A vertical piezoelectric stick-slip driving platform and method based on inertia-friction dynamic balance method for inhibiting back-off

Abstract

The application provides a vertical piezoelectric stick-slip driving platform and method for inhibiting rollback based on an inertia-friction dynamic balance method, and belongs to the technical field of micro driving and precise positioning. The platform is mainly composed of a base, a support seat, a linear slide, a connecting piece, a right-angle adapter plate, a working slide, a cross roller guide, a double-drive transmission module and a fastening screw. The transmission module adopts a triangular structure, and the contact deformation between the transmission module and the working slide can be adjusted through the linear slide, so that the platform has high bearing capacity and load adaptability, and is suitable for vertical large-load driving. The application proposes an inertia-friction dynamic balance method, adopts a single-layer inertia-friction balance mode and a double-layer collaborative friction joint mode to respectively complete forward and reverse driving in the vertical direction, and through adjustment of the initial contact deformation, effective inhibition of rollback movement can be realized, and the vertical driving precision and system stability are improved.

Description

Technical Field

[0001] This invention belongs to the field of micro-drive precision positioning technology, and relates to a vertical piezoelectric stick-slip drive platform and method based on inertial-friction dynamic balance to suppress backlash. Background Technology

[0002] Piezoelectric actuators utilize the inverse piezoelectric effect of piezoelectric elements. By applying a specific voltage signal, they control the piezoelectric element to produce micro- and nano-scale mechanical deformation. This deformation is then converted, transmitted, and amplified through a compliant structure, ultimately acting on a mover to achieve precision actuation. Piezoelectric actuators possess significant advantages such as simple and compact structure, fast response speed, high precision, no electromagnetic pollution, immunity to electromagnetic interference, and strong environmental adaptability. They have been successfully applied in optical systems, aerospace, robotics, ultra-precision machining, and biomedicine. Piezoelectric stick-slip actuators, with their advantages of high output speed, high resolution, compact structure, small size, and simple control, have also found widespread application.

[0003] Piezoelectric stick-slip actuation utilizes the difference between dynamic and static friction to achieve periodic "stickiness" and "slippage." Current research on piezoelectric stick-slip actuation focuses on the horizontal direction. However, in the vertical direction, the addition of gravity has a significant impact on the performance of stick-slip inertial piezoelectric actuation devices. Gravity exacerbates the inherent backlash phenomenon of stick-slip actuation, making it more difficult to suppress. Furthermore, due to the limitations of its actuation principle, stick-slip actuation suffers from limited load-bearing capacity; the introduction of gravity essentially increases the load, further complicating the actuation process. Therefore, vertical actuation requires a structure with stronger load-bearing capacity while maintaining the normal deformation of the flexible structure, necessitating a balance between the two.

[0004] To address the backlash phenomenon during piezoelectric stick-slip actuation, various methods and structures for suppressing backlash have been proposed. In 2022, Yan Peng et al., in their Chinese invention patent "A Stick-Slip Actuator and Method for Actively Suppressing Backlash Motion" (publication number CN115085581B), designed a stick-slip actuator employing dual piezoelectric ceramics for synergistic driving. This actuator effectively suppresses backlash by separating or pressing the friction head against the mover. However, this method cannot be used for vertical driving; the separation of the friction head from the mover causes the mover to fall under gravity, preventing normal driving. In 2023, Cheng Yabing et al. published a Chinese invention patent, "A Stick-Slip Actuator for Driving Foot with Variable Friction to Suppress Retreat," with publication number CN116111874A. This device designed a stick-slip actuator for driving foot with variable friction to suppress retreat. The device uses structural design to make the driving foot at the fixed end and the moving end produce different deformations during forward and backward movements, thereby generating different frictional force differences to complete forward movement and suppress retreat. However, it does not consider the adaptability in the vertical direction. The unidirectional nature of gravity places higher demands on the structural design, which may cause the retreat suppression method to fail and make it difficult to achieve vertical bidirectional driving.

[0005] Therefore, it is urgent to design a piezoelectric stick-slip drive platform for vertical bidirectional drive and propose a drive method to effectively suppress vertical retraction. Summary of the Invention

[0006] This invention addresses the shortcomings and needs of existing technologies by proposing a vertical piezoelectric stick-slip drive platform and method based on an inertial-friction dynamic balance approach to suppress backlash. The inertial-friction dynamic balance method utilizes a single-layer inertial friction balance mode and a double-layer cooperative friction relay mode to achieve forward and reverse vertical drive, respectively, taking advantage of the unidirectional characteristics of gravity. By adjusting the initial contact deformation, backlash can be effectively suppressed, improving vertical drive accuracy and system stability. This method can meet the drive requirements of different loads in the vertical direction and exhibits strong load capacity and adaptability.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A vertical piezoelectric stick-slip drive platform for suppressing backlash based on an inertial-friction dynamic balance method is disclosed. The platform includes a base 1, a support base 2, a first linear slide 3.1, a second linear slide 3.2, a first connector 4.1, a second connector 4.2, a first right-angle adapter plate 5.1, a second right-angle adapter plate 5.2, a working slide 6, a first crossed roller guide rail 7.1, a second crossed roller guide rail 7.2, a first drive transmission module 8.1, a second drive transmission module 8.2, and multiple fastening screws. Specifically: The base 1 is a horizontally placed flat plate structure. The support 2 is a vertical plate, with its bottom mounted on the base 1 by a fifth fastening screw 9.5, located on one side. A first crossed roller guide 7.1 and a second crossed roller guide 7.2 are mounted on the vertical side of the support 2 by a sixth fastening screw 9.6, enabling vertical relative movement between the working slide 6 and the support 2. The working slide 6 is mounted on the first crossed roller guide 7.1 and the second crossed roller guide 7.2 by a fourth fastening screw 9.4. The first linear slide 3.1 and the second linear slide 3.2 have identical structures and are symmetrically mounted on the base 1 by a seventh fastening screw 9.7, located on the other side. Each linear slide is mounted with a right-angle adapter plate via a connector. A drive module is mounted on the right-angle adapter plate. Specifically: the first connector 4.1 and the second connector 4.2 are respectively mounted on the first linear slide 3.1 and the second linear slide 3.2 via a first fastening screw 9.1; the first right-angle adapter plate 5.1 and the second right-angle adapter plate 5.2 are respectively mounted on the first connector 4.1 and the second connector 4.2 via a second fastening screw 9.2; the first drive module 8.1 and the second drive module 8.2 are respectively mounted on the opposite vertical sides of the first right-angle adapter plate 5.1 and the second right-angle adapter plate 5.2 via a third fastening screw 9.3. The first drive module 8.1 is a drive module used to vertically drive the working slide 6, and the second drive module 8.2 is an auxiliary module used to balance the force on the working slide 6 and suppress retraction.

[0008] Furthermore, both the first drive transmission module 8.1 and the second drive transmission module 8.2 are composed of piezoelectric stacks, flexible structures, and preload screws. The flexible structures of both modules include a symmetrical flexible preload beam 11.1, a triangular flexible hinge structure 11.2, a flexible hinge frame 11.3, and a drive foot 11.4, all manufactured as a single unit. The piezoelectric stack of the first drive transmission module 8.1 includes a first piezoelectric stack 10.1 and a second piezoelectric stack 10.2, and the preload screws include a first preload screw 12.1 and a second preload screw 12.2. The piezoelectric stack of the second drive transmission module 8.2 includes a third piezoelectric stack 10.3 and a fourth piezoelectric stack 10.4, and the preload screws include a third preload screw 12.3 and a fourth preload screw 12.4. Specifically: In the first drive module 8.1: the flexible structure is a vertically symmetrical structure, which includes two identical sets of symmetrical flexible preload beams 11.1, symmetrically distributed on the upper and lower sides inside the flexible hinge frame 11.3; the triangular flexible hinge structure 11.2 is located between the two sets of symmetrical flexible preload beams 11.1, and is connected to the flexible hinge frame 11.3 through the symmetrical flexible preload beams 11.1 on the upper and lower sides; the first preload screw 12.1 is installed in the threaded hole on the lower surface of the flexible hinge frame 11.3, and the second preload screw 12.2 is installed in the threaded hole on the upper surface of the flexible hinge frame 11.3; the first piezoelectric stack 10.1 is a vertically upward drive source; the space between the lower flexible symmetrical preload beam 11.1 and the first preload screw 12.1 is the mounting groove for the first piezoelectric stack 10.1, and the upper and lower surfaces of the first piezoelectric stack 10.1 are in contact with the lower surface of the flexible symmetrical preload beam 11.1 and the bottom surface of the first preload screw 12.1, respectively. By rotating the first pre-tightening screw 12.1, the flexible symmetrical pre-tightening beam 11.1 is deformed, thereby generating a pre-tightening force to fix the first piezoelectric stack 10.1; the second piezoelectric stack 10.2 is a vertically downward driving source; the upper flexible symmetrical pre-tightening beam 11.1 and the second pre-tightening screw 12.2 form a mounting groove for the second piezoelectric stack 10.2. The upper and lower surfaces of the second piezoelectric stack 10.2 are in contact with the bottom surface of the second pre-tightening screw 12.2 and the upper surface of the flexible symmetrical pre-tightening beam 11.1, respectively. By rotating the second pre-tightening screw 12.2, the upper flexible symmetrical pre-tightening beam 11.1 is deformed, thereby generating a pre-tightening force to fix the second piezoelectric stack 10.2; when the knob of the working slide 3.1 is rotated, the first drive transmission module 8.1 moves in the vertical direction along the surface of the working slide 6, causing the drive foot 11.4 to make contact deformation with the working slide 6, which is used to balance the gravity of the working slide 6 and generate driving force.

[0009] In the second drive module 8.2: the flexible structure composition and layout of the first drive module 8.1 and the second drive module 8.2 are the same, and the overall structure is symmetrical; the third preload screw 12.3 is installed in the threaded hole on the lower surface of the flexible hinge frame 11.3, and the fourth preload screw 12.4 is installed in the threaded hole on the upper surface of the flexible hinge frame 11.3; the third piezoelectric stack 10.3 is a vertically upward auxiliary drive source; the lower flexible symmetrical preload beam 11.1 and the third preload screw 12.3 form a mounting groove for the third piezoelectric stack 10.3, and the upper and lower surfaces of the third piezoelectric stack 10.3 contact the lower surface of the flexible symmetrical preload beam 11.1 and the bottom surface of the third preload screw 12.3, respectively. By rotating the third preload screw 12.3, the flexible symmetrical preload beam 11.1 is deformed. This generates a preload force to fix the third piezoelectric stack 10.3; the upper flexible symmetrical preload beam 11.1 and the fourth preload screw 12.4 form a mounting groove for the fourth piezoelectric stack 10.4. The upper and lower surfaces of the fourth piezoelectric stack 10.4 are in contact with the bottom surface of the fourth preload screw 12.4 and the upper surface of the flexible symmetrical preload beam 11.1, respectively. By rotating the fourth preload screw 12.4, the upper flexible symmetrical preload beam 11.1 is deformed, thereby generating a preload force to fix the fourth piezoelectric stack 10.4; when the knob of the second working slide 3.2 is rotated, the second drive transmission module 8.2 moves in the vertical direction along the surface of the working slide 6, causing the drive foot 11.4 to contact and deform with the working slide 6, generating auxiliary friction force to balance the force on the working slide 6, thereby suppressing retraction.

[0010] A vertical piezoelectric stick-slip drive method for suppressing backlash based on an inertial-friction dynamic balance approach is implemented using the aforementioned vertical piezoelectric stick-slip drive platform. Before the vertical piezoelectric stick-slip drive platform operates, the knob of the first linear slide 3.1 is rotated to cause the driving foot 11.4 of the first drive module 8.1 to make contact deformation with the working slide 6, thereby generating a normal contact force, so that the static friction force and gravity of the working slide 6 are in equilibrium, and the working slide 6 remains stationary in the vertical direction under the initial preload state; the knob of the second linear slide 3.2 is rotated to position the second drive module 8.2 in a specific position.

[0011] The vertical piezoelectric stick-slip drive method has two modes: a single-layer inertial balance mode and a double-layer cooperative friction relay mode. The single-layer inertial balance mode is used for vertical downward drive, with the first drive module 8.1 providing single-layer drive and the second piezoelectric stack 10.2 serving as the sole drive source. The double-layer cooperative friction relay mode is used for vertical upward drive, with the first drive module 8.1 and the second drive module 8.2 providing cooperative drive, the first piezoelectric stack 10.1 serving as the drive source, and the third piezoelectric stack 10.3 serving as the auxiliary drive source.

[0012] The first mode: The single-layer inertial balance mode is used for vertical downward drive. The first drive transmission module 8.1 participates in the drive, while the second drive transmission module 8.2 does not participate in the drive. The specific steps are as follows: Step 1: Apply an initial voltage U to the second piezoelectric stack 10.2 2_initial The static friction force f is 0. There is an initial contact force between the drive foot 11.4 of the first drive transmission module 8.1 and the working slide 6. The working slide 6 remains stationary. sd Vertically upward, it balances the downward gravitational force Mg, i.e., f sd =Mg; Step 2: Apply a voltage signal U to the second piezoelectric stack 10.2 2_step Initially, the voltage signal is 0, and the second piezoelectric stack 10.2 is at its natural length. As the voltage gradually increases, the second piezoelectric stack 10.2 elongates, and the deformation of the triangular flexible hinge structure 11.2 gradually increases. This generates a coupled clamping and feeding motion at the drive foot 11.4. The clamping motion increases the normal preload of the drive foot 11.4 and the working slide 6, while the feeding motion causes the working slide 6 and the drive foot 11.4 to move downwards synchronously. The nonlinear deformation of the flexible hinge structure 11.2 causes the working slide 6 to have a downward acceleration, resulting in a force balance relationship f for the working slide 6. sd +Ma=Mg; Step 3: Apply a sudden drop in voltage signal U to the second piezoelectric stack 10.2 2_back During this stage, the voltage signal originates from U. 2_max The pressure drops sharply to 0, the second piezoelectric stack 10.2 quickly recovers its natural length, and the working slide 6 maintains a vertical downward motion tendency due to inertia, with static friction f sd Switching to kinetic friction f cd The direction is vertically upward. By rotating the knob of the working slide 3.1, the initial contact deformation between the drive foot 11.4 and the working slide 6 is precisely adjusted, thereby precisely controlling the initial normal contact force. This achieves a balance between inertial force, dynamic friction, and gravity at this stage, thus suppressing the retraction of the working slide 6, i.e., f. cd =Mg+F I .

[0013] The second mode: The dual-layer cooperative friction relay mode is used for vertical upward driving. The second driving module 8.1 and the second auxiliary module 8.2 drive in coordination. The specific steps are as follows: Step 1: Apply an initial voltage U to the first piezoelectric stack 10.1 1_initial The initial voltage U applied to the third piezoelectric stack is 0, which is 10.3. 3_initial For U 3_max An initial preload F exists between the drive foot 11.4 of the first drive module 8.1 and the working slide 6. 0dThe second auxiliary module 8.2 has an initial preload F under the action of the second linear slide 3.2. 0a And F 0d >F 0a The working slide 6 remains stationary, and the static friction force f it experiences is... sd Vertically upward, it balances the downward gravitational force Mg, i.e., f sd =Mg; Step 2: Apply a rising voltage signal U1 to the first piezoelectric stack 10.1. Initially, the voltage signal is 0, and the first piezoelectric stack 10.1 is at its natural length. The voltage gradually increases to U1. 1_rise The first piezoelectric stack 10.1 elongates, and the triangular flexible hinge structure 11.2 deforms gradually, driving the foot 11.4 to generate a coupled action of clamping motion and upward feeding motion; a voltage signal U is applied to the third piezoelectric stack 10.3. 3_step The initial voltage signal is U 3_max The third piezoelectric stack 10.3 is in an elongated state, and the voltage gradually decreases to 0. The third piezoelectric stack 10.3 recovers its deformation, the triangular flexible hinge structure 11.2 recovers its deformation, and the driving foot 11.4 generates a coupled action of release motion and downward feed motion; the initial preload F between the first drive transmission module 8.1 and the working slide 6 0d The initial preload F between the second drive module 8.2 and the working slide 6 is less than the initial preload F. 0a The working slide 6 moves upward synchronously with the first drive transmission module 8.1, with an acceleration of a1. The frictional forces acting on the working slide 6 are the vertically upward static frictional forces f from the first drive transmission module 8.1. sd The vertically downward dynamic friction force f from the second drive module 8.2 ca There exists a force balance relationship f sd +Ma1=Mg+f ca ; Step 3: The voltage signal U1 of the first piezoelectric stack 10.1 continues to increase to U 1_max The voltage U3 of the third piezoelectric stack 10.3 increases from 0 to U 3_max As U3 increases in slope, it becomes greater than U1. The working slide 6 and the second drive module 8.2 move upward synchronously with an acceleration of a2. The frictional force on the working slide 6 comes from the vertically downward kinetic friction force f from the first drive module 8.1. cd The vertically upward static friction force f from the second drive transmission module 8.2 sa There exists a force balance relationship f sa +Ma2=Mg+f cd ; Step 4: Apply a sudden drop in voltage signal U to the first piezoelectric stack 10.1 1_back During this stage, the voltage signal originates from U.1_max The voltage drops sharply to 0, the first piezoelectric stack 10.1 quickly recovers its natural length, and the voltage of the third piezoelectric stack 10.3 rises to U. 3_max And maintain; the frictional force on the working slide 6 comes from the vertically downward dynamic frictional force f of the first drive transmission module 8.1. cd and the upward kinetic friction force f from the second drive module 8.2 ca By rotating the knobs of the first linear slide 3.1 and the second linear slide 3.2, the initial contact deformation between the drive foot 11.4 of the first drive transmission module 8.1 and the second drive transmission module 8.2 and the working slide 6 is adjusted respectively, thus achieving force balance. ca +F I =Mg+f cd This suppresses the retraction motion of the working slide 6.

[0014] The beneficial effects of this invention are as follows: (1) By adopting a double-layer triangular flexible structure, the initial contact deformation between the drive module and the working slide is adjusted by the linear slide, and the initial gravity balance is achieved. This piezoelectric stick-slip drive platform solves the problem of gravity load in the vertical direction and has strong load capacity and load adaptability. (2) An inertial-friction dynamic balance method is proposed. Given the unidirectional nature of gravity, two driving modes are proposed based on this method, which are applicable to vertical downward and vertical upward driving respectively. The vertical downward driving adopts a single-layer inertial friction balance mode. By adjusting the initial contact deformation of the single layer, the balance of friction, inertial force and gravity during the retraction phase of the working slide is achieved. The vertical upward driving adopts a double-layer cooperative friction relay mode. By adjusting the initial contact deformation of the two driving modules respectively, the force balance during the retraction phase of the working slide is achieved, and the vertical bidirectional retraction motion is effectively suppressed. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the overall structure; Figure 2 This is a schematic diagram of the internal structure; Figure 3 This is a schematic diagram of the connection at the base; Figure 4 This is a schematic diagram of the drive and transmission module; Figure 4 (a) in the diagram is a structural schematic of the first drive transmission module 8.1; Figure 4 (b) in the diagram is a schematic diagram of the second drive transmission module 8.2; Figure 5 This is a schematic diagram of the driving principle for a single-layer inertial friction balance mode. Figure 5 (a) in the diagram is a schematic diagram of step one of the single-layer inertial friction balance mode; Figure 5(b) is a schematic diagram of step two of the single-layer inertial friction balance mode; Figure 5 (c) in the diagram is a schematic diagram of step three of the single-layer inertial friction balance mode; Figure 6 Schematic diagram of the driving principle of the dual-layer cooperative friction relay mode; Figure 6 (a) in the diagram is a schematic diagram of step one of the two-layer cooperative friction relay mode; Figure 6 (b) in the diagram is a schematic diagram of step two of the double-layer cooperative friction relay mode; Figure 6 (c) in the diagram is a schematic diagram of step three of the double-layer cooperative friction relay mode; Figure 6 (d) in the diagram is a schematic diagram of step four of the double-layer cooperative friction relay mode; In the diagram: 1. Base; 2. Support base; 3.1 First linear slide; 3.2 Second linear slide; 4.1 First connector; 4.2 Second connector; 5.1 First right-angle adapter plate; 5.2 Second right-angle adapter plate; 6. Working slide; 7.1 First crossed roller guide; 7.2 Second crossed roller guide; 8.1 First drive transmission module; 8.2 Second drive transmission module; 9.1 First fastening screw; 9.2 Second fastening screw; 9.3 Third fastening screw; 9.4 Fourth fastening screw ; 9.5 Fifth fastening screw; 9.6 Sixth fastening screw; 9.7 Seventh fastening screw; 10.1 First piezoelectric stack; 10.2 Second piezoelectric stack; 10.3 Third piezoelectric stack; 10.4 Fourth piezoelectric stack; 11.1 Symmetrical flexible preload beam; 11.2 Triangular flexible hinge structure; 11.3 Flexible hinge frame; 11.4 Drive foot; 12.1 First preload screw; 12.2 Second preload screw; 12.3 Third preload screw; 12.4 Fourth preload screw. Detailed Implementation

[0016] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and technical solutions.

[0017] This embodiment provides a vertical piezoelectric stick-slip drive platform based on an inertial-friction dynamic balance method to suppress backlash. The complete structure is as follows: Figure 1 As shown, the internal structure is as follows Figure 2 As shown. The vertical piezoelectric stick-slip drive platform includes a base 1, a support base 2, a first linear slide 3.1, a second linear slide 3.2, a first connector 4.1, a second connector 4.2, a first right-angle adapter plate 5.1, a second right-angle adapter plate 5.2, a working slide 6, a first crossed roller guide rail 7.1, a second crossed roller guide rail 7.2, a first drive transmission module 8.1, a second drive transmission module 8.2, and multiple fastening screws; specifically: The base 1 is a horizontally placed flat plate structure. The support 2 is a vertical plate, with its bottom mounted on the base 1 via a fifth fastening screw 9.5, located on one side. A first crossed roller guide 7.1 and a second crossed roller guide 7.2 are mounted on the vertical side of the support 2 via a sixth fastening screw 9.6, enabling vertical relative movement between the working slide 6 and the support 2. The working slide 6 is mounted on the first crossed roller guide 7.1 and the second crossed roller guide 7.2 via a fourth fastening screw 9.4. The first linear slide 3.1 and the second linear slide 3.2 have identical structures and are symmetrically mounted on the base 1 via a seventh fastening screw 9.7, located on the other side. The mounting positions of the support 2, the first linear slide 3.1, and the second linear slide 3.2 on the base 1 are as follows: Figure 3 As shown. Each linear slide is equipped with a right-angle adapter plate via a connector. A drive module is mounted on the right-angle adapter plate. Specifically: the first connector 4.1 and the second connector 4.2 are respectively mounted on the first linear slide 3.1 and the second linear slide 3.2 via the first fastening screw 9.1; the first right-angle adapter plate 5.1 and the second right-angle adapter plate 5.2 are respectively mounted on the first connector 4.1 and the second connector 4.2 via the second fastening screw 9.2; the first drive module 8.1 and the second drive module 8.2 are respectively mounted on the opposite vertical sides of the first right-angle adapter plate 5.1 and the second right-angle adapter plate 5.2 via the third fastening screw 9.3. The first drive module 8.1 is a drive module used to vertically drive the working slide 6, and the second drive module 8.2 is an auxiliary module used to balance the force on the working slide 6 and suppress retraction.

[0018] Furthermore, both the first drive transmission module 8.1 and the second drive transmission module 8.2 are composed of piezoelectric stacks, flexible structures, and preload screws, such as... Figure 4 As shown in (a) and (b); the flexible structures of the first drive transmission module 8.1 and the second drive transmission module 8.2 both include a symmetrical flexible preload beam 11.1, a triangular flexible hinge structure 11.2, a flexible hinge frame 11.3, and a drive foot 11.4, all integrally manufactured using 7075 aluminum alloy material; the piezoelectric stack of the first drive transmission module 8.1 includes a first piezoelectric stack 10.1 and a second piezoelectric stack 10.2, and the preload screws include a first preload screw 12.1 and a second preload screw 12.2; the piezoelectric stack of the second drive transmission module 8.2 includes a third piezoelectric stack 10.3 and a fourth piezoelectric stack 10.4, and the preload screws include a third preload screw 12.3 and a fourth preload screw 12.4. All four piezoelectric stacks have the same specifications, with dimensions of 5mm × 5mm × 18mm and a maximum nominal displacement of 18μm. Specifically: In the first drive module 8.1: the flexible structure is a vertically symmetrical structure, which includes two identical sets of symmetrical flexible preload beams 11.1, symmetrically distributed on the upper and lower sides inside the flexible hinge frame 11.3; the triangular flexible hinge structure 11.2 is located between the two sets of symmetrical flexible preload beams 11.1, and is connected to the flexible hinge frame 11.3 through the symmetrical flexible preload beams 11.1 on the upper and lower sides; the first preload screw 12.1 is installed in the threaded hole on the lower surface of the flexible hinge frame 11.3, and the second preload screw 12.2 is installed in the threaded hole on the upper surface of the flexible hinge frame 11.3; the first piezoelectric stack 10.1 is a vertically upward drive source; the space between the lower flexible symmetrical preload beam 11.1 and the first preload screw 12.1 is the mounting groove for the first piezoelectric stack 10.1, and the upper and lower surfaces of the first piezoelectric stack 10.1 are in contact with the lower surface of the flexible symmetrical preload beam 11.1 and the bottom surface of the first preload screw 12.1, respectively. By rotating the first pre-tightening screw 12.1, the flexible symmetrical pre-tightening beam 11.1 is deformed, thereby generating a pre-tightening force to fix the first piezoelectric stack 10.1. The second piezoelectric stack 10.2 is a vertically downward driving source. The upper flexible symmetrical pre-tightening beam 11.1 and the second pre-tightening screw 12.2 form a mounting groove for the second piezoelectric stack 10.2. The upper and lower surfaces of the second piezoelectric stack 10.2 are in contact with the bottom surface of the second pre-tightening screw 12.2 and the upper surface of the flexible symmetrical pre-tightening beam 11.1, respectively. By rotating the second pre-tightening screw 12.2, the upper flexible symmetrical pre-tightening beam 11.1 is deformed, thereby generating a pre-tightening force to fix the second piezoelectric stack 10.2. When the knob of the working slide 3.1 is rotated, the first drive transmission module 8.1 moves in the vertical direction along the surface of the working slide 6, causing the drive foot 11.4 to make contact deformation with the working slide 6, which is used to balance the gravity of the working slide 6 and generate driving force.

[0019] In the second drive module 8.2: the flexible structure composition and layout of the first drive module 8.1 and the second drive module 8.2 are the same, and the overall structure is symmetrical; the third preload screw 12.3 is installed in the threaded hole on the lower surface of the flexible hinge frame 11.3, and the fourth preload screw 12.4 is installed in the threaded hole on the upper surface of the flexible hinge frame 11.3; the third piezoelectric stack 10.3 is a vertically upward auxiliary drive source; the lower flexible symmetrical preload beam 11.1 and the third preload screw 12.3 form a mounting groove for the third piezoelectric stack 10.3, and the upper and lower surfaces of the third piezoelectric stack 10.3 contact the lower surface of the flexible symmetrical preload beam 11.1 and the bottom surface of the third preload screw 12.3, respectively. By rotating the third preload screw 12.3, the flexible symmetrical preload beam 11.1 is deformed. This generates a preload force to fix the third piezoelectric stack 10.3; the upper flexible symmetrical preload beam 11.1 and the fourth preload screw 12.4 form a mounting groove for the fourth piezoelectric stack 10.4. The upper and lower surfaces of the fourth piezoelectric stack 10.4 are in contact with the bottom surface of the fourth preload screw 12.4 and the upper surface of the flexible symmetrical preload beam 11.1, respectively. By rotating the fourth preload screw 12.4, the upper flexible symmetrical preload beam 11.1 is deformed, thereby generating a preload force to fix the fourth piezoelectric stack 10.4; when the knob of the second working slide 3.2 is rotated, the second drive transmission module 8.2 moves in the vertical direction along the surface of the working slide 6, causing the drive foot 11.4 to contact and deform with the working slide 6, generating auxiliary friction force to balance the force on the working slide 6, thereby suppressing retraction.

[0020] Example 1 (Single-layer inertial balance mode) Applying a periodic sawtooth wave signal to the second piezoelectric stack 10.2 involves the following steps: Step 1: Initial stage, an initial voltage U is applied to the second piezoelectric stack 10.2. 2_initial The value is 0, and the second piezoelectric stack is at its natural length, such as... Figure 5 As shown in (a), there is an initial contact force between the drive foot 11.4 of the first drive transmission module 8.1 and the working slide 6. The working slide 6 remains stationary, and the static friction force f it experiences is... sd Vertically upward, it balances the downward gravitational force Mg, i.e., f sd =Mg; Step Two: Driving Phase, such as Figure 5 As shown in (b), a voltage signal U is applied to the second piezoelectric stack 10.2. 2_stepInitially, the voltage signal is 0, and the second piezoelectric stack 10.2 is at its natural length. As the voltage gradually increases, the second piezoelectric stack 10.2 elongates, and the deformation of the triangular flexible hinge structure 11.2 gradually increases. This generates a coupled clamping and feeding motion at the drive foot 11.4. The clamping motion increases the normal preload of the drive foot 11.4 and the working slide 6, while the feeding motion causes the working slide 6 and the drive foot 11.4 to move downwards synchronously. The nonlinear deformation of the flexible hinge structure 11.2 causes the working slide 6 to have a downward acceleration, resulting in a force balance relationship f for the working slide 6. sd +Ma=Mg; Step 3: Voltage sag stage, such as Figure 5 As shown in (c), a sudden voltage signal U is applied to the second piezoelectric stack 10.2. 2_back During this stage, the voltage signal originates from U. 2_max The pressure drops sharply to 0, the second piezoelectric stack 10.2 quickly recovers its natural length, and the working slide 6 maintains a vertical downward motion tendency due to inertia, with static friction f sd Switching to kinetic friction f cd The direction is vertically upward. By rotating the knob of the working slide 3.1, the initial contact deformation between the drive foot 11.4 and the working slide 6 is precisely adjusted, thereby precisely controlling the initial normal contact force. This achieves a balance between inertial force, dynamic friction, and gravity at this stage, thus suppressing the retraction of the working slide 6, i.e., f. cd =Mg+F I .

[0021] Example 2 (Dual-layer cooperative friction relay mode) A periodic sawtooth wave signal is applied to the first piezoelectric stack 10.1, and a periodic reverse sawtooth wave signal is applied to the third piezoelectric stack 10.3. The specific steps are as follows: Step 1: Initial stage, such as Figure 6 As shown in (a), the initial voltage U applied to the first piezoelectric stack 10.1 1_initial The initial voltage U applied to the third piezoelectric stack is 0, which is 10.3. 3_initial For U 3_max An initial preload F exists between the drive foot 11.4 of the first drive module 8.1 and the working slide 6. 0d The second auxiliary module 8.2 has an initial preload F under the action of the second linear slide 3.2. 0a And F 0d >F 0a The working slide 6 remains stationary, and the static friction force f it experiences is... sd Vertically upward, it balances the downward gravitational force Mg, i.e., f sd =Mg; Step Two: Driving Phase, such as Figure 6As shown in (b), a rising voltage signal U1 is applied to the first piezoelectric stack 10.1. Initially, the voltage signal is 0, and the first piezoelectric stack 10.1 is at its natural length. The voltage gradually increases to U1. 1_rise The first piezoelectric stack 10.1 elongates, and the triangular flexible hinge structure 11.2 deforms gradually, driving the foot 11.4 to generate a coupled action of clamping motion and upward feeding motion; a voltage signal U is applied to the third piezoelectric stack 10.3. 3_step The initial voltage signal is U 3_max The third piezoelectric stack 10.3 is in an elongated state, and the voltage gradually decreases to 0. The third piezoelectric stack 10.3 recovers its deformation, the triangular flexible hinge structure 11.2 recovers its deformation, and the driving foot 11.4 generates a coupled action of release motion and downward feed motion; the initial preload F between the first drive transmission module 8.1 and the working slide 6 0d The initial preload F between the second drive module 8.2 and the working slide 6 is less than the initial preload F. 0a The working slide 6 moves upward synchronously with the first drive transmission module 8.1, with an acceleration of a1. The frictional forces acting on the working slide 6 are the vertically upward static frictional forces f from the first drive transmission module 8.1. sd The vertically downward dynamic friction force f from the second drive module 8.2 ca There exists a force balance relationship f sd +Ma1=Mg+f ca ; Step 3: Secondary driving stage, such as Figure 6 As shown in (c), the voltage signal U1 of the first piezoelectric stack 10.1 continues to increase to U 1_max The voltage U3 of the third piezoelectric stack 10.3 increases from 0 to U 3_max As U3 increases in slope, it becomes greater than U1. The working slide 6 and the second drive module 8.2 move upward synchronously with an acceleration of a2. The frictional force on the working slide 6 comes from the vertically downward kinetic friction force f from the first drive module 8.1. cd The vertically upward static friction force f from the second drive transmission module 8.2 sa There exists a force balance relationship f sa +Ma2=Mg+f cd ; Step 4: Voltage sag phase, such as Figure 6 As shown in (d), a sudden voltage signal U is applied to the first piezoelectric stack 10.1. 1_back During this stage, the voltage signal originates from U. 1_max The voltage drops sharply to 0, the first piezoelectric stack 10.1 quickly recovers its natural length, and the voltage of the third piezoelectric stack 10.3 rises to U. 3_maxAnd maintain; the frictional force on the working slide 6 comes from the vertically downward dynamic frictional force f of the first drive transmission module 8.1. cd and the upward kinetic friction force f from the second drive module 8.2 ca By rotating the knobs of the first linear slide 3.1 and the second linear slide 3.2, the initial contact deformation between the drive foot 11.4 of the first drive transmission module 8.1 and the second drive transmission module 8.2 and the working slide 6 is adjusted respectively, thus achieving force balance. ca +F I =Mg+f cd This suppresses the retraction motion of the working slide 6.

[0022] In summary, this invention proposes a vertical piezoelectric stick-slip drive platform based on an inertial-friction dynamic balance method to suppress backlash, solving the problem of vertical gravity load and exhibiting high load-bearing capacity and load adaptability. Based on the proposed inertial-friction dynamic balance method, a single-layer inertial friction balance mode and a double-layer cooperative friction relay mode are derived. By adjusting the initial contact deformation between the single or double layer and the working slide, force balance during the backlash phase is achieved, effectively suppressing backlash motion during the vertical stick-slip drive process and improving vertical drive accuracy and system stability.

[0023] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A vertical piezoelectric stick-slip drive platform based on an inertial-friction dynamic equilibrium method to suppress backlash, characterized in that, The vertical piezoelectric stick-slip drive platform includes a base (1), a support base (2), a first linear slide (3.1), a second linear slide (3.2), a first connector (4.1), a second connector (4.2), a first right-angle adapter plate (5.1), a second right-angle adapter plate (5.2), a working slide (6), a first crossed roller guide rail (7.1), a second crossed roller guide rail (7.2), a first drive transmission module (8.1), and a second drive transmission module (8.2); specifically: The base (1) is a horizontally placed flat plate structure; The support base (2) is a vertical plate, and its bottom is fixedly installed on the base (1) and located on one side; the first cross roller guide (7.1) and the second cross roller guide (7.2) are fixedly installed on the vertical side of the support base (2), which enables the working slide (6) and the support base (2) to generate relative movement in the vertical direction; The first linear slide (3.1) and the second linear slide (3.2) have the same structure and are symmetrically installed on the base (1) on the other side. Each linear slide is equipped with a right-angle adapter plate through a connector, and a drive transmission module is installed on the right-angle adapter plate. The components include a first connector (4.1), a second connector (4.2), a first right-angle adapter plate (5.1) and a second right-angle adapter plate (5.2), a first drive transmission module (8.1), and a second drive transmission module (8.2). Specifically, the first connector (4.1) and the second connector (4.2) are respectively fixedly installed on the first linear slide (3.1). The first right-angle transition plate (5.1) and the second right-angle transition plate (5.2) are fixedly installed on the first connector (4.1) and the second connector (4.2); the first drive transmission module (8.1) and the second drive transmission module (8.2) are respectively installed on the opposite vertical sides of the first right-angle transition plate (5.1) and the second right-angle transition plate (5.2), wherein the first drive transmission module (8.1) is a drive module used to vertically drive the working slide (6), and the second drive transmission module (8.2) is an auxiliary module used to balance the force on the working slide (6) and suppress retraction.

2. The vertical piezoelectric stick-slip drive platform for suppressing backlash based on the inertia-friction dynamic balance method according to claim 1, characterized in that, Both the first drive transmission module (8.1) and the second drive transmission module (8.2) consist of piezoelectric stacks, flexible structures, and preload screws. The two piezoelectric stack structures are different, but the flexible structures are the same. Specifically: The flexible structures of the first drive transmission module (8.1) and the second drive transmission module (8.2) both include a symmetrical flexible preload beam (11.1), a triangular flexible hinge structure (11.2), a flexible hinge frame (11.3), and a drive foot (11.4), which are manufactured as a single unit. The piezoelectric stack of the first drive transmission module (8.1) includes a first piezoelectric stack (10.1) and a second piezoelectric stack (10.2), and the preload screws include a first preload screw (12.1) and a second preload screw (12.2). The piezoelectric stack of the second drive transmission module (8.2) includes a third piezoelectric stack (10.3) and a fourth piezoelectric stack (10.4), and the preload screws include a third preload screw (12.3) and a fourth preload screw (12.4).

3. A vertical piezoelectric stick-slip drive platform for suppressing backlash based on an inertial-friction dynamic balance method according to claim 2, characterized in that, In the first drive transmission module (8.1): The flexible structure is a symmetrical structure, containing two sets of identical symmetrical flexible preload beams (11.1), symmetrically distributed on the upper and lower sides inside the flexible hinge frame (11.3); the triangular flexible hinge structure (11.2) is located in the middle of the two sets of symmetrical flexible preload beams (11.1), and is connected to the flexible hinge frame (11.3) through the symmetrical flexible preload beams (11.1) on the upper and lower sides; the first preload screw (12.1) is installed in the threaded hole on the lower surface of the flexible hinge frame (11.3), and the second preload screw (12.2) is installed in the threaded hole on the upper surface of the flexible hinge frame (11.3); The first piezoelectric stack (10.1) is a vertically upward driving source; the upper and lower surfaces of the first piezoelectric stack (10.1) are in contact with the lower surface of the flexible symmetrical flexible preload beam (11.1) and the bottom surface of the first preload screw (12.1), respectively. By rotating the first preload screw (12.1), the flexible symmetrical flexible preload beam (11.1) is deformed, thereby generating a preload force to fix the first piezoelectric stack (10.1); The second piezoelectric stack (10.2) is a vertically downward driving source; the upper and lower surfaces of the second piezoelectric stack (10.2) are in contact with the bottom surface of the second pre-tightening screw (12.2) and the upper surface of the flexible symmetrical pre-tightening beam (11.1), respectively. By rotating the second pre-tightening screw (12.2), the upper flexible symmetrical pre-tightening beam (11.1) is deformed, thereby generating a pre-tightening force to fix the second piezoelectric stack (10.2); When the knob of the first linear slide (3.1) is rotated, the first drive transmission module (8.1) moves in the vertical direction along the surface of the working slide (6), causing the drive foot (11.4) to make contact deformation with the working slide (6) to balance the gravity of the working slide (6) and generate driving force.

4. A vertical piezoelectric stick-slip drive platform for suppressing backlash based on an inertial-friction dynamic balance method according to claim 3, characterized in that, In the first drive transmission module (8.1): The lower flexible symmetrical flexible pre-tightening beam (11.1) and the first pre-tightening screw (12.1) form the mounting groove for the first piezoelectric stack (10.1); the upper flexible symmetrical flexible pre-tightening beam (11.1) and the second pre-tightening screw (12.2) form the mounting groove for the second piezoelectric stack (10.2).

5. A vertical piezoelectric stick-slip drive platform for suppressing backlash based on an inertial-friction dynamic balance method according to claim 4, characterized in that, In the second drive transmission module (8.2): The first drive transmission module (8.1) and the second drive transmission module (8.2) have the same flexible structure composition and layout, and the overall structure is symmetrical; the third pre-tightening screw (12.3) is installed in the threaded hole on the lower surface of the flexible hinge frame (11.3), and the fourth pre-tightening screw (12.4) is installed in the threaded hole on the upper surface of the flexible hinge frame (11.3); The third piezoelectric stack (10.3) is a vertically upward auxiliary drive source; the upper and lower surfaces of the third piezoelectric stack (10.3) are in contact with the lower surface of the flexible symmetrical pre-tightening beam (11.1) and the bottom surface of the third pre-tightening screw (12.3), respectively. By rotating the third pre-tightening screw (12.3), the flexible symmetrical pre-tightening beam (11.1) is deformed, thereby generating a pre-tightening force to fix the third piezoelectric stack (10.3); the upper and lower surfaces of the fourth piezoelectric stack (10.4) are in contact with the bottom surface of the fourth pre-tightening screw (12.4) and the upper surface of the flexible symmetrical pre-tightening beam (11.1), respectively. By rotating the fourth pre-tightening screw (12.4), the upper flexible symmetrical pre-tightening beam (11.1) is deformed, thereby generating a pre-tightening force to fix the fourth piezoelectric stack (10.4); When the knob of the second linear slide (3.2) is rotated, the second drive module (8.2) moves in the vertical direction along the surface of the working slide (6), causing the drive foot (11.4) to make contact deformation with the working slide (6), generating auxiliary friction force, balancing the force on the working slide (6), and thus suppressing retraction.

6. A vertical piezoelectric stick-slip drive platform for suppressing backlash based on an inertial-friction dynamic balance method according to claim 5, characterized in that, In the second drive transmission module (8.2): The lower flexible symmetrical flexible preload beam (11.1) and the third preload screw (12.3) form the mounting groove for the third piezoelectric stack (10.3), and the upper flexible symmetrical flexible preload beam (11.1) and the fourth preload screw (12.4) form the mounting groove for the fourth piezoelectric stack (10.4).

7. A vertical piezoelectric stick-slip drive platform for suppressing backlash based on an inertial-friction dynamic balance method according to claim 6, characterized in that, The working slide (6) is mounted on the first cross roller guide (7.1) and the second cross roller guide (7.2).

8. A vertical piezoelectric stick-slip drive method based on inertia-friction dynamic equilibrium to suppress backlash, characterized in that, Based on the vertical piezoelectric stick-slip drive platform described in any one of claims 1-7, before the vertical piezoelectric stick-slip drive platform is put into operation, the knob of the first linear slide (3.1) is rotated to generate a normal contact force by the contact deformation between the drive foot (11.4) of the first drive module 8.1 and the working slide (6), so that the static friction force of the working slide (6) and gravity are in equilibrium, and the working slide (6) remains stationary in the vertical direction in the initial pre-tightened state; the knob of the second linear slide (3.2) is rotated to position the second drive transmission module (8.2) in a specific position; The vertical piezoelectric stick-slip drive method has two modes: a single-layer inertial balance mode and a double-layer cooperative friction relay mode. The single-layer inertial balance mode is used for vertical downward drive, with the first drive transmission module (8.1) driving in a single layer and the second piezoelectric stack (10.2) being the sole drive source. The double-layer cooperative friction relay mode is used for vertical upward drive, with the first drive transmission module (8.1) and the second drive transmission module (8.2) driving in tandem, the first piezoelectric stack (10.1) being the drive source and the third piezoelectric stack (10.3) being the auxiliary drive source.

9. A vertical piezoelectric stick-slip drive method for suppressing backlash based on an inertial-friction dynamic equilibrium method according to claim 8, characterized in that, In the single-layer inertial balance mode, for vertical downward driving, the first drive transmission module (8.1) participates in the driving, while the second drive transmission module (8.2) does not participate in the driving. The specific steps are as follows: Step 1: Applying an initial voltage U to the second piezoelectric stack (10.2) 2_initial The initial contact force is 0, meaning there is an initial contact force between the drive foot (11.4) of the first drive transmission module (8.1) and the working slide (6). The working slide (6) remains stationary, and the static friction force f is zero. sd Vertically upward, it balances the downward gravitational force Mg, i.e., f sd =Mg; Step 2: Apply a voltage signal U to the second piezoelectric stack (10.2). 2_step Initially, the voltage signal is 0, and the second piezoelectric stack (10.2) is at its natural length. As the voltage gradually increases, the second piezoelectric stack (10.2) elongates, and the deformation of the triangular flexible hinge structure (11.2) gradually increases. The driving foot (11.4) generates a coupled action of clamping motion and feeding motion. The clamping motion increases the normal preload of the driving foot (11.4) and the working slide (6). The feeding motion causes the working slide (6) and the driving foot (11.4) to move downward synchronously. The nonlinear deformation of the flexible hinge structure 11.2 causes the working slide (6) to have a downward acceleration. The working slide (6) has a force balance relationship f. sd +Ma=Mg; Step 3: Apply a sudden drop in voltage signal U to the second piezoelectric stack (10.2). 2_back During this stage, the voltage signal originates from U. 2_max The length of the second piezoelectric stack (10.2) drops rapidly to 0, and the working slide (6) maintains a vertical downward motion due to inertia. The static friction force f sd Switching to kinetic friction f cd The direction is vertically upward. By rotating the knob of the first linear slide (3.1), the initial contact deformation between the drive foot (11.4) and the working slide (6) is precisely adjusted, thereby accurately controlling the initial normal contact force and achieving a balance between inertial force, dynamic friction force and gravity at this stage, thus suppressing the retraction of the working slide (6), i.e., f cd =Mg+F I .

10. A vertical piezoelectric stick-slip drive method for suppressing backlash based on an inertial-friction dynamic equilibrium method according to claim 8, characterized in that, The aforementioned dual-layer cooperative friction relay mode is used for vertical upward driving. The second driving module 8.1 and the second auxiliary module 8.2 cooperate for driving, and the specific steps are as follows: Step 1: Applying an initial voltage U to the first piezoelectric stack (10.1) 1_initial The initial voltage U applied to the third piezoelectric stack (10.3) is 0. 3_initial For U 3_max An initial preload F exists between the drive foot (11.4) of the first drive module 8.1 and the working slide (6). 0d The second auxiliary module 8.2 has an initial preload F under the action of the second linear slide (3.2). 0a And F 0d >F 0a The working slide (6) remains stationary, and the static friction force f it experiences is... sd Vertically upward, it balances the downward gravitational force Mg, i.e., f sd =Mg; Step 2: Apply a rising voltage signal U1 to the first piezoelectric stack (10.1). Initially, the voltage signal is 0, and the first piezoelectric stack (10.1) is at its natural length. The voltage gradually increases to U1. 1_rise The first piezoelectric stack (10.1) elongates, the triangular flexible hinge structure (11.2) deforms gradually, and the driving foot (11.4) generates a coupled action of clamping motion and upward feeding motion; a voltage signal U is applied to the third piezoelectric stack (10.3). 3_step The initial voltage signal is U 3_max The third piezoelectric stack (10.3) is in an elongated state, and the voltage gradually decreases to 0. The third piezoelectric stack (10.3) recovers its deformation, the triangular flexible hinge structure (11.2) recovers its deformation, and the driving foot (11.4) generates a coupled action of release motion and downward feed motion; the initial preload F between the first drive transmission module (8.1) and the working slide (6) 0d The initial preload F between the second drive module (8.2) and the working slide (6) is less than the initial preload F. 0a The working slide (6) moves upward synchronously with the first drive transmission module (8.1) with an acceleration of a1. The frictional forces acting on the working slide (6) are the vertically upward static frictional forces f from the first drive transmission module (8.1). sd The vertically downward dynamic friction force f from the second drive module (8.2) ca There exists a force balance relationship f sd +Ma1=Mg+f ca ; Step 3: The voltage signal U1 of the first piezoelectric stack (10.1) continues to increase to U 1_max The voltage U3 of the third piezoelectric stack (10.3) increases from 0 to U 3_max As U3 increases in slope, it becomes greater than U1. The working slide (6) and the second drive transmission module (8.2) move upward synchronously with an acceleration of a2. The frictional force on the working slide (6) comes from the vertically downward kinetic friction force f from the first drive transmission module (8.1). cd The vertically upward static friction force f from the second drive transmission module (8.2) sa There exists a force balance relationship f sa +Ma2=Mg+f cd ; Step 4: Apply a sudden drop in voltage signal U to the first piezoelectric stack (10.1). 1_back During this stage, the voltage signal originates from U. 1_max The voltage drops sharply to 0, the first piezoelectric stack (10.1) quickly recovers its natural length, and the voltage of the third piezoelectric stack (10.3) rises to U. 3_max And maintain; the frictional force on the working slide (6) comes from the vertically downward dynamic frictional force f from the first drive transmission module (8.1). cd and the upward kinetic friction force f from the second drive module (8.2) ca By rotating the knobs of the first linear slide (3.1) and the second linear slide (3.2), the initial contact deformation between the drive feet (11.4) of the first drive transmission module (8.1) and the second drive transmission module (8.2) and the working slide (6) is adjusted respectively, thereby achieving force balance. ca +F I =Mg+f cd This suppresses the retraction motion of the working slide (6).

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