US3830031A

US3830031A - Three-dimensional depolyable and collapsible structures

Info

Publication number: US3830031A
Application number: US00254209A
Authority: US
Inventors: G Soisson
Original assignee: Individual
Current assignee: Individual
Priority date: 1971-05-19
Filing date: 1972-05-17
Publication date: 1974-08-20
Anticipated expiration: 1991-08-20
Also published as: DE2223621A1; CH552725A; IT957905B; GB1388633A; FR2138244B1; FR2138244A1

Abstract

Three-dimensional collapsible structure having the form of a system of bars articulated to one another, which comprises a twodimensional lattice made of parallelograms of hinged bars, acting as a first carrier element, a second carrier element which has preferably the same construction as the first one and a number of pivoting rods connecting together some of the joints of the two carrier elements, said rods being inclined with respect to the planes of the carrier elements when the structure is deployed.

Description

States atent n91 Soisson THREE-DIMENSIONAL DEPOLYABLE AND COLLAPSIBLE STRUCTURES Inventor: Gerard Charles Jean Soisson, 40 rue du Bac 75, Paris, France Filed: May 17, 1972 Appl. No.: 254,209

Foreign Application Priority Data May 19, 1971 France. 71.18308 us. (31...; 52/645, 52/109, 52/648 1m. (:1 E04h 12/18, E04b 1/343 Field 01 Search 52/645, 109, 648

References Cited UNITED STATES PATENTS 11/1889 Edwards .,,52/109 Edwards 52/109 11] 3,830,031 1451 Aug. 20, 1974 1,095,391 5/1914 Fogle ct a1. 52/109 1,51 1,679 10/1924 Schwarz 3,053,351 9/1962 Fulcher 52/632 Primary Examiner-Frank L. Abbott Assistant Examiner-James L. Ridgill, Jr. Atmrne Agent, or Firm-William .1. Daniel 5 7 ABSTRACT Three-dimensional collapsible structure having the form of a system of bars articulated to one another, which comprises a two-dimensional lattice made of parallelograms of hinged bars, acting as a first carrier element, a second carrier element which has preferably the same construction as the first one and a number of pivoting rods connecting together some of the joints of the two carrier elements, said rods being inclined with respect to the planes of the carrier elements when the structure is deployed.

10 Claims, 21 Drawing Figures PATENTEDAUBZO 1974 30830 O 31 sum 3 BF 6 PATENTEDmszo lam 3.830.031

SHEET 5 0f 6 The present invention relates to a three-dimensional deployable and collapsible structure, which enables the factory production of assembled units as well as the storage and transportation of these units in a compact form.

The present invention is concerned in particular with reducing the factory production time and shopfloor assembly time, thus with reducing the cost price, with making it easy for these various operations to be carried out by semi-skilled labour, and with giving the structure a design which enables it to be dismantled for subsequent reuse after storing in the collapsed (folded) state.

The invention therefore has as its objects:

a structure which can be collapsed flat and can therefore be transported in its entirety, on a trailer;

a structure which can be factory assembled throughout and which avoids the need for the building of subassemblies on the shopfloor;

a structure with standard components in which the number of different components is very small so that substantial production runs of identical components become possible;

structural assemblies obtained by very small numbers of assembly sequences which are both logical and repetitive;

a structure with modular sub-assemblies the components of which are designed so that their size and scale can be modified without difficulty;

multiple and varied structures having a large variety of possible shapes (flat, cylindrical, spherical, saddleshaped, etc.) produced simply by a choice of the lengths of the bars or rods, of the spacings of drilled holes and of the types of connecting elements used in the joints;

an extremely simple, straightforward and rapid method of assembly on the shopfloor (tractive deploying force on the ground, is applied in one direction only, the structure maintained in the deployed position by the fitting of a rigid integrated element, raising and fixing the deployed structure).

In accordance with the invention the structure comprises:

a first carrier element which is a two-dimensional lattice structure with an assembly of articulated chain links or parallelograms constituted by networks of straight bars certain ones at least of which are coplanar and make a certain angle with one another with the structure is deployed, the bars of one and the same network being parallel to one another and joints being provided at certain ones, at least, of the corners of said chain links;

at least one second carrier element at an interval from the first and provided with joints;

and pivoting rods connecting at least certain ones of the joints of the other carrier element, said rods being inclined in relation to the alignment of the plan of collapse of the structure, said alignment being defined by a plane direction in which, by and large, there are placed the bars which become adjacent to one another when the angles which they make with each other are virtually closed.

In accordance with a particularly advantageous embodiment, the second aforesaid carrier element has a structure similar to that of the first and isconstituted by a second lattice structure, certain ones at least of the bars of said second lattice structure defining parallelograms or chain links which are identical to those of the first lattice structure and whose geometric centres are located upon perpendiculars to said first lattice structure struck at the points of intersection between the bars thereof. Certain ones at least of the joints of one lattice structure may be connected in each case to four joints of the other lattice structure, by four inclinedrods which form the corners of a right pyramid. The inclined rods, in projection onto a collapsed plane, may form with the bars of the two lattice structures, adjacent triangles whose apices are directed alternately towards one and then the other of the lattice structures.

In at least part of the structure, at least one prismatic volume having one of these triangles for a base, is pref erably defined by three bracing arrangements comprising two pairs of rods and two bar elements, the ends of these rods and said elements being connected in pairs by the aforesaid joints and said rods and said elements of said volume likewise being connected together at their points of intersection, by pivots.

In order to produce a flat structure, the projected triangles converging towards a lattice structure are preferably of isoceles form and are identical to the projected triangles converging towards the other lattice structure, the pivots of the bracing arrangements of the aforesaid prismatic volume, said arrangements being assembled at the points of intersection, being located at the centres of the rods and bar elements.

Other embodiments of the structure are possible by varying the proportions of these elements, bars and rods.

Various other features and advantages of the invention will become apparent furthermore, from the detailed description which now follows, and the accompanying drawings.

In the drawings:

FIG. 1 is a perspective view, showing in the collapsed position a first embodiment of the structure;

FIG. 2 is a perspective view illustrating said first form of embodiment in the deployed position and clearly illustrating that the envelope obtained is flat;

FIG. 3 is an elevational view projected onto the collapsing plane R" in FIG. 1;

FIG. 4 is a schematic view of the embodiment of FIGS. 1 to 3, showing the two lattice structures of the assembly of inclined rods, and illustrating them in three exploded perspective views marked 4A, 4B and 4C and linked with one another by joining lines a and b and because FIG. 4C can only provide a rather confused impression of the distribution of the inclined rods, FIG. 4 also comprises a fourth perspective view 4D where the zigzag sheet defined by these rods has been flattened and the correspondence between the flattened sheet of FIG. 4D and the true sheet of FIG. 4C is indicated by the joining lines da and db;

FIG. 5 is a schematic plan view of the structure shown in FIGS. 1 to 4, in which view there can be seen;

in thick full line, the bars of the lattice structure of FIG. 4A;

in thin full line, the bars of the lattice structure of FIG. 4B;

in chain dotted line, the inclined rods of FIG. 4D;

marked by solid circles, the joints connecting the bars of the lattice structure of FIG. 4A, with the inclined rods;

marked by open circles, the joints connecting the bars of the lattice structure of FIG. 48, with the inclined rods;

marked by crosses, the other points of intersection between the bars or rods, whether or not said bars or rods do or do not have joints at these points;

in long broken line, the transverse imaginary lines T or t which, perpendicularly to a collapsing plane, R, link the points of intersection of the bars of one lattice structure or the other, respectively;

in short broken line, the imaginary longitudinal lines L or I which, parallel to the collapsing plane R, link the points of intersection between the bars of one lattice structure or the other, respectively;

FIGS. 6 and 7 are views similar to those of FIGS. 1 and 2 and relate to a structure of saddle-shape, related to a hyperbolic paraboloid, in the deployed state;

FIGS. 8 and 9 are views similar to those of FIGS. 1 and 2 relating to a structure which, in the deployed state, has a cylindrical form;

FIG. 10 is a view of similar kind (in plan form) to that shown in FIG. but showing another embodiment;

FIG. I1 is a side elevation of the embodiment shown in FIG.

FIG. 12 is a plan view showing a joint for connection between a lattice structure and the inclined rods;

FIGS. 13 and 14 are sections taken on the lines XXX-XXX and XXXl-XXXI respectively, of FIG. 12, the tubes shown in one section, not appearing in the other; and

FIGS. I5, 16 and 17 illustrate in plan, section and side elevation, a variant embodiment of a joint.

It is important to point out that FIGS. 1, 6 and 8 on the one hand and FIGS. 2, 7 and 9 on the other hand are perspective views which reproduce the result'obtained by photographing, respectively in collapsed and deployed states, models produced in accordance with the other corresponding Figures of the drawing. They prove, therefore, that all the structures can be rendered perfectly flat when they are collapsed (folded) and that they adopt a flat. saddle-shaped or cylindrical form when they are deployed. In addition, they make it possible to define in space the exact positions of the bars and rods, according to whether the structure is collapsed or deployed, something which would be much more difficult if they were not there and from a consideration purely of the other, conventional figures.

In accordance with the first embodiment shown in FIGS. 1 to 5, the three-dimensional deployable structure is of the kind with an imaginary flat envelope and is designed to be hyperstable that is to say that it has a large number of superfluous connections. To facilitate description and understanding, we will assume that it is horizontal as would be the case if it constituted the framework of a ceiling or the framing of a flat roof.

It comprises a top lattice structure 1 (FIGS. 4A and 5) constituted by a first network of mutually parallel bars 2, and by a second network of likewise mutually parallel bars 3 which intersect the bars 2, however, to form X' all these bars being shown in thick full line in FIG. 5.

The

bars

2 and 3 are connected by joints 4 schematically indicated by solid circles and located at the points of intersection between even imaginary longitudinal lines L and even imaginary transverse lines T as defined hereinbefore. Thus, at the intersection between the lines L1; and T there is a joint 4 linking a bar 2 with a bar 3.

The structure likewise comprises a bottom lattice structure 5 (FIGS. 48 and 5) constituted, as before, by two intersecting networks of

bars

6 and 7 shown in thin line in FIG. 5.

The

bars

6 and 7 are connected by joints 8 indicated by open circles and located at the points of intersection between the even longitudinal imaginary lines 1 and the odd transverse imaginary lines t as defined in the foregoing, it being understood furthermore that the lines of the two lattice structures extend in one and the same plane perpendicular to those of the same order. Thus, at the intersection between the lines 1., and I there is a joint 8 connecting a bar 6 to a bar 7.

The two lattice structures 1 and 5 are idendical in the sense that the chain links defined by their respective bars are deformable parallelograms or lozenges of the same shape and orientation. However, these lattice structures are located in such a manner in relation to one another that each bottom joint 8 is aligned with the geometric centre of the corresponding top chain line and, consequently, each top joint 4 is aligned with the geometric centre of the corresponding bottom chain link.

Finally, the structure comprises inclined rods which are attached in such a fashion as to be able to pivot at their ends, to the top joints 4 and the bottom joints 8, thus linking them together.

However, these inclined rods are arranged in a special fashion in order to enable the structure to be collapsed and deployed. Thus, considering FIGS. 4D and 5, it will be observed that:

the rods of a first series, marked by the reference 9, each link a top joint 4 to a bottom joint 8, disposed at the intersection of a transverse line whose order is higher by one unit, and a longitudinal line whose order is higher by two units; for example, a rod 9 connects the top joint 4 (T L to the bottom joint 8 1 the rods of a second series, designated by the reference 10, each link a top joint 4 to a bottom joint 8 located at the intersection between the transverse line whose order is higher by one unit and a longitudinal line whose order is lower by two units; for example, a rod 10 connects the top joint 4 (T L aforementioned, to the bottom joint 8 (t the rods of a third series, marked 11, each link a top joint 4 to a bottom joint 8 located at the intersection between a transverse line whose order is less by one unit and a longitudinal line whose order is higher by two units; for example a rod 11 connects the aforesaid top joint 4 (T L to the bottom joint 8 (t the rods of a fourth series, indicated by reference 12, each connect a top joint 4 to a bottom joint 8 located at the intersection between a transverse line whose order is less by one unit and a longitudinal line whose order is less by two units; for example, a rod 12 connects the top joint 4 (T L aforementioned, to the bottom joint 8 (t It will be observed, therefore, that each of the joints 4 of the top lattice structure 1 is connected to four joints 8 of the bottom lattice structure 5, by four inclined rods 9 to 12 extending along the corners of a right pyramid. It will be observed, too, that two consecutive pyramids 13 and 14 (FIG. 4D) overlap, their respecti-ve rods crossing one another in pairs. The same applies if we consider the pyramids and 16 whose apices coincide with the bottom joints 8.

In a different manner, it will be observed, from a comparison of FIGS. 4C and 4D, that the inclined rods 9 to 12 form a collapsible sheet 17 which, projected onto the collapsing plane R, defines a zigzag line.

This zigzag sheet is encountered in all the variant embodiments in which the degree of hyperstability" is diminished although not at the expense of the stability of the overall structure.

In the structure described hereinbefore, it has already been mentioned that a series of bars can also be distinguished which bars form X' such as a b,, a b a b (FIG. 5) or a -b' a -b a;,b;,, etc for the top lattice structure and (lg-B2, etc for the bottom lattice structure, this quite apart from the terminal parts. To give the deployed structure greater stability, it is also possible to provide pivots such as those i,, i;, or 1",, i at the points of intersection of these X", or at any rate at certain ones, these pivots being perpendicular to therelevant pairs of bars. Also, advantageously, pivots of this kind can be provided at the points of intersection, or at least certain ones of them, between the pivoting rods, where these are present. These pivots have been shown at 21 and 24 in FIG. 3.

It should be pointed out that in this fashion columns of these X' are formed in the one case a 14 b a b these columns, each of the X*, for example a b is connected to the X in the contiguous column, by joints 4.

In the present case, namely that of the production of the flat design shown in FIGS. 1 to 5, the various columns are coplanar in each lattice structure, whether top or bottom; however, this does not apply to other possible embodiments, which we shall call shaped ones, and which fall within the scope of the invention, such for example as those shown in FIGS. 6 and 7' or 8 and 9.

In accordance with the embodiment shown in FIGS. 6 and 7, the external envelope of the deployed structure has a saddle shape related to a hyperbolic paraboloid; in effect, as FIG. 7 shows, it has a convex curvature in the transverse directions and a concave curva ture in the longitudinal directions. In this case, all the triangles l9 and 20 are of isoceles form, preferably equilateral and identical to one another, the pivots not being located at the centres of the bars.

In the embodiment shown in FIGS..8 and 9, the external envelope of the deployed structure is cylindrical. In this case and as shown in FIG. 8, all the projected triangles are isoceles triangles, but the triangles 19 whose apices are directed towards the top lattice structure, have a shorter base than the triangles 20 whose apices are directed towards the bottom lattice structure; in order words, the bottom bars are-shorter than the top bars. Here, the pivots are located strictly at the centre of the bars.

We will now consider the structure shown in FIG. 10. Like FIG. 5, this figure illustrates a deployed structure with an articulated top lattice structure (in thick line) and an articulated bottom lattice structure (in thin line), these being connected to one another by pivoting rods which link the joints together. Contrary to the case shown in FIG. 5, however, where the bars of a network form X'* with one another, here they form V"" articulated at their ends and at the vertex, so that equivalent possibilities are created as a consequence. However, because the chain links of the structure have more of a floating nature as a consequence, it is a useful expedient to additionally provide, as links between the two lattice structures, articulated bars such as those c etc which connect the top bars a b, to the bottom bars a,, B, The conventional collapsing plane" will in this case be the projection plane of FIG. II; it is worth pointing out, however, that any flat structure in accordance with the invention, whether it be that of FIG. 10 or that of FIG. 5, has another possible collapsing plane, namely that of the two base lattice structures.

In order to maintain the structure, whatever its type, in the deployed position, several means are open.

In accordance with a first embodiment, the marginal joints 4 and/or 8 of the structure are attached to the edge beams (for example P in FIG. 4c), of the construction into which this structure is to be integrated.

In a second embodiment, certain ones of the top joints 4 and/or certain ones of the bottom joints 8 of the structure, are rigidly spaced apart by elongated elements extending perpendicular or parallel to the col- Iapsing plane R and following the shape of the structure envelope. Elements of this kind can of course be replaced by ties (chains, cables or the like), permanently hooked to certain joints.

In accordance with a third embodiment, certain ones of the top joints 4 and/or certain ones of the bottom joints 8 and/or certain ones of the pivots, are locked so that no pivoting can take place in relation to the

bars

2, 3 and the rods 9 to 12.

These various embodiments can of course be combined with one another. Moreover, the bars and rods can be constituted by iron members with flats, or by profiled sections having at least one flat flange; they can also be constituted by tubes of circular, square, rectangular or other section.

The design of the joints 4 and 8 at each of which there terminate either elements, bars and inclined rods, will be illustrated by way of example hereinafter making reference to FIGS. 12 to I4 where said elements are constituted by tubes.

Each joint comprises a fitting 30 exhibiting a halfsleeve 31 into which there can be slid and fixed in place, for example by a bolt, a tube 32 which is to act as an element to maintain the structure in the deployed position.

This half-sleeve is integral with four convergent lugs 33 to 36.

The

lugs

33 and 34 are coplanar because they are designed to support the pivoting elements 37 of the

bar components

2a and 3a which are to constitute the top lattice structure 1 for example. These pivoting elements 37 are located in four holes 38.1 and 38.2 formed at the corners of said lugs 33 and 34.

The

lugs

35 and 36 subtend with one another an angle corresponding to that of the triangles l9 and 20. In the case of the embodiment shown in FIG. 3, this angle is 60.

The lug 35 has two holes at its corners, 39.1 (FIG. 13) and 39.2 (FIG. 14), for the accommodation of the pivoting elements 37 which articulate the

inclined rods

9 and 10 respectively.

The lug 36 likewise has two holes 40.1 (FIG. 13), and 40.2 (FIG. 14), at its corners, to take the pivoting elements 37 for the articulation of the

inclined rods

11 and 12 respectively.

It is important to point out that, considering the holes 38.1, 39.1 and 40.1 located close to the plane of section XXX-XXX, the tube 2a is assembled above the lug 34 (FIG. 13) whilst the

other tubes

9, 11 and 3a are arranged at the same side, moving around the tube 32, of the

lugs

35, 36 and 33, as that at which the tube 2a is located in relation to said lug 34. It will be observed, on the other hand, that considering the holes 38.2, 39.2 and 40.2 located close to the plane of section XXXl- -XXXI, the tube 3a is located beneath the lug 34 (FIG. 14) whilst the

other tubes

10, 12 and 2a, as be fore, have the same position in relation to their

respective lugs

35, 36 and 33, as the tube 311.

Under these conditions, if the structure is fitted with joints of this kind, the

tubes

2a and 3a never being located in the same plane, can cross one another; the same applies to the

tubes

6a and 7a, 9 and 10, 11 and 12. In addition, the fitting of the tubes to the lugs 33 to 36 and the assembly of the pivoting elements 37, are made possible and straightforward by the fact that the two tubes and the two elements of one and the same lug, cannot interfere since they are arranged at opposite sides.

Self-evidently, variant embodiments are possible: the

tubes

20, 9, 11, etc could be flattened to a greater or lesser extent, at least at their ends, and the float 31 is not essential and could be omitted.

If the structure is flat (FIGS. 1 and 2), the pivoting elements 37 will be simple rods with a single degree of freedom; they can then be constituted by bolts, rivets or the like.

By contrast, if the structure is shaped, that is to say other than flat (FIGS. 6, 7, 8 and 9) it may be sufficient to provide adequate clearance between the rods constituting the pivoting elements 37 and the holes formed in the fitting 30 and/or the tubes, in order to produce at least one extra degree of freedom.

However, it would appear a better idea to provide a crimped knuckle, with a certain degree of mobility about its centre, in the tubes and to fix a rod extending said knuckle to the corresponding lug ofthe fitting. The same type of assembly can be provided in this case for the pivots 21 to 24.

The joints 4 and 8 can also be given a simpler design, in particular in the case of shaped structures. In other words, and as shown in FIG. 3, the bar elements 20 or 30 (or 6a and 711) as well as the rods 9 to 12 can be threaded over a toroidal ring 41 which is open prior to assembly and afterwards closed by suitable means.

Whatever the case, in all the joints 4, 8 and the pivots 21 to 24, the axes ofpivot are parallel, at least when the structure is collapsed, to the collapsing plane R.

In FIGS. 15 to 17, a variant embodiment ofajoint designed especially for a structure of the kind shown in FIGS. 10 and 11 and using bars which form collapsible V in each of the lattice structures, can be seen; the joint belongs to the top lattice structure and is shown in the deployed position.

The centre" of the joint is constituted by a rigid metal component 30, star-shaped in section, with radiating lugs in the manner shown in FIG. 16, which may however be asymmetrical in the manner shown in FIG. 17. To the lugs of this centre" the bars (for example tubes) and the rods are pivotally attached by pivots such as 38.1, 39.1, perpendicular to the lugs. By analogy with FIGS. 12 to 14, the

references

2a and 30 have been used to designate the elements of a V in the top lattice structure; the V" of opposite vertex is marked 2a, 3a. The pivoting rods 9, 9' are articulated to the lugs having the corresponding inclination. The bars 0 likewise articulated to the lugs, constitute supplementary links belonging to the structure of FIGS. 10 and II.

This kind of joint enables the forces to converge at a single imaginary point, and enables the structure to be folded. To this end, when it is desired to fold the structure, the bars of the

V

2a and 31!, 2'41 and 3a, pivot about their respective joint centres until they are practically parallel.

The structure in accordance with the invention can be utilised for the production of floors, false ceilings, suspended partitions, fiat, cylindrical or hyperbolic paraboloid roofs, domes or cupolas, etc., in permanent or dismantlabel form, for the manufacture of firebreak screens, windbreaks, snowbreaks, etc., installed outdoors, for the production of scaffolding and for many other applications.

to produce foldable frameworks for buildings, for example in order to build roof trusses, hangers, bridges, etc., several preferably flat and differently orientated pieces can be assembled, each of which is constituted by a three-dimensional structure in accordance with the invention, a series of bars of one of said pieces being common with a series of bars in the contiguous piece, so that they are assembled to produce the frameword.

What I claim is:

1. A three-dimensional collapsible structure comprising in combination at least one pair of spaced apart generally parallel two-dimensional lattice assemblies each comprised of straight bars arranged in X-shaped pairs articulated together at their intersections, each X-Shaped pair of bars in each such lattice, exclusive of those on the periphery of the structure, having each of the four ends thereof pivotally connected to the end of at least one adjacent X-shaped pair of bars, all such articulations and pivotal connections of each assembly being fitted on axes perpendicular to the general plane of that assembly, the assemblies of each adjacent pair of such assemblies being displaced laterally relative to one another so that a straight line passing through any axis of articulation of said bar pairs in such assemblies extends at an oblique angle to the general planes of said assemblies, and connecting rods between such assemblies, each rod having its respective ends pivotally connected on axes inclined with respect to the general plane of the corresponding assembly to the pivotally connected ends of two adjacent bar pairs in the same assembly and extending obliquely to the general planes of the assemblies.

2. The structure of claim 1 wherein the assemblies of each adjacent pair of assemblies are displaced laterally so that a perpendicular line drawn through each such articulation or pivotal connection in one assembly passes through a point approximately equidistant from two adjacent articulations or pivotal connections in the other assembly of such pair of assemblies.

3. The structure of claim 1 wherein each of the pivotally connected two ends of two adjacent bar pairs are connected on said inclined axes to two generally oppositely extending connecting rods.

4. The structure of claim 1 wherein said connecting rods extend obliquely between said lattice assembliesin generally zig-zag fashion.

5. The structure of claim 1 wherein pairs of said connecting rods are articulated together intermediate their ends to form X-Shaped pairs of such rods intervening between said lattice assemblies.

6. The structure of claim 1 wherein the X-shaped pairs of connecting rods corresponding to one row of said X-shaped bar pairs in said assemblies are inclined in one oblique direction while the rod pairs corresponding to the next adjacent row of bar pairs are inclined in a generally opposite oblique direction.

7. The structure of claim 1 wherein the X-shaped rod pairs are inclined in alternating directions in each row of said bar pairs.

8. The structure of claim 1 wherein each of the pivotally connected two ends of two adjacent bar pairs are connected on said inclined axes to four generally oppositely extending connecting rods.

9. The structure of claim 1 wherein the ends of said bar pairs and said connecting rods are connected by rings which provide both said perpendicular and said inclined axes.

10. The structure of claim 1 further comprising rigid multi-legged joint elements to constitute the intersection between said inclined and perpendicular axes of

Claims

4. The structure of claim 1 wherein said connecting rods extend obliquely between said lattice assemblies in generally zig-zag fashion.

10. The structure of claim 1 further comprising rigid multi-legged joint elements to constitute the intersection between said inclined and perpendicular axes of pivotal connection.