Three-stage multivariable controllable dalton plate general experiment method and platform

Abstract

This invention belongs to the technical field of probability and statistics physics experimental devices. It proposes a three-segment, multivariable, controllable Dalton plate general experimental method and platform. The method involves preparing and assembling a ball-throwing segment, a collision segment, and a collection trough module. A target nail is installed in the collision segment module. Balls are thrown from the ball-throwing segment module, randomly collide with each other in the collision segment module, and then fall into different sections of the collection trough module. A mobile terminal collects images of the ball distribution. A native app uses a 2D graphics rendering engine for offline image recognition, sequentially performing image preprocessing, threshold segmentation, contour detection, and size calibration, outputting the ball stacking height for each section. Based on the ball height in each section, ball distribution data and distribution curves are generated. The statistical results and curves are displayed on the app interface, completing the random distribution experiment. This invention solves the problems of fixed structure, non-adjustable parameters, and low efficiency of manual ball counting in existing Dalton plates, making large-scale, multivariable, and multi-group repeated experiments possible.

Description

Technical Field

[0001] This invention belongs to the technical field of probability and statistics physics experimental devices, and in particular relates to a general experimental method and platform for a three-stage multivariable controllable Dalton plate. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] The Dalton Board, officially known as the Galton Board, was designed by Francis Galton in 1873 and was the first physical teaching aid to visually demonstrate the normal distribution. Galton used the random collision of small balls to verify that the superposition of a large number of random factors follows a normal distribution, which was used to explain the mean regression phenomenon in genetic statistics and is widely used in statistical physics demonstration teaching.

[0004] In the classroom, the Dalton board, as a classic physics teaching demonstration instrument for binomial distribution approaching normal distribution, plays a certain role in helping students understand the transition from randomness to regularity. However, it has certain limitations: due to its integrated structure and single experimental variable, students can only passively observe the statistical results and cannot control the changes in parameters, making it difficult to touch the deeper laws of random processes and regularities; in the traditional Dalton board experiment, it is difficult to collect the number of balls in each slot, and manual counting of balls is inefficient and prone to subjective errors, making it impossible to conduct a large number of multi-group experiments. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, this invention provides a three-stage multivariable controllable Dalton plate general experimental method and platform, which solves the problems of fixed structure, non-adjustable parameters, and low efficiency of manual counting of small balls in the existing Dalton plate.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides a general experimental method for a three-stage, multivariable, controllable Dalton plate, comprising: Prepare and assemble the ball-throwing section module, the collision section module, and the collection trough module, and select a target nail to install on the collision section module; Select a small ball and throw it from the ball throwing section module. After being randomly collided with by the collision section module, the ball falls into the collection section of the collection trough module. The mobile terminal is used to collect images of the ball distribution. The native mini-program uses a two-dimensional graphics rendering engine to perform offline image recognition, and sequentially performs image preprocessing, threshold segmentation, contour detection and size calibration, and outputs the stacking height of the balls in each collection zone. Based on the height of the balls in each collection zone, generate ball distribution data, plot distribution curves, and display the statistical results and curves on the mini-program interface to complete the random distribution experiment process.

[0007] As a further technical solution, the ball-throwing section module is provided with a ball-throwing port and a ball-falling channel to guide the ball into the collision section module; the collision section module is provided with a nail array installation area, in which nail plate positioning holes are arranged in an array, and removable nails are installed in the nail plate positioning holes; the collection trough module is located below the collision section module, and its interior is divided into several collection zones along the horizontal direction to receive the balls that fall into each zone after being hit by the nails; the ball-throwing section module, the collision section module, and the collection trough module are three independently manufactured modules, which are spliced ​​together from top to bottom.

[0008] As a further technical solution, the specific manufacturing process of the ball-throwing section module, the collision section module, and the collection tank module includes: Transparent sheets were laser-engraved to form the ball-throwing section module, the collision section module, the collection trough module, and other components. Three independent modules were formed by bonding them together with acrylic adhesive. The three independent modules were positioned and aligned from top to bottom through a V-shaped mechanical interface and locked together with a snap-fit ​​structure to complete the assembly of the whole machine. According to the experimental plan, target nails were selected and inserted into the nail plate positioning holes of the collision section module to form a nail array.

[0009] As a further technical solution, the specific process of offline image recognition includes: Image preprocessing includes converting the acquired image into a grayscale image and performing noise suppression; threshold segmentation separates the ball region from the background region by setting a grayscale threshold; contour detection uses the OpenCV algorithm to identify the ball stacking contours in each collection partition and calculates the pixel height; size calibration converts the pixel height into the ball stacking height according to the pre-calibrated ratio between the unit pixel and the actual height.

[0010] As a further technical solution, the experimental method also includes: adjusting experimental parameters, conducting multiple control experiments under different variable conditions, and quantitatively statistically analyzing the impact of different parameter settings on the statistical distribution results.

[0011] As a further technical solution, the experimental parameters include nail array density, nail material, nail size, nail shape, nail arrangement, ball size, ball material, and initial collision velocity.

[0012] As a further technical solution, after the native mini-program is identified, a visual verification interface is overlaid on the two-dimensional graphics rendering engine, including: marking the upper and lower physical boundaries of the collection partition with the first type of lines, marking the boundaries between each collection partition with the second type of lines, marking the top position of the small ball stack in each collection partition with the third type of lines, and marking the collection partition number at the corresponding position of each collection partition, so that the experimenters can manually review the identification results.

[0013] A second aspect of the present invention provides a three-stage, multivariable, controllable Dalton plate universal experimental platform, comprising: A pitching section module, wherein the pitching section module is provided with a pitching port and a ball landing channel; The collision segment module is provided with a nail array installation area, which has an array of nail plate positioning holes, in which detachable nails are installed. A collection trough module is located below the collision section module, and its interior is divided into several collection zones along the horizontal direction. The mobile terminal offline image recognition module is used to collect images of the ball distribution in the collection slot module. The native mini-program performs offline image recognition based on the two-dimensional graphics rendering engine and outputs the stacking height of the balls in each collection zone. The ball-throwing section module, the collision section module, and the collection trough module are three independently manufactured modules, which are spliced ​​together from top to bottom and are detachably connected through V-shaped mechanical interfaces and snap-fit ​​structures set on the module joint surfaces.

[0014] As a further technical solution, the project directory structure of the native mini-program includes: The root directory configuration file includes a global lifecycle entry file, which defines global experiment parameters, and a global configuration file, which is used to complete page registration, permission declaration, and global window configuration. The business logic folder includes a page folder and a utility function folder. The page folder stores the image capture and recognition logic code, and the utility function folder encapsulates general utility functions for numerical fitting, distribution curve plotting, and data export. Version management files, including core configuration files and ignore rule configuration files, are used to manage code iterations and filter compilation cache and temporary resource files; The mobile terminal offline image recognition module adopts a pure front-end offline computing architecture, in which all image processing, height calculation and visual annotation are completed locally on the mobile terminal.

[0015] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of a three-stage multivariable controllable Dalton board general experimental method as described in the first aspect of the present invention.

[0016] The above one or more technical solutions have the following beneficial effects: The device of this invention consists of three independent parts: an upper ball-throwing section, a middle collision section, and a lower collection trough. The connection between the three parts adopts a standardized V-shaped mechanical interface and is locked with buckles, requiring no calibration and being easy to assemble and disassemble. Each part can be independently maintained, replaced, and expanded, and has the ability to be continuously iterated. It solves the problem that students find it difficult to grasp the deep-seated patterns of random processes and regularities. Based on the offline image recognition module of the mobile terminal to collect the height of the balls in the multi-slot, it solves the problem of difficulty in collecting the number of balls in each slot and the inability to carry out large-scale, multi-group experiments.

[0017] This invention, for the first time, enables the independent and controllable quantitative exploration of collision distribution patterns using variables such as pin array density, pin shape, arrangement, ball diameter, type, and drop height on a single platform. It allows for the analysis of the synergistic effects of multiple variables on the post-collision ball distribution curve. This breakthrough allows the platform to systematically study the influence of individual variables and the synergistic effects of multiple variables on the final distribution characteristics (such as mean, standard deviation, and kurtosis), filling a gap in current teaching instruments for multivariate collaborative exploration of stochastic processes. It truly evolves the Dalton Plane from a "fixed demonstrator" into a "programmable stochastic process experimental platform."

[0018] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0020] Figure 1 The flowchart of the general experimental method for the three-stage multivariable controllable Dalton plate in the first embodiment is shown. Figure 2 This is a structural diagram of the three-segment multivariable controllable Dalton plate of the first embodiment; Figure 3 This is a structural diagram of the pitching section module in the first embodiment; Figure 4 This is a structural diagram of the collision segment module in the first embodiment; Figure 5 This is a structural diagram of the collection tank module in the first embodiment; Figure 6 A schematic diagram of the collision segment module in AutoCAD modeling for the first embodiment; Figure 7 This is a schematic diagram of laser engraving on the collision segment module of the first embodiment; Figure 8 A SolidWorks modeling diagram of the nail in the first embodiment; Figure 9 This is a schematic diagram of the 3D-printed nail from the first embodiment; Figure 10 This is a schematic diagram of the pin array module assembly in the first embodiment; Figure 11 A schematic diagram of the spare ball in the first embodiment; Figure 12 This is a comparison diagram of experiments with nails made of different materials in the first embodiment; Figure 13 A comparative diagram of experiments with nails of different sizes in the first embodiment; Figure 14 A comparative diagram of experiments with nails of different shapes in the first embodiment; Figure 15 This is a comparison diagram of experiments with small balls of different materials in the first embodiment; Figure 16 This is a comparison diagram of experiments with small balls at different drop heights in the first embodiment; Figure 17 This is a schematic diagram of the bimodal curve of the first embodiment; Figure 18 This is a schematic diagram of the bimodal curve pin array arrangement in the first embodiment; Figure 19 This is a schematic diagram of the three-peak curve of the first embodiment; Figure 20 This is a schematic diagram of the three-peaked curve pin array arrangement in the first embodiment.

[0021] In the diagram, 1 is the throwing section module; 2 is the collision section module; 3 is the collection trough module; and 4 is the snap-fit ​​structure. Detailed Implementation

[0022] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0023] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0024] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0025] Because existing Dalton Plate experiments involve an integrated structure and a single experimental variable, students can only passively observe statistical results and cannot change parameters and variables, making it difficult to grasp the deeper patterns of random processes and regularities. Therefore, this invention divides the device into three independent parts: an upper ball-throwing section, a middle collision section, and a lower collection trough. These parts are connected using standardized V-shaped mechanical interfaces and locked with snap-fit ​​mechanisms, eliminating the need for calibration, facilitating easy assembly and disassembly, and allowing for the modification of experimental parameters. Since traditional Dalton Plate experiments involve inefficient manual counting of balls and significant subjective errors, this invention develops a lightweight offline image recognition counting module that records the height of the balls in each trough to represent the number of balls, overcoming the difficulties of data acquisition through parameter transformation. Specific implementation methods are illustrated in the following examples.

[0026] Example 1 like Figure 1 As shown, this embodiment discloses a general experimental method for a three-stage multivariable controllable Dalton plate, including: S1: Prepare and assemble the ball-throwing section module 1, the collision section module 2, and the collection groove module 3, and select the target nail to install on the collision section module 2.

[0027] like Figure 2 As shown, the ball-throwing module 1 has a ball-throwing port and a ball-falling channel to guide the ball into the collision module 2; the collision module 2 has a nail array mounting area with nail plate positioning holes arranged in an array, and removable nails are installed in the nail plate positioning holes; the collection trough module 3 is located below the collision module 2, and its interior is divided into several collection zones along the horizontal direction to receive the balls that fall into each zone after being hit by the nails; the ball-throwing module 1, the collision module 2, and the collection trough module 3 are three independently manufactured modules, which are spliced ​​together from top to bottom.

[0028] Specifically: (1) The structure and manufacturing process of the ball-throwing section module, the collision section module, and the collection tank module are as follows: like Figure 3 As shown, the ball-throwing module 1 has a rectangular frame structure with acrylic panels on its sides and top. The middle of the ball-throwing module 1 has a V-shaped ball-loading container composed of two support plates, which are perpendicular to the two large, oppositely positioned plates of the ball-throwing module 1. The lower part of the V-shaped ball-loading container has an opening with a removable baffle to control the flow of the ball from the V-shaped container into the collision module 2. Rectangular guide plates are located on both sides of the opening to guide the ball back to the V-shaped container when the device is inverted. After the ball returns, the baffle can be inserted into the opening to prepare for the next experiment.

[0029] like Figure 4As shown, the collision segment module 2 has a rectangular frame structure, including two opposing first and second plate walls, and two side plates connecting the two plate walls. The second plate wall is formed by bonding the first acrylic plate and the second acrylic plate together. The first plate wall has a plurality of first positioning holes arranged in an array, and the second plate wall has a plurality of second positioning holes that are coaxially corresponding to each of the first positioning holes.

[0030] In this embodiment, the first positioning hole is a circular hole with a diameter of 4.00 mm, arranged in 21 rows at equal intervals on the first plate wall (the spacing is generally between 10.00 and 20.00 mm). The first positioning holes in adjacent rows are staggered by half a spacing in the horizontal direction. The second positioning hole includes a first square hole and a second square hole arranged coaxially. The first square hole is opened on the first acrylic plate close to the first plate wall, with a side length of 6.00 mm. The second square hole is opened on the second acrylic plate away from the first plate wall, with a side length of 8.00 mm. The first and second acrylic plates are limited by a positioning frame to ensure that the first square hole and the second square hole are coaxial. The second positioning holes on the second plate wall are arranged coaxially and correspondingly with the first positioning holes on the first plate wall.

[0031] like Figure 5 As shown, the collection tank module 3 is a container structure with an open top and an acrylic panel wall enclosed at the bottom and all four sides. The surrounding acrylic panel wall includes two large, oppositely arranged first and second side walls, and two smaller, oppositely arranged third and fourth side walls. Sixteen partitions are evenly spaced horizontally between the first and second side walls, dividing the interior of the collection tank module 3 into 17 equally wide collection zones for receiving small balls that fall into each collection zone after being collided with the collision section module 2. The number of small balls in each collection zone is different, and their height within the collection zone is also different, thus forming a distribution curve at the top of the small balls in each collection zone.

[0032] First, after assembling and calibrating the three sections, standard V-shaped mechanical interfaces are installed on each section. These interfaces consist of V-shaped protruding interfaces and V-shaped recessed interfaces. The hooks of the snap-fit ​​structure 4 are glued to the V-shaped protruding interfaces, and the locking rings of the snap-fit ​​structure 4 are glued to the V-shaped recessed interfaces. The installation process between the throwing section module 1 and the impact section module 2 is as follows: the V-shaped protruding interfaces with hooks are installed on the outside of the side plate of the impact section module 2, and the V-shaped recessed interfaces with locking rings are snapped onto the outside of the two smaller, oppositely positioned plates of the throwing section module 1. The same installation process is used between the impact section module 2 and the collection tank module 3: the V-shaped protruding interfaces with hooks are installed on the outside of the side plate of the impact section, and the V-shaped recessed interfaces with locking rings are installed on the outside of the third and fourth side walls of the collection tank. The three sections are then sequentially locked together with snap-fit ​​mechanisms to form a fixed, parameter-controllable Dalton plate experimental platform.

[0033] Accessories of different heights can be added between the throwing section module 1 and the collision section module 2. The accessory is a rectangular structure with the same length and width as the throwing section, and acrylic walls on all sides. In the middle of the accessory is a vertical channel with the same length and width as the ball outlet of the throwing section module 1, ensuring that the ball passes through smoothly and collides vertically with the pin array.

[0034] In this embodiment, the graphics of different components of the throwing section module 1, the collision section module 2, and the collection trough module are drawn using AutoCAD software. Precision laser cutting technology is then used to cut the acrylic sheet. Finally, acrylic adhesive is used to bond the components of the different modules, resulting in the throwing section module 1, the collision section module 2, and the collection trough module 3, all made of 3.00mm thick transparent acrylic sheet. Wherein, as... Figure 6 As shown, two-dimensional machining drawings of nail arrays with different spacings of 10.00cm, 15.00cm, and 20.00cm were drawn using AutoCAD software. Simultaneously, the diameter of the circular positioning hole was designed based on the diameter of the cylindrical high-precision stainless steel shaft, allowing it to accommodate steel shafts of different diameters (2 / 3 / 4 / 5 / 6 mm), forming collision segments with nails of different diameters and nail array densities. Figure 7 As shown, the acrylic sheet is imported into a precision laser cutting machine. Leveraging the machine's high-precision processing capabilities, positioning holes for the nails are cut, ensuring all holes are neatly arranged and evenly spaced. This effectively avoids the problems of hole misalignment and dimensional deviation caused by manual drilling. These cut sheets are then bonded together to create collision segment modules 2 with different nail array densities. The throwing segment, collision segment, and collecting groove have the same length and width. When the three parts are locked together with clips, they form a closed cuboid with unchanged length and width and a height consisting of three superimposed segments.

[0035] (2) The structure and manufacturing process of the nail are as follows: One end of the nail has a cylindrical section that fits into the first positioning hole, and the other end of the nail has two square sections that fit into the second positioning hole. The cylindrical section and the square sections are coaxially arranged. The nail is inserted into the first positioning hole through the cylindrical section and into the corresponding second positioning hole through the square section, so that the nail is perpendicular to the surface of the first plate wall and the second plate wall.

[0036] In this embodiment, as Figure 8 As shown, models of nails of different sizes and shapes were designed using Solidworks software, and the two ends of the nails were standardized to have the same size and shape. Figure 9 As shown, ABS nails are printed using 3D printing technology; the steel nails are sourced directly from standard high-precision stainless steel shafts; such as... Figure 10 As shown, the nail array module is assembled manually.

[0037] S2: Select a ball and throw it into the ball throwing section module 1. After being randomly collided with by the collision section module 2, the ball falls into the collection section of the collection slot module 3.

[0038] like Figure 11 As shown, in this embodiment, four types of industrial standard small balls are selected, uniformly divided into two diameters of 3mm and 6mm, covering high / low density and high / low elasticity materials: PS polystyrene balls: low density, high friction; Glass beads: high density, high elasticity; POM (Polyoxymethylene) balls: medium density, low friction; Steel ball: high density, high rigidity.

[0039] In this embodiment, the three-section structure and the replaceable and addable accessories of the collision section nails solve the problem of adjusting the nail material, size, shape and nail array arrangement parameters; and the adjustment of parameters such as the material and size of the ball and the initial conditions (velocity) of the collision.

[0040] S3: The mobile terminal collects images of the ball distribution. The native mini-program uses a 2D graphics rendering engine to perform offline image recognition, sequentially performing image preprocessing, threshold segmentation, contour detection and size calibration, and outputs the stacking height of the balls in each collection zone.

[0041] In this embodiment, a lightweight offline image recognition and counting module is developed based on a native WeChat mini-program. Utilizing the Canvas 2D engine, it completes the entire process of image acquisition, pixel analysis, target detection, and data conversion. No backend server or third-party vision library is required; the distribution data of balls in collection slots 1-17 can be output simply by capturing images on-site with a mobile device. The overall processing flow consists of four stages: image preprocessing, threshold segmentation, contour detection, and size calibration. Image preprocessing includes converting the acquired image to grayscale and performing noise suppression; threshold segmentation separates the ball region from the background region by setting a grayscale threshold; contour detection uses the OpenCV algorithm to identify the stacked contours of the balls in each collection zone and calculates the pixel height; size calibration converts the pixel height into the stacked height of the balls based on a pre-calibrated ratio between unit pixels and actual height.

[0042] Specifically: (1) Image preprocessing: After taking a photo of the platform collection slot with a mobile phone, the photo is grayscaled and Gaussian blurred to reduce noise and eliminate reflection and shadow interference.

[0043] (2) Threshold segmentation: Set a grayscale threshold to separate the sphere region from the transparent acrylic background and generate a binary image.

[0044] (3) Contour detection: The OpenCV algorithm identifies the contour of the small balls stacked in each collection slot and calculates the pixel height.

[0045] (4) Size calibration: Pre-calibrate the actual height corresponding to the unit pixel, convert the pixel height into the stacking height of the balls, and automatically output the height of the balls in slots 1 to 17.

[0046] In this embodiment, the principle of step-by-step image recognition is as follows: (1) Image acquisition stage The `wx.chooseMedia` API, officially provided by the WeChat Mini Program, allows users to take photos or select images from their albums, returning a temporary local path to the image: `tempFilePath`. This path is a temporary resource address within the Mini Program, valid only for the current session, and serves as the data source for subsequent image processing.

[0047] (2) Obtain the Canvas rendering node Query the page using wx.createSelectorQuery <canvas id="canvas">The component enables the new standard Canvas2D by enabling node:true mode and obtaining the canvas instance and canvas size.

[0048] (3) Loading image resources canvas.createImage() creates an internal image object for the mini-program, and assigns a temporary image path to img.src to load the image.

[0049] Image loading is an asynchronous operation; drawing operations can only be performed after img.onload is triggered.

[0050] (4) Image preprocessing (subsequent logic within onload) Core image processing is implemented using the Canvas context ctx: `ctx.drawImage()` draws the original image onto the canvas, allowing for scaling, cropping, and background removal as needed; `ctx.getImageData()` retrieves the canvas pixel array (RGBA pixel data); grayscale conversion, Gaussian blur noise reduction, and threshold binarization: iterate through the pixel array to convert the color image to grayscale, suppressing shooting reflections and acrylic shadow noise; contour traversal detection: identify the ball regions in each collection slot and calculate pixel height; pixel size calibration: based on a pre-calibrated ratio, obtain the ball distribution data in each collection slot and store it in `result[]`.

[0051] S4: Generate ball distribution data based on the ball height of each collection zone, draw the distribution curve, and display the statistical results and curves on the mini-program interface to complete the random distribution experiment process.

[0052] After the native mini-program completes the recognition, a visual verification interface is overlaid on the two-dimensional graphics rendering engine, including: marking the upper and lower physical boundaries of the collection partition with the first type of lines, marking the boundaries between each collection partition with the second type of lines, marking the top position of the small ball stack within each collection partition with the third type of lines, and marking the collection partition number at the corresponding position of each collection partition, so that the experimenters can manually review the recognition results.

[0053] Specifically: After the calculation is completed, the program overlays a visual annotation interface on the Canvas layer, making it easier for experimenters to manually verify the recognition results. (1) Set the legend in the upper left corner to distinguish the four types of annotation lines: blue line of the slot boundary, yellow dashed line of the slot separator, red line of the stack top, and green line of the fitting.

[0054] (2) The blue solid lines mark the upper and lower physical boundaries of all collection slots, and the yellow dashed lines divide the 17 slots equally.

[0055] (3) Mark the corresponding slot number below each card slot to intuitively match the height value with the physical position and quickly locate the recognition error caused by reflection or abnormal shooting angle.

[0056] S5: Adjust experimental parameters, conduct multiple control experiments under different variable conditions, and quantitatively analyze the impact of different parameter settings on the statistical distribution results.

[0057] In step S5, the adjustment of each parameter variable includes: (1) The collision segment module 2 with different pin array densities can be manually replaced.

[0058] (2) You can manually change nails of different sizes and shapes as well as different nail arrangements; for example, you can change the three-dimensional models of nails with three cross sections: round, square, and equilateral triangle, with diameters covering 3 / 4 / 5 / 6mm.

[0059] (3) By opening the buckle and removing the ball throwing section module 1, the type, size and other parameters of the ball can be changed manually; by adding auxiliary modules to the ball throwing section module 1 and the collision section module 2, the falling height of the particles can be adjusted so as to change the initial collision conditions of the particles.

[0060] A WeChat mini-program based on image recognition can quickly identify the height of the balls in each slot by collecting photos of the slots and generate a distribution curve, which greatly improves efficiency and makes it possible to conduct a large number of repeated experiments and multivariate experiments.

[0061] In this embodiment, by changing variables such as the diameter, material, and shape of the nails, the material of the ball, the falling height of the ball, and the direction and arrangement of the triangular nails, the distribution curve characteristics of the small ball after the collision were systematically studied, and the mechanism was explored from the microscopic and macroscopic levels of the collision. The specific experimental plan is shown in Table 1.

[0062] Table 1. Summary of Experimental Schemes

[0063] Experiment 1: Results and Pattern Analysis of Nail Variable Experiment like Figure 12 As shown, within the range of slots 2–16, the ranges of the coefficient of restitution of steel nails, ABS nails and PS balls of the same diameter are similar, their landing point distributions are similar, their standard deviations σ of the normal distributions are similar, and their curves are similar.

[0064] like Figure 13 As shown, within the range of slots 2–16, the larger the nail diameter, the smaller the gap between nails, the stronger the lateral constraint, the smaller the standard deviation σ, the narrower the curve, and the higher the peak value; the smaller the nail diameter, the larger the gap between nails, the weaker the lateral constraint, the more dispersed the distribution, the larger the standard deviation σ, and the shorter and wider the curve.

[0065] like Figure 14 As shown, within the range of slots 2–16, the triangular nail exhibits the strongest lateral disturbance from collisions, the largest standard deviation σ, and the most dispersed distribution; the round nail experiences symmetrical force, conforming to a standard normal distribution; the square nail demonstrates a significant effect in constraining lateral offset, with the smallest standard deviation σ and the highest concentration of impact points.

[0066] like Figure 15 As shown, within the range of slots 2–16, the coefficient of restitution e of the ps ball and the glass ball is small, the collision kinetic energy loss is large, the landing point is more concentrated, the standard deviation σ is smaller, and the curve is higher and narrower.

[0067] like Figure 16 As shown, the curves of each group of steel balls have a high degree of overlap and the numerical differences are slight; the current experimental results show that the initial velocity has a very small effect on the distribution curve of the small ball.

[0068] like Figure 17-20 As shown, the characteristic curve of the bimodal distribution of the small balls indicates that the nails with equilateral triangular cross sections are arranged in a specific way, which changes the symmetrical situation where the probability of the small balls colliding with each other is equal in a specific area. This results in the small balls appearing in some areas with a higher probability, and the number of balls in the corresponding collection tank is greater, thus presenting a bimodal distribution. If the arrangement of the nails in different areas is further adjusted, a trimodal distribution curve will be obtained.

[0069] Example 2 like Figure 2 As shown, this embodiment discloses a three-stage, multivariable, controllable Dalton plate general experimental platform, including: The pitching section module is equipped with a pitching opening and a ball landing channel; The collision section module is equipped with a nail array installation area, which has an array of nail plate positioning holes for installing removable nails. The collection trough module is located below the collision section module, and its interior is divided into several collection zones along the horizontal direction. The mobile terminal offline image recognition module is used to collect images of the ball distribution in the collection slot module. The native mini-program performs offline image recognition based on the two-dimensional graphics rendering engine and outputs the stacking height of the balls in each collection zone. The throwing section module, the collision section module, and the collection trough module are three independently manufactured modules. They are spliced ​​together from top to bottom and are detachably connected through V-shaped mechanical interfaces and snap-fit ​​structures set on the module joint surfaces.

[0070] Furthermore, the project directory structure of a native mini-program includes: The root directory configuration file includes a global lifecycle entry file, which defines global experiment parameters, and a global configuration file, which is used to complete page registration, permission declaration, and global window configuration. The business logic folder includes a page folder and a utility function folder. The page folder stores the logic code for image capture and recognition, while the utility function folder encapsulates general utility functions for numerical fitting, distribution curve plotting, and data export. Version management files, including core configuration files and ignore rule configuration files, are used to manage code iterations and filter compilation cache and temporary resource files; The mobile terminal offline image recognition module adopts a pure front-end offline computing architecture, where all image processing, height calculation, and visual annotation are completed locally on the mobile terminal.

[0071] In this embodiment, the mobile terminal offline image recognition module belongs to a standard native WeChat mini-program project. The project directory structure is clearly divided, and the functions of each directory are as follows: (1) Root directory configuration file appjs is the global lifecycle entry file for the mini-program, used to define global experimental parameters; appjson completes page registration, album and camera permission declarations, and global window configuration; appwxss0 unifies the global page style; and projectconfigjson stores the compilation and real device debugging configurations for developer tools, adapting to the needs of multi-device debugging.

[0072] (2) Business Logic Folder The pages folder stores all functional pages, with the image capture and recognition logic code deployed on the image detection page; the utils folder encapsulates general utility functions, including methods for numerical fitting, distribution curve plotting, and data export and reuse.

[0073] (3) Version management files The git and gitignore files are used for code iteration control, filtering compilation cache and temporary resource files, which facilitates subsequent simulation algorithms and parameter identification for iterative optimization.

[0074] The entire system adopts a pure front-end offline computing architecture. All image processing, height calculation, and visualization annotation operations are completed locally on the mobile phone, eliminating network transmission delays and making it suitable for batch quantitative experiments in laboratory environments without network access.

[0075] Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0076] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in a three-stage, multivariable, controllable Dalton board general experimental method as described in Embodiment 1 of this disclosure.

[0077] The steps and methods involved in the apparatus of Embodiments 2 and 3 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0078] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0079] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.< / canvas>

Claims

1. A general experimental method for a three-stage, multivariable, controllable Dalton plate, characterized in that, include: Prepare and assemble the ball-throwing section module, the collision section module, and the collection trough module, and select a target nail to install on the collision section module; Select a small ball and throw it from the ball throwing section module. After being randomly collided with by the collision section module, the ball falls into the collection sections of the collection trough module. The mobile terminal is used to collect images of the ball distribution. The native mini-program uses a two-dimensional graphics rendering engine to perform offline image recognition, and sequentially performs image preprocessing, threshold segmentation, contour detection and size calibration, and outputs the stacking height of the balls in each collection zone. Based on the height of the balls in each collection zone, generate ball distribution data, plot distribution curves, and display the statistical results and curves on the mini-program interface to complete the random distribution experiment process.

2. The three-stage, multivariable, controllable Dalton plate general experimental method as described in claim 1, characterized in that, The ball-throwing section module has a ball-throwing port and a ball-falling channel to guide the ball into the collision section module; the collision section module has a nail array installation area with arrayed nail plate positioning holes for installing removable nails; the collection trough module is located below the collision section module and its interior is divided into several collection zones along the horizontal direction to receive balls that fall into each zone after being struck by nails; the ball-throwing section module, the collision section module, and the collection trough module are three independently manufactured modules, which are assembled sequentially from top to bottom.

3. The three-stage, multivariable, controllable Dalton plate general experimental method as described in claim 2, characterized in that, The specific manufacturing processes for the ball-throwing section module, the collision section module, and the collection tank module include: Transparent sheets were laser-engraved to form the ball-throwing section module, the collision section module, the collection trough module, and other components. Three independent modules were formed by bonding them together with acrylic adhesive. The three independent modules were positioned and aligned from top to bottom through a V-shaped mechanical interface and locked together with a snap-fit ​​structure to complete the assembly of the whole machine. According to the experimental plan, target nails were selected and inserted into the nail plate positioning holes of the collision section module to form a nail array.

4. The three-stage, multivariable, controllable Dalton plate general experimental method as described in claim 1, characterized in that, The specific process of offline image recognition includes: Image preprocessing includes converting the acquired image into a grayscale image and performing noise suppression; threshold segmentation separates the ball region from the background region by setting a grayscale threshold; contour detection uses the OpenCV algorithm to identify the ball stacking contours in each collection partition and calculates the pixel height; size calibration converts the pixel height into the ball stacking height according to the pre-calibrated ratio between the unit pixel and the actual height.

5. The three-stage, multivariable, controllable Dalton plate general experimental method as described in claim 1, characterized in that, The experimental methods also include: adjusting experimental parameters, conducting multiple control experiments under different variable conditions, and quantitatively analyzing the impact of different parameter settings on the statistical distribution results.

6. The three-stage, multivariable, controllable Dalton plate general experimental method as described in claim 5, characterized in that, The experimental parameters include nail array density, nail material, nail size, nail shape, nail arrangement, ball size, ball material, and initial collision velocity.

7. The three-stage, multivariable, controllable Dalton plate general experimental method as described in claim 1, characterized in that, After the native mini-program is identified, a visual verification interface is overlaid on the two-dimensional graphics rendering engine, including: marking the upper and lower physical boundaries of the collection partition with the first type of lines, marking the boundaries between each collection partition with the second type of lines, marking the top position of the small ball stack in each collection partition with the third type of lines, and marking the collection partition number at the corresponding position of each collection partition, so that the experimenters can manually review the identification results.

8. A three-segment, multivariable, controllable Dalton plate universal experimental platform, characterized in that, include: A pitching section module, wherein the pitching section module is provided with a pitching port and a ball landing channel; The collision segment module is provided with a nail array installation area, which has an array of nail plate positioning holes, in which detachable nails are installed. A collection trough module is located below the collision section module, and its interior is divided into several collection zones along the horizontal direction. The mobile terminal offline image recognition module is used to collect images of the ball distribution in the collection slot module. The native mini-program performs offline image recognition based on the two-dimensional graphics rendering engine and outputs the stacking height of the balls in each collection zone. The ball-throwing section module, the collision section module, and the collection trough module are three independently manufactured modules, which are spliced ​​together from top to bottom and are detachably connected through V-shaped mechanical interfaces and snap-fit ​​structures set on the module joint surfaces.

9. The three-segment multivariable controllable Dalton plate universal experimental platform as described in claim 8, characterized in that, The project directory structure of the native mini-program includes: The root directory configuration file includes a global lifecycle entry file, which defines global experiment parameters, and a global configuration file, which is used to complete page registration, permission declaration, and global window configuration. The business logic folder includes a page folder and a utility function folder. The page folder stores the image capture and recognition logic code, and the utility function folder encapsulates general utility functions for numerical fitting, distribution curve plotting, and data export. Version management files, including core configuration files and ignore rule configuration files, are used to manage code iterations and filter compilation cache and temporary resource files; The mobile terminal offline image recognition module adopts a pure front-end offline computing architecture, where all image processing, height calculation, and visual annotation are completed locally on the mobile terminal.

10. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps of the general experimental method for a three-stage multivariable controllable Dalton board as described in any one of claims 1-7.

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