Adjustable, fully compliant guide device with constant force, its design method and adjustment

Abstract

The invention relates to an adjustable fully compliant guide device with constant force, which enables the setting of a force operating point by changing the preload of compliant elements, an associated method for setting the device for a predetermined force, and for dimensioning the compliant elements of the guide device. The adjustable, fully compliant guide device with constant force has a wide range of applications. These include metrology, weighing technology, precision engineering, nanofabrication, biomedical engineering, sports and rehabilitation equipment, the automotive industry, and robotics.

Description

Field of invention

[0001] The invention relates to an adjustable fully compliant guide device with constant force, which enables the setting of a force operating point by changing the preload of compliant elements, an associated method for setting the device for a predetermined force, and for dimensioning the compliant elements of the guide device.

[0002] The adjustable, fully compliant guide device with constant force has a wide range of applications. These include metrology, weighing technology, precision engineering, nanofabrication, biomedical engineering, sports and rehabilitation equipment, the automotive industry, and robotics. State of the art

[0003] The compliant constant-force guide devices known from the prior art exhibit a large movement for a small change in force around a force operating point; thus, a small change in force ΔF causes a large change in position, i.e., a large displacement Δs. Their advantages include the elimination of the need for lubrication, no wear and no backlash (i.e., the elimination of undesirable dead travel), as well as the possibility of miniaturization and very easy scalability. Furthermore, such devices are passive, meaning that no additional control with sensors and actuators is required to ensure a constant force. This makes such devices inexpensive and easy to assemble [1].

[0004] Two variants for the design of fully compliant guide devices with constant force are known from the prior art. In the first variant, a constant force is achieved by optimizing the shape of the compliant elements. By varying the cross-section, curvature, and material along the length of the element, a constant force is achieved [2, 3]. Due to its complex structure, this variant is prone to production defects, which affect the quality of the device. In addition, this variant is based on individual, structure-specific optimization methods, making the calculation complex and time-consuming [10, 11, 12]. Furthermore, adjusting the force operating point is not possible with this variant.

[0005] In the second variant of the device, the constant force is achieved by combining compliant elements with positive and negative stiffnesses. These are designed such that the different stiffnesses of the elements cancel each other out, creating a region with a constant force [4, 5]. Thus, the device has a stiffness, defined as the difference quotient ΔF / Δs (F - force, s - displacement), of zero and achieves a constant force over the considered range of motion Δs. By using a spring as a compliant element with positive stiffness (ΔF / Δs > 0), the force operating point can be adjusted based on the spring's preload [6]. A disadvantage of this variant is that several different elements are required, which must be coordinated with each other. Furthermore, the use of a conventional spring in the device makes scalability (miniaturization) difficult or even impossible.While using flexible elements as springs can achieve a certain degree of miniaturization, this would result in a complex shape. Therefore, this variant has similar disadvantages to the first one. Both variants require significant development effort to enable a specific, constant force for a given application.

[0006] The influence of the connection angle, length, and cross-section of the beam elements of a complex beam mechanism on its stiffness has already been investigated in the literature [7]. However, the results of these investigations focus only on a specific, fixed force application point. Further investigations into the dependence of the parameters have not been carried out, which means that the application to an adjustable guide device with an adjustable force application point is not possible.

[0007] Based on a literature review, [8] and [9] are the only sources known to the applicants that utilize the bending behavior under different clamping conditions to adjust the force application point for a region with a constant force. In patent US11047458B1 [8], the area moment of inertia along the bending axis is changed by torsion to adjust the force application point. To still guarantee movement in one plane, this method requires a rigid external frame. Thus, the device is not a purely compliant device. The means for adjusting the force application point are located on the mechanism and move with it, resulting in higher energy consumption. This necessitates multiple components, leading to increased assembly effort and costs. In [9], the interaction of the angles of two elements with respect to the direction of movement is used to adjust the force application point.This requires adjusting not only the angle but also the length of an element at various points. Several flexible elements are needed for this, each individually controlled and coordinated. This increases the potential for errors and the control / regulation effort. Furthermore, the use of multiple elements leads to a more complex design. The guide elements and the elements to be adjusted are functionally separate and are distinct components.

[0008] The disadvantages of adjustable, compliant guide devices known from the prior art can be summarized as follows: The guide devices have complex shapes and structures, and their design requires complex and time-consuming design processes, which makes simple scalability difficult, especially because rigid body elements are present. None of the devices has the means to adjust the force application point in such a way that the guide elements and the elements to be adjusted are the same component. Furthermore, the known devices require several different compliant components that must be precisely matched to one another. Object of the invention

[0009] The presented invention aims to provide a guide device that overcomes the disadvantages of adjustable guide devices known from the prior art. This objective also includes providing a method for designing and adjusting such a guide device. Solution to the task

[0010] The object of the invention is achieved by an adjustable, fully compliant guide device for guiding a table, having the features specified in claim 1. Advantageous embodiments of the guide device are disclosed in dependent claims 2 to 12. Furthermore, the object of the invention is achieved by a method for designing and adjusting such a guide device according to claim 13.

[0011] The term "table" is to be interpreted broadly in this application. It encompasses any platforms that are movable in one spatial direction x (i.e., linearly), in two spatial directions x, y (i.e., in a plane), or in three spatial directions x, y, z (i.e., in three-dimensional space). This includes, for example, xy-moving tables (xy stages) that allow precise positioning in the nanometer range in a plane.

[0012] As is customary in the present technical field, flexible elements in this application are also referred to as beams or beam elements. Brief description of the drawings Fig. 1 - Front view of a guide device with a table to be guided, having a rectangular cross-section and mirrored flexible elements Fig. 2 - Top view of the guide device with the table to be guided, having a rectangular cross-section and mirrored flexible elements Fig. 3 - Top view of a guide device with a table to be guided, having a triangular cross-section and mirrored compliant elements Fig. 4 - Top view of a guide device with a table to be guided, having a round cross-section and mirrored flexible elements Fig. 5 - Front view of a guide device with a table to be guided, having a rectangular cross-section and flexible elements attached below the table Fig. 6 - Top view of the guide device with the table to be guided, having a rectangular cross-section, and flexible elements attached below the table. Fig. 7 - Front view of a guide device with a rectangular cross-section table to be guided for zero-force applications Fig. 8 - Front view of a guide device with a table to be guided, having a rectangular cross-section and a slight angular deviation φ of the guide device from the guide direction Fig. 9 - Characteristic curve of the guide device with slight angular deviation φ from the guide direction Fig. 10 - Front view of a guide device with a table to be guided, having a rectangular cross-section and an inclination angle ζ of the frame relative to the direction orthogonal to the guide direction Fig. 11 - Front view of a guide device with a table to be guided, having a rectangular cross-section and a movable mounting point for the flexible elements parallel to the guide direction Fig. 12 - Basic structure of the adjustable fully compliant guide device with constant force (free on one side, with a straight compliant element) Fig. 13 - Basic structure of the adjustable fully compliant guide device with constant force (clamped, smaller force operating point) Fig. 14 - Basic structure of the adjustable fully compliant guide device with constant force (clamped, larger force operating point) Fig. 15 - Rectangular cross-section of a flexible element Fig. 16 - Circular cross-section of a flexible element Fig. 17 - Characteristic curve for minimum and maximum force operating point Fig. 18 - Flowchart of the procedure for dimensioning the compliant elements and determining their number for the adjustable constant-force fully compliant guide device Detailed description of the solution

[0013] The invention is explained in detail below using the drawings described above.

[0014] The basic idea of ​​the fully compliant guide device with constant force considered here consists of the use of simple, preferably straight, compliant elements with a constant cross-section. The constant force is achieved by utilizing the preload of the compliant elements through adjustment of the connection distance to the table and the connection angle to the frame, taking into account the dimensions of the compliant elements.

[0015] The fully compliant guide device with constant force according to the invention comprises one or more compliant elements with a constant cross-section. The guide device derives its function solely from the compliance of these elements; therefore, it is referred to as a fully compliant guide device. These elements are preferably of identical construction and suitable for guiding a table. The elements are preferably manufactured straight, but when clamped in the guide device, they generally assume a curved shape. The use of straight compliant elements has the advantage that a guide device equipped with such straight elements is simple and inexpensive to manufacture and particularly easy to dimension, as is explained in detail in embodiments 1 and 2.The flexible elements can also be pre-bent, however, the dimensioning of the guide device is then much more complicated and requires an additional adjustment of the parameters connection angle β and connection distance p, which results in additional calculation effort for each radius of curvature (see embodiment 3).

[0016] If several flexible elements are used, they are preferably arranged in parallel in groups. Each flexible element is rigidly connected at one end to the table to be guided. Flexible elements are rigidly connected to the table on at least two sides. Thus, each flexible element is rigidly connected at one end to the table to be guided. The end of the flexible element is perpendicular to the side of the table, so that the connection is orthogonal to the table's guide direction. The other end of the element is connected to the frame at a distance p from the table, measured orthogonally to the guide direction. This connection is designed such that a connection angle β is formed between the frame and the tangent to the end of the flexible element.The parameters p and β are adjustable by providing a means on the frame for each flexible element. This means consists of linear and rotary joints with actuators, or is preferably a single-actuator mechanism. This means connects the flexible element to the frame and, by changing the connection distance to the table and the connection angle to the frame, allows for the adjustment of a characteristic curve for the guide device. The characteristic curve of the guide device with constant force describes the relationship between the table's displacement s and the force F in the same direction; it is therefore a force-displacement characteristic. The characteristic curve can also be adjusted during operation of the guide device, for example, when objects of different weights are placed on the table. The dimensions of the flexible elements determine the range of motion and force application of the guide device.The connection distance and angle determine the force operating point. Depending on the selected dimensions of the compliant elements, the force operating point can range from nanonewtons to kilonewtons, making the device suitable for applications such as force compensation, force limiting, and force measurement in both nanofabrication and robotics.

[0017] The characteristic curve of a guide device with constant force typically consists of three sections. In the first section, the curve rises; in the next section, a constant force is established, forming a plateau; and in the last section, the curve rises again. The point with the force value, known as the force operating point, is located in the middle of the second, nearly horizontal section, i.e., the plateau. This point lies in the middle of the travel range with a nearly constant force profile, which is the travel range for the constant force, referred to as the range of motion. The range of motion thus extends across the plateau.

[0018] If the connection spacing p is smaller than the length of the flexible element and the connection angle β ≠ π, the flexible element bends, thus prestressing it. Reducing the connection angle β and / or increasing the connection spacing p increases the stiffness of the flexible element and, consequently, the entire guide device. By correctly selecting the connection spacing p and the connection angle β, deformations can be found that result in a region of zero stiffness, i.e., a stiffness ΔF / Δs = 0, and thus a constant force distribution.

[0019] Similarly, a suitable connection angle can be found for various connection distances, resulting in a range of motion where the stiffness is zero. Smaller connection distances lead to greater curvature of the flexible element. Consequently, greater forces are required in the guiding direction to move the flexible element. This also raises the point of force application. Therefore, it is possible to adjust the point of force application by changing the connection distance and the connection angle without altering the dimensions of the flexible element.

[0020] The fully compliant guide device with constant force can incorporate a varying number of compliant elements. If only one element is used, additional frictionless or low-friction guidance of the table is required. Two or more elements are attached to the table in such a way that all reaction forces and moments in all directions perpendicular to the guidance direction cancel each other out. This is achieved as follows: If the compliant elements are attached to two sides of the table, an arrangement should be chosen that results from a mirroring or from rotating the elements by an angle of 180° around an axis parallel to the guidance direction. The elements can also be attached to three, four, or more sides / areas of the table and in groups. Here, too, the positions of the elements for each side / area of ​​the table should be determined in groups, e.g.,These can be obtained by reflection or by rotation about the axis parallel to the guide direction at an angle of 360° / m, where m is the number of sides / areas on the table. The term "area" here refers to tables that do not have straight sides, such as round or elliptical tables, or to sections of a table's side. Possible arrangements are shown in [reference]. Fig. 1 to Fig. 4 is shown. Here, it shows Fig. Figure 1 shows the front view of a guide device with six flexible elements 3. The elements 3 form two groups of three, each grouped in a mirror-symmetrical manner. One end of each flexible element 3 is attached to two opposite sides of a rectangular table 4 to be guided. The other end of each flexible element 3 is connected to a section of a frame 2. This connection is achieved by means of a device 8, which is slidable along the respective section of the frame 2. The sections of the frame 2 are also positioned mirror-symmetrically on both sides of the table 4, without being directly connected to it. On each side, three sections of the frame 2 are positioned parallel to each other at a distance 6. The position of the device 8 sets a connection distance p and a connection angle β, thereby adjusting the stiffness of the flexible elements 3.The table 4 can be moved with a constant force F within a range of motion between the stops 5a and 5b. By shifting the means 8, the connection distance p and the connection angle β, and thus the stiffness of the flexible elements 3, can be changed, thereby adjusting the magnitude of the constant force F, i.e., the force operating point of the guide device. This will be explained in more detail in embodiment 1. Fig. 2, Fig. 3 and Fig. Figure 4 shows the guide device from above for rectangular, triangular, and round tables. In these, an additional force is achieved by an object 10 positioned on the table. It is also possible to attach the elements 3 below the table. This results in smaller dimensions for the flexible guide device. Such an arrangement is shown in Fig. 5 from the front and in Fig. Shown from above, number 6. In the top view ( Fig. 6) The table 4 is indicated only by two side edges. This reveals two groups of four flexible elements 3 located below the table 4, which are connected to two opposite sides of the table 4. In Fig. The elements of a group overlap in 5. Fig. 6 the sections of the frame 2 are covered by the flexible elements 3.

[0021] If the flexible elements are mirrored with respect to the plane orthogonal to the guide direction and all elements are additionally pre-tensioned in the guide direction up to the force work point, then, with negligible weight of the table or with additional compensation of its weight, a guide with zero force F is achieved. Null realized (F Null = 0). Such an embodiment is in Fig. Figure 7 shows that the elements 3 connected to the left side of table 4 exert a force F on table 4. The elements 3 connected to the right side of table 4 exert an oppositely directed but equal-magnitude force -F on table 4, resulting in a force F Null This results in a value of 0. Table 4 can therefore be moved freely in the guide direction. The weight of the table is negligible if the connection distance is distorted by no more than 5%. The table's weight can be compensated for by orienting the guide direction horizontally, which requires additional low-friction guidance of the table, for example, by a mechanism that moves almost horizontally.

[0022] Preferably, the guide direction should be parallel to gravity, with the frame positioned horizontally. A slight deviation ±φ of the table (5%) from the guide direction, which should be orthogonal to the frame (or of the frame from the horizontal position), as shown in Fig. 8. This is permissible, particularly if the groups of compliant elements are arranged on opposite sides / areas of the table. In this case, the inaccuracies in the characteristic curves of opposite elements cancel each other out, resulting in the desired constant force characteristic curve. This is also shown in the force-displacement diagram in Fig. 9. The halved sum of the force-displacement relationship with the positive deviation +φ and the force-displacement relationship with the negative deviation -φ is almost identical to the force-displacement relationship without deviation (φ = 0). Thus, the adjustable, fully compliant guide device with constant force is invariant with respect to a slight tilt of the frame.

[0023] If an additional angle ζ is set for the frame, as in Fig. As shown in Figure 10, the range of motion is given a proportional angle ζ. d to the force axis in the force-displacement diagram Fig. 17. This changes the force-displacement relationship within the range of motion. With a suitable choice, the behavior with constant force over the entire force range can be improved, resulting in less force deviation within the range of motion. A similar effect can also be achieved if the means 8 for adjusting the connection distance p and angle β has an additional vertically adjustable distance 9, as in Fig. Shown in 11. This allows the position of the range of motion to be determined in the force-displacement diagram. Fig. 17 can be moved to the left or right.

[0024] To prevent exceeding the range of motion, stops can be used to mechanically limit the range of motion. In the arrangement according to Fig. 1. The stops 5a and 5b limit the upper and lower range of motion, respectively. This ensures that the permissible elongations of prestressed flexible elements are not exceeded. List of reference symbols and formula symbols 1 Parallel guidance 2 frames 3. Flexible element 4 Table 5 keystrokes 6. Spacing of sections of the frame 7 Range of motion 8 Medium 9. Distance of the frame from the basic position 10 objects 11. Force work point p Connection distance β Connecting angle L beam length h beam height b Beam width R beam radius E modulus of elasticity σ permissible voltage F Force work point F min minimum force work point F max maximum force work point F̃ dimensionless force constant I Z Area moment of inertia of the z-axis I y Area moment of inertia of the y-axis r radius of curvature n number of bars M̃ dimensionless moment constant ζ Angle of the frame ζ d angle proportional to ζ φ Deviation of the table from the guide direction Σ halved sum Example 1

[0025] In Fig. 12 to Fig. Figure 14 shows a flexible element 3. This element is connected on one side to a guided table 4, which is supported by an additional frictionless parallel guide 1. The element is connected to the table 4 in a direction orthogonal to the guide direction. On the other side, it is connected to the frame 2 via a means 8 for adjusting the connection distance and angle. The frame 2 is positioned orthogonally to the guide direction.

[0026] The preferred connection distance p lies in the range p ∈ [0.5 L; 0.85 L], where L denotes the length of the compliant element. The parallel guide should preferably be selected with negligible friction. Frictionless guidance without an additional frictionless parallel guide can be achieved, for example, by a symmetrical arrangement of the compliant elements. This cancels out forces orthogonal to the direction of motion and moments acting on the table 4. The relationships (F1), (F2), (F4), and (F7) are represented by polynomials. It is not excluded that other forms of mathematical relationships exist between the parameters, as long as similar values ​​result for the parameters involved. All calculation methods are given in SI units. Quantities marked with a tilde are dimensionless.

[0027] For the guide device under consideration, there is a connection angle β for every connection distance p at which guiding with constant force occurs. Fig. 13 is a compliant element for a small force work point 11 (see Fig. 17) and in Fig. Figure 14 shows a large force operating point 11. The connection distance p and the connection angle β must have a ratio that can be described by the following polynomial: β(p)=a1L2p2+a2Lp+a3

[0028] The polynomial coefficients preferably lie in the intervals: a1 ∈ [1.98; 2.52]; a2 ∈ [-0.12; 0.6]; a3 ∈ [-0.14; 0.098]. Polynomial coefficients of a1 = 2.248; a2 = 0.2363; a3 = -0.0223 are particularly preferred.

[0029] The range of motion 7 begins at the same level as the connection point of the flexible element 2 on the frame, measured orthogonally to the guide direction. Outside the range of motion, stiffness increases. The characteristic curves are for a maximum F max and a minimal F min Power work point in Fig. Figure 17 shows the maximum force work point F. max preferably smaller than 2.3 times the minimum force operating point F min The point of force operation F can be set between the curves shown by adjusting the connection distance p and the angle β. The point of force operation F and the connection distance p are related in a polynomial form: p(F)=b1LF˜FminF2+b2LF˜FminF+b3L

[0030] The polynomial coefficients preferably lie in the intervals b1 ∈ [0.00029; 0.00048]; b2 ∈ [-0.048; -0.043]; b3 ∈ [1.14; 1.17] . Polynomial coefficients of b1 = 0.000385; b2 = -0.04547; b3 = 1.156 are particularly preferred.

[0031] For a maximum connection distance p of 0.85 times the length L, the force constant F̃ preferably lies in the range F̃ ∈ [7.0525; 7.2171] with a particularly preferred value of F̃ = 7.08105. A different force constant corresponds to each deviating maximum connection distance.

[0032] To obtain a constant force within the range of motion 7, the length L of the compliant element should be significantly longer than the range of motion 7, preferably as follows: L≥10.15⋅range of motion 7

[0033] To prevent bending outside the considered plane, the area moment of inertia I must be zthe cross-sectional area of ​​the element about the axis parallel to the guide direction must be significantly smaller than the area moment of inertia I y around the axis orthogonal to it. Furthermore, the cross-sectional dimensions should be significantly smaller, preferably ten times smaller, than the length and radius of curvature r of the loaded flexible element (slenderness condition). For rectangular or circular cross-sections, the y- and z-axes are in Fig. 15 or Fig. Figure 16 shows the maximum radius of curvature r, which is subject to the following relationship: r(F˜)=c1LFmaxF˜4Fmin+c2LFmaxF˜3Fmin+c3LFmaxF˜3Fmin+c4LFmaxF˜3Fmin+c5L.

[0034] The polynomial coefficients are preferentially located in the intervals: c1 ∈ [7,45 ∗ 10 -06 ; 1,053 ∗ 10 -05 ]; c2 ∈ [-0.00061; -0.00045]; c3 ∈ [0.01; 0.014]; c4 ∈ [-0.15; -0.12]; c s ∈ [0.75; 0.81] . Polynomial coefficients of c1 = 8.993e ​​are particularly preferred. -06; c2 = -0.0005298 ; c3 = 0.01219; c4 = -0.136; c5 = 0.7778 .

[0035] The following relationship is used to determine the cross-sectional dimensions for an area of ​​force work points 11: Iz=FminL2F˜En

[0036] Here, E is the modulus of elasticity of the material of the compliant element and n is the number of elements attached parallel to the table 4.

[0037] At high load points with short lengths of flexible elements, conflicts with the slenderness condition can occur. In this case, their number n can be increased. It must be noted that the flexible elements are loaded in parallel. The higher number of elements reduces their cross-sectional dimensions and thus their area moment of inertia. The bending of the beams must be considered when arranging the flexible elements. Therefore, the connections to the frame 2 should have at least a preferred spacing 6, see [reference]. Fig. 1, exhibiting 0.35 times the length of the flexible element in the direction of movement.

[0038] To guarantee purely elastic deformation, the following must also apply to a rectangular or round cross-section: h2≤σLM˜E or R≤σLM˜E

[0039] Here, σ is the permissible stress of the material, h is the height of the cross-section or R is the radius of a round cross-section, see. Fig. 15 or Fig. 16, and M̃ results from M˜(F˜)=d1FmaxF˜2Fmin+d2FmaxF˜Fmin+d3

[0040] The polynomial coefficients preferably lie in the intervals: d1 ∈ [-0.011; -0.0098]; d2 ∈ [0.58; 0.61]; d3 ∈ [0.093; 0.2]. Polynomial coefficients of d1 = -0.01025; d2 = 0.5952; d3 = 0.1428 are particularly preferred.

[0041] Using the relationships (F3) to (F7), a method can be defined which allows the dimensions and number of the compliant elements to be determined. These elements constitute the adjustable, fully compliant guide device with constant force. Such a method is described in Fig. 18 is schematically represented using a flowchart. The range for the force work points FE [F ] is specified as input for the development of the guide device.min ; F max ], i.e., the force work range, which should be greater than zero, the range of motion 7, which should be greater than zero, the number n ∈ ℕ of the flexible elements, the modulus of elasticity E, and the allowable stress σ of the material of the flexible elements. Using these values, the length L of the elements according to (F3), the dimensionless moment constant M̃ according to (F7), the maximum radius of curvature r according to (F4), and the maximum value for h or R according to (F6) are determined. The inputs and the quantities sought can be chosen freely. The order of the calculations should only be followed insofar as the parameters required in the relationships are calculated first. For example, the cross-sectional dimensions can be determined using the area moment of inertia I. zThe slenderness conditions are determined according to (F5). Subsequently, the slenderness conditions are checked. If these are not met and it turns out that the parameter h or R is too large, it is reduced; otherwise, the number n of elements is increased. If the slenderness conditions are met with the determined cross-sectional dimensions, they can be accepted.

[0042] The procedure for setting the force application point 11 consists of determining the connection spacing p(F) according to (F2) and the connection angle β(p) according to (F1). Any beam can be used as a flexible element as long as it fulfills the slenderness conditions, has a constant cross-section over its length L, and does not exceed the allowable stresses σ during deformation. The cross-sectional dimensions of flexible elements, their length L, as well as the modulus of elasticity E and the allowable stresses σ are then known. By rearranging (F5), the minimum force application point F can be determined. min to be determined. The maximum force work point F max results from (F6) with (F7), the slenderness conditions taking into account (F4) and the preferred force work range F min < F max < 2.3°F min. During the application of the adjustable compliant guide device with constant force, the connection distance and the connection angle can also be adjusted according to (F2) and (F1) so that a desired force operating point 11 is set. Example 2

[0043] A typical cross-section for flexible elements is rectangular. In particular, a cross-section with a width b that is significantly greater than the height h of a flexible element fulfills the requirements for deformation in one plane and results in the linear movement of the table. The formulas for calculating the width b and the height h are derived from formulas (F5) and (F6) for the area moment of inertia and the elastic limit of motion: h≤2σLM˜E b=12FminL2F˜Eh3n

[0044] To meet the slimming requirements, the following should preferably be fulfilled: h≤r10; h≤L10 h≤r10;h≤L10

[0045] As in embodiment 1, the number of elements can be increased to meet the slimness requirements. Example 3

[0046] By using pre-bent, flexible elements, the maximum stress in the element can be reduced within the range of motion. The flexible element should preferably have a similar curvature to a straight element of the same dimensions in the pre-stressed state, corresponding to the desired force operating point. To minimize deviations from the constant force characteristic curve, the radius of curvature and / or at least one parameter setting (connection angle β, connection distance p) must be adjusted. With significantly deviating curvatures, an adjustable constant force can no longer be guaranteed. Advantages of the invention • Loss of lubrication • no wear and play • easy scalability • No regulation necessary • Simple beam shape, resulting in easier production and assembly • Identical flexible elements can be used simultaneously as guide elements and adjustable elements. • Low production error rates • Simple and quick design of the device using simple calculation formulas • adaptable to changing environmental conditions • versatile areas of application Commercial applicability

[0047] The adjustable, fully compliant guide device with constant force has a wide range of applications: measurement technology, weighing technology, precision engineering, nanofabrication, biomedical engineering, sports and rehabilitation equipment, automotive industry, robotics, etc.

[0048] An example of the application of a constant-force guide device is gravity compensation. Here, the device is designed so that the force-operating point of the table to be moved (even with an object on it) lies at the value of its gravitational force. Thus, the compliant elements are pre-tensioned by the table's gravity, and the potential energy is added to the system by the table's gravity. Very little energy is then required to move the table within the specified range of motion. This makes it ideal for use in nanopositioning machines. Since the objects to be moved on the table can have different weights, a device is needed that can be adjusted to different force-operating points. This is achieved by adjusting the connection distance and angle using a suitable mechanism.

[0049] The adjustable, fully compliant guide can also be used to determine the weight of an object. An object is placed on the table, and then all compliant elements (connection distance and angle) are adjusted until the point of force application is reached. By reading the settings and the position of the table with the object, the object's weight can be determined. Therefore, the guide can also be used in weighing technology.

[0050] Another application is force limitation. In robotics and medical technology, it is crucial not to exceed a maximum force within a defined range of motion to prevent injury to people or damage to objects. The required constant force between a work object guided by the guide device and the person or object being processed can vary depending on the application and can be adjusted using this device.

[0051] Furthermore, the fully compliant guide mechanism with constant force can be used in sports and rehabilitation equipment. A compliant guide mechanism with constant force is required to load muscles with the same force over a predetermined range of motion. Adjusting the force application point also allows for adaptation to different training intensities. Cited literature [1] Howell, Larry L.; Magleby, Spencer P.; Olsen, Brian M. (2013): Handbook of Compliant Mechanisms. S. 6. DOI: 10.1002 / 9781118516485. [2] Rahman, Minhaz Ur; Zhou, Hong (2014): Design of Constant Force Compliant Mechanisms. In: INTERNATIONAL JOURNAL OF ENGINEER-ING RESEARCH & TECHNOLOGY (IJERT) 3 (7), S. 14-19. DOI: 10.17577 / IJERTV3IS070028. [3] Radaelli, G.; Herder, J. L. (2017): Gravity balanced compliant shell mechanisms. In: International Journal of Solids and Structures 118-119, S. 78-88. DOI: 10.1016 / j.ijsolstr.2017.04.021. [4] Tong, Zongdi; Zhang, Xiaozhi; Wang, Guangwei (2023): Automatic Optimization for Compliant Constant Force Mechanisms. In: Actuators 12(2) (61). DOI: 10.3390 / act12020061. [5] Hoetmer, Karin; Woo, Geoffrey; Kim, Charles; Herder, Just (2010): Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing. In: Journal of Mechanisms and Robotics 2 (4), Artikel 041007. DOI: 10.1115 / 1.4002247. [6] Wu, Yi-Syuan; Lan, Chao-Chieh (2014): Linear Variable-Stiffness Mechanisms Based on Preloaded Curved Beams. In: Journal of Mechanical Design 136 (12), Artikel 122302. DOI: 10.1115 / 1.4028705. [7] Tong, Zongdi; Zhang, Xiaozhi; Wang, Guangwei (2023): Automatic Optimization for Compliant Constant Force Mechanisms. In: Actuators 12(2) (61). DOI: 10.3390 / act12020061. [8] Hasara, Steven Lawrence; Lusk, Craig Perry (2019): Load-adjustable constant-force mechanisms. Veröffentlichungsnr: US11047458B1. [9] Tolman, Kyler A.; Merriam, Ezekiel G.; Howell, Larry L. (2016): Compliant constant-force linear-motion mechanism. In: Mechanism and Machine Theory 106, S. 68-79. DOI: 10.1016 / j.mechmachtheory.2016.08.009.

[10] Bilancia, Pietro, and Giovanni Berselli. „Design and Testing of a Monolithic Compliant Constant Force Mechanism.“ Smart materials and structures 29.4 (2020): 44001. DOI: 10.1088 / 1361-665X / ab6884

[11] Zhang, Qingyi, Peng Yan, and Haipeng Wang. „A Curved-Beam Based Quasi Constant Force Mechanism Supporting Large Range and Force-Sensitive Robotic Manipulation.“ Mechanism and machine theory 172 (2022): 104799. DOI: 10.1016 / j.mechmachtheory.2022.104799

[12] Liu, Chih-Hsing et al. „Optimal Design of a Compliant Constant-Force Mechanism to Deliver a Nearly Constant Output Force Over a Range of Input Displacements.“ Soft robotics 7.6 (2020): 758-769. DOI: 10.1089 / soro.2019.0122

Claims

[1] Adjustable fully compliant guide device for guiding a table (4) with constant force along a guide direction in a range of motion (7), comprising a frame (2), at least one compliant element (3), at least one means (8) for adjusting a preload state of the at least one compliant element (3), characterized by , that one end of the at least one flexible element (3) can be connected to the table (4) orthogonally to its guide direction and the other end of the at least one flexible element (3) is connected to the frame (2) via the means (8), so that a connection distance p to the table (4) and a connection angle β to the frame (2) can be adjusted using the means (8), whereby a preload state of the at least one flexible element (3) and a force operating point (11) of the guide device can be adjusted. [2] Guide device according to claim 1 characterized by, that the frame (2) can be positioned orthogonally to the guide direction of the table (4). [3] Guide device according to claim 1 or 2, characterized by that it has one or more prestressed flexible elements (3) for connection with one side of the table (4) and an additional parallel guide (1) for the table (4). [4] Guide device according to claim 1 or 2, characterized by , that it has several prestressed flexible elements (3) arranged such that all reaction forces and moments cancel each other out in all directions orthogonal to the guiding direction. [5] Guide device according to claim 1, characterized by , that several flexible elements (3) are arranged in groups in at least two groups, wherein the flexible elements (3) of each group have the same cross-sectional area in sum and are arranged either mirrored or rotationally symmetric. [6] Guide device according to claim 5, characterized by , that a force-free guidance is achieved by at least two groups of flexible elements (3) prestressed up to the force work point (11) which are mirrored with respect to a plane orthogonal to the guidance direction. [7] Guide device according to claim 5, characterized by , that a slight angular deviation φ of the guide direction from orthogonality to the frame (2) is compensated by the fact that the groups of compliant elements (3) can be arranged on opposite sides of the table (4). [8] Guide device according to claim 5, characterized by , that the frame (2) can be tilted by an additional angle ζ relative to its horizontal position, whereby the range of motion (7) of the table (4) is tilted proportionally to the angle ζ and less force deviation is achieved in the range of motion (7). [9] Guide device according to claim 5, characterized by, that the means (8) for adjusting the connection distance p and the connection angle β additionally has a vertically adjustable distance (9) to the frame (2), whereby the position of the movement range (7) of the table (4) can be moved with constant force along the guide direction. [10] Guide device according to any one of claims 1 to 5, characterized by , that it can be connected to a table (4) with small or negligible mass, so that the frame (2) can be positioned in any orientation in space. [11] Guide device according to any one of claims 1 to 10, characterized by , that it has mechanical stops (5a, 5b) to prevent exceeding a predetermined range of movement (7) for the table (4). [12] Guide device according to any one of claims 1 to 11, characterized by , that the flexible elements (3) are straight in the unstressed state. [13] Method for dimensioning and adjusting a guide device according to claim 12, characterized by the following steps: a) Dimensioning of the flexible elements (3) and finding their number by specifying a force range of a force work point using formulas (F3) to (F7): L≥10.15⋅range of motion 7 r=c1LFmaxF˜4Fmin+c2LFmaxF˜3Fmin+c3LFmaxF˜2Fmin+c4LFmaxF˜Fmin+c5L Iz=FminL2F˜En h2≤σLM˜E or R≤σLM˜E M˜=d1FmaxF˜2Fmin+d2FmaxF˜Fmin+d3 b) Adjustment of the flexible elements (3) before or during the use of the guide device by changing the connection angle β and the connection distance p according to formulas (F1) and (F2): β=a1L2p2+a2Lp+a3 p=b1LF˜Fmin2F2+b2LF˜FminF+b3L which allows any force operating point to be set within the specified force range, with L as beam length, r as radius of curvature, c1, ..., c5 as polynomial coefficients of the maximum radius of curvature r, F max as maximum force operating point, F̃ as dimensionless force constant, F min for minimum force operating point, I Z as area moment of inertia of the cross-section of the element about the axis parallel to the guide direction, E as modulus of elasticity, n as number of beams, h as beam height, σ as allowable stress, M̃ as dimensionless moment constant, R as beam radius, d1, ..., d3 as polynomial coefficients of the dimensionless moment constant M̃, β as connection angle, a1, ..., a3 as polynomial coefficients of the connection angle β, p as connection spacing and b1, ..., b3 as polynomial coefficients of the connection spacing p, where The polynomial coefficients of the connecting angle β preferably lie in the intervals: a1 ∈ [1.98; 2.52]; a2 ∈ [-0.12; 0.6]; a3 ∈ [-0.14; 0.098], the polynomial coefficients of the connecting distance p preferably lie in the intervals b1 ∈ [0.00029; 0.00048]; b2 ∈ [-0.048; -0.043]; b3 ∈ [1.14; 1.17], the polynomial coefficients of the maximum radius of curvature r preferably lie in the intervals: c1 ∈ [7.45 ∗ 10 -06 ; 1,053 ∗ 10 -05 ]; c2 ∈ [-0.00061; -0.00045]; c3 ∈ [0.01; 0.014]; c4 ∈ [-0.15; -0.12]; c5 ∈ [0.75; 0.81] lies, and the polynomial coefficients of the dimensionless moment constant M̃ preferentially lie in the intervals: d1 ∈ [-0.011; -0.0098]; d2 ∈ [0.58; 0.61]; d3 ∈ [0.093; 0.2]. [14] Table (4) equipped with a guide device according to one of claims 1 to 12. [15] Use of the guide device according to one of claims 1 to 12 and / or the table (4) according to claim 14 for moving the table (4) with an optional object (10) located on the table (4) with constant force for gravitational compensation, force limitation, in nanopositioning machines, in force measurement and weighing technology for determining mass, in robot and gripper technology, in medical technology and for force adjustment in sports and rehabilitation equipment.

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