Two-dimensional motion trail tracking device based on permanent magnet positioning

Abstract

The invention discloses a two-dimensional motion trail tracking device based on permanent magnet positioning. The two-dimensional motion trail tracking device comprises an induction positioning plate, a signal acquisition module, a data transmission interface, a position calculation module and a display device, a three-axis magnetic sensor array is arranged on an induction positioning plate, magnetic field changes during movement of a permanent magnet are collected in real time, the three-dimensional position of the permanent magnet is inversed in combination with a magnetic dipole model, and the positioning precision is improved through an adaptive weighted fusion algorithm for multi-point position estimation. The signals are transmitted to display equipment after being processed, so that real-time drawing and physical quantity analysis of a motion track are realized; the permanent magnet serves as a passive projectile, power supply is not needed, and trajectory tracking of various motion modes such as horizontal projectile, free falling and simple pendulum can be achieved by matching with an optional auxiliary module. Through the synergistic effect of the passive permanent magnet and the magnetic sensor array, maintenance-free and high-precision real-time tracking and visual analysis of a two-dimensional motion track in a middle school physical experiment are realized.

Description

TECHNICAL FIELD

[0001] The application relates to the field of two-dimensional motion trajectory tracking, and particularly relates to a two-dimensional motion trajectory tracking device based on permanent magnet positioning. BACKGROUND

[0002] In middle school physics teaching, in order to intuitively show the concepts of horizontal projectile motion, inclined projectile motion and motion synthesis, it is often necessary to draw the motion trajectory of an object through experiments. At present, the traditional experimental devices commonly used in schools include: stroboscopic photography and electric spark tracing, etc. These methods have some obvious inconveniences and errors. Indirect measurement is usually required, the coordinate position of the object cannot be directly read, manual drawing and marking are required, which not only increases the difficulty of the experiment, but also reduces the success rate of one-time experiments. In order to solve these problems, in recent years, new technical solutions such as ultrasonic positioning, iron powder adsorption, magnetic writing board, magnetic dispersion liquid and magnet ball adsorption have been introduced into the field of education technology. Although these new technologies are simpler in structure and more intuitive in display effect compared with traditional methods, they still have problems such as low success rate of one-time experiments, low data accuracy, unstable performance, etc. Moreover, these technologies have high requirements for the temperature and humidity conditions of the experimental environment. They are easily affected by temperature and humidity, resulting in large experimental errors and poor stability. In the recent stage, the physical teaching experimental device (such as patent CN105845000A) commonly uses an electromagnetic positioning scheme, and the projectile needs to be integrated with a battery, a circuit and an electromagnetic coil to generate an alternating magnetic field. This active design has obvious defects such as the need to replace or charge the battery regularly, increasing the maintenance cost. Although these technologies have improved in some aspects, they still cannot fully meet the needs of modern physics teaching, especially in improving the convenience, accuracy and environmental adaptability of the experiment.

[0003] In view of these deficiencies, the application proposes a passive permanent magnet positioning scheme, which replaces the traditional active projectile with a permanent magnet, combines a high-sensitivity magnetic sensor array with a position estimation algorithm, and realizes maintenance-free, high-precision motion trajectory tracking. SUMMARY

[0004] In order to solve the above problems, the application proposes a two-dimensional motion trajectory tracking device based on permanent magnet positioning. The application uses a permanent magnet as a passive motion target, combines a three-dimensional position inversion algorithm based on a magnetic dipole model and an adaptive weighted fusion method of multi-sensor position estimation values, solves the problems of traditional experimental devices in physics teaching, such as dependence on active projectiles, inconvenience of maintenance, manual trajectory drawing, low data precision and low experimental success rate, and realizes automatic, real-time and high-precision visual tracking of the motion trajectory of the permanent magnet.

[0005] The specific scheme is as follows:

[0006] In one aspect, a two-dimensional motion trajectory tracking device based on permanent magnet positioning comprises:

[0007] An induction positioning plate for sensing the magnetic field change generated by the movement of the permanent magnet in a two-dimensional plane in real time to obtain an original magnetic field signal; the permanent magnet is a moving target, and the magnetization direction thereof is configured to be always perpendicular to the plane of the induction positioning plate during the movement;

[0008] A signal acquisition module connected to the induction positioning plate for dynamically filtering and integrating the original magnetic field signal to obtain preprocessed magnetic field data;

[0009] A data transmission interface connected to the signal acquisition module for transmitting the preprocessed magnetic field data to a position calculation module in real time;

[0010] A position calculation module connected to the data transmission interface for inversely calculating the real-time position coordinates of the permanent magnet on the two-dimensional plane according to the received preprocessed magnetic field data to obtain a coordinate sequence;

[0011] A display device for receiving the coordinate sequence to draw a trajectory and display numerical values, and display the motion trajectory curve and motion parameters of the permanent magnet in real time.

[0012] Further, the induction positioning plate is provided with a sensor array composed of a plurality of three-axis magnetic sensing units arranged in a predetermined pattern; each three-axis magnetic sensing unit includes three orthogonal single-axis magnetic sensors or one three-axis magnetic sensor for calculating the three-dimensional position of the permanent magnet; the single-axis magnetic sensor and the three-axis magnetic sensor are both magnetic sensors based on the Hall effect, anisotropic magnetoresistance, giant magnetoresistance, or tunnel magnetoresistance principle.

[0013] Further, the three-dimensional position of the permanent magnet is calculated by one three-axis magnetic sensing unit, specifically as follows:

[0014] A three-axis magnetic sensing unit in the sensor array is used to establish a sensor coordinate system {s} along the three axes of the sensing unit, and the position of the permanent magnet in the coordinate system is (x, y, z), the magnetization direction of which is consistent with the positive direction of the z-axis; the permanent magnet is equivalent to a magnetic dipole, and the magnetic field intensity (B x ,B y ,B z ) generated at the sensing unit is:

[0015]

[0016] Wherein, K represents a constant related to the magnetic moment of the permanent magnet; represents the distance from the permanent magnet to the magnetic sensor;

[0017] The ratio of the magnetic field components is calculated as follows:

[0018]

[0019] Substitute y = ax into the expression for B z and divide by B x Introducing the ratio t = z / x, we finally get a quadratic equation in t:

[0020]

[0021] After obtaining t, we can calculate the expression of distance r with respect to x:

[0022]

[0023] Substitute it into the formula of B x , and we can solve the x coordinate:

[0024]

[0025] Then we can find the coordinate y component:

[0026] y = ax.

[0027] Further, in the position calculation module, the real-time position coordinates of the permanent magnet on the two-dimensional plane are inversely calculated according to the received preprocessed magnetic field data, specifically including: calculating a plurality of permanent magnet position estimation values corresponding to each magnetic sensor from a plurality of preprocessed magnetic field data, assigning adaptive weights to each estimation value according to the difference degree between a plurality of permanent magnet position estimation values, and then weighting and fusing a plurality of permanent magnet position estimation values according to the adaptive weights to output the final permanent magnet position coordinates.

[0028] Further, the difference degree between the plurality of permanent magnet position estimation values is determined by calculating the average Euclidean distance between any position estimation value and all other position estimation values, and the adaptive weight is inversely proportional to the average Euclidean distance.

[0029] Further, the signal acquisition module is also provided with a self-checking unit for monitoring the working state of each magnetic sensing unit, and if an abnormality is detected, an alarm is triggered and the data acquisition process is stopped.

[0030] Further, the self-checking unit in the signal acquisition module is configured to support excitation response detection, zero drift monitoring, spatial consistency verification or range check to monitor the working state of the magnetic sensing unit:

[0031] The excitation response detection specifically applies a test excitation signal to the magnetic sensing unit, and diagnoses hardware failure by judging whether the output response deviates from the expected characteristics;

[0032] The zero-bias drift monitoring specifically involves recording the reference readings of each sensor in a static environment and monitoring whether the readings undergo abrupt drift during operation.

[0033] The spatial consistency verification specifically involves comparing the readings of adjacent sensors and identifying abnormal reading units by judging their spatial consistency.

[0034] The range check specifically determines whether the sensor output exceeds the preset valid data range.

[0035] The self-testing unit obtains diagnostic results through the above configuration, marks and alarms abnormal sensors based on the diagnostic results, and prevents their data from entering the position calculation process.

[0036] Furthermore, the data transmission interface can be a wired interface or a wireless interface.

[0037] Furthermore, the two-dimensional motion trajectory tracking device based on permanent magnet positioning also includes one or more optional auxiliary modules, which are mechanically connected to the sensing positioning plate, and are used to provide specific initial motion conditions for the permanent magnet or constrain its motion trajectory.

[0038] Furthermore, the optional auxiliary module is one or a combination of the following:

[0039] An adjustable sliding track, one end of which is fixed to the edge of the induction positioning plate, is used to install and guide the permanent magnet to perform projectile motion at a set initial velocity and angle;

[0040] The vertical release bracket is equipped with an electromagnet adsorption device to fix the permanent magnet at a preset height and allow it to fall freely after being triggered.

[0041] The variable pendulum length mechanism includes a pendulum string, a length adjuster, and a fixed support, used to suspend the permanent magnet to form a simple pendulum, and to simulate different simple pendulum motion conditions by changing the pendulum length;

[0042] A vertical oscillator guide rail is provided, which is perpendicular to the plane of the induction positioning plate and is equipped with a spring to guide the permanent magnet to perform damped vibration or simple harmonic motion in the vertical direction.

[0043] A curved track is a shaped guide rail with a specific radius of curvature, used to guide the permanent magnet in circular motion or other complex curved motion to verify the law of conservation of centrifugal force or mechanical energy.

[0044] The present invention adopts the above technical solution and has the following beneficial effects:

[0045] (1) By using permanent magnets as the moving target, this invention eliminates the need for built-in batteries or power supply devices, replacing traditional active electromagnetic projectiles. This fundamentally avoids the maintenance requirements of battery replacement or charging, reduces usage costs, and improves the stability and durability of the device.

[0046] (2) This invention performs three-dimensional position inversion based on the magnetic dipole model and effectively suppresses single-point measurement errors through an adaptive weighted fusion algorithm of multi-sensor position estimates, significantly improving positioning accuracy and system robustness, and ensuring that motion trajectory data is true and reliable.

[0047] (3) The device of the present invention can collect, calculate and display motion trajectory curves in real time, and automatically complete coordinate acquisition and image drawing, avoiding the tedious process of manually plotting points and drawing in traditional methods, greatly improving the success rate of experiments and teaching efficiency, and making it easier for students to intuitively understand the laws of motion. Attached Figure Description

[0048] Figure 1 This is a structural block diagram of a two-dimensional motion trajectory tracking device based on permanent magnet positioning according to an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of a projectile motion experimental device based on a permanent magnet positioning device according to an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of the mechanical energy conservation experimental apparatus based on a permanent magnet positioning device according to an embodiment of the present invention;

[0051] Figure 4 This is a schematic diagram of a damped vibration test apparatus based on a permanent magnet positioning device according to an embodiment of the present invention;

[0052] Figure 5 This is a schematic diagram of a centrifugal track experimental device based on a permanent magnet positioning device according to an embodiment of the present invention;

[0053] Figure 6 This is a schematic diagram of a pendulum experimental apparatus based on a permanent magnet positioning device according to an embodiment of the present invention;

[0054] Figure 7 This is a structural diagram of a permanent magnet positioning device for middle school physics teaching according to an embodiment of the present invention;

[0055] Figure 8 This is a system workflow diagram according to an embodiment of the present invention. Detailed Implementation

[0056] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0057] This invention discloses a two-dimensional motion trajectory tracking device based on permanent magnet positioning, comprising:

[0058] The sensing positioning plate is used to sense the changes in the magnetic field generated by the permanent magnet moving in a two-dimensional plane in real time and obtain the original magnetic field signal; the permanent magnet is the moving target, and its magnetization direction is configured to always be perpendicular to the plane of the sensing positioning plate during the movement.

[0059] Figure 1 In this embodiment, the permanent magnet 1 is connected to the induction positioning plate 3 via an optional auxiliary module 2. The induction positioning plate 3 is connected to the signal acquisition module 4, which is connected to the position calculation module 6 via a data transmission interface 5. The signal acquisition module calculates the real-time position coordinates of the permanent magnet on a two-dimensional plane. After receiving the position coordinates, the display device 7 displays the motion trajectory curve and motion parameters of the permanent magnet in real time. Specifically, the induction positioning plate is equipped with a sensor array consisting of multiple triaxial magnetic sensing units arranged according to a preset pattern. Each triaxial magnetic sensing unit includes three orthogonal single-axis magnetic sensors or one triaxial magnetic sensor. The triaxial magnetic sensing unit is used to calculate the three-dimensional position of the permanent magnet. Both the single-axis and triaxial magnetic sensors are magnetic sensors based on the Hall effect, anisotropic magnetoresistance, giant magnetoresistance, or tunneling magnetoresistance principles.

[0060] Specifically, the three-dimensional position of the permanent magnet is calculated using a triaxial magnetic sensing unit, as follows:

[0061] Establish a sensor coordinate system {s} along the three axes of a triaxial magnetic sensing unit in the sensor array. Let the position of the permanent magnet in this coordinate system be (x, y, z), and its magnetization direction be consistent with the positive z-axis. Equivalently representing the permanent magnet as a magnetic dipole, the magnetic field strength (B) generated at this sensing unit is... x B y B z )for:

[0062]

[0063] Where K represents a constant related to the magnetic moment of the permanent magnet; This indicates the distance from the permanent magnet to the magnetic sensor;

[0064] The ratio of the magnetic field components is calculated as follows:

[0065]

[0066] Substitute y = αx into B z The expression, and its relationship with B x Dividing by the ratio t = z / x, we finally obtain a quadratic equation in t:

[0067]

[0068] Once t is obtained, the expression for distance r with respect to x can be calculated:

[0069]

[0070] Substitute it into B x The x-coordinate can be obtained by reversing the formula:

[0071]

[0072] Then, the y-components of the coordinates are determined:

[0073] y = αx.

[0074] Specifically, the calculation process can be summarized as follows:

[0075] a) Obtain the magnetic field strength component (B) measured by the magnetic sensing unit. x B y B z );

[0076] b) Calculate the ratio α of the magnetic field components α = B y / B x and β = B z / B x ;

[0077] c) Substitute the ratio into the equation And solve for the key ratio t;

[0078] d) Using the formula Calculate the x-coordinate of the permanent magnet;

[0079] e) Then calculate the y-coordinate: y = αx.

[0080] The signal acquisition module, connected to the sensing positioning plate, is used to dynamically filter and integrate the original magnetic field signal to obtain preprocessed magnetic field data.

[0081] Specifically, the signal acquisition module is also equipped with a self-testing unit to monitor the working status of each magnetic sensing unit. If an abnormality is detected, an alarm is triggered and the data acquisition process is stopped. The sampling frequency of the signal acquisition module is adjustable in the range of 10Hz to 1000Hz.

[0082] The data transmission interface is connected to the signal acquisition module and is used to transmit the preprocessed magnetic field data to the position calculation module in real time.

[0083] Specifically, the data transmission interface can be a wired interface or a wireless interface, specifically a USB, Bluetooth, or Wi-Fi module.

[0084] The position calculation module, connected to the data transmission interface, is used to invert and calculate the real-time position coordinates of the permanent magnet on the two-dimensional plane based on the received preprocessed magnetic field data, and obtain a coordinate sequence.

[0085] Specifically, the position calculation module is further configured to: calculate multiple preprocessed magnetic field data to obtain multiple permanent magnet position estimates corresponding to each magnetic sensor; assign adaptive weights to each estimate based on the degree of difference between the multiple permanent magnet position estimates; and then perform weighted fusion of the multiple permanent magnet position estimates based on the adaptive weights to output the final permanent magnet position coordinates.

[0086] Specifically, the self-test unit in the signal acquisition module can be configured to perform excitation response detection, zero-bias drift monitoring, spatial consistency verification, or range check to monitor the operating status of the magnetic sensing unit.

[0087] The excitation response detection specifically involves applying a test excitation signal to the magnetic sensing unit and diagnosing hardware faults by determining whether its output response deviates from the expected characteristics.

[0088] The zero-bias drift monitoring specifically involves recording the reference readings of each sensor in a static environment and monitoring whether the readings undergo abrupt drift during operation.

[0089] The spatial consistency verification specifically involves comparing the readings of adjacent sensors and identifying abnormal reading units by judging their spatial consistency.

[0090] The range check specifically determines whether the sensor output exceeds the preset valid data range.

[0091] The self-testing unit obtains diagnostic results through the above configuration, marks and alarms abnormal sensors based on the diagnostic results, and prevents their data from entering the position calculation process.

[0092] Specifically, the degree of difference between the multiple permanent magnet position estimates is determined by calculating the average Euclidean distance between any position estimate and all other position estimates, and the adaptive weight is inversely proportional to this average Euclidean distance.

[0093] The display device is used to receive the coordinate sequence, draw the trajectory and display the values, and display the motion trajectory curve and motion parameters of the permanent magnet in real time.

[0094] A permanent magnet is used as a moving target, and its magnetization direction is configured to always be perpendicular to the plane of the sensing positioning plate during the movement. Its movement trajectory is captured in real time by the sensing positioning plate and transmitted to the position calculation module for position inversion through the signal acquisition module and data transmission interface. Finally, the movement parameters and movement trajectory of the permanent magnet are displayed on the display device.

[0095] Specifically, in this embodiment, the two-dimensional motion trajectory tracking device based on permanent magnet positioning also includes one or more optional auxiliary modules, which are mechanically connected to the sensing positioning plate or the device base, and are used to provide specific initial motion conditions for the permanent magnet or constrain its motion trajectory.

[0096] Specifically, the optional auxiliary modules are one of the following or a combination thereof:

[0097] An adjustable sliding track, one end of which is fixed to the edge of the induction positioning plate, is used to install and guide the permanent magnet to perform projectile motion at a set initial velocity and angle;

[0098] The vertical release bracket is equipped with an electromagnet adsorption device to fix the permanent magnet at a preset height and allow it to fall freely after being triggered.

[0099] The variable pendulum length mechanism includes a pendulum string, a length adjuster, and a fixed support, used to suspend the permanent magnet to form a simple pendulum, and to simulate different simple pendulum motion conditions by changing the pendulum length;

[0100] A vertical oscillator guide rail is provided, which is perpendicular to the plane of the induction positioning plate and is equipped with a spring to guide the permanent magnet to perform damped vibration or simple harmonic motion in the vertical direction.

[0101] Curved track, which is a shaped guide rail with a specific radius of curvature, is used to guide the permanent magnet to perform circular motion or other complex curved motion to verify the law of conservation of centrifugal force or mechanical energy.

[0102] Specifically, in this embodiment, each magnetic sensor calculates its own observed value (B). x B y B z This paper uses a position estimation method to calculate an estimated position of a permanent magnet. First, the location of the magnetic sensor is defined as the origin (0,0,0), and a corresponding coordinate system is established. Then, based on the magnetic dipole model, the position of the permanent magnet in space (x,y,z) is calculated through inversion. One inversion method involves calculating the ratio of the horizontal components of the magnetic field (B...). y / B x B z / B x To eliminate common coefficients in the formula and establish a proportional relationship between position coordinates, a quadratic equation about the ratio of position coordinates is constructed and solved by substituting the magnetic dipole model and introducing intermediate variables, and real solutions with physical meaning are selected. Finally, the obtained ratio is substituted back into the magnetic field formula to solve for the specific three-dimensional spatial coordinates. Another inversion calculation method is based on sensor measurements of B. zGiven the known magnetic moment and height of the permanent magnet, the distance from the permanent magnet to the sensor can be calculated. Next, B is measured using a sensor. x B y The value can determine the orientation of the permanent magnet in a two-dimensional plane.

[0103] Because the distance, angle, and noise level of each sensor differ from the target, the reliability (weight) of their estimation results also differs. The residual-weighted adaptive least squares fusion algorithm dynamically assigns weights by calculating the residual of each sensor's estimate (i.e., its consistency with other sensor estimates). The smaller the residual, the larger the weight. Finally, an optimal estimate is obtained through weighted least squares fusion. The specific steps are as follows:

[0104] a) Calculate the position estimate for each sensing unit. Assume the estimated position of the i-th magnetic sensing unit in the sensor coordinate system {s} is... Its estimated position p in the global coordinate system {g} i for

[0105]

[0106] in, Let be the position of the i-th magnetic sensing unit in the global coordinate system {g}.

[0107] b) Calculate the residual between every two estimates. For the i-th sensor, the residual r i It can be defined as the average Euclidean distance between the sensor estimate and all other sensor estimates.

[0108]

[0109] Where M is the total number of sensors. Residual r i This reflects the degree of consistency between the estimated value of the i-th sensor and other sensors. i The larger the value, the greater the potential interference or error of the sensor.

[0110] c) Calculate initial weights for each sensor's estimated value based on the residuals, such that the smaller the residual, the larger the weight.

[0111]

[0112] Where ∈ is a very small positive number used to prevent division by zero errors.

[0113] d) Normalize all initial weights to obtain the final weights w used for fusion. i ,Right now

[0114]

[0115] e) Calculate a weighted average of all location estimates based on the normalized weights to output the final fused location.

[0116]

[0117] This position calculation method and fusion algorithm have low computational complexity, making them very suitable for high-speed two-dimensional tracking scenarios.

[0118] Specifically, the inductive positioning plate used in this embodiment consists of a sensor array composed of multiple magnetic sensors, capable of sensing changes in the magnetic field generated by the permanent magnet. By acquiring and processing the magnetic field signals, the position information of the permanent magnet during its movement is determined. These magnetic sensors are arranged in a specific pattern to form an array, improving the accuracy and precision of the positioning. A signal acquisition module is integrated inside or connected to the inductive positioning plate. The microcontroller (MCU) acquires the signals sensed by the magnetic sensors through a data transmission bus, such as SPI, I2C, or RS485, performs preprocessing such as filtering and integration, and finally transmits the data to a computer or other data processing equipment. The permanent magnet, as the tracking target of the motion trajectory, possesses strong magnetism so that the magnetic sensors can clearly sense its magnetic field. Its shape and mass can be selected according to experimental requirements; generally, a regular shape and moderate mass are required to ensure the stability and repeatability of the projectile motion. The data transmission interface is a wired interface (such as a USB interface) or a wireless transmission module (such as a Bluetooth or Wi-Fi module), used to transmit the permanent magnet position data processed by the signal processing circuit to external devices such as computers and data acquisition units for further analysis, display, and recording. The base is used to support and fix the induction positioning plate and other related components, and the height, angle and other parameters can be adjusted according to experimental needs to place the induction positioning plate in a suitable working position.

[0119] Specifically, the principle of the positioning algorithm in this embodiment is that the target to be tracked performs two-dimensional motion on the inductive positioning plate. Based on the magnetic field model of the permanent magnet, the two-dimensional position of the permanent magnet is derived by inverting the three-dimensional magnetic field measurement values. For example, the position of the permanent magnet on the two-dimensional plane can be calculated using a single triaxial magnetometer LIS3MDL. The inductive positioning plate consists of multiple magnetometers. Although a single triaxial magnetometer can also locate the permanent magnet, multiple magnetometers can expand the positioning range and achieve higher positioning accuracy through data fusion (such as fusion based on residual adaptive weighting and fusion based on confidence criteria).

[0120] Sensor data acquisition involves placing the LIS3MDL magnetic sensor within the plane where the permanent magnet's position needs to be detected, ensuring it can sense changes in the magnetic field generated by the permanent magnet. The magnetic field strength data (B) along three axes output by the sensor is read via its measurement interface (such as I2C or SPI).x B y B z ).

[0121] Specifically, the permanent magnet positioning device in this embodiment has the following different applications in middle school physics teaching.

[0122] like Figure 2 The projectile motion experimental apparatus shown is constructed by adding an adjustable sliding track to a permanent magnet positioning device, thus forming a projectile motion experimental device. One end of the adjustable sliding track is fixed to the edge of the induction positioning plate, and the other end can be fitted with a permanent magnet, allowing for flexible adjustment of the initial position and height of the permanent magnet to simulate different initial conditions for projectile motion. The permanent magnet positioning device measures and records the trajectory of the permanent magnet, verifying the combined motion mechanism of horizontal uniform velocity and vertical free fall in projectile motion.

[0123] like Figure 3 The free-fall experimental apparatus shown is constructed by adding a vertical release bracket to a permanent magnet positioning device, thus forming a free-fall experimental device. The vertical release bracket is fixed to the top of the induction positioning plate and integrates an electromagnet adsorption device. The permanent magnet is fixed by the electromagnet and falls freely the instant the power is cut off, ensuring an initial velocity of zero. The permanent magnet positioning device measures and records the trajectory of the permanent magnet, allowing for qualitative observation and quantitative study of the motion laws of the object under free fall conditions.

[0124] A damped vibration testing apparatus is constructed by adding a vertical oscillator rail to a permanent magnet positioning device, thus forming a damped vibration testing device. Figure 4 As shown, the vertical oscillator guide rail can be constructed from transparent acrylic rails. One end of a spring is fixed above the induction positioning plate, and the other end suspends a permanent magnet oscillator. Limit grooves are located on both sides of the oscillator. In the damped vibration experiment, the permanent magnet undergoes damped vibration motion in front of the induction positioning plate. A magnetic sensor array senses the changes in the magnetic field of the permanent magnet in real time, collecting data on its trajectory and decay process. Through data analysis, the laws and characteristics of damped vibration are studied, helping students understand the influence of damping on vibration.

[0125] like Figure 5 The centrifugal track experimental apparatus shown is constructed by adding a curved track to a permanent magnet positioning device. This curved track consists of both semi-circular and straight sections, with a permanent magnet ball released from the top of the track. In the centrifugal track experiment, the permanent magnet moves in a circular motion along the specific track. A sensing positioning plate tracks the positional changes of the permanent magnet in real time, collecting data on its trajectory. Data analysis is used to study centrifugal force, the laws of circular motion, etc., primarily for demonstrating centrifugal phenomena, the laws of circular motion, and trajectory analysis of projectile motion.

[0126] like Figure 6The mechanical energy conservation experiment apparatus shown (simple pendulum method) is constructed by adding a variable pendulum length mechanism to the permanent magnet positioning device. The variable pendulum length mechanism is mounted above the induction positioning plate, with the end of the pendulum string connected to a permanent magnet pendulum bob. The pendulum length is adjusted via a spool winch. In the mechanical energy conservation experiment, the permanent magnet acts as the pendulum bob, swinging in front of the induction positioning plate. A magnetic sensor array senses the changes in the pendulum's magnetic field in real time, collecting its trajectory and periodic data. By analyzing the position data and calculating physical quantities such as velocity and potential energy, the law of conservation of mechanical energy is verified, helping students understand the conversion relationship between kinetic and potential energy.

[0127] All of the aforementioned high school physics experimental setups are based on permanent magnet positioning devices. Through the interaction between permanent magnets and magnetic sensor arrays, they achieve real-time tracking and data acquisition of different physical motion trajectories. They have significant application value in high school physics teaching, enabling the intuitive demonstration of various physical phenomena and laws, thereby improving teaching effectiveness and students' learning interest.

[0128] Specifically, the experimental procedure in this embodiment will be illustrated using projectile motion as an example:

[0129] (1) Device initialization: Fix the induction positioning plate horizontally on the base, ensuring that the plate surface is stable and not tilted. Zero and calibrate the position of the induction positioning plate through the host computer (host computer calibration operation is supported).

[0130] (2) Adjusting the initial conditions of the permanent magnet: Install the permanent magnet on the adjustable sliding track (one end fixed to the edge of the induction positioning plate). According to the experimental requirements, adjust the height and horizontal position of the sliding track, and set the initial release point coordinates of the permanent magnet to simulate projectile motion with different initial velocities.

[0131] (3) Start data acquisition: Turn on the signal acquisition module and set the tracking frequency to ≥200Hz. Confirm that the data transmission interface (USB or Bluetooth) is properly connected to the host computer to ensure real-time reception of coordinate data.

[0132] (4) Release the permanent magnet so that it slides horizontally along the end of the track and enters a projectile motion state. When the permanent magnet moves in the two-dimensional space above the induction positioning plate, the magnetic sensor array captures its magnetic field changes in real time, calculates and outputs the (x,y) coordinate sequence to the host computer through the positioning algorithm.

[0133] (5) Data recording and analysis: The host computer displays the trajectory curve in real time and records the complete motion trajectory of the permanent magnet from the release point to the landing point. After the experiment, the data is exported (wired / wireless transmission is supported), and the relationship between horizontal displacement, vertical displacement and time is analyzed to verify the laws of projectile motion.

[0134] The above experiments show that projectile motion can be considered as the combined motion of uniform linear motion in the horizontal direction and free fall motion in the vertical direction. Compared with traditional electromagnetic positioning devices, this invention provides a maintenance-free, highly reliable motion trajectory tracking device. Specifically, it eliminates the power supply requirement of the projectile to reduce maintenance costs; and supports real-time data acquisition and visualization analysis for various physical experiments such as projectile motion, pendulum motion, and free fall.

[0135] like Figure 7 The diagram shows a structural representation of a permanent magnet positioning device for middle school physics teaching according to an embodiment of the present invention. The device mainly consists of the following parts: a base serving as the supporting foundation for the entire system, providing stable mechanical fixation for the upper components, and a leveling mechanism to ensure the induction positioning plate remains horizontal, laying the foundation for accurate measurement; the induction positioning plate is the core sensing component of the system, its surface integrating a magnetic sensor array arranged in a grid pattern. This array consists of multiple high-precision triaxial magnetic sensing units, used to collect, in real-time and synchronously, the spatial distribution data of the magnetic field generated when the permanent magnet moves near the plate surface; a data transmission interface (such as USB Type-C) is provided on the side or rear of the device, responsible for high-speed transmission of the pre-processed magnetic field data from the signal acquisition module to an external computing device, and can receive control commands from a host computer.

[0136] The permanent magnet positioning device of this invention can demonstrate the trajectory of a moving object in a two-dimensional plane in middle school physics teaching. These experiments include projectile motion, free fall, centrifugal motion, damped motion, and conservation of mechanical energy. The device is used in conjunction with a computer, which has dedicated software installed to display the object's trajectory on the screen. The computer can also demonstrate that projectile motion is a composite motion of uniform linear motion in the horizontal direction and free fall in the vertical direction.

[0137] Specifically, Figure 8 The workflow of the device in this embodiment is demonstrated. After system startup, initialization is performed first, followed by a self-test procedure for the magnetic sensor unit. If the self-test passes, the system enters the multi-channel magnetic signal synchronous acquisition stage, with a sampling frequency of no less than 200Hz, and performs signal filtering, integration, and bias calibration. The processed magnetic field signal is sent to the positioning algorithm module via a wired (e.g., Type-C) or wireless (e.g., Bluetooth, Wi-Fi) interface. Based on single-sensor position inversion estimation and multi-sensor positioning fusion algorithms, the coordinate position of the permanent magnet is calculated in real time. After receiving the data, the host computer or mobile device can display the motion trajectory, record data, and perform further analysis in real time, and support experimental control. The entire process runs in a loop until the system receives a stop command, realizing closed-loop processing from magnetic field sensing to positioning output and visualization analysis.

[0138] Although the invention has been specifically shown and described in conjunction with preferred embodiments, those skilled in the art should understand that various changes in form and detail may be made to the invention without departing from the spirit and scope of the invention as defined in the appended claims, all of which shall be within the scope of protection of the invention.

Claims

1. A two-dimensional motion trajectory tracking device based on permanent magnet positioning, characterized in that, include: The induction positioning plate is used to sense the changes in the magnetic field generated by the permanent magnet moving in a two-dimensional plane in real time, and to obtain the original magnetic field signal. The permanent magnet is a moving target, and its magnetization direction is configured to always be perpendicular to the plane of the sensing positioning plate during the movement. The signal acquisition module, connected to the sensing positioning plate, is used to dynamically filter and integrate the original magnetic field signal to obtain preprocessed magnetic field data. A data transmission interface is connected to the signal acquisition module and is used to transmit the preprocessed magnetic field data to the position calculation module in real time. The position calculation module, connected to the data transmission interface, is used to invert and calculate the real-time position coordinates of the permanent magnet on the two-dimensional plane based on the received preprocessed magnetic field data, and obtain a coordinate sequence; The display device is used to receive the coordinate sequence, draw the trajectory and display the values, and display the motion trajectory curve and motion parameters of the permanent magnet in real time.

2. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 1, characterized in that, The sensing positioning plate is equipped with a sensor array consisting of multiple triaxial magnetic sensing units arranged according to a preset pattern; each triaxial magnetic sensing unit includes three orthogonal single-axis magnetic sensors or one triaxial magnetic sensor, used to calculate the three-dimensional position of the permanent magnet; both the single-axis magnetic sensors and the triaxial magnetic sensors are magnetic sensors based on the Hall effect, anisotropic magnetoresistive, giant magnetoresistive or tunneling magnetoresistive principles.

3. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 2, characterized in that, The three-dimensional position of the permanent magnet is calculated using a triaxial magnetic sensing unit, as detailed below: Establish a sensor coordinate system {s} along the three axes of a triaxial magnetic sensing unit in the sensor array. Let the position of the permanent magnet in this coordinate system be (x, y, z), and its magnetization direction be consistent with the positive z-axis. Equivalently representing the permanent magnet as a magnetic dipole, the magnetic field strength (B) generated at this sensing unit is... x B y B z )for: Where K represents a constant related to the magnetic moment of the permanent magnet; This indicates the distance from the permanent magnet to the magnetic sensor; The ratio of the magnetic field components is calculated as follows: Substitute y = αx into B z The expression, and its relationship with B x Dividing by the ratio t = z / x, we finally obtain a quadratic equation in t: Once t is obtained, the expression for distance r with respect to x can be calculated: Substitute it into B x The x-coordinate can be obtained by reversing the formula: Then, the y-components of the coordinates are calculated: y = αx.

4. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 1, characterized in that, In the position calculation module, the real-time position coordinates of the permanent magnet on the two-dimensional plane are calculated based on the received preprocessed magnetic field data. Specifically, this includes: calculating multiple estimated positions of the permanent magnet corresponding to each magnetic sensor by processing multiple preprocessed magnetic field data; assigning adaptive weights to each estimated value based on the degree of difference between the multiple estimated positions of the permanent magnet; and then weighting and fusing the multiple estimated positions of the permanent magnet according to the adaptive weights to output the final position coordinates of the permanent magnet.

5. The method as described in claim 4, characterized in that, The degree of difference between the multiple permanent magnet position estimates is determined by calculating the average Euclidean distance between any position estimate and all other position estimates, and the adaptive weight is inversely proportional to this average Euclidean distance.

6. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 1, characterized in that, The signal acquisition module also includes a self-testing unit to monitor the working status of each magnetic sensing unit. If an abnormality is detected, an alarm will be triggered and the data acquisition process will be stopped.

7. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 6, characterized in that, The self-test unit in the signal acquisition module can be configured to perform excitation response detection, zero-bias drift monitoring, spatial consistency verification, or range check to monitor the operating status of the magnetic sensing unit. The excitation response detection specifically involves applying a test excitation signal to the magnetic sensing unit and diagnosing hardware faults by determining whether its output response deviates from the expected characteristics. The zero-bias drift monitoring specifically involves recording the reference readings of each sensor in a static environment and monitoring whether the readings undergo abrupt drift during operation. The spatial consistency verification specifically involves comparing the readings of adjacent sensors and identifying abnormal reading units by judging their spatial consistency. The range check specifically determines whether the sensor output exceeds the preset valid data range. The self-testing unit obtains diagnostic results through the above configuration, marks and alarms abnormal sensors based on the diagnostic results, and prevents their data from entering the position calculation process.

8. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 1, characterized in that, The data transmission interface can be either a wired or wireless interface.

9. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 1, characterized in that, It also includes one or more optional auxiliary modules, mechanically connected to the sensing positioning plate, for providing specific initial motion conditions for the permanent magnet or constraining its motion trajectory.

10. The two-dimensional motion trajectory tracking device based on permanent magnet positioning according to claim 9, characterized in that, The optional auxiliary module is one or a combination of the following: An adjustable sliding track, one end of which is fixed to the edge of the induction positioning plate, is used to install and guide the permanent magnet to perform projectile motion at a set initial velocity and angle; The vertical release bracket is equipped with an electromagnet adsorption device to fix the permanent magnet at a preset height and allow it to fall freely after being triggered. The variable pendulum length mechanism includes a pendulum string, a length adjuster, and a fixed support, used to suspend the permanent magnet to form a simple pendulum, and to simulate different simple pendulum motion conditions by changing the pendulum length; A vertical oscillator guide rail is provided, which is perpendicular to the plane of the induction positioning plate and is equipped with a spring to guide the permanent magnet to perform damped vibration or simple harmonic motion in the vertical direction. A curved track is a shaped guide rail with a specific radius of curvature, used to guide the permanent magnet in circular motion or other complex curved motion to verify the law of conservation of centrifugal force or mechanical energy.

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