With the title: TRAPEZOIDAL CYLINDRICAL KINEMATISM

Analysis of the prior art before the innovation: by observing the technical and structural aspects of existing linear motion systems, in particular the electromechanical actuators, it can be seen that linear displacement systems (herein also referred to as linear motion/displacement systems/actuators, linear motion/displacement electromechanical systems/actuators) able to combine in the same product aspects of compactness, simplicity, power and speed, also suitable for applications in autonomous systems, do not currently exist on the market. The reason is simple: linear motion electromechanical actuators, or electromechanical actuators, known today, make use of trapezoidal leadscrews or ball screws or kinematic mechanisms based on the use of belts or chains, or are hydraulic and/or pneumatic. Linear motion actuators made on the basis of the aforementioned mechanisms are mainly activated by electric motors, and are bulky and expensive. It is therefore difficult and/or expensive to embed/enclose/encase these mechanisms inside an electric motor, and to overcome this problem very expensive and complex mechanical components must be used. Furthermore, the choice of one of these solutions, namely, screws or belts or chains, always implies to renounce to one or more actuator features, that is compactness, operative speed or simplicity. Hydraulic Linear Actuators, also called "hydraulic rams", and pneumatic systems are, at a first sight, the most compact actuators, but this is only an apparent compactness. In fact these devices need to be connected, respectively, to a hydraulic pump or to a compressor that, even by not considering the connecting tubes, is always very bulky or heavy, because it must generate high pressures or flow rates. For the same reason said hydraulic pumps or compressors are realized with massive metallic components and therefore are massive, heavy and/or bulky. Since the hydraulic ram or the pneumatic actuator are not operational in absence of the corresponding pump or compressor, the final and actual volume and mass of actuation systems or linear movement systems incorporating these hydraulic or pneumatic components will necessary include also the volumes and masses of said pumps or compressors.

Objective that the here described innovation intends to achieve: the objective of the here described invention is a system capable of converting rotary motion into translational motion, characterized by compactness, operative speed and simplicity, so to allow the realization of systems enabling linear motions characterized by compactness, operative speed and simplicity, which in turn benefit from the advantages associated to these desirable features. The trapezoidal cylindrical kinematism identified from now on with the acronym CTC which stands for "Cinematismo Trapezio Cilindrico" as in the Italian Patent, is constituted by flexible bands, translating and rotating parts which, assembled together with appropriate degrees of freedom and in the manner that will be described below, allow the creation of systems enabling linear motion, even of powered ones, characterized by a small footprint, a simplicity of construction and unmatched performances. The CTC mechanism is therefore a system that constitutes a completely different alternative to trapezoidal or to ball screws or to kinematisms based on belts or on chains or on hydraulic rams or on pneumatic- based mechanisms, and a system that can accommodate any motor of any type, provided that this is suitable for operating the CTC parts, completely inside the actuator, giving thus to the so-obtained assembly characteristics of compactness that other systems do not have. The advantages that the CTC can give overcome the simple compactness, and include an extreme simplicity and the capability to be assembled with components that both allow accelerations higher than that of existing systems, and are much less expensive that those of currently available systems, as can be inferred by the description of the CTC operations that will be given hereafter. With the aid of tables 01 , 02, 03, 04, 05, 06, and of Figures 01 to 19, all in isometric view, we describe the operation of a system that converts the relative rotary motion of two elements in translational motion of a third element relative to the two aforementioned elements, by means of CTC, which is a kinematism based on bands, rings and cylinders. Figures 01 to 05 belonging to Tables 01 and 02 show acronyms, most of which are enclosed in rectangles having outgoing arrows that indicate the element of the figures to which they refer to. The following description, after having properly defined the nomenclature of the involved elements, will use either the so-defined names of the system parts and/or the corresponding symbols, as reported in said figures and tables.

Names and descriptions of the constituent parts of the CTC: in Figures 01 , 02 and 03 of Table 01- attached to this patent application - with the acronym CUR, in yellow, the Cursor, i.e. the yellow ring, is identified. This is the part of CTC that receives or transmits linear translational motion along the axis Z, which is also represented and labeled in the same figures. At the base of the figure 01 and 03 of Table 01 , it is possible to notice two concentric rings, one red and one blue, marked by the initials BR and BB, which are the red base and the blue base, respectively. BR has a parallelepiped-shaped appendix of reduced thickness, called red fin, that will be indicated with the acronym AR, as shown in Figures 01 and 03 of Table 01. The same applies for BB, in which case the parallelepiped- shaped appendix is named blue fin and is labeled AB. The two BR and BB rings are concentric, and BB is partially within BR. Moreover, their axis is coincident with the rotation axis and with Z. BR and BB are bound to rotate around the Z axis, while any other possible movement of said parts is hindered. The AR and AB fins have the additional function to mark the angular positions a and ,\ying in the XY plan, orthogonal to the Z axis, of BR and BB with respect to angular zero represented in figure 01 by the gray surface parallel to and passing through Z, marked in turn and from now on called, 0°. AR and A B are therefore not to be considered essential for the functioning of the CTC and are not to be considered as a vital part for it. In Figures 04 and05 of Table 02 two semitransparent tubes can be noticed one external in gray and one internal in green which are marked respectively by the abbreviations CE and CI; these are to be considered to all intents and purposes as not deformable tubes hence provided with an empty volume inside them. CE and CI are the acronyms respectively for the external column and internal columns. The transparency is not binding in any respect for the purposes of the operation of CTC; it has the only usefulness of making more understandable the dynamics of the parts. The non-void volume always present between CE and CI is called the Domain of the Bands which depends on the diameters of CE and CI. Inside it the motion of the CUR is confined. The columns are concentric and coaxial to Z, moreover they are static along Z compared to BR and BB, even though the immobility is not necessary for the CTC's functioning and is therefore not to be considered binding for the purposes of the patent. In the other Tables, CE and CI are both represented in gray: CE much more transparent than CI. In Figures 01 , 02 and 03 of Table 01 it is possible to see bands, one red and one blue, that are partially wrapped up around CI assuming a cylindrical spiral shape having as axis Z , which are respectively identified by the acronyms FR and FB and are named respectively red band or red principle and blue band or principle. They jointly to CE and CI carry out the task of transforming the rotatory motion of BR and BB in CUR's translational motion by moving and changing their shape inside the "Domain of the Bands". These are to all intents and purposes bands or stripes or belts segments of flexible material provided with a section represented in Figure 18 of Table 05 and marked with S. Each end of each band is bound to the CUR via a hinge shown in Figures 01 , 02, 03, 04, 05 of the Tables 01 and 02 as a gray little cylinder adjacent to it and marked on Tables 01 and 02 with the acronym CER. The other end of the FR is bound on the BR with a hinge shown in Figures 01 , 02, 03, 04, 05 of the Tables 01 and 02 as a gray little cylinder adjacent to it and marked on Tables 01 and 02 with the acronym CER. The other end of the FB is bound on the BB via a hinge shown in Figures 01 , 02, 03, 04, 01 and 05 of Table 02 as little gray cylinder adjacent to it and marked on Tables 01 and 02 with the acronym CER. The CERs enable bands to rotate around their axis but not the removal of the ends from the bond's points. The axes of the CERs, in turn, are to be considered orthogonal to and intersecting Z. The length of the shortest path that joins the hinges' grafting points of a band calculated along the surface of the band itself, it is also the band length. The bands or principles are to be considered able to change their shape depending on the position of the CUR but also capable of preserving their length in the same conditions. The figures from 01 to 19 in Tables 01 to 06 represent the CTC unless the fact that FR and FB ends respectively hinged on BR and BB are actually outside of the Domain of the Bands as defined in reality the length of CE and CI must be considered such as to include inside also said ends and thus also the BR and BB, even though this is not a binding condition for the functioning of the system that is the CTC works fine even if the ends remain outside the domain of the Bands for a length approximately equal to the width of the band itself. The choice of not strictly represent in the figures the system according to the definition of the parts given above has been taken to simplify the three-dimensional perception of the invention making clearer the illustrations.

Operation of CTC as a whole: Figure 06 of Table 03 presents the isometric vision of all the elements above depicted assembled so as to constitute the CTC in its entirety and in position ZERO: to which correspond the angles α = β = 0 with respect to 0° . Let's assume now to act with approp riate force pairs (by hand, for example) on the AR and AB fins, and then operate BR and BB, by rotating them by an angle a and β respectively different from 0 with respect to the 0° reference . Said displacements are represented in Figure 07, 08 , 09 , 10, 1 1 of the Tables 03 and 04 by red and blue curved arrows placed adjacent to the symbols a and β respectively. As bands FR and FB cannot change their length, being flexible but not extendible, being forcedly confined within the Domain of the Bands by CE and CI, as a result of the hinges they will be dragged by the BR and BB and will wrap around the CI trailing, in turn and towards the bases, the CUR . By increasing further a and β, see Figure 08 of Table 03, the bands will wrapped up even more causing further lowering of the CUR. By following Figures 09, 10, 1 1 of Table 04, one can see how the gradual increase of a and β in the respective directions implies the approach of the CUR to the BR and BB more and more increased in response to the progressively growing amplitude of the angles. The principles FR and FB are antagonistic between themselves on the XY plane while they are concordant along the Z axis so that for their particular arrangement, at the kinematism's operation according to its structure and binding constraints defined above, the application of appropriate pairs of forces that put BR in rotation with respect to BB, they transmit forces on FR and FB respectively, through the CERs, such that their components in the XY plane are opposed each other while those along Z are concordant and get summed up. If BB was placed parallel to BR then the principles would not be antagonistic because neither the components on the XY plane nor those along Z would be in opposition to each other. If the CTC had two parallel principles it could not convert the relative rotatory motion of BR and BB in the translational motion of the CER.

Therefore, the CTC is such only if it has at least two principles that are antagonistic or have components in the XY plane of the forces applied by the BR or BB or by the CUR in opposition to each other. By inverting the direction of rotation of the BR and BB one gets the effect of removing the CUR from BR and BB. This is easily seen by imagining of inverting arrows which indicate the magnitude of the angles a and β and following Figures 06 to 11 of the Tables 03 and 04 in reverse order starting from Figure 11 of Table 04. By analyzing the forces perpendicular to section S it is possible to see how they have section by section, however small, a component in the XY plane of centripetal or centrifugal type according to CUR displacement towards or away from the bases respectively. This component would be responsible for the immediate exit of the FR and FB from the Domain of the Bands if there were no CE and CI carrying out the function of receiving and cancelling any displacement of the bands away from the Domain of the Bands and ensuring in this way their functional position.

Exposition of advantages compared to the state-of-the-art: as can be seen all the space inside the CI, shared entirely with CE, is not functional to CTC therefore it is usable for any purpose, such as the insertion of a motor that through appropriate intermediate mechanical organs actuates the CTC. These mechanical organs together with a possible engine are not an integral part of the invention and therefore of the patent application. The CTC is a very compact and lightweight kinematism with respect to other solutions discussed in the analysis of the prior art reported above. The CTC can be operated, even in the presence of different types of deformations of the CE or CI; unlike other systems which normally lose their functionalities if they were to undergo deformations to the stem. The CTC is easily reversible, that is by moving the CUR a relative rotation of the bases can be achieved; normally, this feature is very difficult if not impossible in screw-based or hydraulic systems. The CTC benefits of significant translations of the CUR against few turns of relative rotation of the BR and BB ; in the case of screw-based systems, a comparable result requires screws with very long pitch and of difficult and limited fabrication. The CTC can be made with many principles and as an example Figures 12, 13 , 14, 15, 16 and 17 of Table 05 illustrate the steps of the operation of Figures 06, 07 , 08, 09, 10, 11 of the Tables 03 and 04 seen before with a CTC based on six principles antagonistic two by two and in Figure 19 of Table 06 it is possible to see the CTC at the end of a descending cycle of the CUR corresponding to the same position taken by the CTC based on 2 principles of Figure 11 of Table 03 but equipped with as many as 16 principles. The increased number of principles makes the system's operation smoother and allows the transmission of a greater force from the bases to the CUR and vice versa. The CTC is a kinematism that can be used to make mechanical systems for linear motion, lifting, opening and closing, rotation, conversion of motion. Given the particular compactness, one of the applications that would most benefit is the robotics, particularly in the context of autonomous systems, today mainly hindered by the bulkiness, the low accelerating capacity and the weight of the handling systems of the various elements that constitute the parts of the autonomous system . Starting from an engine and suitable organs for the transmission of motion to the bases BR and BB, the CTC can be assembled around them so as to minimize the footprint of the system as a whole. The CTC is also extremely simple to be made even with inexpensive materials and does not require particularly precise mechanical parts because it is perfectly functioning and performing. Moreover, the CTC compared to the biological motor systems that generate only traction forces, is able to produce both traction and pushing forces.