Non-contact floating suction transport device and slip instability suppression method thereof

Abstract

The application discloses a kind of non-contact suction floating transport devices and its slip instability suppression method, the non-contact suction floating transport device includes motion platform, motion platform is cylindrical, four hinged points distributed on its upper surface and four hinged points distributed on circumferential surface jointly constitute a cuboid, each hinged point is connected with a flexible cable, the flexible cable is wound around fixed pulley on parallel frame and then wound on roller, and the roller is driven by motor;Bernoulli suction cup is arranged below the motion platform, and the Bernoulli suction cup is connected with air source through pipeline, and flow valve is arranged on the pipeline;The flexible cable is wound on the roller by driving the roller to rotate by motor, and then the rope length is continuously changed, and the pose and position of the motion platform are converted.The application has the advantages of large working space, high degree of freedom, lightweight, low cost and the like.

Description

Technical Field

[0001] This invention relates to contactless transportation, specifically to a contactless buoyancy transport device and a method for suppressing slippage instability. Background Technology

[0002] Compared to traditional transportation methods, contactless transportation offers lower frictional resistance and energy consumption, and in particular, it enables precise load control and positioning, reducing the risk of workpiece damage during transport. Therefore, it shows promise for applications in the transportation of workpieces (such as wafers) in the semiconductor industry.

[0003] Bernoulli suction cups are one method of achieving contactless transportation. The principle of Bernoulli suction cups is as follows: Figure 1 As shown, airflow flows in from the air supply channel of the Bernoulli chuck, forming an air film in the gap between the chuck and the workpiece. According to Bernoulli's principle, the pressure is low where the flow velocity is high, and the workpiece is "held up" by atmospheric pressure, thus the workpiece is adsorbed by the chuck.

[0004] CN115799131A discloses a non-contact suction and buoyancy transport device and control method with adjustable suction force. It utilizes a parallel platform and servo cylinders to enable Bernoulli suction cups to translate, adjust suction force, and change angle and posture. The existing technical problem is that the parallel platform is a rigid structure, resulting in a small workspace and a large weight (leading to high inertia during movement, reduced stability, and hindering movement control), and low degrees of freedom. Summary of the Invention

[0005] Purpose of the invention: The first purpose of the present invention is to provide a non-contact suction and flotation transport device with a large working space; the second purpose of the present invention is to provide a method for suppressing slippage instability of the non-contact suction and flotation transport device.

[0006] Technical solution: The contactless suction and conveying device of the present invention includes a parallel frame and a moving platform. Each side of the parallel frame is provided with two sets of fixed pulleys and a motor. The fixed pulleys are located at the bottom of the frame beam, one at each end, and the base of the fixed pulley is rotatably connected to the frame beam. The motor is located on the outside of the parallel frame, and its position corresponds to the fixed pulley. The output end of the motor is provided with a roller, and a flexible cable is wound on the roller.

[0007] The motion platform is cylindrical, with four hinge points on its upper surface and four hinge points on its circumferential surface forming a cuboid. On each side of the parallel frame, the flexible cable on the left side passes over the fixed pulley at the upper left end of the parallel frame and connects to the hinge point at the upper right end of the cuboid, and the flexible cable on the right side passes over the fixed pulley at the upper right end of the parallel frame and connects to the hinge point at the lower left end of the cuboid. The hinge points at the upper right end and the lower left end of the cuboid are coplanar.

[0008] A Bernoulli suction cup is installed below the exercise platform. The Bernoulli suction cup is connected to the air source through a pipeline, and a flow valve is installed on the pipeline to regulate the air supply flow.

[0009] Furthermore, the fixed pulley base includes a U-shaped bracket rotatably mounted on the base plate, the fixed pulley is hinged to the U-shaped bracket, and the base plate is fixed to the frame beam.

[0010] Furthermore, four Bernoulli suction cups are set below the motion platform, evenly distributed circumferentially; four sets of pressure measuring holes are radially distributed on the Bernoulli suction cups, with n pressure measuring holes in each set, n≥5, and a pressure sensor is set at the upper end of each pressure measuring hole to detect the pressure of the air film between the Bernoulli suction cup and the workpiece; the four sets of pressure measuring holes are in a cross-shaped symmetrical structure about the center of the Bernoulli suction cup.

[0011] The slip instability suppression method of the non-contact suction and buoyancy transport device of the present invention includes:

[0012] (1) Establish a moving coordinate system o-xyz and an external fixed coordinate system O-XYZ, wherein the origin o of the moving coordinate system o-xyz is located at the center of the upper surface of the motion platform; calculate the direction vector and length of the flexible cable suspension part by means of vector operation rules and the attitude angle and position vector required by the motion platform, and then calculate the angle that the motor needs to rotate.

[0013] (2) When the motion platform deviates, the direction of deviation is determined according to the asymmetry of the pressure values ​​detected by each pressure sensor, and the motion platform rotates around the z-axis of the moving coordinate system. The angle is adjusted so that the two Bernoulli suction cups coincide with the offset direction of the motion platform;

[0014] (3) When the two Bernoulli chucks coincide with the offset direction of the motion platform, the workpiece rotates only in the xz plane or yz plane of the moving coordinate system around an axis parallel to the y-axis or an axis parallel to the x-axis, while the motion platform is offset relative to the workpiece. Based on the pressure values ​​detected by each pressure sensor along the workpiece rotation axis, and combined with the air film pressure distribution formula, the corresponding gap height is obtained; then, based on the gap height, the tilt angle of the workpiece relative to the motion platform and the position coordinates of the workpiece's center of gravity relative to the motion platform are calculated; based on this, the position and posture of the motion platform to be moved are calculated, and then the angle of motor rotation is obtained to eliminate the offset.

[0015] (4) After eliminating the offset, while maintaining the ability to overcome the workpiece's gravity, calculate the adsorption force required by the Bernoulli chuck through the kinematic equation, substitute the required adsorption force into the formula of the vertical adsorption force generated by the Bernoulli chuck on the workpiece, and calculate the real-time air supply flow required by the Bernoulli chuck according to the Newton method iteratively, pull the workpiece back to the horizontal, and suppress slippage instability.

[0016] (5) In steps (1) to (4), during the process of the motion platform continuously changing position and posture, the conditions of force balance equation and torque balance equation need to be met. When the tension of the flexible cable is greater than or equal to the minimum tension and less than or equal to the maximum tension that the flexible cable can withstand, the motion platform can follow the workpiece in real time. When the tension of the flexible cable is less than the minimum tension or greater than the maximum tension that the flexible cable can withstand, the motion platform cannot move to the designated position or cannot rotate to the designated posture angle, thus failing to suppress the workpiece slippage and instability, and the workpiece eventually becomes unstable and falls.

[0017] Further, step (1) includes:

[0018] Let the entry point of the i-th flexible cable at the fixed pulley be... The cable hinge point of the motion platform is The roller's entry point is ; The coordinates of the point on the fixed coordinate system are , The coordinates of the point on the fixed coordinate system are The coordinates of the origin o of the moving coordinate system on the fixed coordinate system are: , The coordinates of the point on the moving coordinate system are ;

[0019] In a fixed coordinate system, formula (1) is obtained according to the rules of vector operations:

[0020] (1)

[0021] Define the distances by which the origin o of the moving coordinate system is translated towards the x-axis, y-axis, and z-axis of the moving coordinate system, respectively. The Euler angles for rotation about the x-axis, y-axis, and z-axis of the moving coordinate system are respectively: , , ;

[0022] Will , and Substituting the point coordinates into formula (1), we get formula (2):

[0023] (2)

[0024] in, The direction vector of the flexible cable suspension section;

[0025] (3)

[0026] in, The coordinates of the origin o of the moving coordinate system on the fixed coordinate system when the motion platform has not translated or undergone attitude angle changes;

[0027] T is the coordinate transformation matrix, as shown in the following formula:

[0028] (4)

[0029] The angle that the i-th motor should rotate is obtained by formula (5). :

[0030] (5)

[0031] in, This refers to the current length of the flexible cable suspension section. This refers to the initial length of the flexible cable suspension section. The value is the diameter of the roller; the direction of cable retraction is counterclockwise, a negative sign indicates that the motor rotates counterclockwise, and a positive sign indicates that the motor rotates clockwise.

[0032] Further, step (2) includes:

[0033] The pressure values ​​measured by the two sets of pressure sensors along a diameter direction on the Bernoulli suction cup are P1, P2, ..., P 2n The pressure values ​​measured by the two sets of pressure sensors along another diametrical direction are P1', P2', ..., P 2n ';

[0034] The four Bernoulli suction cups are arranged clockwise as Bernoulli suction cups a, b, c, and d. One diameter direction of each Bernoulli suction cup is always parallel to the x-axis of the moving coordinate system, and the other diameter direction is always parallel to the y-axis of the moving coordinate system. Bernoulli suction cups a and c are located along the y-axis, and Bernoulli suction cups b and d are located along the x-axis. When the moving platform begins to move in a direction parallel to the xy plane of the moving coordinate system o-xyz, two Bernoulli suction cups must always coincide with this direction.

[0035] For Bernoulli suction cup a, calculate ; ; ; Then the motion platform needs to rotate around the z-axis of the moving coordinate system o-xyz. 'angle:

[0036] (8)

[0037] According to formula (9) 'Angle conversion to Within the interval, obtain the final result. angle:

[0038] (9).

[0039] Further, step (3) includes: the motion platform offsets relative to the workpiece. At this time, the vertical projection E of the center of the motion platform onto the surface of the workpiece does not coincide with the center of gravity e of the workpiece, and the workpiece rotates around its own center of gravity e.

[0040] when At this time, the two Bernoulli chucks coinciding with the offset direction of the motion platform are Bernoulli chucks b and d. The workpiece will only tilt in the xz plane of the moving coordinate system and rotate about an axis parallel to the y-axis of the moving coordinate system. Each Bernoulli chuck corresponds to P1'~P 2n The gap height below the pressure measuring hole is the same;

[0041] The air film pressure distribution within the gap between the Bernoulli chuck and the workpiece is represented by formula (6):

[0042] (6)

[0043] in, Where is the standard atmospheric pressure, R is the air constant, T is the temperature, G is the mass flow rate of the air supply channel, h is the clearance height between the Bernoulli chuck and the workpiece, D is the diameter of the Bernoulli chuck, and r is the radial distance from the pressure measuring hole to the center of the Bernoulli chuck. Gas viscosity;

[0044] The pressure values ​​P1', P2', ..., P collected by the pressure sensors on Bernoulli suction cups a and c are used to... 2n Substituting into formula (6), given the initial air supply flow rate q, the gap height is obtained. ;

[0045] The average clearance height from the center of the motion platform on the lower surface of the Bernoulli chuck to the workpiece surface is obtained using formula (10). :

[0046] (10)

[0047] The pressure values ​​P1', P2', ..., P collected by the pressure sensors on Bernoulli suction cups b and d are used to... 2n Substitute the values ​​into formula (6) to obtain the gap height. ; ;

[0048] The average clearance height between the Bernoulli chuck b and the workpiece is obtained using formula (11). :

[0049] (11)

[0050] The average clearance height from the Bernoulli chuck to the workpiece is obtained using formula (12). ;

[0051] (12)

[0052] The workpiece rotates around its own center of gravity e, and the clearance height... , The same change occurs; at this point, the adsorption forces of Bernoulli chucks b and d on the workpiece... , Changes may occur, leading to increased instability of the workpiece; in this case, it is necessary to rotate the motion platform so that its tilt angle matches the tilt angle of the workpiece, and to make the center of the motion platform and the center of gravity of the workpiece lie on the same straight line.

[0053] Using the moving coordinate system o-xyz as the reference coordinate system, projected onto the lower surface of the Bernoulli suction cup, the coordinates of the center of the motion platform are known to be... The coordinates of the center of Bernoulli suction cup b The coordinates of the center of Bernoulli's suction cup d Projected onto the workpiece surface, the center coordinates of the motion platform are... Projected coordinates of the center of Bernoulli suction cup b The projected coordinates of the center of Bernoulli's suction cup d ;

[0054] The tilt angle of the motion platform relative to the workpiece is obtained using formula (13). :

[0055] (13)

[0056] in, In the first and fourth quadrants;

[0057] The coordinates of the workpiece's center of gravity are obtained using formula (14). :

[0058] When an offset exists, formula (14) is:

[0059]

[0060] in, For point and points The slope between;

[0061] When there is no offset, formula (14) is:

[0062]

[0063] in, The initial clearance height between the Bernoulli chuck and the workpiece;

[0064] The position coordinates that the origin o of the moving coordinate system should be moved to can be obtained by formula (15). :

[0065] (15)

[0066] Will Substituting into formula (3) can update the position of the origin of the moving coordinate system in the fixed coordinate system. By adding the tilt angles of the platform relative to the workpiece in each movement, the attitude angle can be obtained. Substituting into formula (2), the orientation vector of the suspended part of the i-th flexible cable can be calculated. Then, substituting into formula (5), the angle that the i-th motor should rotate through can be calculated. Complete the follow;

[0067] After the motion platform completes one translation and rotation, the offset is eliminated. Therefore, the offset Reassign the value to 0.

[0068] Further, step (4) includes:

[0069] When the motion platform moves to the designated position and is relatively parallel to the workpiece, the offset... Since the initial gap height h is already 0, all Bernoulli chucks relative to the workpiece have a gap height equal to the initial gap height h. At this point, it is necessary to change the air flow rate at Bernoulli chucks b and d respectively, thereby changing the magnitude of the suction force generated by Bernoulli chucks b and d on the workpiece. , Then, the magnitude of the torque of Bernoulli suction cups b and d on the workpiece is changed, and the workpiece is pulled back to parallel.

[0070] The tilt angle of the workpiece is very small, so the component of the horizontal force is ignored; the torque M of the Bernoulli suction cups b and d on the workpiece can be obtained by formula (16). At the same time, when the workpiece is pulled and rotated back to parallel, it must satisfy formula (17) to ensure that the vertical suction force can overcome the gravity and prevent the workpiece from falling.

[0071] (16)

[0072] Where l is the distance from the center of the Bernoulli suction cup to the center of the motion platform in the yz plane of the moving coordinate system, and the torque M is positive in the counterclockwise direction;

[0073] (17)

[0074] Where m is the mass of workpiece (9); It is the acceleration due to gravity;

[0075] Set a parameter k greater than 0 to control different attitude angles. The torque at that time is shown in formula (18);

[0076] (18)

[0077] Combining equations (16) to (18), we obtain equation (19), which is the suction force required by Bernoulli suction cups b and d. ;

[0078] (19)

[0079] The formula for the perpendicular adsorption force exerted by a Bernoulli suction cup on a workpiece is:

[0080] (7)

[0081] Where d is the diameter of the air supply channel. This is the loss coefficient;

[0082] Adsorption force Substituting the initial gap height h into formula (7) yields the required air flow rate for Bernoulli suction cups b and d. , ;

[0083] The required air supply flow rates for Bernoulli suction cups b and d are determined iteratively using Newton's method. , ;

[0084] Let the function ,Will The multivariable function is expanded to its second derivative using Taylor expansion, as shown in formula (20). By taking the derivative and setting its value to 0, we obtain the iterative formula (21). When the iteration meets the preset accuracy, the iteration ends, and the required gas supply flow rate is calculated. , ;

[0085] (20)

[0086] in, For gas supply flow or , For gas supply flow or The initial value;

[0087] (twenty one)

[0088] in, The gas supply flow rate obtained in the nth iteration or , The gas supply flow rate obtained in the (n-1)th iteration or .

[0089] Furthermore, when or At that time, the two Bernoulli chucks coinciding with the offset direction of the motion platform are Bernoulli chucks a and c; the slip instability suppression method and similar.

[0090] Further, step (5) includes:

[0091] When the motion platform is translated and its pose is transformed by Euler angles, force balance and torque balance must be satisfied as shown in formula (22):

[0092] (twenty two)

[0093] in, Let be the tension vector of the i-th flexible cable. Let G be the unit vector of the i-th flexible cable suspension section, G be gravity, M' be the external torque on the motion platform, and T be the coordinate transformation matrix.

[0094] Solving formula (22) yields =( , ,..., ),like Not satisfied If the motion platform cannot be translated to the specified position or change to the specified attitude angle, the workpiece will immediately become unstable and fall off. This is the minimum tension force required for the flexible cable. This is the maximum tensile force that a flexible cable can withstand.

[0095] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0096] (1) The contactless adsorption and transportation device based on the parallel platform of flexible cable designed in this invention has a larger working space than the traditional rigid structure, and can realize contactless transportation over a wide range. In addition, it has advantages such as high degree of freedom, lightweight and low cost. The motor drives the roller to control the winding and unwinding of the cable, and controls the translation distance and the transformation of the Euler angle of the motion platform. The motion platform has six degrees of freedom and can translate to the x, y and z axes of the moving coordinate system and rotate around the x, y and z axes.

[0097] (2) By collecting pressure data in real time through the pressure sensor on the Bernoulli suction cup, the offset direction and gap height of the motion platform relative to the workpiece can be indirectly obtained, realizing the coordinated control of flow regulation and motion platform posture change. The installation of positioning auxiliary device is omitted, preventing the workpiece from becoming unstable and slipping in the non-contact transport state, and achieving true complete non-contact. Attached Figure Description

[0098] Figure 1 This is a schematic diagram of a Bernoulli suction cup.

[0099] Figure 2 This is a schematic diagram of the non-contact suction and flotation transport device provided in an embodiment of the present invention;

[0100] Figure 3 and Figure 4 This is a schematic diagram of the hinge point of the motion platform in an embodiment of the present invention;

[0101] Figure 5 This is a schematic diagram of the structure of the fixed pulley base in an embodiment of the present invention;

[0102] Figure 6 This is a schematic diagram of the Bernoulli suction cup in an embodiment of the present invention;

[0103] Figure 7 This is a cross-sectional view of the Bernoulli suction cup in an embodiment of the present invention;

[0104] Figure 8 This is a top view of the motion platform in an embodiment of the present invention;

[0105] Figure 9 This is a schematic diagram of workpiece offset and tilt in an embodiment of the present invention;

[0106] Figure 10 This is a schematic diagram of the motion platform rotating and following in an embodiment of the present invention;

[0107] Figure 11 This is a schematic diagram of the workpiece tilting in the plane in an embodiment of the present invention;

[0108] Figure 12 This is a schematic diagram of the motion platform following the workpiece in an embodiment of the present invention;

[0109] Figure 13 This is a flowchart illustrating the motion platform following the workpiece in an embodiment of the present invention;

[0110] Figure 14 This is a schematic diagram illustrating the change in gas supply flow rate in an embodiment of the present invention;

[0111] Figure 15 This is a flowchart of obtaining gas supply flow rate in an embodiment of the present invention;

[0112] Figure 16This is a force analysis diagram of the motion platform in an embodiment of the present invention.

[0113] Figure 17 This is a flowchart of the slip instability suppression method of the non-contact suction and flotation transport device in the embodiments of the present invention. Detailed Implementation

[0114] The invention will now be further described with reference to the accompanying drawings.

[0115] Appendix Figures 1 to 17 The accompanying figure labels are as follows:

[0116] 1. Parallel frame; 2. Fixed pulley; 201. Base plate; 202. Double-ended stud; 203. Nut; 204. U-shaped bracket; 205. Smooth washer; 3. Motion platform; 301. Small hole; 4. Flexible cable; 5. Bernoulli suction cup; 501. Pressure measuring hole; 6. Roller; 7. Coupling; 8. Motor; 9. Workpiece; 10. Pressure sensor; 11. Connecting plate;

[0117] like Figure 2 As shown, an embodiment of the present invention provides a contactless suction and buoyancy conveying device, comprising a parallel frame 1 and a motion platform 3, wherein the motion platform 3 is located inside the parallel frame 1. Each side of the parallel frame 1 is provided with two sets of fixed pulleys 2 and a motor 8. The fixed pulleys 2 are located at the bottom of the frame beam, one at each end. The motor 8 is located on the outside of the parallel frame 1, corresponding to the fixed pulleys 2. The output end of the motor 8 is connected to a roller 6 via a coupling 7, and a flexible cable 4 is wound around the roller 6.

[0118] like Figure 3 and Figure 4 As shown, the motion platform 3 is cylindrical, with four hinge points on its upper surface and four hinge points on its circumferential surface (at a certain distance from the lower surface of the motion platform 3). These eight hinge points together form a cuboid. To facilitate the fixing of the flexible cable 4, the hinge points are specifically small holes 301 on the surface of the motion platform 3. The motor 8 drives the roller 6 to rotate, and the flexible cable 4 winds around the roller 6, continuously changing its length and thus altering the posture and position of the motion platform 3.

[0119] Viewed from each side of the parallel frame 1, the starting end of the flexible cable 4 on the left side is at the point of contact with the roller. The exit point is around the fixed pulley 2 at the upper left end of the parallel frame 1. The rear hinge point with the upper right end of the cuboid Connected, the starting end of the flexible cable 4 on the right is cut into the roller. The exit point is around the fixed pulley 2 at the upper right end of the parallel frame 1. The rear hinge point with the lower left end of the cuboid The upper right hinge point of the cuboid is coplanar with the lower left hinge point of the cuboid. This avoids cable interference caused by changes in the pose of the motion platform 3 due to the length of the flexible cable 4, and also prevents collisions between the cable and the Bernoulli suction cup located below the motion platform 3.

[0120] like Figure 5 As shown, the fixed pulley base includes a base plate 201, a double-ended stud 202, a U-shaped bracket 204, and a smooth pad 205. The fixed pulley 2 and the U-shaped bracket 204 are hinged by a cylindrical hinge. The base plate 201 is fixed on the frame beam. One end of the double-ended stud 202 passes through the base plate 201 and connects to the frame beam, and the other end passes through the U-shaped bracket 204 and the smooth pad 205. Finally, it is tightened with a nut 203, so that the fixed pulley 2 can rotate on the U-shaped bracket 204. At the same time, the U-shaped bracket 204 can rotate around the double-ended stud 202, so that when the Euler angle of the motion platform 3 changes, the suspended part of the flexible cable 4 and the fixed pulley 2 remain in the same horizontal plane.

[0121] Combination Figures 6 to 8 A vertically intersecting connecting plate 11 is fixed to the lower surface of the motion platform 3. Four Bernoulli suction cups 5 are respectively located at the four corners of the connecting plate 11, parallel to the motion platform 3 and evenly distributed circumferentially (adjacent Bernoulli suction cups 5 are at 90°). Four sets of pressure measuring holes 501 are radially distributed on the Bernoulli suction cups 5, with five holes in each set. Each pressure measuring hole 501 is equipped with a pressure sensor 10 at its upper end to detect the pressure of the air film in the gap between the Bernoulli suction cup 5 and the workpiece 9. The four sets of pressure measuring holes 501 are arranged in a cross-shaped symmetrical structure about the center of the Bernoulli suction cup 5. The Bernoulli suction cup 5 is connected to an air source via a pipeline, and a flow valve is installed on the pipeline to regulate the air supply flow.

[0122] Pressure sensor 10 sends analog signals to the data acquisition card, which then sends digital signals to the PC. The PC controls each motor 8 and the flow valve.

[0123] like Figure 17 As shown, this embodiment of the invention also provides a method for suppressing slip instability of the contactless suction and buoyancy transport device described in this embodiment, which specifically includes the following steps:

[0124] (1) Establish a moving coordinate system o-xyz and an external fixed coordinate system O-XYZ, wherein the origin o of the moving coordinate system o-xyz is located at the center of the upper surface of the motion platform 3; calculate the direction vector and length of the suspended part of the flexible cable 4 by means of vector operation rules and the attitude angle and position vector required by the motion platform 3, and then calculate the angle that the motor 8 needs to rotate.

[0125] Step (1) includes:

[0126] An external fixed coordinate system O-XYZ is established at the lower left corner of the parallel frame 1; the entry point of the i-th flexible cable 4 at the fixed pulley 2 is calculated as follows. The cable hinge point of the motion platform 3 is The entry point of roller 6 is ; The coordinates of the point on the fixed coordinate system are , The coordinates of the point on the fixed coordinate system are The coordinates of the origin o of the moving coordinate system on the fixed coordinate system are: , The coordinates of the point on the moving coordinate system are ;

[0127] In a fixed coordinate system, formula (1) is obtained according to the rules of vector operations:

[0128] (1)

[0129] Define the distances by which the origin o of the moving coordinate system is translated towards the x-axis, y-axis, and z-axis of the moving coordinate system, respectively. The Euler angles for rotation about the x-axis, y-axis, and z-axis of the moving coordinate system are respectively: , , ;

[0130] Will , and Substituting the point coordinates into formula (1), we get formula (2):

[0131] (2)

[0132] in, The direction vector of the suspended portion of the flexible cable 4;

[0133] The coordinates of the origin o of the moving coordinate system on the fixed coordinate system It can be obtained from formula (3):

[0134] (3)

[0135] in, The coordinates of the origin o of the moving coordinate system on the fixed coordinate system when the motion platform 3 has not translated or undergone attitude angle transformation;

[0136] T is the coordinate transformation matrix, as shown in the following formula:

[0137] (4)

[0138] The angle that the i-th motor 8 should rotate is obtained by formula (5). :

[0139] (5)

[0140] in, This refers to the current length of the flexible cable 4 suspension section. This refers to the initial length of the suspended portion of the flexible cable 4. The diameter of roller 6 is shown; the direction of cable retraction is counterclockwise, the negative sign represents the counterclockwise rotation of motor 8, and the positive sign represents the clockwise rotation of motor 8. According to fluid dynamics analysis, the air film pressure distribution in the gap between Bernoulli chuck and workpiece 9 is represented by formula (6), and the vertical adsorption force generated by Bernoulli chuck on workpiece 9 can be represented by the integral form of formula (7).

[0141] (6)

[0142] in, Where is the standard atmospheric pressure, R is the air constant, T is the temperature, G is the mass flow rate of the air supply channel, h is the clearance height between the Bernoulli chuck and the workpiece, D is the diameter of the Bernoulli chuck, and r is the radial distance from the pressure measuring hole to the center of the Bernoulli chuck. Gas viscosity;

[0143] (7)

[0144] Where d is the diameter of the gas supply channel; This is the loss coefficient, typically taken as 0.5;

[0145] (2) When the motion platform 3 deviates, the direction of deviation is determined according to the asymmetry of the pressure values ​​detected by each pressure sensor 10, and the motion platform 3 rotates around the z-axis of the moving coordinate system. The angle is adjusted so that the two Bernoulli suction cups 5 coincide with the offset direction of the motion platform 3;

[0146] Step (2) includes:

[0147] like Figure 6 As shown, the pressure values ​​measured by the two sets of pressure sensors 10 along a diameter direction on the Bernoulli suction cup 5 are P1, P2, ..., P 10 The pressure values ​​measured by the two sets of pressure sensors 10 along another diametrical direction are P1', P2', ..., P 10 '.like Figure 7 As shown, the pressure measuring hole 501 connects the upper and lower surfaces of the Bernoulli chuck, and the pressure at the air film between the workpiece and the Bernoulli chuck can be measured by the pressure sensor 10 through the pressure measuring hole 501.

[0148] like Figure 8As shown, the four Bernoulli suction cups 5 are arranged clockwise as Bernoulli suction cups a, b, c, and d; each Bernoulli suction cup 5 has P1-P... 10 The orientation of the pressure measuring holes is always parallel to the x-axis of the moving coordinate system, P1'-P 10 The pressure measuring holes are always arranged parallel to the y-axis of the moving coordinate system. There are Bernoulli chucks a and c in the y-axis direction and Bernoulli chucks b and d in the x-axis direction. When the moving platform 3 starts to move in a certain direction parallel to the xy plane of the moving coordinate system o-xyz, there must always be two Bernoulli chucks 5 coinciding with this direction.

[0149] For Bernoulli suction cup a, calculate ; ; ; Then the motion platform 3 needs to rotate around the z-axis of the moving coordinate system o-xyz. The angle can be obtained from formula (8):

[0150] (8)

[0151] According to formula (9) 'Angle conversion to Within the interval, obtain the final result. angle:

[0152] (9)

[0153] (3) When the offset directions of the two Bernoulli chucks 5 coincide with those of the motion platform 3, the workpiece 9 rotates only in the xz plane or yz plane of the moving coordinate system, around an axis parallel to the y-axis or an axis parallel to the x-axis. At the same time, the motion platform 3 is offset relative to the workpiece 9. Based on the pressure values ​​detected by each pressure sensor 10 along the rotation axis of workpiece 9, and combined with the air film pressure distribution formula, the corresponding gap height is obtained; then, based on the gap height, the tilt angle of workpiece 9 relative to motion platform 3 and the position coordinates of the center of gravity of workpiece 9 relative to motion platform 3 are calculated; based on this, the position and posture of motion platform 3 to be moved are calculated, and then the rotation angle of motor 8 is obtained to eliminate the offset.

[0154] Step (3) includes:

[0155] like Figure 9 As shown, the motion platform 3 is offset relative to the workpiece 9. At this time, the vertical projection E of the center of the motion platform 3 onto the surface of the workpiece 9 does not coincide with the center of gravity e of the workpiece 9. As a result, the workpiece 9 will generate an eccentric torque and thus rotate around its own center of gravity e.

[0156] like Figure 10As shown, the motion platform 3 is rotated around the z-axis of the moving coordinate system so that the two Bernoulli suction cups always coincide with the direction of motion of the motion platform 3. At that time, the two Bernoulli suction cups 5 that coincide with the offset direction of the motion platform 3 are Bernoulli suction cups b and d (when or When the two Bernoulli suction cups 5 that coincide with the offset direction of the motion platform 3 are Bernoulli suction cups a and c, then d needs to be replaced with c, b with a, and x with y. Change to Calculating the gap height requires P1', P2', ..., P 10 Replace with P1, P2, ..., P 10 Therefore, the torques generated by Bernoulli chucks a and c on workpiece 9 are equal in magnitude and opposite in direction within the yz plane of the moving coordinate system, existing only within the xz plane of the moving coordinate system. Similarly, the torques generated by Bernoulli chucks b and d on workpiece 9 also exist only within the xz plane of the moving coordinate system. Therefore, workpiece 9 will only tilt within the xz plane of the moving coordinate system, meaning it will only rotate around an axis parallel to the y-axis of the moving coordinate system. Thus, each Bernoulli chuck 5 corresponds to P1'-P 10 The gap height below the pressure test hole 501 is the same.

[0157] The pressure values ​​P1', P2', ..., P collected by pressure sensor 10 on Bernoulli suction cups a and c are used to collect pressure values ​​P1', P2', ..., P 10 Substituting into formula (6), given the initial air supply flow rate q, the gap height can be obtained. ;

[0158] To reduce errors, the average gap height projected from the center of the motion platform (3) on the lower surface of the Bernoulli chuck to the workpiece surface is obtained using formula (10). :

[0159] (10)

[0160] The pressure values ​​P1', P2', ..., P collected by pressure sensor 10 on Bernoulli suction cups b and d are used to collect pressure values ​​P1', P2', ..., P 10 Substitute the values ​​into formula (6) to obtain the gap height. ; ;

[0161] To reduce errors, the average clearance height between Bernoulli chuck b and workpiece 9 is obtained using formula (11). :

[0162] (11)

[0163] To reduce errors, the average clearance height from the Bernoulli chuck d to the workpiece 9 is obtained using formula (12). ;

[0164] (12)

[0165] like Figure 11 As shown, workpiece 9 will rotate around its own center of gravity e in the moving coordinate system xz plane, with a gap height. , The same change occurs; at this point, the adsorption forces of Bernoulli chucks b and d on workpiece 9... , Changes can also occur, leading to increased instability in workpiece 9. For example... Figure 12 As shown, at this time, it is necessary to rotate the motion platform 3 so that its tilt angle is consistent with the tilt angle of the workpiece 9, and make the center of the motion platform 3 and the center of gravity of the workpiece 9 on the same straight line.

[0166] Using the moving coordinate system o-xyz as the reference coordinate system, projected onto the lower surface of the Bernoulli suction cup, the coordinates of the center of the moving platform 3 are known to be... The coordinates of the center of Bernoulli suction cup b The coordinates of the center of Bernoulli's suction cup d Projected onto the surface of workpiece 9, the center coordinates of motion platform 3 are... Projected coordinates of the center of Bernoulli suction cup b The projected coordinates of the center of Bernoulli's suction cup d ;

[0167] The tilt angle of the motion platform 3 relative to the workpiece 9 is obtained by formula (13). :

[0168] (13)

[0169] in, In the first and fourth quadrants;

[0170] The coordinates of the center of gravity of workpiece 9 are obtained by formula (14). :

[0171] When an offset exists, formula (14) is:

[0172]

[0173] in, For point and points The slope between;

[0174] When there is no offset, formula (14) is:

[0175]

[0176] in, The initial clearance height between the Bernoulli chuck and the workpiece;

[0177] The position coordinates that the origin o of the moving coordinate system should be moved to can be obtained by formula (15). :

[0178] (15)

[0179] Will Substituting into formula (3) can update the position of the origin of the moving coordinate system in the fixed coordinate system. By adding the tilt angles of the moving platform 3 relative to the workpiece 9 each time, the attitude angle can be obtained. Substituting into formula (2), the orientation vector of the suspended part of the i-th flexible cable 4 can be calculated. Then, substituting into formula (5), the angle that the i-th motor 8 should rotate through can be calculated. Complete the follow;

[0180] The method flow for obtaining the workpiece's tilt angle relative to the motion platform and the position of its center of gravity relative to the motion platform is as follows: Figure 13 As shown. After the motion platform 3 completes one translation and rotation, the offset is eliminated. Therefore, the offset Reassign the value to 0.

[0181] (4) After eliminating the offset, while maintaining the ability to overcome the gravity of the workpiece 9, calculate the adsorption force required by the Bernoulli suction cup 5 through the kinematic equation, substitute the required adsorption force into the formula of the vertical adsorption force generated by the Bernoulli suction cup on the workpiece 9, and calculate the real-time air supply flow required by the Bernoulli suction cup 5 according to the Newton method iterative calculation, pull the workpiece 9 back to the horizontal, and suppress slippage instability (the adsorption force of the Bernoulli suction cup is very sensitive to the gap height, and the motion platform must follow the workpiece in real time to be relatively parallel in order to suppress instability and prevent the workpiece from falling).

[0182] Step (4) includes:

[0183] like Figure 12 As shown, when the motion platform 3 moves to the designated position and is parallel to the workpiece 9, the offset is... The initial clearance height (h) is now 0, meaning all Bernoulli chucks have a clearance height equal to the initial clearance height (h) relative to workpiece 9. For example... Figure 14 As shown, it is necessary to change the air flow rate at Bernoulli chucks b and d respectively, thereby changing the magnitude of the adsorption force generated by Bernoulli chucks b and d on workpiece 9. , Then, the torque of Bernoulli suction cups b and d on workpiece 9 is changed, and workpiece 9 is pulled back to parallel.

[0184] The tilt angle of workpiece 9 is very small, so the component of the horizontal force is ignored. The torque M of Bernoulli suction cups b and d on workpiece 9 can be obtained by formula (16). At the same time, when workpiece 9 is pulled and rotated back to parallel, it must satisfy formula (17) to ensure that the vertical suction force can overcome the gravity and prevent workpiece 9 from falling.

[0185] (16)

[0186] Where l is the distance from the center of the Bernoulli suction cup to the center of the motion platform in the yz plane of the moving coordinate system, and the torque M is positive in the counterclockwise direction;

[0187] (17)

[0188] Where m is the mass of the workpiece; It is the acceleration due to gravity;

[0189] When workpiece 9 has been pulled back to a parallel state, there should be no torque to cause workpiece 9 to rotate excessively. Therefore, a parameter k greater than 0 is set to control the rotation at different attitude angles. The torque at that time is shown in formula (18);

[0190] (18)

[0191] Combining equations (16) to (18), we obtain equation (19), which is the suction force required by Bernoulli suction cups b and d. ;

[0192] (19)

[0193] Adsorption force Substituting the initial gap height h into formula (7) yields the required air flow rate for Bernoulli suction cups b and d. , ;

[0194] The required air supply flow rates for Bernoulli suction cups b and d are determined iteratively using Newton's method. , ;

[0195] Let the function ,Will The multivariable function is expanded to its second derivative using Taylor expansion, as shown in formula (20). By taking the derivative and setting its value to 0, we obtain the iterative formula (21). When the iteration meets the preset accuracy, the iteration ends, and the required gas supply flow rate is calculated. , ;

[0196] (20)

[0197] in, For gas supply flow or , For gas supply flow or The initial value;

[0198] (twenty one)

[0199] in, The gas supply flow rate obtained in the nth iteration or , The gas supply flow rate obtained in the (n-1)th iteration or ;

[0200] The procedure for obtaining the air supply flow rate of a Bernoulli suction cup is as follows: Figure 15 As shown.

[0201] (5) In steps (1) to (4), during the process of the motion platform 3 continuously changing its position and posture, it is necessary to satisfy the conditions of the force balance equation and the torque balance equation. When the tension of the flexible cable 4 is greater than or equal to the minimum tension and less than or equal to the maximum tension that the flexible cable 4 can withstand, the motion platform 3 can follow the workpiece 9 in real time. When the tension of the flexible cable 4 is less than the minimum tension or greater than the maximum tension that the flexible cable 4 can withstand, the motion platform 3 cannot move to the designated position or cannot rotate to the designated posture angle, thus failing to suppress the slippage and instability of the workpiece 9, and the workpiece 9 eventually becomes unstable and falls.

[0202] Step (5) includes:

[0203] like Figure 16 The force analysis diagram of the motion platform is shown. Static analysis is performed on the motion platform 3. When the motion platform 3 is translated and transformed by Euler angles, it must satisfy force balance and torque balance as shown in formula (22):

[0204] (twenty two)

[0205] in, Let be the tension vector of the i-th flexible cable 4. Let G be the unit vector of the suspended part of the i-th flexible cable 4, G be the gravity, M' be the external torque on the motion platform, and T be the coordinate transformation matrix.

[0206] Since the cable can only withstand tension during the movement of the motion platform, the minimum tension of the cable is calculated as follows: The maximum tensile force that the cable can withstand is Solving formula (22) yields =( , ,..., ),like Not satisfied If the motion platform 3 cannot be translated to the specified position or change to the specified attitude angle, the workpiece 9 will immediately become unstable and fall off.

Claims

1. A contactless suction and buoyancy conveying device, characterized in that, It includes a parallel frame and a motion platform. Each side of the parallel frame is equipped with two sets of fixed pulleys and a motor. The fixed pulleys are located at the bottom of the frame beam, one at each end, and the base of the fixed pulley is rotatably connected to the frame beam. The motor is located on the outside of the parallel frame, corresponding to the fixed pulleys. The output end of the motor is equipped with a roller, and a flexible cable is wound on the roller. The motion platform is cylindrical, with four hinge points on its upper surface and four hinge points on its circumferential surface forming a cuboid. On each side of the parallel frame, the flexible cable on the left side passes over the fixed pulley at the upper left end of the parallel frame and connects to the hinge point at the upper right end of the cuboid, and the flexible cable on the right side passes over the fixed pulley at the upper right end of the parallel frame and connects to the hinge point at the lower left end of the cuboid. The hinge points at the upper right end and the lower left end of the cuboid are coplanar. A Bernoulli suction cup is installed below the exercise platform. The Bernoulli suction cup is connected to the air source through a pipeline. A flow valve is installed on the pipeline to regulate the air supply flow. Four Bernoulli suction cups are set under the motion platform and are evenly distributed around the circumference. There are four sets of pressure measuring holes distributed radially on the Bernoulli suction cups. Each set has n pressure measuring holes, n≥5. Each pressure measuring hole is equipped with a pressure sensor at the top to detect the pressure of the air film between the Bernoulli suction cup and the workpiece. The four sets of pressure measuring holes are arranged in a cross-shaped symmetrical structure about the center of the Bernoulli suction cup.

2. The contactless suction and buoyancy conveying device according to claim 1, characterized in that, The fixed pulley base includes a U-shaped bracket rotatably mounted on the base plate, the fixed pulley is hinged to the U-shaped bracket, and the base plate is fixed to the frame beam.

3. A method for suppressing slip instability in the non-contact suction and buoyancy transport device according to claim 1, characterized in that, include: (1) Establish a moving coordinate system o-xyz and an external fixed coordinate system O-XYZ, wherein the origin o of the moving coordinate system o-xyz is located at the center of the surface of the moving platform; By using vector operation rules and the attitude angle and position vector required by the motion platform, the direction vector and length of the flexible cable suspension part are calculated, and then the angle that the motor needs to rotate through is calculated. (2) When the motion platform deviates, the direction of deviation is determined according to the asymmetry of the pressure values ​​detected by each pressure sensor, and the motion platform rotates around the z-axis of the moving coordinate system. The angle is adjusted so that the two Bernoulli suction cups coincide with the offset direction of the motion platform; (3) When the two Bernoulli chucks coincide with the offset direction of the motion platform, the workpiece rotates only in the xz plane or yz plane of the moving coordinate system around an axis parallel to the y-axis or an axis parallel to the x-axis, while the motion platform is offset relative to the workpiece. Based on the pressure values ​​detected by each pressure sensor along the workpiece rotation axis, and combined with the air film pressure distribution formula, the corresponding gap height is obtained; then, based on the gap height, the tilt angle of the workpiece relative to the motion platform and the position coordinates of the workpiece's center of gravity relative to the motion platform are calculated; based on this, the position and posture of the motion platform to be moved are calculated, and then the angle of motor rotation is obtained to eliminate the offset. (4) After eliminating the offset, while maintaining the ability to overcome the workpiece's gravity, calculate the adsorption force required by the Bernoulli chuck through the kinematic equation, substitute the required adsorption force into the formula of the vertical adsorption force generated by the Bernoulli chuck on the workpiece, and calculate the real-time air supply flow required by the Bernoulli chuck according to the Newton method iteratively, pull the workpiece back to the horizontal, and suppress slippage instability. (5) In steps (1) to (4), during the process of the motion platform continuously changing position and posture, the conditions of force balance equation and torque balance equation need to be met. When the tension of the flexible cable is greater than or equal to the minimum tension and less than or equal to the maximum tension that the flexible cable can withstand, the motion platform can follow the workpiece in real time. When the tension of the flexible cable is less than the minimum tension or greater than the maximum tension that the flexible cable can withstand, the motion platform cannot move to the designated position or cannot rotate to the designated posture angle, thus failing to suppress the workpiece slippage and instability, and the workpiece eventually becomes unstable and falls.

4. The method for suppressing slip instability of the non-contact suction and buoyancy transport device according to claim 3, characterized in that, Step (1) includes: Let the entry point of the i-th flexible cable at the fixed pulley be... The cable hinge point of the motion platform is The roller's entry point is ; The coordinates of the point on the fixed coordinate system are , The coordinates of the point on the fixed coordinate system are The coordinates of the origin o of the moving coordinate system on the fixed coordinate system are: , The coordinates of the point on the moving coordinate system are ; In a fixed coordinate system, formula (1) is obtained according to the rules of vector operations: （1） Define the distances by which the origin o of the moving coordinate system is translated towards the x-axis, y-axis, and z-axis of the moving coordinate system, respectively. The Euler angles for rotation about the x-axis, y-axis, and z-axis of the moving coordinate system are respectively: , , ; Will , and Substituting the point coordinates into formula (1), we get formula (2): （2） in, The direction vector of the flexible cable suspension section; （3） in, The coordinates of the origin o of the moving coordinate system on the fixed coordinate system when the motion platform has not translated or undergone attitude angle changes; T is the coordinate transformation matrix, as shown in the following formula: （4） The angle that the i-th motor should rotate is obtained by formula (5). : （5） in, This refers to the current length of the flexible cable suspension section. This refers to the initial length of the flexible cable suspension section. The value is the diameter of the roller; the direction of cable retraction is counterclockwise, a negative sign indicates that the motor rotates counterclockwise, and a positive sign indicates that the motor rotates clockwise.

5. The method for suppressing slip instability of the non-contact suction and buoyancy transport device according to claim 4, characterized in that, Step (2) includes: The pressure values ​​measured by the two sets of pressure sensors along a diameter direction on the Bernoulli suction cup are P1, P2, ..., P 2n The pressure values ​​measured by the two sets of pressure sensors along another diametrical direction are P1', P2', ..., P 2n '; The four Bernoulli suction cups are arranged clockwise as Bernoulli suction cups a, b, c, and d. One diameter direction of each Bernoulli suction cup is always parallel to the x-axis of the moving coordinate system, and the other diameter direction is always parallel to the y-axis of the moving coordinate system. Bernoulli suction cups a and c are located along the y-axis, and Bernoulli suction cups b and d are located along the x-axis. When the motion platform begins to move in a direction parallel to the xy-plane of the moving coordinate system o-xyz, two Bernoulli suction cups must always coincide with this direction. For Bernoulli suction cup a, calculate ; ; ; Then the motion platform needs to rotate around the z-axis of the moving coordinate system o-xyz. 'angle: （8） According to formula (9) 'Angle conversion to Within the interval, obtain the final result. angle: （9）。 6. The method for suppressing slip instability of the non-contact suction and buoyancy transport device according to claim 5, characterized in that, Step (3) includes: the motion platform offsets relative to the workpiece. At this time, the vertical projection E of the center of the motion platform onto the surface of the workpiece does not coincide with the center of gravity e of the workpiece, and the workpiece rotates around its own center of gravity e. when At this time, the two Bernoulli chucks coinciding with the offset direction of the motion platform are Bernoulli chucks b and d. The workpiece will only tilt in the xz plane of the moving coordinate system and rotate about an axis parallel to the y-axis of the moving coordinate system. Each Bernoulli chuck corresponds to P1'~P 2n The gap height below the pressure measuring hole is the same; The air film pressure distribution within the gap between the Bernoulli chuck and the workpiece is represented by formula (6): （6） in, Where is the standard atmospheric pressure, R is the air constant, T is the temperature, G is the mass flow rate of the air supply channel, h is the clearance height between the Bernoulli chuck and the workpiece, D is the diameter of the Bernoulli chuck, and r is the radial distance from the pressure measuring hole to the center of the Bernoulli chuck. For gas viscosity; The pressure values ​​P1', P2', ..., P collected by the pressure sensors on Bernoulli suction cups a and c are used to... 2n Substituting into formula (6), given the initial air supply flow rate q, the gap height is obtained. ; The average clearance height from the center of the motion platform on the lower surface of the Bernoulli chuck to the workpiece surface is obtained using formula (10). : （10） The pressure values ​​P1', P2', ..., P collected by the pressure sensors on Bernoulli suction cups b and d are used to... 2n Substitute the values ​​into formula (6) to obtain the gap height. ; ; The average clearance height between the Bernoulli chuck b and the workpiece is obtained using formula (11). : （11） The average clearance height from the Bernoulli chuck to the workpiece is obtained using formula (12). ; （12） The workpiece rotates around its own center of gravity e, and the clearance height... , The same change occurs; at this point, the adsorption forces of Bernoulli chucks b and d on the workpiece... , Changes may occur, leading to increased workpiece instability; in this case, it is necessary to rotate the motion platform so that its tilt angle matches the workpiece's tilt angle, and to align the center of the motion platform with the workpiece's center of gravity on the same straight line. Using the moving coordinate system o-xyz as the reference coordinate system, projected onto the lower surface of the Bernoulli suction cup, the coordinates of the center of the motion platform are known to be... The coordinates of the center of Bernoulli suction cup b The coordinates of the center of Bernoulli's suction cup d Projected onto the workpiece surface, the center coordinates of the motion platform are... Projected coordinates of the center of Bernoulli suction cup b The projected coordinates of the center of Bernoulli's suction cup d ; The tilt angle of the motion platform relative to the workpiece is obtained using formula (13). : （13） in, In the first and fourth quadrants; The coordinates of the workpiece's center of gravity are obtained using formula (14). : When an offset exists, formula (14) is: in, For point and points The slope between; When there is no offset, formula (14) is: in, The initial clearance height between the Bernoulli chuck and the workpiece; The position coordinates that the origin o of the moving coordinate system should be moved to can be obtained by formula (15). : （15） Will Substituting into formula (3) can update the position of the origin of the moving coordinate system in the fixed coordinate system. By adding the tilt angles of the platform relative to the workpiece in each movement, the attitude angle can be obtained. Substituting into formula (2), the orientation vector of the suspended part of the i-th flexible cable can be calculated. Then, substituting into formula (5), the angle that the i-th motor should rotate through can be calculated. Complete the follow; After the motion platform completes one translation and rotation, the offset is eliminated. Therefore, the offset Reassign the value to 0.

7. The method for suppressing slip instability of the non-contact suction and buoyancy transport device according to claim 6, characterized in that, Step (4) includes: When the motion platform moves to the designated position and is relatively parallel to the workpiece, the offset... Since the initial gap height h is already 0, all Bernoulli chucks relative to the workpiece have a gap height equal to the initial gap height h. At this point, it is necessary to change the air flow rate at Bernoulli chucks b and d respectively, thereby changing the magnitude of the suction force generated by Bernoulli chucks b and d on the workpiece. , Then, the magnitude of the torque of Bernoulli suction cups b and d on the workpiece is changed, and the workpiece is pulled back to parallel. The tilt angle of the workpiece is very small, so the component of the horizontal force is ignored; the torque M of the Bernoulli suction cups b and d on the workpiece can be obtained by formula (16). At the same time, when the workpiece is pulled and rotated back to parallel, it must satisfy formula (17) to ensure that the vertical suction force can overcome the gravity and prevent the workpiece from falling. （16） Where l is the distance from the center of the Bernoulli suction cup to the center of the motion platform in the yz plane of the moving coordinate system, and the torque M is positive in the counterclockwise direction; （17） Where m is the mass of workpiece (9); It is the acceleration due to gravity; Set a parameter k greater than 0 to control different attitude angles. The torque at that time is shown in formula (18); （18） Combining equations (16) to (18), we obtain equation (19), which is the suction force required by Bernoulli suction cups b and d. ; （19） The formula for the perpendicular adsorption force exerted by a Bernoulli suction cup on a workpiece is: （7） Where d is the diameter of the air supply channel. This is the loss coefficient; Adsorption force Substituting the initial gap height h into formula (7) yields the required air flow rate for Bernoulli suction cups b and d. , ; The required air supply flow rates for Bernoulli suction cups b and d are determined iteratively using Newton's method. , ; Let the function ,Will The multivariable function is expanded to its second derivative using Taylor expansion, as shown in formula (20). Taking the derivative and setting its value to 0, we obtain the iterative formula (21); When the iteration meets the preset accuracy, the iteration ends, and the required gas supply flow rate is calculated. , ; （20） in, For gas supply flow or , For gas supply flow or The initial value; （21） in, The gas supply flow rate obtained in the nth iteration or , The gas supply flow rate obtained in the (n-1)th iteration or .

8. The method for suppressing slip instability of the non-contact suction and buoyancy transport device according to claim 6 or 7, characterized in that, when or At that time, the two Bernoulli chucks coinciding with the offset direction of the motion platform are Bernoulli chucks a and c; the slip instability suppression method and similar.

9. The method for suppressing slip instability of the non-contact suction and buoyancy transport device according to claim 7, characterized in that, Step (5) includes: When the motion platform is translated and its pose is transformed by Euler angles, force balance and torque balance must be satisfied as shown in formula (22): （22） in, Let be the tension vector of the i-th flexible cable. Let G be the unit vector of the i-th flexible cable suspension section, G be gravity, M' be the external torque on the motion platform, and T be the coordinate transformation matrix. Solving formula (22) yields =( , ,..., ),like Not satisfied If the motion platform cannot be translated to the specified position or change to the specified attitude angle, the workpiece will immediately become unstable and fall off. This is the minimum tension force required for the flexible cable. This is the maximum tensile force that a flexible cable can withstand.

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