Classroom teaching method and teaching device based on digital twin technology

文档序号:193166 发布日期:2021-11-02 浏览:43次 中文

阅读说明:本技术 一种基于数字孪生技术的课堂教学方法及教学装置 (Classroom teaching method and teaching device based on digital twin technology ) 是由 潘卫清 戴恩文 苏衍峰 于 2021-08-02 设计创作,主要内容包括:本发明公开了一种基于数字孪生技术的课堂教学方法及教学装置,本发明通过终端选择需进行的实验,并发送指令至对应的实验装置进行实验,在实验过程中采集实验装置实验的视频图像和数据,并在终端上显示,用于学习者观察实际实验过程和获取实际实验数据,在观察完毕实际实验后在终端上通过数字孪生技术操控虚拟模型演示实验的理论原理和理论模型,最后根据理论原理对采集到的实验数据进行计算,并将结果与理论原理推导的结果进行对比,从而完成教学。因此本发明能够更好的帮助教师完成教学内容的演示与知识的传授,更好的帮助学生从多角度对物理本质进行全方位的综合学习。(The invention discloses a classroom teaching method and a teaching device based on a digital twin technology, wherein a terminal selects an experiment to be performed, and sends an instruction to a corresponding experiment device to perform the experiment, video images and data of the experiment device are collected in the experiment process and displayed on the terminal, so that a learner can observe an actual experiment process and obtain actual experiment data, a virtual model is controlled on the terminal to demonstrate theoretical principles and theoretical models of the experiment through the digital twin technology after the actual experiment is observed, and finally, the collected experiment data is calculated according to the theoretical principles and compared with results deduced from the theoretical principles, thereby completing the teaching. Therefore, the teaching aid can better help teachers to finish teaching content demonstration and knowledge teaching, and better help students to comprehensively learn physical essence from multiple angles in an all-round way.)

1. A classroom teaching method based on a digital twin technology is characterized in that: the terminal and the experimental device are in data transmission, the virtual experimental model on the terminal is enabled to be synchronously interacted with the operation steps and parameter settings of the experimental device in real time through a digital twinning technology, meanwhile, the camera shoots an experimental process video of the experimental device in real time, and the experimental process video is synchronously displayed on the terminal.

2. The classroom teaching method based on digital twinning technology as claimed in claim 1, wherein: the method specifically comprises the following steps:

s1: a user logs in interactive software of a terminal, selects an experimental project to be performed and issues an operation instruction, and the terminal transmits the operation instruction to a corresponding experimental device;

s2: the experimental device receives the operation instruction and starts to perform the experiment;

s3: acquiring an experimental process video of an experimental device experiment, and synchronously displaying an actual experimental process and experimental data on a terminal;

s4, synchronously displaying theoretical principles and theoretical models of the experiment on the terminal;

and S5, calculating the acquired experimental data according to the theoretical principle, and comparing the result with the result deduced by the theoretical principle to finish teaching.

3. The classroom teaching method based on digital twinning technology as claimed in claim 2, wherein: and after the user clicks the real experiment and/or calculation verification in the interactive software, calculating the experiment data in the display area in the interactive software.

4. The teaching device of the classroom teaching method based on digital twin technology as claimed in claim 1, wherein: the device comprises a terminal (11), wherein a digital twin medium (12) is arranged in the terminal (11), and the digital twin medium (12) is connected with an experiment module (14) through a communication module (13); the experiment module (14) is connected with a plurality of experiment devices (16) through a main control module (15); .

5. The teaching device of the classroom teaching method based on digital twin technology as claimed in claim 4, wherein: the terminal is a mobile phone, a computer or a tablet computer.

6. The teaching device of the classroom teaching method based on digital twin technology as claimed in claim 4, wherein: the communication mode of the communication module (13) is network cable connection, WiFi connection and USB connection.

7. The teaching device of the classroom teaching method based on digital twin technology as claimed in claim 4, wherein: the master control module (15) includes one or more processors and memory for storing associated operating instructions.

8. The teaching device of the classroom teaching method based on digital twin technology as claimed in claim 4, wherein: the experiment module (14) is also provided with a camera module (17), a power supply module (18) and an illumination module (19).

9. The teaching device of the classroom teaching method based on digital twin technology as claimed in claim 4, wherein: the experimental device (16) comprises a Brewster angle experimental device (1), an optical diffraction experimental device (2), an equal-thickness interference experimental device (3), a grating diffraction experimental device (4), a Malus law experimental device (5) and a Young double-slit interference experimental device (6).

Technical Field

The invention relates to the technical field of teaching, in particular to a classroom teaching method and a classroom teaching device based on a digital twin technology.

Background

Along with the state continues to vigorously carry out teaching reform, quality education is further realized, and the experiment module can help teaching reform. The experiment module can assist teachers to quickly develop teaching experiments with qualitative demonstration and quantitative verification functions in class. Simultaneously this also helps novel education mode, helping hand teaching reform. The method also increases the ways of pre-study and post-course development of students and assists in developing independent and innovative research-type study. Meanwhile, the vivid and real experimental scene is beneficial to exciting the learning interest of students and deepening the understanding of the students on the physical principle and the physical concept. However, the existing problems include that teachers lack corresponding teaching demonstration means and instruments in classroom teaching, and students lack deep understanding of abstract physical principles and physical concepts.

Disclosure of Invention

The invention aims to provide a classroom teaching method and a classroom teaching device based on a digital twin technology. The invention can better help teachers to finish teaching content demonstration and knowledge teaching, and better help students to comprehensively learn physical essence from multiple angles.

The technical scheme of the invention is as follows: a classroom teaching method based on a digital twinning technology is characterized in that a terminal and an experimental device carry out data transmission, a virtual experimental model on the terminal is enabled to synchronously interact with operation steps and parameter settings of the experimental device in real time through the digital twinning technology, meanwhile, a camera shoots an experimental process video of the experimental device in real time, and the experimental process video is synchronously displayed on the terminal.

The classroom teaching method based on the digital twin technology specifically comprises the following steps:

s1: a user logs in interactive software of a terminal, selects an experimental project to be performed and issues an operation instruction, and the terminal transmits the operation instruction to a corresponding experimental device;

s2: the experimental device receives the operation instruction and starts to perform the experiment;

s3: acquiring an experimental process video of an experimental device experiment, and synchronously displaying an actual experimental process and experimental data on a terminal;

s4, synchronously displaying theoretical principles and theoretical models of the experiment on the terminal;

and S5, calculating the acquired experimental data according to the theoretical principle, and comparing the result with the result deduced by the theoretical principle to finish teaching.

According to the classroom teaching method based on the digital twin technology, after a user clicks real experiments and/or calculation verification in interactive software, experimental data are calculated in a display area in the interactive software.

The classroom teaching method based on the digital twinning technology comprises a terminal, wherein a digital twinning medium is arranged in the terminal and is connected with an experiment module through a communication module; the experimental module is connected with a plurality of experimental devices through the main control module; .

In the classroom teaching method based on the digital twin technology, the terminal is a mobile phone, a computer or a tablet computer.

In the classroom teaching method based on the digital twin technology, the communication modes of the communication module are network cable connection, WiFi connection and USB connection.

In the classroom teaching method based on the digital twin technology, the main control module includes one or more processors and a memory, and is used for storing relevant operation instructions.

In the classroom teaching method based on the digital twin technology, the experiment module is also provided with a camera module, a power supply module and an illumination module

According to the classroom teaching method based on the digital twin technology, the experimental device comprises a Brewster angle experimental device, an optical diffraction experimental device, an equal-thickness interference experimental device, a grating diffraction experimental device, a Malus law experimental device and a Young double-slit interference experimental device.

In the teaching device of the classroom teaching method based on the digital twin technology, the grating diffraction experimental device comprises a fourth base, a plurality of fourth lasers are arranged on the fourth base, and second dichroic mirrors are correspondingly arranged at the front ends of the fourth lasers; a first single slit sheet is arranged on the fourth base and positioned on one side of the second dichroic mirror, a second collimating lens is arranged in front of the first single slit sheet, a second experiment turntable is arranged in front of the second collimating lens, and a plurality of second experiment sheets distributed in an annular mode are arranged on the second experiment turntable; a second Fourier transform lens positioned in front of the second experiment turntable is arranged on the fourth base, and a first observation screen is arranged in front of the second Fourier transform lens; and a second camera facing the first observation screen is further arranged on the fourth base.

According to the teaching device of the classroom teaching method based on the digital twin technology, the Malus law experiment device comprises a fifth base, a fifth laser is arranged on the fifth base, a polarizer is arranged in front of the fifth laser, a second analyzer is arranged in front of the polarizer, and a fifth detector is arranged in front of the second analyzer; and a third motor is further arranged on the fifth base, a second gear is arranged at the output end of the third motor, and second teeth meshed with the second gear are annularly distributed on the second polarization analyzer.

Compared with the prior art, the invention has the following beneficial effects:

1. the method comprises the steps of carrying out data transmission with an experimental device through a terminal, enabling a virtual experimental model on the terminal to be synchronously interacted with operation steps and parameter settings of the experimental device in real time through a digital twinning technology, simultaneously shooting an experimental process video of the experimental device by a camera in real time, synchronously displaying the experimental process video on the terminal, and being used for a learner to observe an actual experimental process and obtain actual experimental data, synchronously displaying a theoretical principle and a theoretical model of an experiment on the terminal after the actual experiment is observed, finally calculating the acquired experimental data according to the theoretical principle, and comparing the result with a result derived from the theoretical principle, thereby completing teaching. Therefore, the teaching aid can better help teachers to complete demonstration of teaching contents and teaching of knowledge, better help students comprehensively learn physical essence from multiple angles, and simultaneously can better help teachers to develop qualitative demonstration and quantitative verification teaching experiments in class, and is also helpful for increasing ways of pre-lesson and post-lesson development of students, stimulating learning interests of students and deepening understanding of physical concepts.

2. The invention also provides an experimental device, wherein a user accesses and controls the experimental module through a digital twin medium of the terminal, a power supply module in the experimental module provides power for the experimental device to ensure the operation of the experimental device, a communication module transmits an operation instruction of the user to a main control module, and the main control module sends a specific instruction to a device in the experimental module to perform a related physical experiment; the main control module sends instructions to the camera module and the lighting module, the camera module is used for collecting physical experiment phenomena, and the lighting module is used for compensating the ambient light intensity.

3. The experimental device has diversity, and can demonstrate Brewster angle experiment, single slit and round hole diffraction experiment, equal thickness interference experiment, grating diffraction experiment, Malus law experiment and Young double slit interference experiment.

In the grating diffraction experiment device, a grating diffraction experiment light path is formed by a fourth laser, a second dichroic mirror, a first single slit sheet, a second collimating lens, a second experiment sheet and a second Fourier transform lens, visible light with different wavelengths is emitted by the fourth laser, enters the single slit of the first single slit sheet after passing through the corresponding second dichroic mirror, is linearly propagated along the light path direction, the collimation of an incident beam is ensured by the second collimating lens, then the second experiment sheet with a grating structure with different parameters is switched by the rotation of a first experiment turntable, so that the grating diffraction phenomenon is generated after the light meets the grating structure in the propagation process, the light is focused into a first observation screen by the first Fourier transform lens, the experiment result of the grating diffraction experiment is observed by the first observation screen, and the experiment result of the grating diffraction experiment is collected by a second camera, therefore, the invention can demonstrate grating diffraction experiments and meet the requirements of students on watching and actual understanding, thereby improving the teaching result and quality.

In the Malus law experiment device, a Malus law experiment light path is formed by a fifth laser, a polarizer and a second analyzer, the fifth laser is used for emitting a light beam, the light beam enters the second analyzer after being polarized by the polarizer, the rotation of the second analyzer is controlled by a third motor and a second gear, the light beam emitted by the laser is changed into linearly polarized light, a detector is used for collecting a real-time video image of an experiment and the light intensity of red light after passing through the second analyzer, and therefore the Malus law experiment phenomenon that the light intensity changes along with the change of angles is demonstrated.

Drawings

FIG. 1 is a schematic flow diagram of the process of the present invention;

FIG. 2 is a schematic view of an experimental set-up according to the present invention;

FIG. 3 is a schematic diagram of an experimental module of the present invention;

FIG. 4 is a schematic diagram of the structure of a grating diffraction experimental apparatus;

FIG. 5 is a schematic diagram of the structure of another embodiment of a grating diffraction experimental apparatus;

FIG. 6 is a schematic diagram of a grating structure of a second test piece;

FIG. 7 is a schematic diagram of the Malus' law experimental setup;

fig. 8 is a schematic structural diagram of a second analyzer.

Reference numerals

1. Brewster's angle experimental apparatus; 2. an optical diffraction experimental apparatus; 3. an equal thickness interference experimental device; 4. a grating diffraction experimental device; 5. a Malus law experimental device; 6. young double slit interference experimental device; 11. a terminal; 12. a digital twinning medium; 13. a communication module; 14. an experiment module; 15. a main control module; 16. an experimental device; 17. a camera module; 18. a power supply module; 19. a lighting module; 401. a fourth base; 402. a fourth laser; 403. a second dichroic mirror; 404. a first single-slit sheet; 405. a second collimating lens; 406. a second experiment turntable; 407. a second test piece; 408. a second Fourier transform lens; 409. a first viewing screen; 410. a second camera; 411. isolating the chamber; 412. inserting a block; 413. a slot; 414. a second rotating electric machine; 415. a second turntable fixing frame; 416. a second installation chamber; 501. a fifth base; 502. a fifth laser; 503. a polarizer; 504. a second analyzer; 505. a fifth detector; 506. a third motor; 507. a second gear; 508. a second tooth; 509. the chamber is protected.

Detailed Description

The invention is further illustrated by the following figures and examples, which are not to be construed as limiting the invention.

Example 1: a classroom teaching method based on digital twin technology comprises a terminal, wherein the terminal is a mobile phone, a computer, a panel and the like, and is an electronic device; the terminal carries out real-time interaction and data transmission with an experimental device through a digital twin technology (the digital twin technology is a simulation process which fully utilizes data such as a physical model, sensor updating and operation history, integrates multidisciplinary, multi-physical quantity, multi-scale and multi-probability, and finishes mapping in a virtual space so as to reflect the full life cycle process of corresponding entity equipment, and the digital twin technology is an beyond-reality concept and can be regarded as a digital mapping system of one or more important equipment systems which depend on each other), supports the remote control of the experimental device to carry out real experiments corresponding to teaching contents, and comprises the following steps as shown in figure 1:

s1: a user logs in a digital twin medium (namely interactive software) of a terminal to select a corresponding experiment module, after a corresponding option is selected, the digital twin medium interface is switched to an operation interface corresponding to the experiment module, namely, an experiment to be carried out is selected through the terminal, and an instruction is sent to a corresponding experiment device to carry out the experiment, for example, after the digital twin medium selects a Young double-slit interference experiment, each operation of the digital twin medium is matched with the Young double-slit interference experiment;

s2: based on the operation of the user in the experiment operation selection area in the digital twin medium, the user can send an instruction to control the opening and closing of the experiment module by clicking the option, and can also set options of relevant parameters of the experiment module, specifically, the relevant parameters of the Young double-slit interference experiment module include: wavelength, double-slit spacing, observation distance, etc.;

s3, when the experiment module executes the instruction to perform the experiment, the video module collects the video image of the experiment device experiment, and synchronously displays the actual experiment process and the actual experiment data in the display of the interactive software, wherein the data comprises the total length of the stripes, and is used for the learner to observe the actual experiment process and obtain the actual experiment data;

s3, after the user clicks the theoretical principle, demonstrating the theoretical principle and the theoretical model of the experimental module in the display area of the terminal; the theoretical model is demonstrated in the form of animation, accurately represents the process and characteristics of the experiment, is matched with relevant parameters in the theoretical principle, and is explained by combining the animation;

s4, calculating the acquired experimental data according to the theoretical principle, and comparing the result with the result deduced by the theoretical principle to complete teaching; in this embodiment, after the user clicks the real experiment and/or the calculation verification in the interactive software, the experimental data is calculated in the display area in the interactive software, where the calculation process includes a derivation process and a derivation result of a calculation formula for displaying a theoretical principle, and after the experiment is finished, the acquired experimental data is calculated, and the result is compared with the result derived from the theoretical principle.

According to the technical scheme provided by the embodiment 1 of the invention, the digital twin medium on the terminal is used for demonstrating the virtual model of the teaching content, the method comprises a theoretical principle, a theoretical model and a related calculation process, the digital twin medium can realize the remote control of the opening and closing of the physical classroom teaching experiment device and the setting of related experiment parameters, and real-time video images of the entity device and the experiment process are displayed in the display area of the terminal so as to be used for a user to develop teaching and learning, the display of the physical experiment phenomenon can help the user to understand an abstract physical formula more easily, and the interaction with the user can further deepen understanding and further improve the teaching level.

Example 2: as shown in fig. 2, the teaching apparatus for implementing the classroom teaching method based on the digital twin technology in embodiment 1 includes a terminal 11, the terminal is a mobile phone, a computer, or a tablet, a digital twin medium 12 is provided in the terminal 11, and the digital twin medium 12 is an interactive software, and belongs to a system program; the digital twin medium 12 is connected with an experiment module 14 through a communication module 13 in the terminal 11, and the communication module carries out communication in a wireless or wired mode through 4/5G; the experiment module 14 is connected with a plurality of experiment devices 16 through a main control module 15, which includes one or more processors and a memory for storing relevant operation instructions. As shown in fig. 3, the experimental apparatus 16 includes, but is not limited to, a brewster angle experimental apparatus 1, an optical diffraction experimental apparatus 2, an equal thickness interference experimental apparatus 3, a grating diffraction experimental apparatus 4, a malus law experimental apparatus 5, and a young double slit interference experimental apparatus 6; the experiment module 14 is also provided with a camera module 17, a power supply module 18 and an illumination module 19. A user accesses the experiment module 14 through the digital twin medium 12 of the terminal 11, the power supply module 18 in the experiment module 14 provides power for the experiment device 16 to ensure the operation of the experiment device 16, the communication module 13 transmits the operation instruction of the user to the main control module 15, and the main control module 15 sends a specific instruction to the device in the experiment module 16 to perform a related physical experiment; the main control module 15 further sends instructions to the camera module 17 and the lighting module 18, the camera module 17 is used for collecting physical experiment phenomena, and the lighting module 18 is used for compensating the ambient light intensity.

In an embodiment, as shown in fig. 4 and 5, the grating diffraction experimental apparatus includes a fourth base 401, where the fourth base 401 is provided with 3 fourth lasers 402, where the fourth lasers 402 include three lasers with different wavelengths, and can be switched among the three lasers, and in this embodiment, a laser with a wavelength of 650nm is selected, and the laser emits a beam of red light; a second dichroic mirror 403 is correspondingly arranged at the front end of the fourth laser 402, and a certain angle is formed between the second dichroic mirror 403 and the exit angle of the fourth laser 402; a first single-slit sheet 404 on the fourth base 401 and located on one side of the second dichroic mirror 403, where the first single slit is used for enabling a light beam entering an experimental light path to linearly propagate along a light path direction after passing through the single slit; in this embodiment, after passing through the second dichroic mirror 403, a beam of red light linearly propagating along the light path is obtained through a single slit, a second collimating lens 405 is disposed in front of the first single slit sheet 404, the second collimating lens 405 is for ensuring collimation of the light beam in the light path, a second experiment turntable 406 is disposed in front of the second collimating lens 405, and a plurality of second experiment sheets 407 annularly distributed are disposed on the second experiment turntable 406, as shown in fig. 6, the second experiment sheets 407 have a grating structure, and the parameters of different gratings are selected by rotating the second experiment turntable 406; in this embodiment, the second experiment turntable 406 is connected to a second rotating motor 414; the fourth base 401 is provided with a second turntable fixing frame 415, the upper end of the second turntable fixing frame 415 is provided with a second installation chamber 416 for placing a second rotating motor 414, and the second experiment turntable 406 is controlled to rotate by the second rotating motor 414, so that the operation is simple, convenient and stable. A second Fourier transform lens 408 positioned in front of the second experiment turntable 406 is arranged on the fourth base 401, the second Fourier transform lens 408 has a focusing effect on an emergent light beam passing through the grating, a first observation screen 409 is arranged in front of the second Fourier transform lens 408, and the first observation screen 409 is used for observing an experiment result of a grating diffraction experiment; the fourth base 401 is further provided with a second camera 410 facing the first observation screen 409, and the second camera 410 is used for collecting an experiment result of a grating diffraction experiment. The invention forms a grating diffraction experimental light path by a fourth laser 402, a second dichroic mirror 403, a first single slit sheet 404, a second collimating lens 405, a second experimental sheet 407 and a second Fourier transform lens 408, uses the fourth laser 402 to emit visible light with different wavelengths, enters a single slit of the first single slit sheet 404 after passing through the corresponding second dichroic mirror 403, and linearly propagates along the light path direction, the collimation of an incident beam is ensured by the second collimating lens 405, then the second experimental sheet 407 with grating structures with different parameters is switched by the rotation of a first experimental turntable, so that the light encounters the grating structures in the propagation process to generate a grating diffraction phenomenon, and is focused into a first observation screen 409 by the first Fourier transform lens, the experimental result of the grating diffraction experiment is observed by the first observation screen 409, and the experimental result of the grating diffraction experiment is collected by a second camera 410, therefore, the invention can demonstrate grating diffraction experiments and meet the requirements of students on watching and actual understanding, thereby improving the teaching result and quality.

Further, as shown in fig. 5, a partition chamber 411 is disposed on the fourth base 401, the fourth laser 402 and the second dichroic mirror 403 are disposed in the partition chamber 411, and the influence of impurities such as dust on the experimental apparatus is reduced by disposing the partition chamber 411.

Further, as shown in fig. 4, a plurality of insertion blocks 412 are disposed in the partition chamber 411, and an insertion slot 413 is disposed at an upper end of each insertion block 412; the second dichroic mirror 403 is embedded in the slot 413, and the second dichroic mirror 403 can be conveniently mounted by arranging the insert 412 and the slot 413.

In an embodiment, the malus law experiment apparatus is shown in fig. 7, and includes a fifth base 501, a fifth laser 502 is disposed on the fifth base 501, a light beam emitted by the fifth laser 502 is a stable red light, a polarizer 503 is disposed in front of the fifth laser 502, and the polarizer 503 is used for polarizing and ensuring that the emergent light is linearly polarized light; a second analyzer 504 is arranged in front of the polarizer 503, the second analyzer 504 converts the visible light emitted by the laser into linearly polarized light, and the centers of the fifth laser 502, the polarizer 503 and the second analyzer 504 are on the same straight line; a fifth detector 505 is arranged in front of the second analyzer 504, and the fifth detector 505 collects the rotation angle and the light intensity of the video image and the polarized light of the Malus law experiment; as shown in fig. 8, a third motor 506 is further disposed on the fifth base 501, a second gear 507 is disposed at an output end of the third motor 506, second teeth 508 engaged with the second gear 507 are annularly distributed on the second analyzer 504, and an angular speed of rotation of the second analyzer 504 is controlled by the third motor 506 and the second gear 507. The Malus law experiment light path is formed by the fifth laser 502, the polarizer 503 and the second analyzer 504, the fifth laser 502 is used for emitting light beams, the light beams enter the second analyzer 504 after being polarized by the polarizer 503, the rotation of the second analyzer 504 is controlled by the third motor 506 and the second gear 507, the light beams emitted by the lasers are changed into linearly polarized light, the detector collects real-time video images of the experiment and the light intensity of red light after passing through the second analyzer 504, and therefore the Malus law experiment phenomenon that the light intensity changes along with the angle change is demonstrated, the Malus law experiment light path can meet the requirements of students for viewing and actual understanding, and teaching results and quality are improved.

Further, as shown in fig. 7, a protection chamber 509 is disposed on the fifth base 501, and the protection chamber 509 covers the third motor 506; the polarizer 503 is located on the top surface of the protection chamber 509. The present invention reduces the influence of dust and other impurities on the experimental apparatus by providing the protective chamber 509.

In summary, the invention selects the experiment to be performed through the terminal, sends the instruction to the corresponding experimental device for performing the experiment, collects the video image and data of the experimental device experiment in the experimental process, displays the video image and data on the terminal for the learner to observe the actual experimental process and obtain the actual experimental data, controls the virtual model to demonstrate the theoretical principle and the theoretical model of the experiment through the digital twinning technology on the terminal after the actual experiment is observed, calculates the collected experimental data according to the theoretical principle, and compares the result with the result deduced from the theoretical principle, thereby completing the teaching. Therefore, the teaching aid can better help teachers to complete demonstration of teaching contents and teaching of knowledge, better help students comprehensively learn physical essence from multiple angles, and simultaneously can better help teachers to develop qualitative demonstration and quantitative verification teaching experiments in class, and is also helpful for increasing ways of pre-lesson and post-lesson development of students, stimulating learning interests of students and deepening understanding of physical concepts.

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