A double-degree-of-freedom cosine rocking platform based on rope-tethered cam drive and design method thereof
The double-degree-of-freedom cosine type swing table driven by a rope-tied cam uses a low-speed motor and a cam structure to achieve double-degree-of-freedom swing, which solves the problems of complex control and high cost in the existing technology. It is suitable for small and medium-sized experiments and provides high precision and Flexible swing form.
Patent Information
- Application Number
- CN202411472227.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-22
- Publication Date
- 2024-12-31
- Estimated Expiration
- 2044-10-22
AI Technical Summary
When realizing double-degree-of-freedom swing motion, existing swing tables have problems such as complex control, high cost, large space occupancy and difficulty in realizing specific swing forms, which are especially not suitable for small experimental needs.
A double-degree-of-freedom cosine type swing table based on rope-type cam drive was designed. The swing table was controlled to perform double-degree-of-freedom sway through the constant rotation of two low-speed motors. Different swing forms were achieved using the cam shape, and the trapezoidal structure and the string winding mechanism were used. , simplifies device design and operation.
It realizes high-precision double-degree-of-freedom swing, is easy to operate, adapts to various experimental sites, meets the needs of small and medium-sized experiments, and reduces cost and space occupation.
Smart Images
Figure CN119004707B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of rocking platforms, and relates to a double-degree-of-freedom cosine rocking platform device, and in particular to a double-degree-of-freedom cosine rocking platform driven by a rope-type cam and a design method thereof. Background Art
[0002] When sailing in the ocean, a ship will produce six degrees of freedom motion under the action of waves: sway, surge, heave, roll, pitch and bow pitch. The study of the roll and pitch of a ship is of great significance to ship design, navigation safety and the efficiency of marine operations.
[0003] As an excellent spatial motion mechanism, the rocking table is used in aerospace, ship and offshore equipment, automotive industry, military training and other fields. The invention and use of the rocking table has an important impact on the kinematic and dynamic research of ships and marine engineering structures under marine loads. It can provide accurate simulation and analysis methods, allowing researchers to deeply understand the motion behavior and force characteristics of ships under complex marine conditions, thereby optimizing the design and improving safety and reliability.
[0004] From the perspective of domestic and foreign research, the parallel six-degree-of-freedom platform proposed by Stewart is currently more popular. However, in many cases, only a few degrees of freedom are required to move or swing in a certain plane. It is difficult for the parallel six-degree-of-freedom platform to achieve swinging motion in a single plane or a few degrees of freedom. In addition, the swing table is similar to a simple pendulum, and it is difficult and complicated to control the swing table to swing. Not only is the mathematical model nonlinear, but the control of the pendulum is also nonlinear.
[0005] Nowadays, most swing tables use complex hydraulic control systems, such as the patent "A servo device for a swing table" (application number: 202120425430.3). The structure of this swing table is not only complex, but also cumbersome to operate, and the device itself is costly. Small-scale swing experiments are not suitable for such complex swing tables, but are more suitable for simple, easy-to-operate, and low-cost swing tables, such as the patent "A swing table" (application number: 202022661901.9). For most swing experiments, the required swing form is often in the form of trigonometric functions, and the production of the above-mentioned simple swing table does not mention how to determine the swing form. Therefore, it is very necessary to make a swing table that is simple, easy to operate, low in cost, and can determine the swing form for various small-scale swing experiments.
[0006] In response to the complex control problems of electronic control systems, many scholars have also studied mechanically controlled swing tables. However, most of them also involve electro-hydraulic drive devices such as hydraulic cylinders, and it is also difficult to use these devices to control the movement of the swing table. And because it involves devices such as hydraulic cylinders, the scale of the swing table will be large, which will occupy more experimental space and is not suitable for small swing experiments. Most of the swing tables controlled by hydraulic cylinders also have six degrees of freedom, and it is difficult to achieve a two-degree-of-freedom swing motion. Therefore, it is difficult to simulate the two-degree-of-freedom swing conveniently and quickly.
[0007] In view of the above, the present invention designs a swing table structure suitable for double degrees of freedom, convenient for controlling the movement of the swing table and capable of satisfying the required swing form. The structure can control the swing table to swing with double degrees of freedom simply by rotating two low-speed motors at a constant speed, and realizes the required different swing forms by designing the cam shape. Summary of the invention
[0008] In order to overcome the defects of the prior art, the present invention provides a cosine-type swing platform with two degrees of freedom driven by a rope-type cam and a design method thereof.
[0009] In order to achieve the above object, the technical solution adopted by the present invention is:
[0010] A double-degree-of-freedom cosine-type swing platform based on rope-type cam drive, the double-degree-of-freedom cosine-type swing platform mainly consists of a swing device, a trapezoidal structure 7, two low-speed motors, two cams, and two thin ropes.
[0011] The swing device is mainly composed of a first swing platform 5, a second swing platform 12, two fixing devices, and two swing axes. The length of the first swing platform 5 is defined as L 1 , width d 1 , thickness is h 1 The second swing platform 12 is L long. 2 , width d 2 , thickness is h 2 The first swaying platform 5 is fixedly connected to the first swaying shaft 6, the first swaying shaft 6 is connected to the first fixing device 4 through a bearing, the first fixing device 4 is fixed on the ground, and it is ensured that the first swaying platform 5 and the first swaying shaft 6 can sway in one direction relative to the first fixing device 4. The second swaying platform 12 is fixedly connected to the second swaying shaft 13, the second swaying shaft 13 is connected to the second fixing device 11 through a bearing, and the second fixing device 11 is embedded in the first swaying platform 5. In this way, it can be ensured that the first swaying platform 5 sways with the second swaying platform 12 in one direction, and the second swaying platform 12 itself sways in another direction, so that the second swaying platform 12 can sway freely in two directions.
[0012] The trapezoidal structure 7 is a 3 The structure is a regular trapezoidal plate, wherein the middle horizontal plate is fixed on the first swing platform 5, and motor platforms are provided on both sides of the lower part for placing low-speed motors, which swing in one direction along with the first swing platform 5.
[0013] The low-speed motor is a device that provides a uniform rotation of the cam, which can control the speed and can rotate at a uniform and low speed. The two low-speed motor structures have the same speed. The first low-speed motor 1 is located on the ground and is connected to the groove of the width center line of the first swing platform 5 by a thin rope. The second low-speed motor 8 is located on a motor platform at the bottom of the trapezoidal structure 7 and is connected to the groove of the width center line of the second swing platform 12 by a thin rope. The second low-speed motor 8 swings in one direction along with the first swing platform 5.
[0014] There are two cams with the same structure, both of which are convex wheel-shaped structures. The plane shape of the first cam 2 is represented by the curve L 3 The thickness of the first cam 2 is h 3 , and in thickness The plane shape of the second cam 9 is defined by the curve L 4 The closed figure is formed, and the thickness of the second cam 9 is h 4 , and in thickness An inner groove is provided at the location.
[0015] Furthermore, the inner grooves of the two cams are also convex wheel-shaped structures, and the plane shapes of the inner grooves of the two cams are respectively represented by curves L 5 , L 6 The closed figure is composed of two cams with the thickness of the grooves h 5 、h 6 ; where curve L 5 , L 6 With curve L 3 , L 4 is a similar relationship, and the size ratio is L 5 =n 1 L 3 , L 6 =n 2 L 4 , of which 0.95 <n 1 <1, 0.95 <n 2 <1. Curve L 5 , L 6 The inner groove formed mainly serves to fix the thin rope that is wound around the cam as the cam rotates.
[0016] The two thin ropes are respectively l long 1 , l 2 , and the diameters are a1 、a 2 , where a 1 ≤h 5 、a 2 ≤h 6 The first string 3 is fixed at both ends, one end of which is fixed in the inner groove of the first cam 2 and is wound along with the uniform rotation of the first cam 2; the other end is fixed on the groove of the width center line of the first swing platform 5, and the distance between the groove and the first swing platform 5 is d 4 The first string 3 moves with the first swing platform 5 pulled by one end of the winding. The second string 10 is fixed at both ends, one end of which is fixed in the inner groove of the second cam 9 and is wound with the uniform rotation of the second cam 9; the other end is fixed in the groove of the width center line of the second swing platform 12, and the distance between the groove and the second swing platform is d 5 The thin rope moves along with one end of the winding pulling the second swing platform 12.
[0017] When in use, the two low-speed motors are controlled to rotate at a constant speed at the same time, and the second swing platform 12 can swing with two degrees of freedom under the movement of the first swing platform 5 and itself.
[0018] A design method of a two-degree-of-freedom cosine rocking platform based on a rope-tethered cam drive comprises the following steps:
[0019] The first step is to determine the cosine swing form of the two degrees of freedom required for the experiment: |α 1 |cos(ω 1 t),|α 2 |cos(ω 2 t), mainly including the amplitude |α 1 |、|α 2 | and angular frequency ω 1 ,ω 2 .
[0020] The second step is to use the two amplitudes |α 1 |、|α 2 |Determine the inclination angle α of the two rocking platforms at the initial moment 1 , α 2 , where the absolute value of the tilt angle is the amplitude. Finally, the second swing platform 12 can achieve a degree of freedom in -α 1 ~α 1 Swing within the range, the other degree of freedom is -α 2 ~α 2 Swinging within range.
[0021] The third step is to calculate the angular frequency ω. 1 ,ω 2 Determine the rotation speed of the two cams and the two motors, where the angular frequency ω 1 ,ω2 That is, the angular velocity of the two cams and the motor is ω 1 ,ω 2 .
[0022] Step 4: According to the size of the experimental site, you can design the appropriate device size by yourself: including two ropes of length l 1 , l 2 , the diameter of the two thin ropes is a 1 ′、a 2 ′, the length of the two rocking platforms L 1 , L 2 , width d 1 ,d 2 , thickness h 1 、h 2 , the thickness of the two cams h 3 、h 4 , the thickness of the inner grooves of the two cams h 5 、h 6 , the distance d between the two rocking platform grooves and one side of the rocking platform 4 ,d 5 The height difference between the center of the first swing platform 5 and the center of the second swing platform 12 is H, and the thickness of the trapezoidal structure 7 is d 3 .
[0023] The fifth step is to solve the shape parameters of the first cam 2 of the first swing platform 5. Since the solution method of the first swing platform 5 is the same as that of the second swing platform 12, the first swing platform 5 is explained in detail: when the first swing platform 5 is in a horizontal position, the center of the first cam 2 is taken as the origin, the length direction of the first swing platform 5 is the X direction, the thickness direction of the first swing platform 5 is the Y direction, and the length direction of the first swing platform 5 is the Z direction. Since the first swing platform 5 only swings in the XY plane, the device parameters in the Z direction will not affect the entire solution process. For the convenience of solution, the coordinates of the device in the Z direction can be ignored. The details are as follows:
[0024] 5.1: Determine the number of shape parameters of the first cam 2;
[0025] The present invention selects the shape equation of the first cam 2 as:
[0026] A'xy 2 +B'yx 2 +C'x 2 +D'y 2 +E'xy+F'x+G'y+H'=0 (1)
[0027] Among them, x and y are the coordinates of the above coordinate system, and the equation represents a total of 8 parameters of the first cam 2, namely A', B', C', D', E', F', G', and H'. Due to the large number of parameters, it is difficult to solve the subsequent problem, so the parameters can be reduced.
[0028] Select four points a of the first cam 2 on the coordinate axis 1 ,b 1 ,c 1 ,d 1 , whose coordinates are (a 1 ,0)、(-b 1 ,0)、(0,c 1 )、(0,-d 1 ), the A', B', C', D', E', F', G', H' parameters can be calculated based on the coordinate information of these four points. The formula is:
[0029]
[0030] Therefore, according to formula (2), the eight parameters A', B', C', D', E', F', G', and H' can be converted into four parameters. 1 ,b 1 ,c 1 ,d 1 Parameters, then solve a 1 ,b 1 ,c 1 ,d 1 The parameters can be used to obtain the shape equation of the first cam 2.
[0031] 5.2: Solve the range of the four parameters of the first cam;
[0032] 5.2.1: Solution ideas;
[0033] It is rather complicated to directly obtain the parameters of the first cam 2 by using the known swing form and device parameters of the first swing platform 5. The present invention adopts an inversion method. First, the size of the parameters a, b, c, and d are arbitrarily given, and the parameters A', B', C', D', E', F', G', and H' are calculated by formula (2), substituted into formula (1), and converted into polar coordinate form.
[0034] Then, under the condition of known device parameters, the swing form generated by the first cam 2 and the relative error with the given swing form are calculated. 1 ,b 1 ,c 1 ,d 1 A certain interval range is selected around the parameter value (the larger the relative error, the larger the interval range is selected), and the Monte Carlo method is used to randomly select a 1 ,b 1,c 1 ,d 1 Select points within the parameter range and calculate the swing form and relative error. Record the parameters with relative errors less than 1% and redefine the range of the four cam parameters within these parameters. Then, use the heterogeneous comprehensive learning particle swarm optimization (HCLPSO) method to determine the optimal solution of the four parameters.
[0035] 5.2.2: Based on the given first cam parameters, solve the swing form and relative error produced by the first cam 2.
[0036] When calculating the swing form of the first swing platform 5, it is necessary to know the swing angle of the first swing platform 5 at each moment and the position of the connection point between the first string 3 and the first cam 2. Since the parameters of the first cam are already given, the position information of the connection point can be regarded as an unknown quantity. Therefore, two equations need to be constructed at each moment to calculate the swing angle and the connection point information.
[0037] From the perspective of geometric relationship, the connection point between the first cam 2 and the first string 3 is the tangent point between the first string 3 and the first cam 2. A tangent equation can be established at each moment:
[0038]
[0039] Among them, the subscript D 1 represents the tangent point between the first cam 2 and the first string 3 at time t, with subscript A 1 represents the connection point between the first swing platform 5 and the first string 3 at time t. 1 The point coordinates are only related to the fixed point coordinates of the first swing platform 5 The first swing platform 5 has a length L 1 and the swing angle α 1 Since the length L of the first rocking platform 5 is 1 and the first swing platform 5 fixed point coordinates is known and will not change, so we only need to know the swing angle α 1 Then we can find A 1 Point coordinates, that is:
[0040]
[0041] In addition, when the first cam 2 drives the first swing platform 5 to swing, a portion of the first string 3 will be wrapped around the first cam 2, and the total length of the first string 3 will not change. A string length equation can be established at each moment:
[0042]
[0043] Among them, l 1 is the length of the first rope, l s1(t) is the length of the first string 3 wound around the first cam 2, l 1 (t) is the time from the first string 3 to the connection point A 1 To tangent point D 1 Length; is the initial time point D 1 The polar angle coordinate on the first cam 2, and D 1 Point is the tangent point between the first cam 2 and the first string 3 at time t; 1 (t) is the rotation angle of the first cam 2 around the rotation center at time t; is the initial time point B 1 The polar angle coordinate on the first cam 2, and B 1 The point is the initial time t 0 The tangent point between the first cam 2 and the first string 3; 1 is the polar coordinate of the point on the first cam 2, is the derivative of the polar diameter with respect to the polar angle; D is the rectangular coordinate system 1 Point coordinates, A is the rectangular coordinate system 1 Point coordinates.
[0044] Combining equations (3) and (5), it can be seen that there are two equations and two unknown quantities at each moment: the connection point coordinates and the swing angle. Therefore, the connection point position and the swing angle of each time period can be calculated, thereby calculating the relative error between the actual swing angle of the first cam 2 and the specified swing angle.
[0045] 5.2.3: Select the range of the four parameters of the first cam;
[0046] According to the relative error calculated above, at a given first cam a 1 ,b 1 ,c 1 ,d 1 A certain interval range is selected around the parameter value (the larger the relative error, the larger the interval range is selected). The Monte Carlo method is used to calculate the swing angle error caused by each set of first cam parameters according to 5.2.2, and the parameters with a relative error less than 1% are recorded. Among the four parameter values recorded, the range of each parameter is defined as (minimum value in the record, maximum value in the record).
[0047] 5.2.4: Determine the optimal solution of the four parameters of the first cam;
[0048] After obtaining the range of each first cam shape parameter in 5.2.3, the four first cam parameter values are used as optimization variables, and the swing angle error caused by each set of first cam parameters is calculated according to 5.2.2 as the optimization objective function. The four first cam parameter values that minimize the swing angle error are determined using the heterogeneous comprehensive learning particle swarm optimization (HCLPSO) optimization method.
[0049] The sixth step is to solve the second cam shape parameters of the second swing platform 12. When the first swing platform 5 and the second swing platform 12 are both in a horizontal position, the center of the second cam 9 is taken as the origin, the length direction of the second swing platform 12 is the X direction, the thickness direction of the second swing platform 12 is the Y direction, and the length direction of the second swing platform 12 is the Z direction. Similarly, since the second swing platform 12 only swings in the XY plane, the device parameters in the Z direction will not affect the entire solution process. For the convenience of solution, the coordinates of the device in the Z direction can be ignored. Repeat the solution process of the fifth step to obtain four second cam parameter values that minimize the swing angle error.
[0050] Step 7: According to the cam parameters obtained in Steps 5 and 6, the corresponding cams are manufactured, and the two cams are respectively installed on the two low-speed motors, and connected to the corresponding swing platforms with corresponding thin ropes, that is, the first cam 2 is installed on the first low-speed motor 1, and connected to the first swing platform 5 through the first thin rope 3, and the second cam 9 is installed on the second low-speed motor 8, and connected to the second swing platform 12 through the second thin rope 10. The angular velocities of the first low-speed motor 1 and the second low-speed motor 8 are adjusted to ω respectively. 1 ,ω 2 The inclination angles of the first swing platform 5 and the second swing platform 12 are adjusted to α 1 , α 2 When two low-speed transfer machines are started at the same time, the second swing platform 12 will swing in two designed forms. 1 |cos(ω 1 t),|α 2 |cos(ω 2 t) Perform dual-degree-of-freedom swing, that is, one degree of freedom can be achieved in -α 1 ~α 1 Swing within the range, the other degree of freedom is -α 2 ~α 2 Swinging within range.
[0051] The present invention has the following beneficial effects:
[0052] (1) The present invention can design a dual-degree-of-freedom rocking platform that meets various cosine rocking forms according to the design method of the cam. For some small and medium-sized experiments that require specific cosine rocking forms and dual-degree-of-freedom rocking, a dual-degree-of-freedom cosine rocking platform based on a rope-tethered cam drive designed by the present invention can meet the requirements with high precision.
[0053] (2) The dual-degree-of-freedom cosine swing table designed by the present invention can swing by simply starting two low-speed motors at the same time to rotate at a constant speed according to a specified angular velocity. Compared with the existing dual-degree-of-freedom swing table, which also needs to consider the motion coupling in the two degrees of freedom directions, the dual-degree-of-freedom cosine swing table designed by the present invention is very easy to operate.
[0054] (3) When designing the dual-degree-of-freedom cosine-type oscillating platform, the present invention designs the size of the device according to the space size of the experimental site. Compared with large-scale oscillating platforms, the dual-degree-of-freedom cosine-type oscillating platform designed by the present invention can fully adapt to various experimental site sizes and meet the needs of different working conditions. BRIEF DESCRIPTION OF THE DRAWINGS
[0055] Figure 1 It is a physical diagram of the embodiment of the invention and the established coordinate system; it is composed of a swing device, a trapezoidal structure, two low-speed motors, two cams, and two thin ropes. The swing device is mainly composed of a first swing platform, a second swing platform, two fixing devices, and two swing axes.
[0056] In the figure: 1 first low-speed motor; 2 first cam; 3 first thin rope; 4 first fixing device; 5 first swing platform; 6 first swing shaft; 7 trapezoidal structure; 8 second low-speed motor; 9 second cam; 10 second thin rope; 11 second fixing device; 12 second swing platform; 13 second swing shaft.
[0057] Figure 2 The initial moment of the embodiment of the invention is Figure 1 The projection diagram of the XY plane is mainly used to describe the initial moment of the first swing platform. 1 The angular velocity of the 1 is the cam rotation center, B 1 (t 0 ) is the tangent point between the string and the cam at the initial moment, D 1 (t 0 ) is the tangent point at the next moment, A 1 (t 0 ) is the position where the swing platform is connected to one end of the string, C 1 (x C ,y C ) is the center position of the rocking platform, α 1 (t 0) is the angle between the swing platform and the horizontal line at the initial moment (at this time, it is the angle between the left end and the horizontal line, which is set to negative), L 1 is the total length of the first rocking platform.
[0058] Figure 3 The embodiment of the invention is at time t Figure 1 The projection diagram of the XY plane is mainly used to describe the t moment of the first swing platform. 1 The angular velocity of the 1 is the cam rotation center, D 1 (t) is the tangent point between the string and the cam at time t, B 1 (t) is the tangent point at the initial moment or the previous moment, A 1 (t) is the position of one end of the string connected to the swing platform at time t, C 1 (x C ,y C ) is the center position of the rocking platform, α 1 (t) is the angle between the swing platform and the horizontal line at time t (at this time, it is the angle between the right end and the horizontal line, set to be positive), L 1 is the total length of the rocking platform.
[0059] Figure 4 The initial moment of the embodiment of the invention is Figure 1 The projection diagram of the ZY plane is mainly used to describe the initial moment of the second rocking platform. 2 The angular velocity of the 2 is the cam rotation center, B 2 (t 0 ) is the tangent point between the string and the cam at the initial moment, D 2 (t 0 ) is the tangent point at the next moment, A 2 (t 0 ) is the position where the swing platform is connected to one end of the string, C 2 (x C ,y C ) is the center position of the rocking platform, α 2 (t 0 ) is the angle between the swing platform and the horizontal line at the initial moment (at this time, it is the angle between the left end and the horizontal line, which is set to negative), L 2 is the total length of the rocking platform.
[0060] Figure 5 The embodiment of the invention is at time t Figure 1 The projection diagram of the ZY plane is mainly used to describe the t moment of the second rocking platform. 2 The angular velocity of the 2 is the cam rotation center, D2 (t) is the tangent point between the string and the cam at time t, B 2 (t) is the tangent point at the initial moment or the previous moment, A 2 (t) is the position of one end of the string connected to the swing platform at time t, C 2 (x C ,y C ) is the center position of the rocking platform, α 2 (t) is the angle between the swing platform and the horizontal line at time t (at this time, it is the angle between the right end and the horizontal line, set to be positive), L 2 is the total length of the rocking platform.
[0061] Figure 6 According to the invention example, the swing diagram of the first swing platform is calculated, and it is verified from a mathematical level that the cam can drive the first swing platform to swing.
[0062] Figure 7 According to the invention example, the swing diagram of the second swing platform is calculated, and it is verified from a mathematical level that the cam can drive the second swing platform to swing.
[0063] Figure 8 According to the invention example, the overall structural swing diagram of the first swing platform and the second swing platform is calculated, and it is verified that the first swing platform and the second swing platform can swing at the same time.
[0064] Fig. 9 It is a comparison diagram of the rocking curve and the cosine curve of the first rocking platform in the embodiment of the invention, wherein the solid line is the cosine curve, and the dotted line is the rocking curve formed by the first rocking platform, and the two curves are almost overlapped, which verifies the accuracy of the method for solving the cam shape parameters. DETAILED DESCRIPTION
[0065] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.
[0066] A double-degree-of-freedom cosine-type swing platform based on rope-type cam drive, the double-degree-of-freedom cosine-type swing platform mainly consists of a swing device, a trapezoidal structure 7, two low-speed motors, two cams, and two thin ropes.
[0067] The swing device is mainly composed of a first swing platform 5, a second swing platform 12, two fixing devices, and two swing axes. The length of the first swing platform 5 is defined as L 1 , width d 1 , thickness is h 1 The second swing platform 12 is L long. 2 , width d2 , thickness is h 2 The first swaying platform 5 is fixedly connected to the first swaying shaft 6, the first swaying shaft 6 is connected to the first fixing device 4 through a bearing, the first fixing device 4 is fixed on the ground, and it is ensured that the first swaying platform 5 and the first swaying shaft 6 can sway in one direction relative to the first fixing device 4. The second swaying platform 12 is fixedly connected to the second swaying shaft 13, the second swaying shaft 13 is connected to the second fixing device 11 through a bearing, and the second fixing device 11 is embedded in the first swaying platform 5. In this way, it can be ensured that the first swaying platform 5 sways with the second swaying platform 12 in one direction, and the second swaying platform 12 itself sways in another direction, so that the second swaying platform 12 can sway freely in two directions.
[0068] The trapezoidal structure 7 is a 3 The structure is a regular trapezoidal plate, wherein the middle horizontal plate is fixed on the first swing platform 5, and motor platforms are provided on both sides of the lower part for placing low-speed motors, which swing in one direction along with the first swing platform 5.
[0069] The low-speed motor is a device that provides a uniform rotation of the cam, which can control the speed and can rotate at a uniform and low speed. The two low-speed motor structures have the same speed. The first low-speed motor 1 is located on the ground and is connected to the groove of the width center line of the first swing platform 5 by a thin rope. The second low-speed motor 8 is located on a motor platform at the bottom of the trapezoidal structure 7 and is connected to the groove of the width center line of the second swing platform 12 by a thin rope. The second low-speed motor 8 swings in one direction along with the first swing platform 5.
[0070] There are two cams with the same structure, both of which are convex wheel-shaped structures. The plane shape of the first cam 2 is represented by the curve L 3 The thickness of the first cam 2 is h 3 , and in thickness The plane shape of the second cam 9 is defined by the curve L 4 The thickness of the second cam 9 is h 4 , and in thickness An inner groove is provided at the location.
[0071] Furthermore, the inner grooves of the two cams are also convex wheel-shaped structures, and the plane shapes of the inner grooves of the two cams are respectively represented by curves L 5 , L 6 The closed figure is composed of two cams with the thickness of the grooves h 5 、h 6 ; where curve L 5 , L 6 With curve L 3 , L4 is a similar relationship, and the size ratio is L 5 =n 1 L 3 , L 6 =n 2 L 4 , of which 0.95 <n 1 <1, 0.95 <n 2 <1. Curve L 5 , L 6 The inner groove formed mainly serves to fix the thin rope that is wound around the cam as the cam rotates.
[0072] The two thin ropes are respectively l long 1 , l 2 , and the diameters are a 1 、a 2 , where a 1 ≤h 5 、a 2 ≤h 6 The first string 3 is fixed at both ends, one end of which is fixed in the inner groove of the first cam 2 and is wound along with the uniform rotation of the first cam 2; the other end is fixed on the groove of the width center line of the first swing platform 5, and the distance between the groove and the first swing platform 5 is d 4 The first string 3 moves with the first swing platform 5 pulled by one end of the winding. The second string 10 is fixed at both ends, one end of which is fixed in the inner groove of the second cam 9 and is wound with the uniform rotation of the second cam 9; the other end is fixed in the groove of the width center line of the second swing platform 12, and the distance between the groove and the second swing platform is d 5 The thin rope moves along with one end of the winding pulling the second swing platform 12.
[0073] When in use, the two low-speed motors are controlled to rotate at a constant speed at the same time, and the second swing platform 12 can swing with two degrees of freedom under the movement of the first swing platform 5 and itself.
[0074] A design method of a two-degree-of-freedom cosine rocking platform based on a rope-tethered cam drive comprises the following steps:
[0075] The first step is to determine the cosine swing form of the two degrees of freedom required for the experiment: 0.15cos(0.2πx), 0.15cos(0.2πx), mainly including the amplitude |α 1 |=0.15、|α 2 |=0.15 and angular frequency ω 1 =0.2πrad / s,ω 2 =0.2πrad / s.
[0076] The second step is to determine the inclination angle α of the two rocking platforms at the initial moment based on the two amplitudes.1 =-0.15, α 2 =-0.15, where the absolute value of the tilt angle is the amplitude. Finally, the second swing platform 12 can swing within an angle range of -0.15 to 0.15 on one degree of freedom and within an angle range of -0.15 to 0.15 on another degree of freedom.
[0077] The third step is to determine the rotation speed of the two cams and the motor according to the angular frequency as ω 1 =0.2πrad / s,ω 2 =0.2πrad / s.
[0078] The fourth step is to design the appropriate device size according to the size of the experimental site: including two ropes of length l 1 =1m,l 2 =1m, diameter of two thin ropes a 1 ′=0.002m、a 2 ′=0.002m, length L of two swing platforms 1 =1m, L 2 =1m, width d 1 =0.4m,d 2 =0.4m, thickness h 1 =0.01m,h 2 =0.01m, the thickness of the two cams h 3 =0.01m,h 4 =0.01m, thickness of the two cam grooves h 5 =0.002m,h 6 = 0.002m, the distance d between the groove of the swing platform and one side of the swing platform 4 =0.2m,d 5 = 0.2m, the height difference between the center of the first swing platform 5 and the center of the second swing platform 12 is H = 0.3m, and the thickness of the trapezoidal structure 7 is d 3 =0.01m.
[0079] The fifth step is to solve the shape parameters of the first cam of the first swing platform 5. According to the steps of the fifth step of the invention, the shape parameters of the first cam 2 can be obtained:
[0080]
[0081] Step 6: Solve the shape parameters of the second cam of the second rocking platform 12. Repeat the above step 5 to obtain the shape parameters of the second cam 9:
[0082]
[0083] The seventh step is to manufacture the corresponding cam according to the cam parameters obtained in the fifth and sixth steps, install the two cams on the two low-speed motors respectively, and connect them to the corresponding swing platforms with the corresponding thin ropes. Adjust the angular velocities of the two low-speed motors to 0.2πrad / s and 0.2πrad / s respectively, and adjust the inclination angles of the two swing platforms to -0.15 and 0.15 respectively. Start the two low-speed motors at the same time, and the second swing platform 12 will swing with two degrees of freedom according to the two designed swing forms of 0.15cos(0.2πx) and 0.15cos(0.2πx), that is, it can swing in the range of -0.15 to 0.15 on one degree of freedom and in the range of -0.15 to 0.15 on the other degree of freedom. Figure 8 , Fig. 9 .
[0084] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.
Claims
1. A double-degree-of-freedom cosine rocking platform based on a rope-tethered cam drive, characterized in that: The dual-degree-of-freedom cosine-type swing platform comprises a swing device, a trapezoidal structure (7), two low-speed motors, two cams, and two thin ropes; The swing device comprises a first swing platform (5), a second swing platform (12), two fixing devices, and two swing axes; the first swing platform (5) is defined as having a length of L1, a width of d1, and a thickness of h1, and the second swing platform (12) is defined as having a length of L2, a width of d2, and a thickness of h2; the first swing platform (5) is fixedly connected to the first swing axis (6), the first swing axis (6) is connected to the first fixing device (4) via a bearing, the first fixing device (4) is fixed on the ground, and the first swing platform (5) and the first swing axis (6) can swing in one direction relative to the first fixing device (4); the second swing platform (12) is fixedly connected to the second swing axis (13), the second swing axis (13) is connected to the second fixing device (11) via a bearing, and the second fixing device (11) is embedded in the first swing platform (5), so as to ensure that the first swing platform (5) swings with the second swing platform (12) in one direction, and the second swing platform (12) itself swings in another direction, so that the second swing platform (12) can swing freely in two directions; The trapezoidal structure (7) is a regular trapezoidal plate structure with a thickness of d3, wherein the middle horizontal plate is fixed on the first swing platform (5), and motor platforms are provided on both sides of the lower part, swinging in one direction along with the first swing platform (5); The low-speed motor is a device that provides uniform rotation for the cam, and the two low-speed motor structures have the same rotation speed; wherein the first low-speed motor (1) is located on the ground and is connected to the groove of the width center line of the first swing platform (5) through a first thin rope (3); the second low-speed motor (8) is located on the motor platform at the lower part of the trapezoidal structure (7) and is connected to the groove of the width center line of the second swing platform (12) through a second thin rope (10), and the second low-speed motor (8) swings along one direction with the first swing platform (5); There are two cams with the same structure, both of which are convex wheel-shaped structures; the plane shape of the first cam (2) is composed of a closed figure surrounded by a curve L3, the thickness of the first cam (2) is h3, and The plane shape of the second cam (9) is formed by a closed figure surrounded by the curve L4, the thickness of the second cam (9) is h4, and the thickness An inner groove is provided at the location; The two thin ropes are respectively l1 and l2 in length and a1 and a2 in diameter, wherein a1≤h5 and a2≤h6; the first thin rope (3) is fixed at both ends, one end of which is fixed in the inner groove of the first cam (2) and is wound along with the uniform rotation of the first cam (2); the other end is fixed on the groove of the width center line of the first swing platform (5), the distance between the groove and the first swing platform (5) is d4, and the first thin rope (3) moves along with the winding end pulling the first swing platform (5); the second thin rope (10) is fixed at both ends, one end of which is fixed in the inner groove of the second cam (9), and is wound along with the uniform rotation of the second cam (9); the other end is fixed on the groove of the width center line of the second swing platform (12), the distance between the groove and the second swing platform is d5, and the thin rope moves along with the winding end pulling the second swing platform (12); When in use, the two low-speed motors are controlled to rotate at a uniform speed at the same time, and the second swing platform (12) can swing with two degrees of freedom under the movement of the first swing platform (5) and itself.
2. A double-degree-of-freedom cosine rocking platform based on rope-type cam drive according to claim 1, characterized in that: The inner grooves of the two cams are also convex cam-shaped structures. The planar shapes of the inner grooves of the two cams are respectively formed by closed figures enclosed by curves L5 and L6. The thicknesses of the inner grooves of the two cams are h5 and h6 respectively. Among them, the curves L5 and L6 are similar to the curves L3 and L4, and the size ratios are L5 = n1L3 and L6 = n2L4, where 0.95 < n1 < 1 and 0.95 < n2 < 1. The inner grooves formed by the curves L5 and L6 are used to fix the thin ropes that wind around the cams as the cams rotate.
3. A design method for a dual-degree-of-freedom cosine rocking platform based on a rope-tethered cam drive according to claim 1 or 2, characterized in that: It includes the following steps: In the first step, determine the cosine swing forms in two degrees of freedom: |α1|cos(ω1t), |α2|cos(ω2t), which mainly include the amplitudes |α1|, |α2| and the angular frequencies ω1, ω2. In the second step, determine the tilt angles α1, α2 of the two swing platforms at the initial moment according to the two amplitudes |α1|, |α2|, where the absolute value of the tilt angle is the amplitude. On the second swing platform (12), it can swing within the range of -α1 to α1 in one degree of freedom and within the range of -α2 to α2 in the other degree of freedom. In the third step, determine the rotational speeds of the two cams and the two motors according to the angular frequencies ω1, ω2, where the angular frequencies ω1, ω2 are the rotational angular velocities of the two cams and the motors, which are ω1, ω2. In the fourth step, design the size of the device according to the size of the site: including the lengths l1, l2 of the two ropes, the diameters a1′, a2′ of the two thin ropes, the lengths L1, L2, widths d1, d2, thicknesses h1, h2 of the two swing platforms, the thicknesses h3, h4 of the two cams, the thicknesses h5, h6 of the inner grooves of the two cams, the distances d4, d5 between the grooves of the two swing platforms and one side of the swing platforms, the height difference H between the centers of the first swing platform (5) and the second swing platform (12), and the thickness d3 of the trapezoidal structure (7). In the fifth step, solve the shape parameters of the first cam (2) of the first swing platform (5). The solution methods for the first swing platform (5) and the second swing platform (12) are the same. Taking the first swing platform (5) as an example for detailed description: When the first swing platform (5) is in the horizontal position, with the center of the first cam (2) as the origin, along the length direction of the first swing platform (5) as the X direction, along the thickness direction of the first swing platform (5) as the Y direction, and along the length direction of the first swing platform (5) as the Z direction. Since the first swing platform (5) only swings in the X - Y plane, the Z direction is ignored. In the sixth step, solve the shape parameters of the second cam of the second swing platform (12). When both the first swing platform (5) and the second swing platform (12) are in the horizontal position, with the center of the second cam (9) as the origin, along the length direction of the second swing platform (12) as the X direction, along the thickness direction of the second swing platform (12) as the Y direction, and along the length direction of the second swing platform (12) as the Z direction. Similarly, the Z direction is ignored. Repeat the solution process of the fifth step to obtain four second cam parameter values that minimize the swing angle error. The seventh step is to manufacture the corresponding cam according to the cam parameters obtained in the fifth and sixth steps, install the first cam (2) on the first low-speed motor (1), connect the first swing platform (5) through the first thin rope (3), install the second cam (9) on the second low-speed motor (8), connect the second swing platform (12) through the second thin rope (10); adjust the angular velocities of the first low-speed motor (1) and the second low-speed motor (8) to ω1 and ω2 respectively, and adjust the inclination angles of the first swing platform (5) and the second swing platform (12) to α1 and α2 respectively; start the two low-speed motors at the same time, and the second swing platform (12) swings in two degrees of freedom according to the two designed swing forms |α1|cos(ω1t) and |α2|cos(ω2t), so as to swing in the range of -α1 to α1 on one degree of freedom and swing in the range of -α2 to α2 on the other degree of freedom.
4. The design method of a double-degree-of-freedom cosine-type rocking platform based on a rope-tethered cam drive according to claim 3 is characterized in that: The fifth step is as follows: 5.1: Determine the number of shape parameters of the first cam; The shape equation of the first cam (2) is selected as: A'xy 2 +B'yx 2 +C'x 2 +D'y 2 +E'xy+F'x+G'y+H'=0 (1) in, x, y are the coordinates of the above coordinate system, and the first cam (2) parameters represented by this equation have a total of 8 parameters, namely A', B', C', D', E', F', G', H'; Select four points a1, b1, c1, and d1 of the first cam (2) on the coordinate axis, whose coordinates are (a1, 0), (-b1, 0), (0, c1), and (0, -d1), respectively. According to the coordinate information of these four points, the parameters A', B', C', D', E', F', G', and H' are calculated. The formula is: According to formula (2), the eight parameters A', B', C', D', E', F', G', H' are converted into four parameters a1, b1, c1, d1; 5.2: Solve the range of the four parameters of the first cam; 5.2.1: Solution ideas; Using the inversion method, we first arbitrarily set the values of a, b, c, and d parameters, and calculate the parameters A', B', C', D', E', F', G', and H' using formula (2). Substitute them into formula (1) and convert them into polar coordinates. Under the condition of known parameters, the swing form generated by the first cam (2) and the relative error with the given swing form are calculated; based on the given a1, b1, c1, d1 parameter values, an interval range is selected, and points are randomly selected within the a1, b1, c1, d1 parameter interval range by using the Monte Carlo method to calculate the swing form and relative error generated, and the parameters with relative errors less than 1% are recorded, and the interval ranges of the four cam parameters are re-determined from these parameters; the optimal solutions of the four parameters are determined by a heterogeneous comprehensive learning particle swarm optimization method; 5.2.2: Determine the swing form and relative error of the first cam (2) according to the given first cam parameters; At each moment, the swing angle and connection point information are calculated by two equations; The connection point between the first cam (2) and the first string (3) is the tangent point between the first string (3) and the first cam (2). A tangent equation is established at each moment: Wherein, the subscript D1 represents the tangent point between the first cam (2) and the first string (3) at time t, and the subscript A1 represents the connection point between the first swing platform (5) and the first string (3) at time t; and the coordinates of point A1 are only related to the coordinates of the fixed point of the first swing platform (5). The length L1 of the first swing platform (5) is related to the swing angle α1; the coordinates of the point A1 can be obtained by obtaining the swing angle α1, that is: In addition, during the process of the first cam (2) driving the first swing platform (5) to swing, a rope length equation is established at each moment: Among them, l1 is the length of the first rope, l s1 (t) is the length of the first string (3) wound around the first cam (2), l1(t) is the length of the first string (3) from the connection point A1 to the tangent point D1; is the polar angle coordinate of the initial point D1 on the first cam (2), and point D1 is the tangent point between the first cam (2) and the first string (3) at time t; β1(t) is the rotation angle of the first cam (2) around the rotation center at time t; is the polar angular coordinate of the initial point B1 on the first cam (2), and point B1 is the tangent point between the first cam (2) and the first string (3) at the initial time t0; r1 is the polar radial coordinate of the point on the first cam (2), is the derivative of the polar diameter with respect to the polar angle; is the coordinate of point D1 in the rectangular coordinate system, is the coordinate of point A1 in the rectangular coordinate system; By finding the connection point position and the swing angle in each time period, the relative error between the actual swing angle of the first cam (2) and the specified swing angle can be calculated; 5.2.3: Select the range of the four parameters of the first cam; According to the relative error calculated above, select the interval range based on the given first cam parameter values a1, b1, c1, d1, and use the Monte Carlo method according to 5.2.2 to calculate the swing angle error caused by each set of first cam parameters, and record the parameters with relative errors less than 1%; 5.2.4: Determine the optimal solution of the four parameters of the first cam; After obtaining the range of each first cam shape parameter interval in 5.2.3, take the four first cam parameter values as optimization variables, and calculate the swing angle error caused by each group of first cam parameters according to 5.2.2 as the optimization objective function; use the heterogeneous comprehensive learning particle swarm optimization method to determine the four first cam parameter values that minimize the swing angle error.