The role of the shape in industrial design.

Marin, Dumitru ; Raicu, Lucian ; Simion, Ionel 等

1. INTRODUCTION

The shape concept appears in almost all design definitions, formulated by different schools or personalities. For exemple "The International Council of the Societies of Industrial Design" (I.C.S.I.D) gives following definition: "The design is a creative activity which consists in determination of the shape properties of the industrially made objects. The object shape properties, include not only exterior characteristics, but also all the structural relations which make a coherent unity from an object or from an objects system, regarding the point of view of both the producer and the consumer." (Quarante, 1994)

The cylindrical shape is the most frequently used shape in structure of industrial products (shafts, spindles, cylindrical bars and pipes, cylinder bores etc.). It is either manufactured by machine tools through lathing, drilling, boring or through wrapping from sheet, plastic materials etc., the rotation cylinder is the most technological shape, therefore it is more easily achieved than other shapes (conical, spherical, hyperboloidal shape etc.). Also the cylindrical shape can be turned onto a hyperboloidal shape.

Consequently, we suppose a rotation cylindrical shape, such as Fig.1. The circles [C.sub.1] and [C.sub.2] with radius R are fastened between themselves through inextensible generatrices G. The circles [C.sub.1] and [C.sub.2] can be in practice rings or disks and the generatrix G can be rigid bars. When the circle [C.sub.1] is turned in its plane all around the cylinder axis with a certain angle and the circle [C.sub.2] remains fixed, then the cylinder from Fig.1 turns into a rotation hyperboloid (Fig.2).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The rotation hyperboloid from Fig. 2 is a surface generated by a straight line (the generatrix G), which rotates all around [O.sub.1][O.sub.2] axis. The generatrix G doesn't intersect the axis [O.sub.1][O.sub.2] and isn't in a parallel direction with it.

2. CYLINDER TURNING INTO HYPERBOLOID. CALCULATIONS AND REMARKS.

For simplification, we suppose that a new position of the one generatrix G (segment AB) is [A.sub.1][B.sub.1]; then the circle [C.sub.1] turns and changes one's place with distance h and the cylinder turns into (changes in) hyperboloid such as in Fig.3.

In succession, we calculate displacement h. From the rectangular triangle [b'e'a.sub.1'] can write (Marin et al., 2006):

[b'e'.sup.2] = [b'a'.sub.1.sup.2] - [e'a'.sub.1.sup.2] (1)

With dimensions from Fig. 3, formula (1) becomes:

[(H - h).sup.2] = [H.sup.2] - 4[R.sup.2] [sin.sup.2][alpha] (2)

After calculations, finally we obtain:

h = H - [square root of [H.sup.2] - 4[R.sup.2][sin.sup.2][alpha]] (3)

The value of h displacement depends on invariable parameters H and R of cylinder and the variable angle [alpha].

We distinguish following cases:

a) H>2R.

The radical is positive and theoretically the circle [C.sub.1] can be rotated with the angle [alpha] = [pi]/2 and the cylinder becomes a cone that is the generatrix G intersects the [O.sub.1][O.sub.2] axis.

[FIGURE 3 OMITTED]

b) H=2R

The formula 3 becomes:

h = 2R(1 - cos[alpha]) (4)

For [alpha] = [pi]/6; 2[alpha] = [pi]/3 and h = R(2 - [square root of 3]) [congruent to] 0,27R.

For [alpha] = [pi]/6]; 2[alpha] = 2 [pi]/6 and h = 2R(1 - 1/2) = R.

For [alpha] = [pi]/2; 2[alpha] = n and h = 2R = H, the circle [C.sub.1] coincides with the circle [C.sub.2], it is a theoretical case.

c) H<2R.

Because [H.sup.2] - 4[R.sup.2][sin.sup.2][alpha] [greater than or equal to] 0, then [alpha] [less than or equal to] arcsin H/2R and the rotation angle [alpha] is limited.

For example if H = R [??] [alpha] [less than or equal to] [pi]/6.

A rotation hyperboloid can be generated, also, by a hyperbola, which rotates all around [O.sub.1][O.sub.2] axis; the hyperbola and the axis are in the same plane (see Fig.3).

3. APPLICATIONS

If the circle [C.sub.1] and [C.sub.2] in Figure 1 are special rings made from special fibre fastened between themselves through a very strong elastic fibres, then is achieved a Linear to Angular Displacement Device (LADD). Several elements LADD fastened among them can help a robot to raise the leg and it can step (Fig.4). In Fig. 5 is represented a Concentric Linear to Angular Displacement Device (CLADD), made from two concentric LADD. An electric motor turns an extremity of the interior LADD and the other extremity is fastened to an extremity of an exterior LADD. The advantages of LADD elements are: low weight, low noise and the absence of lubricant (Mennitto & Buehler, 1996).

The reduction of fluid flow, even its closing, when the fluid flows through an elastic pipe. This can be realized by spinning of a textile threads bunch fixed around of the pipe with two cylindrical disks. (see the circles [C.sub.1] and [C.sub.2] in Fig. 1). The cylindrical fragment changes into hyperboloidal fragment with variable section (Plahteanu & Belous, 2000).

Pressing, grasping mechanisms; when the ring [C.sub.1] turns and the ring [C.sub.2] remains fixed, can be created axial forces in a direction or the other. The cylinder changes into hyperboloid and the distance between rings decreases or the hyperboloid ctanges into cylinder and the distance between rings increases (Marin, 2007).

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Rolls, rotors, adjustable abrasive or cutting tools based on the hyperboloid's property to change its profile until it becomes cylinder.

Different ornamental items, for example a lamp-shade, can be changed from a cylinder in many hyperboloid shapes (Fiell & Fiell, 2000).

4. CONCLUSIONS

The change of rotation cylinder in rotation hyperboloid and vice versa is simply from the theoretical point of view and beneficially from practical point of view.

The choosing of rotation angle 2[alpha] and displacement h depends on: constructive parameters H and R of the mechanism, the force which must be obtained, the kinematics and dynamic characteristics of the mechanism.

In different constructive shapes, the principle described in this paper can be the technical solution for obtaining of linear motion and of technological forces for various mechanisms (Raicu, 2002; Simion, 2005).

For the further research, we can calculate and plot the velocity and acceleration variation of the designed mechanisms, starting from formula (3), through the derivation of the axial displacement h and we can use the mechanism in the best dynamic conditions.

5. REFERENCES

Fiell, Ch. & Fiell, P. (2000). Industrial design A-Z, Taschen GmbH, ISBN 3-8228-6310-6, Koln.

Marin, D.; Raicu, L. & Radulescu, C. (2006). Geometrical shape--a design creative resource, Scientific Bulletin, University POLITEHNICA of Bucharest, Serie D: Mechanical Engineering; Vol.68, No 3, pp 55-62, I.S.S.N 1454-2358, Bucharest.

Marin, D. (2007). Design Industrial; Designul Formei (Industrial Design; Shape design), Editura BREN, ISBN 978-973-648-706-4, Bucharest.

Mennitto, G. & Buehler, M (1996). A compliant articulated robot leg for dynamic locomotion, Robotic and Autonomous System--No18.

Plahteanu, B. & Belous, V. (2000). Efecte geometrice in creatia tehnica (Geometrical Effects in Technical Creation), Editura Performantica, ISBN 973-8075-01.7, Iasi.

Quarante, D. (1994). Elements de design industriel, Polytehnica 2e Edition, ISBN 2-84054-018-5, Paris.

Raicu, L. (2002). Grafic si vizual intre clasic si modern (Graphics and Visual between Classic and Modern), Editura Paideia, ISBN 978-596-062-1, Bucuresti.

Simion, I. (2005). AutoCAD for Engineers, TEORA USA LLC, ISBN 1-59496-033-X, Wisconsin, USA.