip-rocal frame be repeated, simulated, and constructed. The spatiality could be used to evaluate the form of 3D reciprocal frame. In the study, we also fo-cused on the bar as the element of the reciprocal frame to simplify the re-search object.

3. Simulation and fabrication of 3D reciprocal frame

Many researches demonstrated the shape of reciprocal frame is influenced by the basic unit and bar size (Baverel and Larsen, 2011). For the 3D recip-rocal frame, the growth rule is also a very important factor (Parigi and Pugnale, 2014). So we extracted three primary factors – growth rule, initial form, and bar size. Based on the Rhino and Grasshopper, we wrote the pro-gram to simulate the growing process with the parameters of initial form and bar size. Afterwards, we constructed a physical model to validate the charac-teristics of 3D reciprocal frame.

In the process of computer simulation, we set single variable to testify the effect of different factor. To avoid the interference, we also set the most basic condition of three factors.

The basic initial form of 3D reciprocal frame is a fan mode of three bars. It is also the smallest unit of a reciprocal frame. The basic size of a bar is 40mm in diameter, 600mm in length. The basic growth rule is “recursive” rule which is much like the “flame” model developed by Parigi and Pugnale (2014). Figure 2 shows the growth rule step by step. Starting form a three bars fan, every turn three new bars were added. And from the third round, the added bar was supported by one bar of the former round and one bar of the round before former one. Follow-ing the same logic, the frame grew recursively.

Figure 2. Diagram of the recursive growth rule.


3.1. THE INITIAL FORM

With the same growth rule and bar size, we tried different initial forms. All initial forms are single unit of fan mode with different bars. Table 1 presents the growing processes of these different initial forms – from three bars to six bars. Every example grew five rounds.

TABLE 1. Growth processes of 3D reciprocal frame with different initial form. (In each im-age, top row is plan view, middle row is front view, and the bottom row is perspective view.)

Initial form Growth processes

3 bars

4 bars


Initial form Growth processes

5 bars

6 bars

As shown in Table 1, with the increase of the bars of initial form, the fi-

nal form gradually tends to be upward and inward. Especially for the six bars fan, the bars grew at the fifth round tend to be horizontal again, which is similar to the initial form.

3.2. THE BAR SIZE

With the same growth rule and initial form, we tried different bar size in-cluding diameter and length of the bar.

Figure 3 is the results of reciprocal frame grown after five rounds with different diameter of the bar. The length is fixed at 600mm, the diameter ranges from 10mm to 60mm. With the increasing diameter, the overall shape from flat gradually become stereo, and more open.


Figure 3. Reciprocal frame with different diameter of the bar.

Figure 4 is the results of reciprocal frame grown after five rounds with different length of the bar. The diameter is fixed at 40mm, the length ranges from 300mm to 900mm. With the increasing length, the overall shape from stereo gradually become flat, and more closed.

Figure 4. 3D reciprocal frame with different lengths of the bar.

Comparing both two groups of the reciprocal frames, we found the close relationship between the form and the bar size. The bar is more slender, the form is more flat and closed. The bar is thicker, the form is more stereo and open.

3.3. THE GROWTH RULE

Besides the basic recursive rule, we developed another growth rules to gen-erate the 3D reciprocal frame.

Other than the basic rule, every round we attempted to generate two bars through one existing bar. All of three bars composed a basic reciprocal


frame. Furthermore, we discarded the symmetrical balance for every round. Each round only one bar was selected to generate two new bars. The rule is named “branch”. Figure 5 demonstrates the one possible growth process with branch rule. The green bar is the one selected to generate new bars which are red. It had grown for 8 rounds. With the branch rule, the reciprocal frame is represented as a spiral. It presents a strong regularity, since the se-lection rule is regular.

Figure 5. Growth process with branch rule.

Although only two rules applied in the study, the result showed that the rule has the different effect compared with other factors. The growth rule is a crucial factor for the shape of the frame.

3.4. THE FABRICATION OF THE 3D RECIPROCAL FRAME

The regularity of the 3D reciprocal frame makes the structure easy to con-struct. And the growth process is also the construction process. To validate the characteristics of 3D reciprocal frame, we constructed a full-scale physi-cal model. We chose a fan mode of three bars as initial form. The diameter of the bar is 60mm, the length is 1800mm. And the final result is the frame grown after 8 rounds with recursive rule.

Because of the complexity of 3D reciprocal frame, the friction of the joint is insufficient to keep the structure stable. During the three families of joint type, we chose the bilateral joint with aligned elements axes which can sup-ply the strongest joint (Parigi and Kirkegaard, 2014). Here we used swivel coupler as the joint which usually used to connect two tubes together at any angle (Figure 6). With the consideration of the thickness of the coupler, we set the diameter of the bar 45mm. In addition, to save the materials, some bars were shortened. The materials used for the final construction included 9 1800mm bars, 15 1455mm bars, and 45 swivel couplers.


Figure 6. Components used for fabrication of the 3D reciprocal frame – wooden bars and

swivel coupler.

Figure 7 shows the process of the fabrication of the 3D reciprocal frame, and figure 8 is the final result. It is much similar with the simulated result. It validated the ability of the fabrication of the 3D reciprocal frame. And it im-plies more potentials of application.

Figure 7. Process of the fabrication of the 3D reciprocal frame.

Figure 8. Result of the fabrication of the 3D reciprocal frame.


4. Conclusion and discussion

In our experiments, including computer simulations and full-scale model, we found the 3D reciprocal frame is more complex than 1D and 2D ones. And the complexity of the 3D reciprocal frame is well organised. It has a close relationship with the growth rule, initial form, and the bar size. The 3D re-ciprocal frame possesses the characteristics of growth, regularity, and spati-ality. Moreover, it can be repeated, simulated, and constructed. Therefore, it is valuable to study and practice.

Within three factors, the growth rule is most crucial to the final shape of the 3D reciprocal frame. As long as the rules are clear, the 3D reciprocal frame can be regarded as a typical parametric structure. By adjusting the in-put parameters, we can get rich and interesting shapes.

Our experiment still applied some simple growth rules. The complicated rules haven’t been applied. If allowing different rules applied in the growing process, the result may become more complex and interesting. All these are subject to our future experiments to verify and explore.

References Baverel O. and Larsen O. P.: 2011, A review of woven structures with focus on reciprocal

systems – nexorades, International Journal of Space Structures, 26(4), 281–288. Douthe C. and Baverel O.: 2009, Design of nexorades or reciprocal frame systems with the

dynamic relaxation method, Computers and Structures, 87, 1296–1307. Larsen O. P.: 2014, Reciprocal frame (RF) structures: real and exploratory, Nexus Network

Journal, 16, 119–134. Parigi D. and Kirkegaard P.H.: 2014, Design and fabrication of free-form reciprocal structures,

Nexus Network Journal, 16, 69–87. Parigi D. and Pugnale A.: 2014, Three-dimensionality in reciprocal structures: concepts and

generative rules, Nexus Network Journal, 16, 151–177. Song P., Fu C., Goswami P., Zheng J., Mitra N. J. and Cohen-Or D.: 2014, An interactive

computational design tool for large reciprocal frame structures, Nexus Network Journal, 16, 109–118.

Thonnissen U.: 2014, A form-finding instrument for reciprocal structures, Nexus Network Journal, 16, 89–107.

Documents

DESIGN AND FABRICATION OF 3D RECIPROCAL FRAME