Proceedings of the First Conference Transformables 2013.In the Honor of Emilio Perez Piñero 18th-20th September 2013, School of Architecture Seville, Spain EDITORIAL STARBOOKS. Felix Escrig and Jose Sanchez (eds.)
Transformable Billboard
A.V. Chesnokov
1, V.V. Mikhaylov
21Dr., Assistant Professor, Lipetsk State Technical University, Lipetsk, Russian Federation, [email protected] 2
Dr., Professor, Lipetsk State Technical University, Lipetsk, Russian Federation, [email protected]
Summary:The billboard belongs to information or advertisement devices. It can be used for demonstrating cyclically changing images on its both sides. The device consists of a set of demonstrating units. Each unit is a four-corner prism. The prism consists of a collapsible frame and a flexible covering. On each of four surfaces of a prism different graphical fragments are printed. When aligned in a line the fragments form an integral picture. To change a picture by another one every demonstrating prisms rotate simultaneously in one direction around their longitudinal axis. To make rotation possible, four-corner prisms, situated in close proximity to each other, decrease their size by partially collapsing of their frames. Rotation of prisms and dynamic changing of their dimensions are performed by one engine. In comparison to similar devices intended for displaying changing images the billboard has the following advantages: smaller dimensions and better quality of displaying images. Two types of mechanisms transforming the billboard are considered. Analytical dependences between parameters of the billboard are offered and analysed.
Keywords: billboard, advertisement, changing image, collapsible frame, flexible covering, rotatable, crankgear INTRODUCTION
In order to increase the effect of using information billboards the devices allowing to change images cyclically are now widely used. The easiest of them consist of three-corner prisms with different graphical fragments printed on their surfaces [1, 2]. When aligned in a line the fragments form an integral picture. To change a picture by another one every demonstrating prisms rotate simultaneously in the same direction around their longitudinal axis.
These billboards can demonstrate changing images on the one side only. In order to show pictures on both sides two sets of three-corner prisms are arranged parallel to each other [3]. In this case the thickness of the billboard increases making it bulky and non convenient in use. The obvious way to reduce the thickness of the billboard is to apply four-corner prisms. To show changing pictures on both sides only one set of prisms is enough. Keeping the thickness of the billboard on an appropriate level the size of four-corner prisms can be bigger in comparison to three-corner ones. The quality of pictures formed on the billboard becomes higher since the number of seams between fragments reduces.
On another hand four-corner prisms have one disadvantage. In case of arrangement in close proximity to each other they can’t easily rotate like three-corner ones. For solution of this problem in [4, 5] the prisms carrying fragments of pictures move on the complex trajectories. It makes the thickness of the billboard essentially non-constant before and during transformation.
For achieving much compactness in [6] four-corner prisms are made transformable. Each prism consists of four rigid units with fragments of pictures on their external sides. The unit in the form of “right angle” is made of two plates connected to each other. For changing images on both sides of the billboard the prisms rotate and are simultaneously transformed by moving rigid units. As a result the size of each prism becomes temporary smaller. The disadvantages of [6] are additional seams between fragments forming pictures, and increased labor input of producing and attaching of multitude narrow strips carrying graphical information.
DESCRIPTION OF THE SYSTEM
It is proposed the billboard which consists of a set of demonstrating four-corner prisms, mounted on a rigid frame (fig. 1).
Fig. 1 The billboard demonstrating an image. a – front view, b – section 1-1;
crossbars connected to the strut with hinges, flexible cables made of steel or polymer. Crossbars are also connected to four corner elements to which the flexible covering is attached. Central strut can move in longitudinal direction and is fixed in tangential direction.
Fig. 2 Four-corner prism in expanded state.
1 – longitudinal strut, 2 – crossbars, 3 – hinges, 4 – cables, 5 – corner elements, 6 – flexible covering,
a – the size of the prism in expanded state
On each of four surfaces of a prism different graphical fragments are printed. When aligned in a line the fragments form an integral picture. To change a picture by another one every demonstrating prisms rotate simultaneously in one direction around their longitudinal axis. The rotational angle is equal for each prism and must be divisible without remainder by 900. To make rotation possible, four-corner prisms, situated in close proximity to each other, decrease their size by partially collapsing of their frames (fig. 3). Changing frame size is performed by moving the longitudinal strut (fig. 4).
Fig. 3 The billboard in process of changing an image. All labels are on fig. 1
Fig. 4 Four-corner prism in collapsed state. The labels are on fig. 2, ∆z – displacement of the strut
Rotation of prisms and dynamic changing of their dimensions (fig. 5, 6) are performed with one engine (not shown in figures).
Shafts 10 rotate crankshafts 11 and element 8. The last one is connected with the longitudinal strut 1, allowing it to move freely up and down.
Crankgear mechanism 11-13 pushes the beam 14 connected to the strut 1 with a hinge. The strut is moved in the vertical direction while the hinge allows it to freely rotate around its axis.
In order to avoid a tilt of the beam 14 two shafts 10 with crankgear mechanisms 11-13 have to be installed (fig. 6). As a result an engine by means of shafts 10 rotates the prism and simultaneously changes its dimensions, allowing four-corner prisms to revolve without collision. The upper brace 15 controls the minimal angle γmin between the crossbars 2 and the strut 1. It allows the prism to leave the collapsed state when required.
In the working position the lower brace 16 presses the element 9 which passes freely through the hole in the plate 7. It causes tensioning of cables 4 and fixation the prisms, demonstrating images.
Guides 17 are joined together with a ring 18. The ring allows the strut 1 to pass freely in the vertical direction. The guides influence crossbars 2 in horizontal direction only. As a result the frame of the prism follows the rotating element 8.
Proceedings of the First Conference Transformables 2013.In the Honor of Emilio Perez Piñero 18th-20th September 2013, School of Architecture Seville, Spain EDITORIAL STARBOOKS. Felix Escrig and Jose Sanchez (eds.)
Fig. 5 Principle structure of the billboard, allowing to rotate the prisms and simultaneously change their dimensions (the prism is in collapsed state). Labels 1-6 are on fig. 2; 7 – parts of the billboard frame; 8 and 9 – upper and lower rotating elements; 10 – shaft with means for rotation of elements 8 and 11; 11, 12, 13 – elements of a crankgear; 14 – supporting beam; 15, 16 – upper and lower braces fixed to the strut 1 motionlessly; 17 – guides for crossbars 2; 18 – connecting ring
Fig. 6 Principle structure of the billboard: section 1-1 on fig. 5 (the prism is in expanded state).
Labels are on fig. 2 and 5
Two types of crankgear mechanism are considered. In the first one shown on fig. 7a the crank rotates always in the one side (e.g. in clockwise direction) changing the angle β by 3600 per cycle.
In the second type (fig. 7b) the crank rotates in one direction on even cycles and in the opposite direction - on odd cycles. The maximum changing of angle β in this case is 1800. To show all four different pictures in every side of the billboard the shaft 10 should be equipped with additional means and ratchet mechanisms (not shown in fig. 5, 6), allowing the prisms to rotate in one side only on each cycle.
length of a crank; R – the length of a connecting rod
RESEARCH OF THE SYSTEM
Basic parameters of the billboard are shown on fig. 8.
Fig. 8 Enlarged fragment A on fig. 5 (the prism is in expanded state).
Labels 1-6 are on fig. 2; 2a is the crossbar 2 in an intermediate state; guides 17 are not shown; Yt, d –distances from the axis of the prism to the cable and the crossbar connection, accordingly;
bc – the distance from external side of the flexible covering to the crossbar connection
Displacement ∆z is calculated from: − − − + ⋅ =
∆z(β)a r k2 sin(β)2 cos(β) k 1 , [1a] − + − − ⋅ = ∆z(β)b r k2 cos(β)2 sin(β) k2 1 , [1b] where ∆z(β)a concerns to the first type of the crankgear (fig. 7a), and ∆z(β)b concerns to the second type of the crankgear (fig. 7b); k=R/r - coefficient.
The graphs of ∆z(β) divided by r for a half of a cycle are shown on fig. 9 and 10.
Fig. 9 The graphs of ∆z(β)a/r for the first type of crankgear (fig. 7a)
On fig. 9 the disadvantage of the first type of crankgear is shown: on early stages of each cycle the growth of ∆za is negligible. It can cause a collision of adjacent demonstrating prisms.
In order to increase the reliability of the billboard, cables 4 (fig. 8) have not to slack anytime. It is achieved if
min
γ
γ > during each cycle, where γ is the angle between the crossbars 2 and the strut 1 (fig. 8), γmin is calculated from: − = Ld d Yt arcsin min γ , [2]
where the crossbar length is:
d b a
Ld= 2⋅ /2− c− . [3]
where a is the size of the prism in expanded state (fig. 2). For reducing the height of the billboard the length H0 (fig. 8) must be totally used when collapsing the prism:H0=∆zmax, where ∆zmax is the maximum displacement of the strut. Together with the condition
min
γ
γ > it leads to the following:
(
Yt1...Yt2)
Yt∈ , [4]
max 2 z
Ld≥ ⋅∆ , [5]
where Yt1, Yt2 are calculated from [6a, 6b] and the maximum displacement of the strut 1 – from [7a, 7b]:
+ ⋅ − − ⋅∆ ⋅ = 2 max 2 1 0.5 Ld 2 d Ld 2 z Yt , [6a] + ⋅ + − ⋅∆ ⋅ = 2 max 2 2 0.5 Ld 2 d Ld 2 z Yt , [6b] r z a= ⋅ ∆ max, 2 , [7a] ) 1 1 ( 2 max, = ⋅ + − − ∆z b r k k , [7b]
where ∆zmax,a concerns to the first type of the crankgear (fig. 7a), and ∆zmax,b concerns to the second type of the crankgear (fig. 7b).
From [5] and [7] maximum lengths of cranks – r – can be easily obtained.
To illustrate the process of rotating of two adjacent prisms the following parameters were taken: a = 300 mm, bc = 30 mm, d = 15 mm, k= 2, ∆=a/500=0.6mm, where
Proceedings of the First Conference Transformables 2013.In the Honor of Emilio Perez Piñero 18th-20th September 2013, School of Architecture Seville, Spain EDITORIAL STARBOOKS. Felix Escrig and Jose Sanchez (eds.)
∆ is the initial distance between two adjacent prisms (fig. 11). The distance g between two rotating and transforming prisms is shown on figs. 12.
Fig. 11 Rotating of two adjacent prisms (top view). α - angle of rotation
Fig. 12 The graphs of the distances g between the prisms a, b – types of the crankgear (fig. 7)
The clearance between two prisms in case of using the crankgear of type b stays positive for all angles. The opposite situation takes place for the crankgear of type a. Increasing the initial distance ∆ between two adjacent prisms is not a permissible solution because the quality of demonstrating images becomes bad. The only way to use the crankgear of type a is to increase lengths of a crank and connecting rod – r and R (fig. 13).
Fig. 13 The graph of the distance g between the prisms using the crankgear of type a: r and R are increased
At point A the crossbars 2 reach the brace 15 (fig. 5). As a result cables 4 slack and the size of the prisms stops to reduce.
CONCLUSION
1. The billboard which consists of a set of rotatable four-corner prisms with different graphical fragments printed on their surfaces is considered. Each prism has a collapsible frame and a flexible covering on its sides. Rotation of prisms and dynamic changing of their dimensions are performed by one engine with the help of crankgear mechanisms.
2. The proposed billboard has the following advantages: possibility of displaying of changing images on its both sides, smaller dimensions and better quality of presentation of information.
3. Two types of the transforming mechanism are considered.
4. The first type of the transforming mechanism (fig. 7a) leads to the slacking of cables 4 (fig. 2) during the process.
5. In case of the second type of the transforming mechanism (fig. 7b) cables 4 (fig. 2) may be replaced with the hinge struts. It will simplify the construction and improve reliability of exploitation of the billboard. 6. The proposed billboard can be used for displaying advertising information and for decorating facades of buildings.
7. With regard to the billboard we have got the favourable verdict about the patent for an invention in Russian Federation.
Bibliography
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[4] Patent 1058698 USA, G09F 11/02. Advertising device / A.O. Goldstein (USA), 08.04.1913.
[5] Patent 7509762 USA, G09F 11/02. Multi-sided display sign apparatus / А.Ajumobi (France), 31.03.2009.
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