Variable-radius chain type ellipse drawing mechanism based on Fourier series thought

Abstract

The invention belongs to the technical field of mathematics teaching aids, and relates to a variable-radius chain type ellipse drawing mechanism based on Fourier series thought, which comprises a central chain wheel, a movable chain wheel, a chain, a movable bottom plate, a first connecting rod, a second connecting rod and a pen holder, a first cylindrical pin and a second cylindrical pin are fixed to the circle centers of the center chain wheel and the movable chain wheel respectively, the chain is in transmission connection with the center chain wheel and the movable chain wheel, and the number of the center chain wheel is two times that of the movable chain wheel. One end of the movable bottom plate sleeves the bottom of the first cylindrical pin and is rotationally connected with the first cylindrical pin; a first sliding groove for the second cylindrical pin to slide is formed in the movable bottom plate; the two first connecting rods and the two second connecting rods form a quadrilateral connecting rod mechanism, and a locking piece and a tensioning wheel are arranged on the pin shaft; a brush is fixedly installed at one end of the penholder, and the distance between the point of the brush and the central axis of the movable chain wheel is adjustable. According to the ellipse drawing mechanism, ellipses of different sizes can be drawn by changing the long semi-axis and the short semi-axis of the ellipse.

Description

Technical Field

[0001] The invention belongs to the technical field of mathematics teaching tools, and in particular relates to a variable-radius chain-type ellipse drawing mechanism based on the Fourier series concept. Background Art

[0002] With the development of human science and technology, the emphasis on basic subjects has increased, and the requirements for high-precision drawing tools in industrial production and school mathematics teaching have become increasingly higher. The traditional method of drawing an ellipse has the disadvantages of complex tools, inability to freely transform the major and minor axes, large limitations, and poor reliability. In order to improve the above disadvantages, the present invention is based on the Fourier series expansion idea, starting from the principle level, decomposing the trajectory of the ellipse into the trajectory of two circles with different radii, and changing the major and minor semi-axes of the ellipse by changing the radii of the two circles, and proposes a variable radius chain type ellipse drawing mechanism. Summary of the invention

[0003] In view of the shortcomings of the prior art, the present invention proposes a variable radius chain-type ellipse drawing mechanism based on the Fourier series concept to solve the problem that the existing ellipse drawing tools mentioned in the above background technology cannot freely transform the major axis and minor axis, and can be used to draw ellipses of different sizes.

[0004] The present invention is achieved through the following technical solutions:

[0005] A variable radius chain type ellipse drawing mechanism based on the Fourier series concept comprises a central sprocket, a movable sprocket, a chain, a movable bottom plate, two first connecting rods, two second connecting rods and a pen holder;

[0006] A first cylindrical pin is fixed at the center of the central sprocket, a second cylindrical pin is fixed at the center of the movable sprocket, the central sprocket and the movable sprocket are connected via a chain transmission, and the number of teeth of the central sprocket is twice the number of teeth of the movable sprocket;

[0007] One end of the movable bottom plate is sleeved on the bottom of the first cylindrical pin, and the movable bottom plate is rotatably connected to the first cylindrical pin, the center sprocket and the movable sprocket are both rotatably arranged on the top surface of the movable bottom plate, the movable bottom plate can be used to support the chain to prevent the chain from falling off, a first sliding groove running through the upper and lower parts is provided on the movable bottom plate, the bottom of the second cylindrical pin is inserted into the first sliding groove, and the second cylindrical pin can slide in the first sliding groove along its extension direction, the second cylindrical pin can rotate relative to the movable bottom plate in the first sliding groove, the extension direction of the first sliding groove is the same as the direction of the line between the center of the center sprocket and the center of the movable sprocket, and the movable sprocket can be moved closer to or away from the center sprocket by sliding the second cylindrical pin to adjust the distance between the two along the first sliding groove;

[0008] The two first connecting rods and the two second connecting rods intersect in a V shape, the intersecting ends of the two first connecting rods are rotatably connected to the top of the first cylindrical pin, the intersecting ends of the two second connecting rods are rotatably connected to the top of the second cylindrical pin, the other ends of the two first connecting rods correspond to the other ends of the two second connecting rods one by one and are hinged through pins to form a quadrilateral connecting rod mechanism; each pin is provided with a locking piece for limiting the free rotation of the first connecting rod and the second connecting rod on the pin, based on the locking restriction of the locking piece, the angle between the first connecting rod and the second connecting rod can be ensured to remain fixed during the process of drawing an ellipse. The first cam is used to move the second cylindrical pin by hand to slide it in the first slide groove to adjust the distance between the center of the active sprocket and the center of the center sprocket when adjusting the drawing radius; each pin is fixed with a tensioning wheel slidably arranged on the top surface of the active bottom plate for tensioning the chain, and the inner side of the chain is wound around the tensioning wheel. When the distance between the center of the active sprocket and the center sprocket is adjusted on the top surface of the active bottom plate, the tensioning wheel can move with the pin to ensure that the chain between the active sprocket and the center sprocket is always tensioned to avoid chain falling;

[0009] The pen shaft is a telescopic rod structure with adjustable length. The pen shaft is fixed at the bottom end of the second pin shaft and is located below the movable bottom plate. A brush for drawing an ellipse is fixedly installed at one end of the pen shaft. The central axis of the brush is parallel to the central axis of the movable sprocket, and the distance from the brush tip to the central axis of the movable sprocket is adjustable.

[0010] When drawing an ellipse, the first cylindrical pin and the center sprocket can be fixed on the drawing plane, and the movable base plate can be moved to make the movable base plate, the second cylindrical pin, the quadrilateral linkage and the movable sprocket rotate synchronously around the central axis of the center sprocket, and the chain can move between the center sprocket and the movable sprocket to transmit power, so that the movable sprocket can rotate, and the revolution and rotation of the movable sprocket can drive the second cylindrical pin, the pen holder and the brush to rotate, and the ellipse is drawn by rotating the brush around the central axis of the center sprocket once; based on the different major semi-axis a and different minor semi-axis b of the ellipse, the distance from the central axis of the movable sprocket to the central axis of the center sprocket and the distance from the brush to the central axis of the movable sprocket can be adjusted accordingly, so that ellipses of different sizes can be drawn, and the above distances all refer to vertical distances.

[0011] Furthermore, a center base is fixed at the bottom end of the first cylindrical pin; when drawing an ellipse, the center base can be placed on the drawing plane. Compared with the first cylindrical pin, the contact area between the center base and the drawing plane is larger, and when pressed and fixed, it can provide stable support for the ellipse drawing mechanism.

[0012] Furthermore, a guide wheel fixed to the top surface of the movable base plate is provided between each tensioning wheel and the center sprocket, and between each tensioning wheel and the movable sprocket. The outer side of the chain is wrapped around the guide wheel. Under the guiding action of the four guide wheels on the chain, the length of the meshing section between the chain and the center sprocket and the movable sprocket can be increased, which can help to improve the stability of chain movement and power transmission.

[0013] Furthermore, the movable base plate is provided with a second slide groove running through the upper and lower parts, the second slide groove and the first slide groove intersect vertically on the movable base plate, the bottom end of each pin shaft is inserted into the second slide groove and slides therewith, and the two first connecting rods are telescopic connecting rod structures with adjustable length; when the locking restriction of the locking piece on the pin shaft is released, the second cylindrical pin is manually moved to slide in the first slide groove to adjust the distance between the center of the movable sprocket and the center of the central sprocket, the quadrilateral connecting rod mechanism is deformed to push the two pin shafts to slide in the second slide groove to move closer to or away from each other, and the two first connecting rods automatically extend and retract to adapt to the distance between the pin shaft and the first cylindrical pin to avoid conflict and inability to slide the pin shaft; the second slide groove is used to guide the sliding direction of the pin shaft and the tensioning wheel, which can avoid conflict between the tensioning wheel and the guide wheel.

[0014] Furthermore, the locking member includes a locking nut threadedly connected to the top of the pin shaft for pressing and fixing the first connecting rod and the second connecting rod, or includes a locking nut threadedly connected to the bottom of the pin shaft for locking and fixing the pin shaft and the tensioning wheel on the movable base plate.

[0015] Furthermore, each of the first connecting rods includes a first plate and a second plate, one end of the first plate is rotatably connected to the top of the first cylindrical pin, and the end face of the other end is provided with a guide slot extending inward, one end of the second plate is inserted into the guide slot, and the second plate can slide in the guide slot to adjust the overall length of the first connecting rod, and the other end is rotatably connected to the pin shaft; after loosening the locking nut, the second cylindrical pin is manually moved to slide in the first slot to adjust the distance between the center of the movable sprocket and the center of the center sprocket, the quadrilateral connecting rod mechanism is deformed and pushes the pin shaft to slide in the second slot, and the second plate can automatically move in and out of the first plate to adaptively adjust the length of the first connecting rod, and the two first connecting rods automatically extend and retract to adapt to the distance between the pin shaft and the first cylindrical pin.

[0016] Furthermore, a spring is installed in each of the guide grooves, and the spring is in a compressed state; when the second cylindrical pin slides in the first groove to approach the center sprocket, the first connecting rod needs to be extended and the pin shaft needs to slide outward in the second groove. The rebound force of the spring can help push the pin shaft outward in the second groove, so that the two pin shafts move away from each other.

[0017] Furthermore, the pen holder includes a perforated base fixed at the bottom end of the second pin shaft, the perforated base is provided with a square socket running through it in the transverse direction, a square rod is passed through the socket, and there is friction resistance between the outer wall of the square rod and the inner wall of the socket, the paintbrush is fixed at one end of the square rod, and a certain external force needs to be applied to slide the square rod along the socket to adjust the distance between the brush tip and the central axis of the movable sprocket.

[0018] Furthermore, the method for adjusting the drawing radius of the ellipse drawing mechanism is as follows:

[0019] S1. Determine the size of the major semi-axis a and the minor semi-axis b of the ellipse to be drawn, based on the ellipse parametric equation Evolution Equations Calculate and size;

[0020] S2. Loosen the locking nut to release the deformation restriction on the quadrilateral linkage mechanism, manually move the second cylindrical pin to make it slide in the first slide groove, and adjust the distance from the central axis of the active sprocket to the central axis of the center sprocket to L1. The quadrilateral linkage mechanism deforms and pushes the two pin shafts to slide in the second slide groove to move closer to or away from each other. The two first connecting rods automatically extend and retract to adapt to the distance between the pin shaft and the first cylindrical pin. After L1 is adjusted to the right position, tighten the locking nut to fix the quadrilateral linkage mechanism, so as to fix the position of the active sprocket and lock L1. Push and pull the pen holder by hand to adjust the distance from the brush tip to the central axis of the active sprocket to L2. Based on the friction between the pen holder and the base with holes, the position of the brush tip is locked after releasing the hand, so that L2 is locked. In the process of drawing an ellipse, ensure that the distance L1 from the central axis of the active sprocket to the central axis of the center sprocket and the distance L2 from the brush tip to the central axis of the active sprocket remain unchanged.

[0021] Furthermore, the method for drawing an ellipse by the ellipse drawing mechanism is:

[0022] When drawing an ellipse, use the thumb of one hand to press the first cylindrical pin or the center sprocket to fix it on the drawing plane. As long as one of them is pressed, the other will be fixed accordingly. Other fingers contact the movable base plate, the quadrilateral linkage mechanism or the second cylindrical pin and move it to rotate around the central axis of the center sprocket. Similarly, only one of the movable base plate, the quadrilateral linkage mechanism and the second cylindrical pin needs to be contacted and moved, and the others will rotate accordingly. Based on the synchronous rotation of the movable base plate, the second cylindrical pin, the quadrilateral linkage mechanism and the movable sprocket around the central axis of the center sprocket, the chain moves between the center sprocket and the movable sprocket to transmit power, causing the movable sprocket to rotate. The movable sprocket drives the second cylindrical pin, the pen holder and the brush to rotate when it revolves and rotates. The brush rotates one circle around the central axis of the center sprocket to draw an ellipse with a major semi-axis a and a minor semi-axis b.

[0023] It can be seen from the above technical solution that the variable radius chain type ellipse drawing mechanism based on the Fourier series concept provided by the present invention has the following beneficial effects:

[0024] The ellipse drawing mechanism can be used to draw ellipses of different sizes. Based on the major semi-axis a and the minor semi-axis b of the ellipse, after releasing the deformation restriction of the locking piece on the quadrilateral linkage mechanism, the movement restriction of the movable sprocket and the second cylindrical pin on the movable bottom plate can be released, and the second cylindrical pin can be manually moved to slide in the first slide groove to adjust the distance between the center of the movable sprocket and the center of the central sprocket to L1, and then the locking piece is tightened to lock the size of L1; the length of the pen shaft can be adjusted, and the distance from the brush tip to the central axis of the movable sprocket is adjusted to L2. In the process of drawing an ellipse, ensure that the distance L1 from the central axis of the movable sprocket to the central axis of the central sprocket and the distance L2 from the brush tip to the central axis of the movable sprocket remain unchanged; when drawing an ellipse, press the first circle with the thumb of one hand. The cylindrical pin or the center sprocket fixes it on the drawing plane, and other fingers contact the movable bottom plate, the quadrilateral linkage mechanism or the second cylindrical pin and turn it to rotate around the central axis of the center sprocket. The chain moves between the center sprocket and the movable sprocket to transmit power, causing the movable sprocket to rotate. The movable sprocket drives the second cylindrical pin, the pen holder and the brush to rotate when it revolves and rotates. The brush rotates one circle around the central axis of the center sprocket to draw an ellipse with a major semi-axis a and a minor semi-axis b; based on the different major semi-axis a and minor semi-axis b of the ellipse, the size of L1 and L2 can be adjusted accordingly, so that ellipses of different sizes can be drawn. The structure of the ellipse drawing mechanism is stable and reliable, which can help improve the accuracy of ellipse drawing, and the ellipse drawing mechanism can be operated with one hand to draw an ellipse. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for the specific embodiments or the description of the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual scale.

[0026] Figure 1 It is a three-dimensional structural schematic diagram of the ellipse drawing mechanism of the present invention;

[0027] Figure 2 A three-dimensional bottom view of the ellipse drawing mechanism of the present invention;

[0028] Figure 3 It is a front view of the ellipse drawing mechanism of the present invention;

[0029] Figure 4 The figure is a schematic diagram of the coordinate system for drawing an ellipse by the ellipse drawing mechanism of the present invention.

[0030] In the attached drawings: 1. center sprocket, 2. first cylindrical pin, 3. first connecting rod, 3.1. first strip, 3.2. second strip, 4. locking piece, 5. pin, 6. second connecting rod, 7. second cylindrical pin, 8. pen holder, 8.1. base with holes, 8.2. square rod, 9. paintbrush, 10. movable bottom plate, 10.1. first slide groove, 10.2. second slide groove, 11. movable sprocket, 12. guide wheel, 13. tensioning wheel, 14. center base, 15. chain, 16. cylindrical rod. DETAILED DESCRIPTION

[0031] The following embodiments of the technical solution of the present invention are described in detail in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore only used as examples, and cannot be used to limit the protection scope of the present invention.

[0032] In the description of the present application, it should be understood that the terms "upper", "lower", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0033] Example 1

[0034] A variable radius chain ellipse drawing mechanism based on Fourier series idea, such as Figures 1 to 3 As shown, it is mainly composed of a central sprocket 1, a movable sprocket 11, a chain 15, a central base 14, a movable bottom plate 10, two first connecting rods 3, two second connecting rods 6, a pen holder 8 and a paintbrush 9;

[0035] The center of the center sprocket 1 is fixed with a first cylindrical pin 2, the center of the movable sprocket 11 is fixed with a second cylindrical pin 7, the center sprocket 1 and the movable sprocket 11 are connected by a chain 15, and the number of teeth of the center sprocket 1 is twice the number of teeth of the movable sprocket 11; the center base 14 is fixed to the bottom end of the first cylindrical pin 2, and when drawing an ellipse, the center base 14 can be placed on the drawing plane. Compared with the first cylindrical pin 2, the center base 14 has a larger contact area with the drawing plane, and can provide stable support for the ellipse drawing mechanism when pressed and fixed; specifically, the center base 14 is made of rubber, which is a rubber base and has an anti-slip effect;

[0036] One end of the movable bottom plate 10 is sleeved on the bottom of the first cylindrical pin 2, and the movable bottom plate 10 is rotatably connected with the first cylindrical pin 2. The center sprocket 1 and the movable sprocket 11 are both rotatably arranged on the top surface of the movable bottom plate 10. The movable bottom plate 10 can be used to support the chain 15 to prevent the chain 15 from falling off. The movable bottom plate 10 is provided with a first slide groove 10.1 that runs through from top to bottom. The bottom of the second cylindrical pin 7 is inserted into the first slide groove 10.1, and the second cylindrical pin 7 can slide along its extension direction in the first slide groove 10.1. The second cylindrical pin 7 can rotate relative to the movable bottom plate 10 in the first slide groove 10.1. The extension direction of the first slide groove 10.1 is the same as the direction of the line between the center of the center sprocket 1 and the center of the movable sprocket 11. By sliding the second cylindrical pin 7, the movable sprocket 11 can be close to or away from the center sprocket 1 to adjust the distance between the two along the first slide groove 10.1.

[0037] The two first connecting rods 3 and the two second connecting rods 6 intersect in a V shape, the intersecting ends of the two first connecting rods 3 are rotatably connected to the top of the first cylindrical pin 2, and the intersecting ends of the two second connecting rods 6 are rotatably connected to the top of the second cylindrical pin 7. The other ends of the two first connecting rods 3 correspond to the other ends of the two second connecting rods 6 one by one and are hinged through the pin shaft 5 to form a quadrilateral connecting rod mechanism; each pin shaft 5 is provided with a locking member 4 for limiting the free rotation of the first connecting rod 3 and the second connecting rod 6 on the pin shaft 5, based on the locking restriction of the locking member 4, the angle between the first connecting rod 3 and the second connecting rod 6 can be kept fixed during the process of drawing an ellipse, ensuring that the movable sprocket 11 The distance from the center of the circle to the center of the center sprocket 1 remains unchanged, and the locking restriction of the locking piece 4 is released. When adjusting the drawing radius, the second cylindrical pin 7 can be manually moved to slide in the first slide groove 10.1 to adjust the distance between the center of the movable sprocket 11 and the center of the center sprocket 1; each pin shaft 5 is fixed with a tensioning wheel 13 slidably arranged on the top surface of the movable bottom plate 10 for tensioning the chain 15, and the inner side of the chain 15 is wound around the tensioning wheel 13. When adjusting the distance from the center of the movable sprocket 11 to the center of the center sprocket 1 on the top surface of the movable bottom plate 10, the tensioning wheel 13 can move with the pin shaft 5 to ensure that the chain 15 between the movable sprocket 11 and the center sprocket 1 is always tensioned to avoid chain falling;

[0038] The pen holder 8 is a telescopic rod structure with adjustable length, which is composed of a base with a hole 8.1 and a square rod 8.2; the base with a hole 8.1 is fixed to the bottom end of the second pin shaft 5 and is located below the movable bottom plate 10. The base with a hole 8.1 is a cylindrical structure, which is coaxial with the second cylindrical pin 7 and the movable sprocket 11. The base with a hole 8.1 is provided with a square plug hole that runs through in the transverse direction. The square rod 8.2 is installed in the plug hole, and there is friction between the outer wall of the square rod 8.2 and the inner wall of the plug hole. The brush 9 used to draw an ellipse is fixed to one end of the square rod 8.2, and the central axis of the brush 9 is parallel to the central axis of the movable sprocket 11. The tip of the brush 9 is parallel to the central axis of the movable sprocket 11. The distance between the lines is adjustable, and a certain external force needs to be applied to slide the square rod 8.2 along the socket to adjust the distance between the tip of the brush 9 and the central axis of the movable sprocket 11; specifically, the inner wall of the socket or the outer wall of the square rod 8.2 is fixed with a non-slip rubber layer or a non-slip coating to generate friction resistance; a cylindrical rod 16 is fixed to the other end of the square rod 8.2, and the bottom surface of the cylindrical rod 16 is flush with the bottom surface of the center base 14. The central axis of the cylindrical rod 16, the central axis of the brush 9 and the central axis of the second cylindrical pin 7 are coplanar. In the process of drawing an ellipse, the cylindrical rod 16 is supported on the drawing plane, which can help improve the stability of the pen shaft 8 and the movable base plate 10 during movement.

[0039] Preferably, in the present embodiment, a guide wheel 12 fixed to the top surface of the movable base plate 10 is provided between each of the tensioning wheels 13 and the center sprocket 1 and between each of the tensioning wheels 13 and the movable sprocket 11. The outer side of the chain 15 is wrapped around the guide wheel 12. Under the guiding action of the four guide wheels 12 on the chain 15, the length of the meshing section between the chain 15 and the center sprocket 1 and the movable sprocket 11 can be increased, which can help to improve the stability of the movement and power transmission of the chain 15.

[0040] Preferably, in this embodiment, the movable bottom plate 10 is provided with a second slide groove 10.2 which runs through the upper and lower parts, and the second slide groove 10.2 and the first slide groove 10.1 are vertically intersected on the movable bottom plate 10, and the bottom end of each pin shaft 5 is inserted into the second slide groove 10.2 to slide with it, and the two first connecting rods 3 are telescopic connecting rod structures with adjustable lengths; when the locking restriction of the locking piece 4 on the pin shaft 5 is released, the second cylindrical pin 7 is manually moved to slide in the first slide groove 10.1 to adjust the distance between the center of the movable sprocket 11 and the center of the central sprocket 1, the quadrilateral connecting rod mechanism is deformed to push the two pin shafts 5 to slide in the second slide groove 10.2 to move closer to or away from each other, and the two first connecting rods 3 automatically extend and retract to adapt to the distance between the pin shaft 5 and the first cylindrical pin 2, avoiding conflict and inability to slide the pin shaft 5; the second slide groove 10.2 is used to guide the sliding direction of the pin shaft 5 and the tensioning wheel 13, which can avoid conflict between the tensioning wheel 13 and the guide wheel 12;

[0041] The locking member 4 is a locking nut threadedly connected to the top of the pin 5 for pressing and fixing the first connecting rod 3 and the second connecting rod 6; tightening the locking nut can press and fix the first connecting rod 3, the second connecting rod 6 and the locking nut in the axial direction, so that the first connecting rod 3 and the second connecting rod 6 are fixed on the pin 5; loosening the locking nut can release the locking of the first connecting rod 3 and the second connecting rod 6, so that the first connecting rod 3 and the second connecting rod 6 can rotate relatively around the pin 5, so that the quadrilateral linkage mechanism can be deformed and the distance between the central axis of the movable sprocket 11 and the central axis of the center sprocket 1 can be adjusted;

[0042] In addition, the locking member 4 can also be a locking nut threadedly connected to the bottom of the pin shaft 5 for locking and fixing the pin shaft 5 and the tensioning wheel 13 on the movable base plate 10; tightening the locking nut can fix the pin shaft 5 and the tensioning wheel 13 on the movable base plate 10, and loosening the locking nut can release the locking of the pin shaft 5 and the tensioning wheel 13, so that the pin shaft 5 can slide in the second slide groove 10.2 to drive the first connecting rod 3 and the second connecting rod 6 to rotate, so that the quadrilateral linkage mechanism can be deformed and the distance between the central axis of the movable sprocket 11 and the central axis of the center sprocket 1 can be adjusted; when the locking nut is turned as mentioned above, the tensioning wheel 13 or the pin shaft 5 can be fixed by hand to prevent the pin shaft 5 from rotating with the locking nut and the locking nut cannot be tightened or loosened.

[0043] Preferably, in the present embodiment, each of the first connecting rods 3 comprises a first strip 3.1 and a second strip 3.2, one end of the first strip 3.1 is rotatably connected to the top end of the first cylindrical pin 2, and the end surface of the other end thereof is provided with a guide slot extending inwardly, one end of the second strip 3.2 is inserted into the guide slot, and the second strip 3.2 can slide in the guide slot to adjust the overall length of the first connecting rod 3, and the other end thereof is rotatably connected to the pin shaft 5; after loosening the locking nut, when the second cylindrical pin 7 is manually moved to slide in the first slot 10.1 to adjust the distance between the center of the movable sprocket 11 and the center of the central sprocket 1, the quadrilateral connecting rod mechanism is deformed and pushes the pin shaft 5 to slide in the second slot 10.2, and the second strip 3.2 can automatically move in and out of the first strip 3.1 to adaptively adjust the length of the first connecting rod 3, and the two first connecting rods 3 automatically extend and retract to adapt to the distance between the pin shaft 5 and the first cylindrical pin 2;

[0044] A spring is installed in each of the guide grooves, and the spring is in a compressed state; when the second cylindrical pin 7 slides in the first groove 10.1 to approach the center sprocket 1, the first connecting rod 3 needs to be extended and the pin shaft 5 needs to slide outward in the second groove 10.2. The rebound force of the spring can help push the pin shaft 5 to move outward in the second groove 10.2, so that the two pin shafts 5 move away from each other.

[0045] Example 2

[0046] A variable radius chain-type ellipse drawing mechanism based on the Fourier series concept, the method for adjusting the drawing radius of the ellipse drawing mechanism is as follows:

[0047] S1. Determine the size of the major semi-axis a and the minor semi-axis b of the ellipse to be drawn, based on the ellipse parametric equation Evolution Equations Calculate and size;

[0048] S2. Loosen the locking nut to release the deformation restriction on the quadrilateral linkage mechanism. Manually move the second cylindrical pin 7 to make it slide in the first slide groove 10.1. Adjust the distance from the central axis of the movable sprocket 11 to the central axis of the center sprocket 1 to L1. The quadrilateral linkage mechanism deforms and pushes the two pin shafts 5 to slide in the second slide groove 10.2 to move closer to or away from each other. The two first connecting rods 3 automatically extend and retract to adapt to the distance between the pin shaft 5 and the first cylindrical pin 2. After L1 is adjusted to the right position, tighten the locking nut to The quadrilateral linkage mechanism is fixed to fix the position of the movable sprocket 11, so that L1 is locked; the pen holder 8 is pushed and pulled by hand to adjust the distance from the tip of the brush 9 to the central axis of the movable sprocket 11 to L2. Based on the friction between the pen holder 8 and the perforated base 8.1, the position of the tip of the brush 9 is locked after releasing the hand, so that L2 is locked; in the process of drawing an ellipse, ensure that the distance L1 from the central axis of the movable sprocket 11 to the central axis of the center sprocket 1 and the distance L2 from the tip of the brush 9 to the central axis of the movable sprocket 11 remain unchanged.

[0049] The drawing radius adjustment principle of the ellipse drawing mechanism is as follows:

[0050] According to the Fourier series expansion idea, any periodic function can be expanded into a superposition of a finite number of sinusoidal functions of different frequencies. Since the equation of the ellipse is It can be seen that x and y are both periodic functions about θ with a period of 2π. The above elliptic equation can be further transformed into make It can be seen that the ellipse can be formed by superimposing two circles with different radii and opposite rotation angles; let L1 be the distance from the central axis of the movable sprocket 11 to the central axis of the center sprocket 1, and L2 be the distance from the tip of the brush 9 to the central axis of the movable sprocket 11;

[0051] When adjusting the drawing radius of the ellipse drawing mechanism, first determine the size of the major semi-axis a and the minor semi-axis b of the ellipse to be drawn, loosen the locking nut to release the deformation restriction of the quadrilateral linkage mechanism, and then release the movement restriction of the movable sprocket 11 and the second cylindrical pin 7 on the movable bottom plate 10. The second cylindrical pin 7 can be manually moved to slide in the first slide groove 10.1 to adjust the distance between the center of the movable sprocket 11 and the center of the central sprocket 1 to L1, and then tighten the locking nut to lock the size of L1; the length of the pen shaft 8 can be adjusted, and the distance from the tip of the brush 9 to the central axis of the movable sprocket 11 is adjusted to L2;

[0052] When adjusting L1, draw a point at the center of the top surface of the first cylindrical pin 2 and the center of the top surface of the second cylindrical pin 7 as the reference point, and use a ruler to measure the distance between the two reference points as L1; similarly, draw a point at the center of the bottom surface of the cylindrical perforated base 8.1 as the reference point, and use a ruler to measure the distance from the tip of the brush 9 to the reference point as L2.

[0053] Example 3

[0054] A variable radius chain type ellipse drawing mechanism based on the Fourier series concept, the method of drawing an ellipse by the ellipse drawing mechanism is as follows:

[0055] When drawing an ellipse, use the thumb of one hand to press the first cylindrical pin 2 or the center sprocket 1 to fix it on the drawing plane. As long as one of them is pressed, the other will be fixed accordingly. Other fingers contact the movable base plate 10, the quadrilateral linkage mechanism or the second cylindrical pin 7 and move it to rotate around the central axis of the center sprocket 1. Similarly, only one of the movable base plate 10, the quadrilateral linkage mechanism and the second cylindrical pin 7 needs to be contacted and moved, and the others will rotate accordingly. Based on the synchronous rotation of the movable base plate 10, the second cylindrical pin 7, the quadrilateral linkage mechanism and the movable sprocket 11 around the central axis of the center sprocket 1, the chain 15 moves between the center sprocket 1 and the movable sprocket 11 to transmit power, so that the movable sprocket 11 rotates. When the movable sprocket 11 revolves and rotates, it drives the second cylindrical pin 7, the pen shaft 8 and the brush 9 to rotate. The brush 9 rotates one circle around the central axis of the center sprocket 1 to draw an ellipse with a major semi-axis a and a minor semi-axis b.

[0056] In this embodiment, the number of teeth of the center sprocket 1 is 32 and the number of teeth of the movable sprocket 11 is 16. Figure 4 As shown, in the plane rectangular coordinate system, the origin of the coordinate is the center point of the center sprocket 1, L1 is the distance from the center axis of the movable sprocket 11 to the center axis of the center sprocket 1, and L2 is the distance from the tip of the brush 9 to the center axis of the movable sprocket 11;

[0057] Use the thumb of one hand to press the top of the first cylindrical pin 2, and firmly fix the center base 14 on the drawing plane to prevent it from sliding on the drawing plane when drawing the ellipse. The first cylindrical pin 2, the center sprocket 1 and the center base 14 are all fixed and stationary relative to the earth coordinate system; other fingers (such as the index finger and the middle finger) touch the top of the second cylindrical pin 7 and move it to rotate around the central axis of the center sprocket 1, and the movable bottom plate 10, the quadrilateral linkage, the second cylindrical pin 7 and the movable sprocket rotate synchronously around the central axis of the center sprocket 1. Due to the gap between the center sprocket 1 and the movable sprocket 11, the movable bottom plate 10, the quadrilateral linkage, the second cylindrical pin 7 and the movable sprocket rotate synchronously around the central axis of the center sprocket 1. The gear ratio is 2 to 1, and the two are driven by a chain 15, and the chain 15 is continuously driven. The line connecting the center of the center sprocket 1 and the center of the movable sprocket 11 is defined as the x-axis of the moving system. The ray y through the center sprocket 1 is perpendicular to the x-axis, and its direction is always 90° ahead of the x-axis of the moving system. That is, the x-axis and the y-axis constitute a moving coordinate system. Since the pen holder 8 (including the base 8.1 with holes and the square rod 8.2), the second cylindrical pin 7 and the paintbrush 9 are relatively stationary, the rotation of the pen holder 8 relative to the moving system can reflect the rotation of the movable sprocket 11 relative to the center sprocket 1.

[0058] like Figure 4 As shown, when the movable sprocket 11 revolves around the center sprocket 1, the center of the movable sprocket 11 rotates counterclockwise around the center of the center sprocket 1 by an angle of θ1. At the same time, the pen holder 8 rotates clockwise by an angle of 2θ1 relative to the moving system. That is, after the two are superimposed, the pen holder 8 rotates counterclockwise by an angle of θ1 relative to the static system, which can also be regarded as a clockwise rotation of an angle of -θ1, thereby satisfying the rotation of the radius L1 of the first circle by an angle of θ1 and the rotation of the radius L2 of the second circle by an angle of -θ1.

[0059] Again, if Figure 4 As shown, when the movable sprocket 11 revolves around the center sprocket 1, the center of the movable sprocket 11 rotates counterclockwise around the center of the center sprocket 1 by an angle of θ2. At the same time, the pen holder 8 rotates clockwise by an angle of 2θ2 relative to the moving system. That is, after the two are superimposed, the pen holder 8 rotates counterclockwise by an angle of θ2 relative to the static system, which can also be regarded as a clockwise rotation of an angle of -θ2, thereby satisfying the rotation of the radius L1 of the first circle by an angle of θ2 and the rotation of the radius L2 of the second circle by an angle of -θ2.

[0060] Finally, when the brush 9 rotates around the coordinate origin on the drawing plane, the trajectory drawn by the tip of the brush 9 on the drawing plane is an ellipse with a major semi-axis a and a minor semi-axis b.

[0061] The ellipse drawing mechanism of the present invention is based on the concept of Fourier series expansion, and solves the problem that the existing ellipse gauge cannot freely transform the major axis and the minor axis and cannot draw ellipses of different sizes by adjusting the drawing radius. Transmission is achieved through the meshing relationship between the chain 15 and the center sprocket 1 and the movable sprocket 11. The ratio of the number of teeth of the center sprocket 1 to the number of teeth of the movable sprocket 11 is 2 to 1. The power of continuous motion is transmitted between them through the chain 15, which improves the accuracy and efficiency of power transmission and helps to improve the accuracy of the drawn ellipse. By changing the spatial distribution of the chain 15 and changing the rotation radius of the movable sprocket, the two circles of different radii are changed, the major semi-axis and the minor semi-axis of the ellipse are changed, and ellipses of different sizes are drawn.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A variable radius chain type ellipse drawing mechanism based on the Fourier series concept, characterized by: The invention comprises a central sprocket (1), a movable sprocket (11) and a chain (15); a first cylindrical pin (2) is fixed at the center of the central sprocket (1), a second cylindrical pin (7) is fixed at the center of the movable sprocket (11), the central sprocket (1) and the movable sprocket (11) are connected by transmission via the chain (15), and the number of teeth of the central sprocket (1) is twice the number of teeth of the movable sprocket (11); The movable bottom plate (10) comprises one end of the movable bottom plate (10) which is sleeved on the bottom of the first cylindrical pin (2) and is rotatably connected thereto; the central sprocket (1) and the movable sprocket (11) are both rotatably arranged on the top surface of the movable bottom plate (10); a first slide groove (10.1) which runs through the movable bottom plate (10) from top to bottom is provided; the bottom of the second cylindrical pin (7) is inserted into the first slide groove (10.1) and is slidably matched therewith; the extension direction of the first slide groove (10.1) is the same as the direction of the line connecting the center of the central sprocket (1) and the center of the movable sprocket (11); The invention comprises two first connecting rods (3) and two second connecting rods (6) which intersect in a V shape, wherein one end of the two first connecting rods (3) is rotatably connected to the top of a first cylindrical pin (2), and one end of the two second connecting rods (6) is rotatably connected to the top of a second cylindrical pin (7). The other ends of the two first connecting rods (3) correspond to the other ends of the two second connecting rods (6) in a one-to-one manner and are hingedly connected through a pin shaft (5), thereby forming a quadrilateral connecting rod mechanism; each pin shaft (5) is provided with a locking member (4) for limiting the free rotation of the first connecting rod (3) and the second connecting rod (6) on the pin shaft (5); and each pin shaft (5) is fixed with a tensioning wheel (13) which is slidably arranged on the top surface of a movable bottom plate (10) and is used for tensioning a chain (15); The invention comprises a pen shaft (8), wherein the pen shaft (8) is a telescopic rod structure with adjustable length, the pen shaft (8) is fixed to the bottom end of a second pin shaft (5), a paintbrush (9) is fixedly mounted on one end of the pen shaft (8), the central axis of the paintbrush (9) is parallel to the central axis of a movable sprocket (11), and the distance from the tip of the paintbrush (9) to the central axis of the movable sprocket (11) is adjustable.

2. The variable radius chain type ellipse drawing mechanism based on the Fourier series concept according to claim 1 is characterized in that: A central base (14) is fixed to the bottom end of the first cylindrical pin (2).

3. The variable radius chain type ellipse drawing mechanism based on the Fourier series concept according to claim 1 or 2, characterized in that: A guide wheel (12) fixed on the top surface of the movable bottom plate (10) is arranged between each of the tensioning wheels (13) and the central sprocket (1) and the movable sprocket (11), and the outer side of the chain (15) is wrapped around the guide wheel (12).

4. The variable radius chain type ellipse drawing mechanism based on the Fourier series concept according to claim 3 is characterized in that: The movable bottom plate (10) is provided with a second slide groove (10.2) which runs through the upper and lower parts. The second slide groove (10.2) intersects the first slide groove (10.1) vertically. The bottom end of each pin shaft (5) is inserted into the second slide groove (10.2) and is slidably matched therewith. The two first connecting rods (3) are both telescopic connecting rod structures with adjustable lengths.

5. The variable radius chain type ellipse drawing mechanism based on the Fourier series concept according to claim 4 is characterized in that: The locking member (4) comprises a locking nut threadedly connected to the top of the pin shaft (5) for pressing and fixing the first connecting rod (3) and the second connecting rod (6), or comprises a locking nut threadedly connected to the bottom of the pin shaft (5) for locking and fixing the pin shaft (5) and the tensioning wheel (13) on the movable base plate (10).

6. The variable radius chain type ellipse drawing mechanism based on Fourier series concept according to claim 4 or 5, characterized in that: Each of the first connecting rods (3) comprises a first strip (3.1) and a second strip (3.2); one end of the first strip (3.1) is rotatably connected to the top end of the first cylindrical pin (2); the end surface of the other end is provided with a guide groove extending inward; one end of the second strip (3.2) is inserted into the guide groove and slidably matched therewith; the other end is rotatably connected to the pin shaft (5).

7. The variable radius chain type ellipse drawing mechanism based on Fourier series concept according to claim 6 is characterized in that: A spring in a compressed state is installed in each of the guide slide grooves.

8. The variable radius chain type ellipse drawing mechanism based on Fourier series concept according to claim 1, characterized in that: The pen holder (8) comprises a base with a hole (8.1) fixed to the bottom end of the second pin shaft (5), the base with a hole (8.1) is provided with a square plug hole running through in the transverse direction, a square rod (8.2) is inserted into the plug hole, and there is friction resistance between the outer wall of the square rod (8.2) and the inner wall of the plug hole, and the paintbrush (9) is fixed to one end of the square rod (8.2).

9. The variable radius chain type ellipse drawing mechanism based on Fourier series concept according to claim 1, characterized in that: The method for adjusting the drawing radius of the ellipse drawing mechanism is as follows: S1. Determine the size of the major semi-axis a and the minor semi-axis b of the ellipse to be drawn, based on the ellipse parametric equation Evolution Equations Calculate and size; S2, adjusting the distance from the central axis of the movable sprocket (11) to the central axis of the center sprocket (1) to L1, adjusting the distance from the tip of the paintbrush (9) to the central axis of the movable sprocket (11) to L2, and locking the sizes of L1 and L2.

10. The variable radius chain type ellipse drawing mechanism based on Fourier series concept according to claim 1 or 9, characterized in that: The method for drawing an ellipse by the ellipse drawing mechanism is: The thumb of one hand is used to press the first cylindrical pin (2) or the center sprocket (1) to fix it on the drawing plane, and the other fingers are used to contact the movable bottom plate (10), the quadrilateral linkage mechanism or the second cylindrical pin (7) and move them around the central axis of the center sprocket (1). The trajectory drawn by the brush (9) rotating one circle on the drawing plane is an ellipse with a major semi-axis a and a minor semi-axis b.

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