A self-rotating intelligent continuous pushing device and method for a steel-concrete composite beam bridge
By using a self-rotating intelligent continuous jacking device, the tray is rotated by vertical power components and rotating components with adjustable height, and the tilt angle is changed alternately. This solves the problems of large damage and low efficiency of existing bridge jacking methods, and realizes low-damage and high-efficiency bridge advancement.
Patent Information
- Application Number
- CN202411759377.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-03
- Publication Date
- 2025-10-17
- Estimated Expiration
- 2044-12-03
AI Technical Summary
Existing bridge launching methods are prone to causing significant damage to the bridge structure and have low construction efficiency. In particular, in the construction of large-span prefabricated beam bridges, the dragging and walking launching methods suffer from low efficiency and poor precision.
The system employs a self-rotating intelligent continuous jacking device, consisting of two sets of self-rotating jacking devices, each composed of four minimum units. The system utilizes adjustable vertical adjustment power components and rotating components to drive the tray to rotate, alternating the tilt angle to achieve continuous advancement of the beam. High-strength rubber pads are fitted onto the surface of the tray to protect the beam.
It achieves low-damage and high-efficiency beam advancement, reduces construction offset, improves construction accuracy and quality, and reduces construction costs and energy consumption.
Smart Images

Figure CN119531270B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of assembled bridge construction, in particular to a self-rotating intelligent continuous jacking device and method for a steel-concrete composite beam bridge. BACKGROUND
[0002] Assembled bridges have the advantages of short construction period and green environmental protection. At present, due to the lack of large hoisting equipment for long-span assembled beam bridges, the jacking method has become the preferred scheme for the superstructure construction of long-span assembled steel-concrete composite beam bridges. The jacking method construction can reduce the quality problems of on-site manual operation, reduce labor, improve engineering quality and progress. At present, the main jacking methods for bridges in China are the tractor type and the walking type. The tractor type jacking construction is easy to cause damage to the beam body and has low efficiency. During the pushing process, the beam body on one side is easy to be lifted. The walking type jacking method has high cost. Due to the discontinuity in the pushing process, the jacking speed is low. Moreover, for curved beam bridges, the construction efficiency and precision of the tractor type and walking type jacking construction methods are further reduced.
[0003] To solve the above problems, the present application aims to provide a self-rotating intelligent continuous jacking device for long-span assembled steel-concrete composite beam bridges. This jacking device not only has low cost and low energy consumption, but also causes less damage to the bridge. It continuously pushes with a small offset, simplifies the construction process, and improves the jacking construction efficiency of the superstructure of long-span assembled steel-concrete composite beam bridges. SUMMARY
[0004] In view of the deficiencies of the prior art, the present application provides a self-rotating intelligent continuous jacking device and method for a steel-concrete composite beam bridge, which solves the problem that the current jacking method for bridges in China is easy to cause damage to the beam body and has low construction efficiency.
[0005] To achieve the above purpose, the present application is implemented by the following technical scheme: a self-rotating intelligent continuous jacking device for a steel-concrete composite beam bridge, which comprises two groups of self-rotating jacking devices, each group consisting of four minimum units, and the minimum unit comprises:
[0006] a base for supporting the entire device body, on the upper part of which an adjustable height vertical adjusting power member is installed;
[0007] a rotating member installed on the upper part of the vertical adjusting power member, for driving the tray installed on the upper part to rotate, and the surface of the tray is sleeved with a rubber pad for buffering contact with the beam bridge;
[0008] The rotating member changes the inclination angle of the tray under the adjustment of the vertical adjustment power member, the inclination angle of the tray in all the minimum units is the same and less than 45°, and during construction, the inclination angle of the tray is alternately changed to the left and to the right, and meanwhile, the drive motors in the two groups of self-rotating jacking devices are alternately started in forward rotation and reverse rotation to drive the tray to rotate counterclockwise or clockwise, and the beam body in contact with the surface rubber pad of the tray realizes continuous advancement under the action of the rotating friction force.
[0009] Preferably, the vertical adjustment power member comprises a support fixedly installed at the top end of the base, and an annular track is further arranged at the upper portion of the support, a plurality of power rods are movably installed around the bottom of the annular track.
[0010] Preferably, the rotating member comprises a rotating ring rotatably connected to the top of the annular track, a first gear rotatably installed at the middle portion of the annular track, and the tray is installed at the upper portion of the first gear, and a drive motor is further installed at one side of the middle portion of the annular track, and the output end of the drive motor is fixedly connected with a second gear meshingly connected with the first gear, and the drive motor is used to drive the tray fixedly connected therewith to rotate.
[0011] A pushing method of a self-rotating intelligent continuous pushing device for a steel-concrete composite beam bridge, comprising the following method steps:
[0012] S1, installation of the device: first, install the minimum units in the two groups of self-rotating jacking devices on the bridge pier or the temporary support device, and adjust the preset angle of the minimum units, and complete the preparation work;
[0013] S2, installation of the automatic positioning device: before construction, set a plurality of displacement measuring points on the precast beam body, and input the theoretical displacement values of the measuring points into the Beidou displacement automatic acquisition receiving equipment terminal;
[0014] S3, pushing construction: alternately start the drive motors in the minimum units in the two groups of self-rotating jacking devices to drive the second gear to rotate, so that the first gear drives the tray with the rubber pad sleeved thereon to rotate, and under the action of the rotating friction force, the beam body is realized to be alternately and continuously pushed forward;
[0015] S4, displacement adjustment: when the measured maximum horizontal transverse bridge displacement exceeds the maximum allowable deviation value of the beam body in the horizontal transverse bridge direction , the control device is reversely operated until the relative difference between the final position of the beam body and the theoretical position satisfies formula (3), and the pushing construction is completed.
[0016] Preferably, in the S2 step, the Beidou displacement automatic acquisition receiving equipment terminal automatically acquires the displacement values of the beam body at each measuring point in the pushing process in real time, and the displacement acquisition frequency satisfies the following formula:
[0017]
[0018] In the formula, f is the displacement acquisition frequency of the beam body (Hz) ; is the maximum allowable deviation value of the beam body in the bridge direction (m) ; r is the radius of the tray of the device (m) ; and ω is the angular velocity of the rotation of the tray driven by the first gear (rad / s).
[0019] Preferably, in the S3 step, the actual displacement values of the measuring points are collected in real time by the Beidou displacement automatic collection and receiving device when the beam bridge is pushed, data comparison is made according to the actual displacement values and the theoretical displacement values of the beam bridge, and the running state of the device is adjusted. The displacement of each measuring point during the pushing process needs to satisfy the following formula:
[0020] ω1≤r2ω / r1 Formula (2)
[0021] In formula (2), ω1 is the rotation angular velocity of the second gear (rad / s) ; r1 is the rotation radius of the second gear (m) ; and r2 is the rotation radius of the first gear (m).
[0022] Preferably, in the S4 step, the relative difference between the final position of the beam body and the theoretical position satisfies the following formula:
[0023]
[0024] In formula (3), Δxi is the difference between the horizontal displacement of the i-th measuring point in the transverse direction of the bridge and the theoretical value (m) ; is the maximum allowable deviation value of the beam body in the transverse direction of the bridge (m) ; in formula (4), is the difference between the horizontal displacement of the i-th measuring point in the longitudinal direction of the bridge and the theoretical value (m).
[0025] The present application provides a self-rotating intelligent continuous pushing device and method for a steel-concrete composite beam bridge. The device has the following beneficial effects:
[0026] 1. The vertical adjusting power member with adjustable height is arranged, the angle of the tray can be adjusted, and the inclination angle of the tray is alternately changed to the left and the right during construction. Meanwhile, the driving motors in the two groups of self-rotating jacking devices are alternately started and reversed, the tray is driven to rotate counterclockwise or clockwise, the beam body in contact with the surface rubber pad of the tray is continuously pushed with a small offset under the action of the rotating friction force, and the construction efficiency and precision are high.
[0027] 2. The oval high-strength tray with a rubber pad arranged on the surface is arranged to contact the beam body, the beam body can be effectively protected from damage, the construction progress is improved, and the construction quality is ensured. BRIEF DESCRIPTION OF DRAWINGS
[0028] Figure 1 A perspective view of the device of the present application;
[0029] Figure 2 A sectional view of the partial structure of the present application;
[0030] Figure 3 An exploded view of the structure of the present application;
[0031] Figure 4 A top view of the partial structure of the present application;
[0032] Figure 5 A schematic view of the power rod height adjustment state of the present application;
[0033] Figure 6 A perspective view of the present application in use;
[0034] Figure 7 A layout diagram of the device of the present application in the bridge installation in the pushing construction;
[0035] Figure 8 A-A sectional view of the present application; Figure 7
[0036] Figure 9 A flow chart of the present application.
[0037] Wherein, 1, base; 2, support; 3, power rod; 4, annular track; 5, rotating ring; 6, first gear; 7, drive motor; 8, second gear; 9, tray. DETAILED DESCRIPTION
[0038] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.
[0039] Please refer to the drawings in the following Figure 1 - the drawings in the following Figure 9 The application provides a self-rotating intelligent continuous jacking device for a steel-concrete composite beam bridge, which comprises two groups of self-rotating jacking devices, each group being composed of four minimum units, and has the characteristics of low cost, low energy consumption, small damage to the beam body, continuous pushing and small offset, and is suitable for the construction of the superstructure of a fabricated large-span steel-concrete composite beam bridge. The minimum unit comprises a base 1 for supporting the whole device, an adjustable height vertical adjusting power member mounted on the upper part of the base 1, a rotating member mounted on the top of the vertical adjusting power member, and a tray 9 for contacting the beam bridge mounted on the upper part of the rotating member. A layer of high-strength rubber pad is arranged on the surface of the tray 9, which mainly serves to prevent the tray 9 from damaging the beam body when the tray 9 contacts the beam body and to provide buffering effect.
[0040] Before construction, two groups of self-rotating intelligent continuous jacking devices are prepared for jacking the beam bridge, each group being equipped with four jacking devices, which are minimum units. Each jacking device further comprises four height-adjustable power rods 3, the top of each power rod 3 is movably connected with the lower part of a ring track 4, and the bottom of each power rod 3 is movably mounted on the upper part of a support 2 around the four power rods 3, which serves to provide mounting positions for the four power rods 3. The base 1 for increasing the supporting area of the device is mounted on the lower part of the support 2.
[0041] The inclination angle of the ring track 4 can be changed by adjusting the power rods 3 perpendicular to the plane of the ring track 4. A rotating ring 5 is rotatably connected to the outer circle of the upper part of the ring track 4, which mainly serves to provide auxiliary support for the lower part of the tray 9. A first gear 6 is mounted on the middle part of the ring track 4, and a driving motor 7 is further mounted on one side of the middle part of the ring track 4, the output end of the driving motor 7 is fixedly connected with a second gear 8 which is meshingly connected with the first gear 6, the second gear 8 serves to drive the tray 9 to rotate and generate a rotating friction force. The two groups of self-rotating jacking devices are alternately changed in the inclination angle of the tray 9 to continuously push the beam body with small offset.
[0042] In the device, the main function of the power rods 3 is to jack up the beam body, and the inclination angle of the tray 9 is adjusted by adjusting the extension degrees of the different power rods 3.
[0043] Specifically, the rotating member drives the tray 9 to change the inclination angle under the adjustment of the vertical adjusting power member. During construction, the inclination angle of the tray 9 is alternately changed to the left and right, and the driving motors 7 in the two groups of self-rotating jacking devices are alternately started and reversed to drive the tray 9 to rotate counterclockwise or clockwise. The beam body contacting the rubber pad on the surface of the tray 9 is continuously pushed under the action of the rotating friction force.
[0044] Further, in the application, the inclination angle of the tray 9 is determined according to the pushing direction, the inclination angle is the same and does not exceed 45°, and the extension degrees of the four power rods 3 in each device are consistent.
[0045] Please refer to the attached Figure 5 - attached Figure 6 As shown, the angle of the tray 9 is changed by adjusting the height of the four adjustable power rods 3, so that the predetermined contact surface of the tray 9 is in contact with the bottom surface of the beam body, the tray 9 is tightly mounted on the rotating ring 5, which can be bonded or connected and fixed by a special nut, and the size of the tray 9 matches the rotating ring 5, and the first gear 6 in the device drives the rotation of the tray 9, and the thickness of the tray 9 can be matched according to the length and weight of the pushing beam body to prevent damage to the beam body.
[0046] The device will be further described in conjunction with specific embodiments:
[0047] Please refer to the attached Figure 9 The working principle of the self-rotating intelligent continuous pushing device provided in the embodiment is as follows:
[0048] Firstly, the smallest unit in the device is divided into two groups, each group has four units mounted on a pier or a temporary support device, and then the beam body is arranged at the top of the device;
[0049] Secondly, the height of the rod body of the power rod 3 in the device is adjusted, and the angle of the tray in each smallest unit is adjusted to 30° to the left, the power rod 3 is a hydraulic rod, a jack or other device with pushing function, which is a prior component in the field, and in the embodiment, the power rod 3 is a jack;
[0050] Thirdly, the displacement measuring point is installed on the beam body, and then the theoretical displacement value of the measuring point is input into the Beidou displacement automatic acquisition receiving equipment terminal, which is a terminal Beidou remote displacement measurement system, the system model is JMBD-1050, and the dynamic positioning plane accuracy is ±8mm, which is used as an automatic positioning device for the beam bridge in the embodiment;
[0051] Fourthly, the displacement acquisition frequency of the measuring point is adjusted according to formula 1:
[0052]
[0053] In formula 1, f is the displacement acquisition frequency (Hz); is the maximum allowable deviation value (m) of the beam body in the bridge direction, r is the radius (m) of the tray 9 of the device, and ω is the angular velocity (rad / s) of the rotation of the tray 9 driven by the first gear 6; when the data acquisition frequency of the measuring point meets formula 1, the automatic positioning device in the embodiment runs, otherwise the value of the acquisition frequency f is increased until f is greater than or equal to The automatic positioning device starts to work;
[0054] Step 5. When the automatic positioning device starts to operate, the power device in the device starts to operate. In this embodiment, the power device is the rotating component mentioned above. The rotating component is equipped with a controller. The controller is electrically connected to the drive motor 7 and can adjust the drive motor 7 to rotate forward or reverse. At the same time, corresponding forward rotation control buttons and reverse rotation control buttons are also provided. During specific operation, the displacement of each measuring point must satisfy Formula 2:
[0055] ω1≤r2ω / r1 Equation 2
[0056] In formula 2, ω1 is the angular velocity of the second gear, (rad / s); r1 is the rotation radius of the second gear, (m); r2 is the rotation radius of the first gear, (m);
[0057] In this process, first, by pressing the forward rotation control button, the controller starts the forward rotation of the drive motor 7 in each minimum unit, driving the tray to rotate counterclockwise, causing the beam to deflect to the left and move forward. During the forward movement, the Beidou displacement automatic acquisition and receiving device terminal will compare the collected actual displacement value of the beam bridge with the theoretical displacement value. When the measuring point position does not satisfy Formula 2, the reverse rotation control button is activated to reverse the drive motor 7, allowing the beam to return to the theoretical offset position.
[0058] Step 6. After the beam is pushed to the preset pushing position, the height of the jack in the smallest unit is adjusted to drive the tray 9 to tilt to the right. At this time, the forward rotation control button is turned on to send a signal to the controller, and the controller starts the reverse rotation of the drive motor, driving the tray to rotate clockwise, so that the beam moves forward to the right. During this process, the Beidou displacement automatic acquisition and receiving equipment terminal maintains the same working state as the above process, and compares the actual displacement value of the beam bridge with the theoretical displacement value. When the measuring point position does not satisfy Formula 2, the reverse rotation control button is turned on to reverse the drive motor 7, driving the tray 9 to rotate counterclockwise, and then the beam returns to the theoretical offset position.
[0059] Step 7: When the beam is pushed to the final position, the relative difference with the theoretical position meets the standard
[0060] The formula is as follows:
[0061]
[0062] In formula (3), is the difference between the horizontal displacement of the bridge at the i-th measuring point and the theoretical value, (m); The maximum allowable deviation value of the beam body in the transverse bridge direction is m, when the deviation value of the beam body in the transverse bridge direction is less than the maximum allowable deviation value, the construction can be ended, when the deviation value of the beam body in the transverse bridge direction is greater than the maximum allowable deviation value, the reverse rotation control button is started again, so that the driving motor 7 reverses to drive the tray 9 to rotate, the displacement of the beam body is generated, the deviation value of the beam body in the transverse bridge direction is adjusted, until formula (3) is satisfied, and the construction can be ended.
[0063] Further, the embodiment of the present application also provides a pushing method of the self-rotating intelligent continuous pushing device for the steel-concrete composite beam bridge.
[0064] S1, as shown in the figure, before construction, the smallest unit in the two groups of self-rotating jacking devices needs to be installed on the pier or the temporary supporting device, and the preset angle of the smallest unit is adjusted, and the preparation work is completed. Figure 7
[0065] S2, install the automatic positioning device: set the displacement measuring point on the beam body, input the theoretical displacement value of the measuring point into the Beidou displacement automatic acquisition receiving equipment terminal Beidou remote displacement measurement system JMBD-1050 before pushing construction, and the dynamic positioning plane accuracy is ±8mm.
[0066] In this step, the displacement acquisition frequency needs to satisfy formula 1:
[0067]
[0068] In formula 1, f is the displacement acquisition frequency of the beam body (Hz); The maximum allowable deviation value of the beam body in the transverse bridge direction is m; r is the radius of the tray 9 (m); and ω is the angular velocity of the rotation of the tray 9 driven by the first gear 6 (rad / s).
[0069] S3, pushing construction: alternately start the driving motor in the smallest unit of the two groups of self-rotating jacking devices to drive the second gear to rotate, so that the first gear drives the tray 9 with the rubber pad to rotate, under the action of the rotating friction force, the alternating continuous pushing of the beam body is realized, in this step, the actual displacement value of the measuring point is collected in real time by the Beidou displacement automatic acquisition receiving equipment when the beam bridge is pushed, the data comparison is made according to the actual displacement value and the theoretical displacement value of the beam bridge, and the running state of the device is adjusted, and the running state specifically refers to the inclination direction, angle and rotation direction of the tray 9.
[0070] In this step, the displacement of each measuring point needs to satisfy formula 2:
[0071] ω1≤r2ω / r1 Formula 2
[0072] In formula 2, ω1 is the rotation angular velocity of the second gear, (rad / s); r1 is the rotation radius of the second gear, (m); and r2 is the rotation radius of the first gear, (m); is the difference between the actual transverse horizontal displacement of the ith measuring point and the theoretical value, (m); is the maximum allowable deviation value of the beam body in the transverse direction, (m);
[0073] S4, displacement adjustment: when the actual maximum horizontal transverse displacement exceeds the maximum allowable deviation value of the beam body in the transverse direction , the control device performs reverse operation until the relative difference between the final position of the beam body and the theoretical position satisfies formula 3, and the jacking construction is completed.
[0074] In this step, the test results of each displacement measuring point should satisfy formula 3.
[0075]
[0076] In formula 3, is the difference between the actual transverse horizontal displacement of the ith measuring point and the theoretical value, (m); is the maximum allowable deviation value of the beam body in the transverse direction, (m).
[0077]
[0078] In formula (4), is the difference between the actual longitudinal horizontal displacement of the ith measuring point and the theoretical value, (m).
[0079] By performing the above steps, the device can accurately, quickly and safely push the precast beam body to the predetermined position. The height-adjustable vertical adjustment power member can push the beam body with a small offset amount by adjusting the angle of the elliptical high-strength tray 9, and can realize continuous pushing during the entire construction process. The elliptical high-strength tray 9 is provided with a rubber pad, which can effectively protect the beam body from damage, improve the construction progress, and ensure the construction quality. The device as a whole has good application value.
[0080] Although embodiments of the present application have been shown and described, it is to be understood that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.
Claims
1. A method for jacking a steel-concrete composite beam bridge using a self-rotating intelligent continuous jacking device, characterized in that: The pushing device comprises two sets of self-rotating lifting devices, each set consisting of four minimum units, the minimum unit including: A base (1) for supporting the entire device body, with a height-adjustable vertical power component mounted on its upper portion; A rotating member, which is mounted on the upper portion of the vertical adjustment power member and is used to drive a tray (9) mounted on the upper portion thereof to rotate, wherein the surface of the tray (9) is provided with a rubber pad for buffering contact with the beam bridge; The rotating member changes the tilt angle of the tray (9) under the adjustment of the vertical adjustment power member. In all minimum units, the tilt angle of the tray (9) is the same and less than 45 degrees. During construction, the tray (9) changes its tilt angle alternately to the left and right. At the same time, by alternately starting the driving motors (7) in the two sets of self-rotating jacking devices to rotate forward and reverse, the tray (9) is driven to rotate counterclockwise or clockwise. The beam body in contact with the surface rubber pad of the tray (9) is alternately continuously advanced under the action of the rotating friction force. The vertical adjustment power component comprises a support (2) fixedly mounted on the top of the base (1); an annular track (4) is further provided on the upper portion of the support (2); a plurality of power rods (3) are movably mounted around the upper portion of the support (2); and the tops of the rod bodies of the plurality of power rods (3) are movably mounted around the bottom of the annular track (4); The rotating member comprises a rotating ring (5) rotatably connected to the top of the annular track (4); a first gear (6) is rotatably mounted in the middle of the annular track (4); the tray (9) is mounted on the upper part of the first gear (6); a driving motor (7) is further mounted on one side of the middle of the annular track (4); an output end of the driving motor (7) is fixedly connected to a second gear (8) meshing with the first gear (6) for driving the tray (9) fixedly connected thereto to rotate; The method specifically comprises the following steps: S1. Installation of the device: First, install the smallest unit of the two sets of self-rotating jacking devices on the bridge pier or temporary support device, and adjust the preset angle of the smallest unit to complete the preparation work; S2. Install the automatic positioning device: Before construction, set up multiple displacement measurement points on the prefabricated beam, and input the theoretical displacement values of the measurement points into the Beidou displacement automatic acquisition and receiving equipment terminal; S3, jacking construction: alternately start the driving motors (7) in the minimum units of the two self-rotating jacking devices to drive the second gear (8) to rotate, so that the first gear (6) drives the tray (9) with a rubber pad on the surface to rotate, and under the action of the rotating friction force, the beam body is alternately and continuously pushed forward; S4. Displacement adjustment: When the measured maximum horizontal transverse displacement exceeds the maximum allowable deviation of the beam body in the transverse direction When , the control device performs reverse operation until the relative difference between the final position of the beam and the theoretical position satisfies formula (3), and the jacking construction is completed; In step S4, the relative difference between the final position of the beam and the theoretical position satisfies the following formula: Formula (3) Formula (4) In formula (3), is the difference between the horizontal displacement of the bridge at the i-th measuring point and the theoretical value, (m); is the maximum allowable deviation of the beam in the transverse direction of the bridge, (m); in formula (4), is the difference between the horizontal displacement of the i-th measuring point along the bridge and the theoretical value, (m).
2. The method for pushing a steel-concrete composite beam bridge using a self-rotating intelligent continuous pushing device according to claim 1 is characterized in that: In step S2, the Beidou displacement automatic acquisition and receiving device terminal automatically acquires the displacement values of each measuring point of the beam body during the jacking process in real time. The displacement acquisition frequency satisfies the following formula: f≥rω / Formula (1) In formula (1), f is the acquisition frequency of beam displacement (Hz); is the maximum allowable deviation of the beam along the bridge direction (m); r is the radius of the tray (9) of this device (m); ω is the angular velocity (rad / s) at which the first gear (6) drives the tray (9) to rotate.
3. The method for pushing a steel-concrete composite beam bridge using a self-rotating intelligent continuous pushing device according to claim 1 is characterized in that: In step S3, when the bridge is pushed forward, the actual displacement values of the measuring points are collected in real time by the Beidou displacement automatic acquisition and receiving equipment. Data comparison is made based on the actual displacement values of the bridge and the theoretical displacement values, and the operating status of the device is adjusted. During the pushing process, the displacement of each measuring point must satisfy the following formula: ≤ ω / Formula (2) In formula (2), is the rotational angular velocity of the second gear (8), (rad / s); is the rotation radius of the second gear (8), (m); is the rotation radius of the first gear (6), (m).
Citation Information
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