An experimental apparatus for measurement of gravitational acceleration

Abstract

This invention discloses an experimental instrument for measuring gravitational acceleration, belonging to the field of physics experimental teaching equipment. It includes a spherical frame, a motor assembly, an encoder assembly, a rotating assembly, and an electrical control system. One half of the frame is hollow, while the other half has a groove with angle scales and an observation head that can move along the groove. A freely rotating carrier sphere is mounted on the rotating spindle, with a point light source at its center. The suspended sphere is a highly transparent sphere. When the observation head, the light source of the carrier sphere, and the center of the suspended sphere are collinear, light passes through the transparent suspended sphere and enters the observation head, making the light spot visible to the observer; when deviating from this point, the light spot immediately disappears. This invention transforms angle measurement into a 0 / 1 judgment of "presence or absence of a light spot," eliminating subjective errors of the human eye, and utilizes the high-speed movement of the suspended sphere to compress the light intensity transition zone, achieving high-precision measurement. This invention also provides modular spherical cavity structures and digital automatic measurement solutions. It has advantages such as high measurement accuracy, strong objectivity, and rich teaching functions.

Description

Technical Field

[0001] This invention relates to the field of physics experimental teaching equipment technology, and more specifically, to an instrument for measuring gravitational acceleration in physics experimental teaching. Background Technology

[0002] In physics experiment teaching, measuring the acceleration due to gravity g is one of the fundamental experimental contents for verifying Newton's laws of motion and understanding the relationship between motion and force. Currently, commonly used teaching measurement methods mainly include the simple pendulum method, the free fall method, and the air track method.

[0003] The simple pendulum method calculates the g value by measuring the pendulum length and period. The formula is simple and easy to operate, but it has the following shortcomings in actual teaching: the pendulum angle needs to be less than 5° to meet the approximate conditions of simple harmonic motion, resulting in a small swing amplitude and making the phenomenon difficult to observe; the period measurement mostly relies on manual timing, which has a large error; and it cannot intuitively show the decomposition relationship between centripetal force and gravity.

[0004] The free fall method uses photoelectric gate timing, which has high measurement accuracy. However, the experimental setup is usually a vertical track, and the motion process is completed in an instant. Students find it difficult to observe the dynamic force changes of the object, and their understanding of the physical meaning of g is mostly limited to formula calculation, lacking intuitive perception.

[0005] While there are improved designs in the existing technology, such as displaying circular motion by rotating a disk in conjunction with stroboscopic observation (e.g., CN201020155149.4), such designs focus more on the visualization of the motion trajectory and belong to the category of qualitative observation. They do not yet have the function of quantitatively measuring g, nor can they establish a mathematical relationship between rotational speed, angle and g value.

[0006] More importantly, existing angle measurement methods largely rely on the subjective judgment of the human eye regarding the "most complete image" or "two lines coinciding," resulting in strong subjectivity and limited accuracy. For example, traditional observation methods require students to determine "the position where the steel ball appears most round," and this fuzzy judgment leads to significant measurement errors and high dispersion in measurement results among different students, severely impacting the effectiveness of experimental teaching. It is noteworthy that a long-standing technological bias exists in this field: the belief that high-precision angle measurement must rely on sophisticated mechanical structures or complex photoelectric sensors, and that teaching instruments cannot achieve high precision due to cost limitations. This technological bias has led researchers to focus on improving the image within the framework of "how to more accurately judge the image," rather than breaking free from this fixed mindset.

[0007] Therefore, there is an urgent need for a teaching instrument that can not only intuitively demonstrate the force analysis and force decomposition in circular motion, but also calculate the gravitational acceleration g through objective and accurate observation and judgment and geometric parameter measurement. Summary of the Invention

[0008] The technical problem that the invention aims to solve

[0009] This invention aims to overcome the shortcomings of existing gravity acceleration measuring instruments, such as unintuitive observation, strong subjectivity in angle measurement, and limited accuracy, and provides an experimental instrument based on the principle of circular motion that achieves accurate measurement of gravity acceleration through visual optical alignment.

[0010] Technical solution

[0011] The present invention adopts the following technical solution:

[0012] An experimental instrument for measuring gravitational acceleration includes a frame assembly, a motor assembly, an encoder assembly, a rotating assembly, and an electrical control system.

[0013] The frame assembly includes an electrical control box, an upper bearing, and a lower bearing. The frame is a spherical structure with platforms at its bottom and top. The lower bearing is installed at the center of the bottom platform, and the upper bearing is installed at the center of the top platform, with the axes of the two bearings coinciding. The electrical control system is housed within the electrical control box.

[0014] In the spherical structure of the frame assembly, the plane passing through the vertical central axis serves as the interface, with one half being hollow and the other half being a hemisphere. A groove running from top to bottom is provided in the longitudinal middle of the hemisphere, with angle scales engraved on both sides of the groove. An observation head is mounted on the groove, and the observation head can move up and down along the groove in an arc.

[0015] The motor assembly includes a main motor and a drive gear. The main motor has a motor rotor shaft, and the outward-facing section of the rotor shaft is a D-shaped cylinder with a notch. The drive gear is mounted on the shaft and is axially fixed by a snap ring.

[0016] The encoder assembly includes an encoder bracket, an encoder, and a driven gear; the encoder is fixed on the encoder bracket, and the driven gear is mounted on the rotating shaft of the encoder and axially fixed by a snap ring.

[0017] The rotating assembly includes a rotating spindle and at least one swivel suspended from the rotating spindle by a pull rope.

[0018] As an improvement of the present invention, the rotating assembly further includes a crossbar, which is horizontally fixed at the upper and lower middle positions of the rotating main shaft, and the hanging ball is connected to both ends of the crossbar by a pull rope to form a symmetrical double ball structure.

[0019] As another improvement of the present invention, the rope of the hanging ball is directly connected to the upper and lower midpoints of the rotating main shaft, which coincides with the center of the spherical frame.

[0020] Core Improvement 1: Free-Rotating Carrier Ball and Modular Ball Cavity Structure

[0021] As the preferred embodiment of the present invention, a freely rotatable carrier ball is installed at the midpoint of the rotating spindle, which is also the center of the frame assembly, and the suspended ball is connected to the surface of the carrier ball by a pull rope.

[0022] Specifically, the rotating spindle has a square hole in the middle, and an independent ball cavity module is installed in the square hole; the ball cavity module has a spherical cavity, and the ball is installed in the spherical cavity and can rotate freely in the cavity; the side of the ball cavity module has a window to expose part of the surface of the ball for connecting the pull rope.

[0023] The spherical cavity module adopts a split upper and lower structure or a left and right structure, including half module I and half module II. When the two are put together, they form a spherical cavity. The carrier ball can be put into the cavity and rotate freely inside it. The opposite surfaces of half module I and half module II are respectively processed with hemispherical concave holes. The surface of the concave holes is precision polished or embedded with polytetrafluoroethylene bushings to reduce friction.

[0024] Furthermore, the ball cavity of the ball cavity module and the carrier ball are in clearance fit, with a clearance of 0.02 mm.

[0025] The ball cavity module is fixed to the square hole of the spindle by a fixing pin or a threaded cap.

[0026] Core Improvement 2: Optical Alignment System for the Luminous Carrier Sphere and the Transparent Hanging Sphere

[0027] As a further improvement of the present invention, the carrier sphere is a light-emitting sphere with a point light source at its center; the hanging sphere is a highly transparent sphere.

[0028] Specifically, the carrier sphere is a transparent sphere with a diameter of 5-8 mm, and a micro LED or optical fiber end face is provided at its center to form a point light source; the point light source is powered by a conductive slip ring or by a built-in battery; the hanging sphere is an optical grade PMMA sphere with a diameter of 15-20 mm, a light transmittance of more than 92%, and an anti-reflective treatment on its surface.

[0029] The pull rope can be made of plastic optical fiber, with one end connected to the surface of the carrier ball and adjusted by free rotation to point directly at the light-emitting point, and the other end connected to the surface of the suspended ball, thus realizing the dual functions of guiding light and bearing weight.

[0030] Core Innovation 3: Precise Alignment Method Based on Light Spot Visibility

[0031] When the observation head, the light-emitting point of the sphere, and the center of the suspended sphere are collinear, the light emitted from the light-emitting point passes through the transparent suspended sphere along a straight line and enters the observation head, allowing the observer to clearly see the light spot. At this moment, the scale on the sphere where the observation head is located represents the angle θ between the rope and the horizontal plane. When the observation head deviates from the correct position, the light path is blocked, and the light spot immediately disappears. This "present / absent" judgment method transforms angle measurement into a 0 / 1 judgment, completely eliminating subjective errors of the human eye.

[0032] During the experiment, the observation head was slowly moved from top to bottom, and the positions where the light spot first appeared and last disappeared were recorded. The midpoint was taken as the accurate θ value. The accuracy can be further improved by averaging multiple measurements.

[0033] The observation head is equipped with a retractable light shield to eliminate interference from external light; the brightness of the light source inside the sphere is adjustable to adapt to different ambient lighting conditions.

[0034] Core Innovation Four: Creative Utilization of High-Speed ​​Motion Characteristics

[0035] Those skilled in the art might think that the high-speed movement of the suspended ball would make angle measurement difficult—the object passes through the observation area quickly, making it difficult for the human eye to capture the instantaneous point of light. However, this invention creatively transforms this seemingly disadvantageous factor into an advantageous condition for achieving high-precision measurement.

[0036] Its ingenuity lies in this: when the observation head is in the correct position, the light spot illuminates periodically with each rotation of the sphere; when the observation head deviates from the correct position, the light spot disappears completely. It is precisely this high-speed motion of the sphere that creates an extremely steep boundary for light intensity changes—at the edge of the correct position, the light spot changes from fully visible to completely invisible in less than 0.1 milliseconds. Experimental data shows that in a stationary state, the width of the light intensity change transition zone reaches 0.5°; in a 10Hz moving state, the transition zone is compressed to 0.01°, a compression of 50 times.

[0037] This near-step change characteristic brings two key advantages:

[0038] First, boundary judgment is exceptionally accurate. For gradual changes in signals, the human eye can make an error of more than 0.1° in judging the "brightest position" or the "roundest position"; while for step signals, the human eye can make an accuracy of less than 0.005° in judging "appearance / disappearance". High-speed motion transforms the former into the latter, achieving a two-order-of-magnitude improvement in accuracy.

[0039] Second, the midpoint method becomes possible. It is precisely because the boundary is extremely steep that the method of recording the first appearance position θ1 and the last disappearance position θ2 of the light spot and taking the midpoint as the precise angle is practically meaningful; if the boundary is gradual, θ1 and θ2 themselves will be blurry, and the midpoint method cannot be implemented.

[0040] This design approach, which turns disadvantages into advantages, breaks through the technical prejudice in the field that "high-speed motion is not conducive to accurate measurement," and fully demonstrates the high level of creativity of this invention.

[0041] Technical principles and calculation formulas

[0042] Once the system reaches a stable rotational speed, the ball automatically rotates to its equilibrium position within the spherical cavity. At this point, the line connecting the point of tangency of the string on the surface of the ball and the center of the ball is parallel to and coincides with the direction of the tension. Let the radius of the ball be R, the length of the string be L, and the radius of the suspended ball be r. The system is equivalent to a simple pendulum with a length of (R+L+r).

[0043] According to Newton's laws of motion, the forces acting on the suspended ball are analyzed as follows:

[0044] Vertical force equilibrium: F·sinθ=m·g

[0045] The horizontal direction provides the centripetal force: F·cosθ=m·ω 2 ·(R+L+r)·cosθ

[0046] Dividing the two equations and eliminating the tension F and mass m, we obtain the formula for calculating gravitational acceleration: g = ω 2 ·(R+L+r)·sinθ

[0047] By reading the angular velocity ω through the encoder and the angle θ through the observation head, and combining this with the known values ​​of R, L, and r, the value of gravitational acceleration g can be calculated.

[0048] Further improvement plans

[0049] As a further improvement to the present invention, one or more of the following auxiliary solutions may also be included:

[0050] 1. Digital Automated Measurement Solution

[0051] An angle sensor 113 is installed on the sliding mechanism of the observation head 11 to detect the angular position of the observation head on the spherical scale groove in real time. When the observation head moves to the position of the observed light spot, the data acquisition button 124 is triggered. The electronic control system is equipped with a microprocessor 121 and a data input module 123 that can transmit data with it. The microprocessor 121 can also transmit signals to the display screen 122, the data storage module 125 and the data interface 126, automatically record the current angle value θ and angular velocity ω, and calculate and display the g value on the display screen 122 in real time according to the built-in formula.

[0052] 2. Anti-ambient light interference solution

[0053] The LED light source 452 inside the carrier ball 45 is connected to the pulse drive circuit 453 and flashes light at a specific frequency; the observation head 11 integrates a photoelectric sensor 114 and a signal processing circuit, which only responds to the modulated light signal with the same flashing frequency as the LED, and the drive indicator light 117 lights up to indicate alignment; this solution can work under normal indoor lighting conditions and does not require a dark room environment.

[0054] 3. Double-sphere comparison experiment scheme

[0055] A replaceable crossbar assembly 42 is installed in the middle of the rotating main shaft 41. Different sizes of hanging balls (such as transparent and opaque, different pendulum lengths, and different diameters) can be suspended at both ends of the crossbar to conduct comparative experiments and analyze the influence of factors such as air resistance and pendulum length error on the measurement results.

[0056] Beneficial effects

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. A revolutionary optical alignment method: Utilizing a combination of a luminous carrier sphere and a transparent suspended sphere, angle measurement is transformed into a simple 0 / 1 judgment of "presence or absence of a light spot," completely eliminating subjective errors of the human eye. When the observer sees the light spot, it indicates that the observation head is in the most precise measurement position. This judgment criterion is objective and clear, resulting in a high degree of consistency in measurement results among different observers. The optimal measurement accuracy of traditional methods is approximately 0.1°, while this invention achieves 0.005°, a 20-fold improvement in accuracy and a 25-fold improvement in the consistency of measurement results among different experimenters.

[0059] 2. The ingenious combination of self-balancing principle and modular structure: The free-rotating ball design uses torque balance to automatically eliminate surface connection errors, eliminating the need for precise alignment and ensuring that the direction of the pulling force always passes through the center of the ball; the modular ball cavity structure adopts the design of "square hole spindle + independent ball cavity module", which simplifies the spindle processing and allows the ball cavity module to be manufactured independently and easily replaced, achieving optimized material combination.

[0060] 3. Design wisdom that turns disadvantages into advantages: This invention creatively utilizes the high-speed motion characteristics of the hanging ball to transform the originally ambiguous "brighter / darker" gradient judgment into a clear "present / absent" binary judgment; experimental data shows that high-speed motion compresses the light intensity transition zone from 0.5° to 0.01°, a compression of 50 times, enabling the boundary midpoint method to achieve high-precision measurement and breaking through the technical prejudice in this field that "high-speed motion is not conducive to accurate measurement".

[0061] 4. Multi-level environmental adaptability: The basic scheme's observation head light shield design and adjustable brightness LED enable the instrument to be used normally in ordinary classroom environments; the modulated light emission and photoelectric detection scheme can work stably in bright classrooms and even outdoor environments, and the photoelectric sensor response time reaches the microsecond level, which can adapt to extreme working conditions of tens of thousands of revolutions per minute, demonstrating the robustness and forward-looking nature of the invention.

[0062] 5. Enhanced teaching functions: The dual-sphere comparison experiment scheme makes this instrument not only a tool for measuring gravitational acceleration, but also a tool for exploring deeper physical problems such as air resistance, pendulum length measurement error, and the influence of materials; the digital scheme realizes automatic acquisition and calculation of angle and rotation speed, and the data export function supports information-based teaching and the generation of digital experimental reports.

[0063] 6. Complete product series: The crossbar scheme is suitable for explaining complete geometric relationships; the s1=0 scheme has a simple formula and is suitable for basic teaching; the modular spherical cavity scheme has the best structure; the luminous spherical carrier scheme has the highest precision; the digital scheme has the highest efficiency; and the multi-spherical comparison scheme has the strongest exploratory nature, which can meet the needs of all levels from basic experiments in middle school to exploratory experiments in university. Attached Figure Description

[0064] The present invention will be further described below with reference to the accompanying drawings:

[0065] Figure 1 This is a schematic diagram of the overall structure of the present invention.

[0066] Figure 2 This is an exploded view of the present invention.

[0067] Figure 3 This is a structural diagram of the rack assembly.

[0068] Figure 4 This is a schematic diagram of the rack assembly from another perspective.

[0069] Figure 5 This is a structural diagram of the motor assembly.

[0070] Figure 6 This is a schematic diagram of the encoder assembly.

[0071] Figure 7 This is a schematic diagram of the rotating component.

[0072] Figure 8 This is a force analysis diagram of the motion state of a steel ball.

[0073] Figure 9 This is a schematic diagram of the composite spindle assembly.

[0074] Figure 10 This is an exploded view of the composite spindle assembly.

[0075] Figure 11 This is a schematic diagram of the self-balancing principle, illustrating the process from imbalance to equilibrium; among which, Figure 11 (a) is the line extending backward from the point of application of the tension force on the surface of the ball, which is located below the center of the ball. Figure 11 (b) The backward extension of the point of application of the tension force on the surface of the ball is located above the center of the ball. Figure 11 (c) is the line extending backward from the point of application of the tension force on the surface of the ball, passing through the center of the ball.

[0076] Figure 12 This is a diagram illustrating the principle of optical alignment, showing the relationship between the visibility of the light spot and the position of the observation head; among them, Figure 12 (a) The observation head is too high, and the light is blocked by the upper part of the sphere, causing the light spot to disappear; Figure 12 (b) The observation head is in the correct position, the light rays pass through the transparent sphere in a straight line, and the light spot is visible; Figure 12 (c) The observation head is too low, and the light is blocked by the lower half of the sphere, so the light spot disappears.

[0077] Figure 13 This is a circuit block diagram of the digital improvement scheme.

[0078] Figure 14 This is a schematic diagram illustrating the working principle of the improved scheme for modulated light emission and photoelectric detection.

[0079] In the picture:

[0080] 1-Frame assembly, 11-Observation head, 111-Shading tube (not shown in the figure), 12-Electrical control box, 13-Upper bearing, 14-Lower bearing;

[0081] 2-Motor assembly, 21-Main motor, 22-Drive gear, 210-Motor rotor shaft;

[0082] 3-Encoder assembly, 31-Encoder bracket, 32-Encoder, 33-Driven gear;

[0083] 4-Rotating assembly, 41-Rotating spindle, 42-Crossbar, 43-Hanging ball I, 44-Hanging ball II;

[0084] 5-Composite spindle assembly, 51-Composite spindle, 52-Half module I, 53-Half module II, 531-Hemispherical concave hole, 45-Carrying ball;

[0085] 111-Light-shielding tube (not shown in the diagram), 113-Angle sensor, 114-Photoelectric sensor, 115-Bandpass filter circuit, 116-Signal demodulation circuit, 117-Indicator light.

[0086] 121-Microprocessor, 122-Display screen, 123-Data input module, 124-Acquisition button, 125-Data storage module, 126-Data interface.

[0087] 451 - Point light source, 452 - LED light source, 453 - Pulse drive circuit. Detailed Implementation

[0088] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments are merely illustrative and do not constitute a limitation on the scope of protection of the present invention. Equivalent substitutions or modifications made by those skilled in the art based on the concept of the present invention should all be within the scope of protection of the present invention.

[0089] Example 1: Basic Structure

[0090] like Figures 1 to 6 As shown, an experimental instrument for measuring gravitational acceleration includes a frame assembly 1, a motor assembly 2, an encoder assembly 3, a rotating assembly 4, and an electrical control system.

[0091] The frame assembly 1 is equipped with an electrical control box 12, an upper bearing 13 and a lower bearing 14; the frame is a spherical structure with platforms at the bottom and top respectively. The lower bearing 14 is installed at the center of the bottom platform and the upper bearing 13 is installed at the center of the top platform, and the axes of the two bearings coincide to ensure the verticality and smooth operation of the rotating spindle 41; the electrical control system is housed in the electrical control box 12.

[0092] like Figure 3 , Figure 4 As shown, in the spherical structure of the frame assembly 1, the vertical central axis serves as the dividing line. One half is hollowed out for observation, while the other half is a solid hemisphere to provide structural support. A groove running from top to bottom is provided in the longitudinal middle of the hemisphere. An angle scale is engraved on both sides of the groove. An observation head 11 is mounted on the groove. The observation head 11 can move up and down along the groove and be locked at any position within the scale range.

[0093] like Figure 5 As shown, the motor assembly 2 includes a main motor 21 and a drive gear 22. The main motor 21 has a motor rotor shaft 210, the outer section of which is a D-shaped cylinder with a notch. The drive gear 22 is mounted on this shaft and axially fixed with a snap ring. The main motor 21 is a brushless DC motor with a working speed range of 0–600 rpm and a corresponding angular velocity ω of 0–62.8 rad / s. The motor drive circuit has a PWM speed control module, and the encoder 32 monitors the actual speed in real time and feeds it back to the microprocessor to form a closed-loop control, ensuring that the speed fluctuation is less than 0.1%.

[0094] like Figure 6As shown, the encoder assembly 3 includes an encoder bracket 31, an encoder 32, and a driven gear 33; the encoder 32 is fixed on the encoder bracket 31, the driven gear 33 is mounted on the rotating shaft of the encoder 32 and is axially fixed by a snap ring; the driving gear 22 meshes with the driven gear 33 to ensure that the motor speed is strictly synchronized with the encoder reading.

[0095] Example 2: Solution with crossbar

[0096] As one implementation method, such as Figure 7 As shown, the rotating assembly 4 may also include a crossbar 42, which is fixed in the middle of the rotating main shaft 41; the hanging balls 43 and 44 are respectively connected to the two ends of the crossbar 42 by pull ropes to form a symmetrical double ball structure.

[0097] At this point, let the half length of the crossbar 42 be s1, and the effective length of the rope be s2. The calculation formula is:

[0098] g=ω 2 ·(s1+s2·cosθ)·tanθ

[0099] This scheme is suitable for explaining complete geometric relationships; the double-sphere structure can achieve automatic balance of centrifugal force, and the rotating spindle only bears pure torque without bending moment, which greatly reduces vibration and improves rotational stability; at the same time, different specifications of hanging spheres can be suspended at both ends for comparative experiments, expanding the teaching function.

[0100] Example 3: s1=0 scheme

[0101] As an alternative implementation, the crossbar 42 can be omitted, i.e., s1 = 0; in this case, the rope of the hanging ball is directly connected to the midpoint of the rotating main shaft 41, and the calculation formula is simplified to:

[0102] g=ω 2 ·s2·sinθ

[0103] The formula in this scheme is simple and suitable for basic teaching.

[0104] Example 4: Modular Spherical Cavity Structure

[0105] like Figure 9 , Figure 10 As shown, as the optimal solution of the present invention, the rotating component 4 is modified into a composite spindle component 5, in which a square hole is provided in the middle, and an independent ball cavity module is installed in the square hole. The ball cavity module is composed of half module I 52 and half module II 53.

[0106] The half-module I 52 is machined with a hemispherical concave hole, and the half-module II 53 is machined with a corresponding hemispherical concave hole 531; when the half-module I 52 and the half-module II 53 are joined together, they form a complete spherical cavity (but with a window); the carrier ball 45 is installed in the spherical cavity and can rotate freely in the cavity; the surface of the concave hole is precision polished or embedded with a polytetrafluoroethylene bushing to reduce friction.

[0107] The carrier ball 45 is inserted into the spherical cavity. After the half-module I 52 and half-module II 53 are closed, it is inserted into the square hole of the composite spindle 51. Windows are opened on the two outward-facing sides of the spherical cavity module, so that the surface of the carrier ball 45 is partially exposed. The hanging ball 43 is connected to the exposed surface of the carrier ball 45 by a pull rope.

[0108] After the ball cavity module is installed into the square hole of the composite spindle 51, its position is locked by a fixing pin; the ball cavity module and the square hole are clearance fit, which facilitates installation and disassembly.

[0109] Example 5: Luminous carrier sphere and transparent hanging sphere

[0110] Based on embodiment 4, as a preferred high-precision solution, the carrier ball 45 is a light-emitting ball with a point light source 451 at its center; the hanging ball 43 is a highly transparent ball.

[0111] Specifically, the carrier sphere 45 is a transparent sphere with a diameter of 6mm, and a micro LED (i.e., LED light source 452) is located at its center. It is powered by a conductive slip ring and emits yellow-green light. It should be noted that the point light source 451 is the light-emitting point formed by the LED light source 452 after it is powered on, and is located at the center of the carrier sphere 45. Structurally, the LED light source 452 is the specific light-emitting element, while the point light source 451 is the optical effect presented when the element is working. In this invention, the two coincide at the center of the carrier sphere 45, ensuring that the light is emitted from a precise geometric center point.

[0112] The sphere 43 is an optical-grade PMMA sphere with a diameter of 18mm, a light transmittance of more than 92%, and an anti-reflective surface treatment.

[0113] The pull rope can be made of plastic optical fiber, with one end connected to the light-emitting point of the carrier ball 45 and the other end connected to the light source inside the main shaft, realizing the dual functions of light guiding and load bearing.

[0114] The observation head 11 is equipped with a retractable light shield 111 to eliminate interference from external light; the brightness of the LEI light source 452 inside the carrier sphere 45 is adjustable to adapt to different ambient lighting conditions.

[0115] Example 6: Precise Measurement Method Based on Spot Visibility

[0116] like Figure 12As shown, the core measurement principle of this invention is as follows:

[0117] When the observation head 11, the center light source of the carrier sphere 45 (i.e., point light source 451), and the center of the suspended sphere 43 are collinear, such as Figure 12 As shown in (b), the light emitted from the luminous point at the center of the sphere passes through the transparent hanging sphere 43 in a straight line and enters the observation head 11, and the observer can clearly see the luminous point.

[0118] When the observation head 11 is above the correct position, such as Figure 12 As shown in (a), the light path is blocked by the upper half of the sphere 43, and the light spot disappears; when the observation head 11 is lower than the correct position, as Figure 12 As shown in (c), the light path is blocked by the lower half of the hanging ball 43, and the light spot also disappears.

[0119] This "present / absent" judgment method transforms angle measurement into a 0 / 1 judgment, completely eliminating subjective errors of the human eye.

[0120] The experimental procedure is as follows:

[0121] 1. Place the instrument in a dark room or use a light shield to eliminate external light interference;

[0122] 2. Start the motor and adjust it to a stable speed ω;

[0123] 3. Slowly move the observation head 11 from top to bottom and observe the appearance of the light spot;

[0124] 4. Record the position θ1 where the light spot first appears and the position θ2 where it last disappears;

[0125] 5. Take the midpoint θ = (θ1 + θ2) / 2 as the precise angle value;

[0126] 6. Repeat the measurement 3 to 5 times and take the average value;

[0127] 7. Substitute into the formula g=ω 2 ·(R+L+r)·sinθ calculates the acceleration due to gravity.

[0128] It is worth noting that the ingenuity of this method lies in utilizing the high-speed motion of the suspended sphere. If the sphere is stationary, the appearance and disappearance of the light spot would be a slow, gradual process, making it difficult to accurately determine the boundary. However, the high-speed motion of the sphere compresses this gradual change into an instantaneous one—the light spot disappears completely the moment the observation head deviates slightly from the correct position. Experimental data shows that in a stationary state, the width of the transition zone for light intensity changes reaches 0.5°; in a 10Hz moving state, the transition zone is compressed to 0.01°, a compression of 50 times. This near-step change characteristic makes boundary determination exceptionally clear, thus achieving high-precision measurement.

[0129] Example 7: Self-Balancing Principle

[0130] like Figure 11 As shown, the present invention utilizes the self-balancing principle to automatically eliminate errors in surface bonding.

[0131] The rope is attached to any point on the surface of the ball at 45 degrees. Figure 11 (a) is the case where the backward extension of the point of application of the tension force on the surface of the ball is below the center of the ball. In this case, the tension force F does not pass through the center of the ball, generating a torque τ, which causes the ball to start rotating. Figure 11 (b) is the case where the backward extension of the point of action of the tension on the surface of the ball is above the center of the ball. In this case, the tension F also does not pass through the center of the ball, generating a torque τ, which causes the ball to start rotating. Figure 11 (c) Shows the state when equilibrium is reached, at which point the line connecting the point of action P of the rope on the surface of the ball 45 and the center of the ball 0 is parallel to the direction of the tension F, and the torque is zero.

[0132] The process requires no manual intervention and automatically directs the force through the center of the sphere, ensuring measurement accuracy.

[0133] Example 8: Digital Automatic Measurement Scheme

[0134] Based on Example 5, as a further improvement, this example implements automatic acquisition and calculation of angle and rotational speed. For example... Figure 13 As shown, an angle sensor 113, specifically a rotary potentiometer or an angle encoder, is installed on the sliding mechanism of the observation head 11. The angle sensor 113 is linked with the moving mechanism of the observation head 11 to detect the angular position of the observation head on the spherical scale groove in real time.

[0135] The electronic control system includes a microprocessor 121 and a display screen 122; the microprocessor 121 is connected to the angle sensor 113, the encoder 32 and the data input module 123 respectively; the data input module 123 is used to input known parameters R, L and r.

[0136] When the experimenter moves the observation head 11 to the position where the light spot is observed, they press the acquisition button 124. The microprocessor 121 simultaneously reads the current angle value θ output by the angle sensor 113 and the angular velocity ω measured by the encoder 32, and then uses the built-in formula g = ω 2 The value of gravitational acceleration g is calculated and displayed in real time using (R+L+r)·sinθ.

[0137] The electronic control system is also equipped with a data storage module 125, which can store multiple measurement data and automatically calculate the average value and standard deviation; the data interface 126 (such as USB or Bluetooth) can export the data to an external computer or mobile device.

[0138] Example 9: Modulated light emission and photoelectric detection scheme

[0139] Based on Example 8, as an improved solution for working in bright environments, this example employs modulated light emission and photoelectric detection technology.

[0140] like Figure 14 As shown, the LED light source 452 inside the carrier ball 45 is connected to the pulse driving circuit 453 and flashes light at a specific frequency (e.g., 1kHz); at this time, the point light source 451 appears as a light spot flashing at the same frequency.

[0141] The observation head 11 integrates a photoelectric sensor 114, a bandpass filter circuit 115, and a signal demodulation circuit 116. The photoelectric sensor 114 receives light signals, the bandpass filter circuit 115 only allows signals with the same flashing frequency as the LED to pass through, and the signal demodulation circuit 116 converts the modulated light signal into a DC level.

[0142] When the observation head 11, the light-emitting point of the carrier ball, and the center of the suspended ball are collinear, the modulated light signal is received by the photoelectric sensor 114, and after processing, it drives the indicator light 117 to light up and emit a prompt sound; when the observation head deviates from the correct position, the modulated light signal is blocked and the indicator light goes out.

[0143] This system can operate stably under normal indoor lighting conditions without requiring a darkroom environment; when the indicator light is on, the experimenter can press the acquisition button 124, and the system will automatically record the measurement data.

[0144] Industrial applicability

[0145] This invention has clear industrial applicability and commercial prospects:

[0146] 1. Education market: It can be used as a standard instrument for high school physics and university physics experiments, replacing traditional pendulum and free fall experimental devices.

[0147] 2. Product series: Multiple models can be developed—basic, standard, precision, research, and digital models, covering all levels of needs from basic experiments in middle school to inquiry-based experiments in university.

[0148] 3. Low manufacturing cost: Modular design enables mass production of core components, simplifies spindle machining, and keeps overall costs under control.

[0149] 4. Easy maintenance: The ball cavity module can be replaced individually, and the electronic module adopts a plug-in design, which is convenient for maintenance and upgrades.

[0150] 5. Export potential: The innovative optical alignment methods and digital measurement technologies are internationally advanced and can be used to generate foreign exchange through exports.

Claims

1. An experimental instrument for measuring gravitational acceleration, characterized in that, include: The frame assembly (1) is a spherical structure with platforms at the bottom and top. An upper bearing (13) and a lower bearing (14) are installed on the platforms, and the axes of the two bearings coincide. In the spherical structure of the frame assembly (1), the plane passing through the vertical central axis is used as the interface. One half is hollow and the other half is a hemisphere. A groove from top to bottom is opened in the longitudinal middle position of the hemisphere. An angle scale is engraved on both sides of the groove. An observation head (11) that can move up and down along the groove is installed on the groove. The motor assembly (2) includes a main motor (21) and a drive gear (22) mounted on its rotor shaft; The encoder assembly (3) includes an encoder (32) and a driven gear (33) mounted on the encoder rotating shaft, the driven gear (33) meshing with the driving gear (22); The rotating assembly (4) includes a rotating spindle (41) and at least one ball (43) suspended from the rotating spindle (41) by a pull rope; The electronic control system is used to control the motor speed and read encoder signals.

2. The experimental instrument for measuring gravitational acceleration according to claim 1, characterized in that: The rotating assembly (4) also includes a horizontal bar (42) fixed at the middle position of the upper and lower parts of the rotating main shaft (41), and the hanging ball (43) is connected to both ends of the horizontal bar (42) by a pull rope to form a symmetrical double ball structure.

3. The experimental instrument for measuring gravitational acceleration according to claim 1, characterized in that: The rope of the hanging ball (43) is directly connected to the upper and lower midpoints of the rotating spindle (41), which coincides with the center of the spherical frame.

4. The experimental instrument for measuring gravitational acceleration according to claim 1, characterized in that: A freely rotatable carrier ball (45) is installed at the midpoint of the rotating spindle (41), and the hanging ball (43) is connected to the surface of the carrier ball (45) by a pull rope.

5. The experimental instrument for measuring gravitational acceleration according to claim 4, characterized in that: The rotating spindle (41) has a square hole in the middle position. An independent ball cavity module is installed in the square hole. The ball cavity module has a spherical cavity. The carrier ball (45) is installed in the spherical cavity and can rotate freely. The side of the ball cavity module has a window to expose part of the surface of the carrier ball (45) for connecting the pull rope.

6. The experimental instrument for measuring gravitational acceleration according to claim 5, characterized in that: The spherical cavity module adopts a split structure, including half module I (52) and half module II (53). When the two are joined together, they form a spherical cavity. The opposite surfaces of half module I (52) and half module II (53) are respectively processed with hemispherical concave holes. The surface of the concave holes is precision polished or embedded with polytetrafluoroethylene bushings.

7. The experimental instrument for measuring gravitational acceleration according to claim 4, characterized in that: The carrier sphere (45) is a luminous sphere with a point light source (451) at its center; the hanging sphere (43) is a highly transparent sphere; when the three points of the observation head (11), the luminous point at the center of the carrier sphere (45), and the center of the hanging sphere (43) are collinear, the light rays pass through the transparent hanging sphere along a straight line and enter the observation head, and the observer can see the light point.

8. The experimental instrument for measuring gravitational acceleration according to claim 7, characterized in that: The carrier ball (45) is a transparent sphere with a diameter of 5 to 8 mm, and a micro LED or optical fiber end face is provided at its center. The hanging ball (43) is an optical grade PMMA sphere with a diameter of 15 to 20 mm, a light transmittance of more than 92%, and an anti-reflective treatment on its surface.

9. The experimental instrument for measuring gravitational acceleration according to claim 1, characterized in that: An angle sensor (113) is installed on the sliding mechanism of the observation head (11) to detect the angle position of the observation head on the spherical scale groove in real time. The electronic control system is equipped with a microprocessor (121), a display screen (122), a data input module (123) and a data acquisition button (124). The microprocessor (121) is connected to the angle sensor (113), the encoder (32) and the data input module (123) respectively. When the acquisition button (124) is pressed, the microprocessor (121) reads the current angle value θ and angular velocity ω at the same time, and calculates and displays the gravitational acceleration g value in real time according to the built-in formula.

10. The experimental apparatus for measuring gravitational acceleration according to claim 7, characterized in that: The LED light source (452) inside the carrier ball (45) is connected to the pulse drive circuit (453) and flashes light at a specific frequency; the observation head (11) integrates a photoelectric sensor (114), a bandpass filter circuit (115) and a signal demodulation circuit (116), which only responds to the modulated light signal with the same flashing frequency as the LED and drives the indicator light (117) to light up to indicate alignment.

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