Variable radius gear 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 gear type ellipse drawing mechanism based on Fourier series thought, which comprises two connecting rods, a central gear, a transmission gear, a tail end gear and a penholder, one ends of the two connecting rods are hinged to form a V-shaped connecting rod mechanism through a pin shaft, and a locking piece used for limiting free rotation of the two connecting rods is arranged on the pin shaft. The center gear and the tail end gear are rotationally connected to the other ends of the two connecting rods respectively, the tail end gear is rotationally connected to the pin shaft, the center gear and the tail end gear are both meshed with the transmission gear, and the number of teeth of the center gear is two times that of teeth of the tail end gear; the middle of the penholder is installed on the bottom face of the tail end gear, an ink-free pen and an ink pen are installed at the two ends of the penholder respectively, the lengths from the center of the penholder to the two end faces of the penholder are adjustable, and the central axes of the ink-free pen and the ink pen are parallel to the central axis of the tail end gear at equal intervals. 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 gear-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 change 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 gear-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 gear-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 gear type ellipse drawing mechanism based on the Fourier series concept comprises two connecting rods, a central gear, a transmission gear, a terminal gear and a pen holder;

[0006] One end of the two connecting rods is hinged to form a V-shaped connecting rod mechanism through a pin shaft, and a locking piece for limiting the free rotation of the two connecting rods on the pin shaft is provided on the pin shaft between the two connecting rods. Based on the limitation of the locking piece, the angle between the two connecting rods can be kept fixed during the process of drawing an ellipse. When the limitation of the locking piece is released, the two connecting rods can be rotated by hand to change the angle between the two connecting rods when adjusting the drawing radius, and the spacing between the other ends of the two connecting rods can be adjusted;

[0007] The central gear and the end gear are rotatably connected to the other ends of the two connecting rods respectively, and the end gear is rotatably connected to the pin shaft between the two connecting rods, and the central gear and the end gear are both meshed with the transmission gear, the number of teeth of the central gear is twice the number of teeth of the end gear, and the transmission gear transmits power between the central gear and the end gear. After fixing the central gear, rotating the transmission gear by hand can make the transmission gear and the end gear revolve around the central axis of the central gear, and at the same time, the transmission gear and the end gear can rotate;

[0008] The pen holder is a telescopic frame structure with adjustable length, the middle of which is fixed to the bottom surface of the terminal gear, and the two ends of the pen holder are respectively installed with a non-ink pen and an ink pen, and the length from the center of the pen holder to its two end surfaces is adjustable to adjust the distance between the non-ink pen and the ink pen, the central axis of the non-ink pen and the central axis of the ink pen are parallel to the central axis of the terminal gear, and the distance from the central axis of the non-ink pen to the central axis of the terminal gear is equal to the distance from the central axis of the ink pen to the central axis of the terminal gear;

[0009] When drawing an ellipse, press and fix the center gear, and use your fingers to move the V-shaped connecting rod mechanism to rotate around the central axis of the center gear. The V-shaped connecting rod mechanism can drive the transmission gear, the end gear and the pen holder to rotate around the central axis of the center gear. The transmission gear can revolve around the central axis of the center gear, and the transmission gear can rotate on its own. The end gear can revolve around the central axis of the center gear, and the end gear can rotate around the transmission gear, thereby driving the pen holder on the bottom of the end gear to rotate, and the ink pen and the ink-free pen rotate with the pen holder. The ink pen draws an ellipse by rotating one circle; 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 end gear to the central axis of the center gear can be adjusted accordingly, and the distance from the ink pen to the central axis of the end gear can be adjusted, thereby drawing ellipses of different sizes.

[0010] Furthermore, the locking member includes a first nut threadedly connected to the top of the pin shaft for pressing and fixing the two connecting rods. By tightening the first nut, the two connecting rods can be pressed and fixed so that the two connecting rods are fixed on the pin shaft. When the first nut is loosened, the lock on the two connecting rods is released, and the two connecting rods can be rotated by hand to change the angle between the two connecting rods, and the distance between the center axis of the end gear and the center axis of the center gear can be adjusted.

[0011] Furthermore, the ellipse drawing mechanism also includes a center gear base, the center of the center gear is fixed with a center cylindrical pin, the bottom of the center cylindrical pin is fixed on the center gear base, and the top of the center cylindrical pin is rotatably connected to the connecting rod; the center gear base can support and fix the center gear and the center cylindrical pin. When drawing an ellipse, pressing the center gear with the thumb can fix the center gear base on the drawing plane, so that the center gear base can be firmly attached to the drawing plane and no sliding is allowed. The center gear, center cylindrical pin and center gear base are all stationary relative to the geodetic coordinate system.

[0012] Furthermore, the pen holder is a length-adjustable scissor frame structure, which includes two first scissor arms; an end cylindrical pin is fixed to the center of the end gear, the top of the end cylindrical pin is rotatably connected to the connecting rod, the middle parts of the two first scissor arms are rotatably connected to the bottom of the end cylindrical pin and the two first scissor arms cross in an X shape, the bottom of the end cylindrical pin is threadedly connected with a second nut for pressing and fixing the two first scissor arms on the end cylindrical pin, and both ends of each first scissor arm are rotatably connected to the second scissor arm, wherein the ends of the two second scissor arms located on the same side are rotatably connected to the top of the inkless pen, and the ends of the other two second scissor arms located on the same side are rotatably connected to the top of the ink pen; after loosening the second nut, the restriction of the second nut on the two first scissor arms is released, and the two first scissor arms can be manually moved to rotate relative to each other to adjust the length of the pen holder, thereby adjusting the spacing between the ink pen and the inkless pen. Based on the scissor frame structure, the distances from the tip of the ink pen and the tip of the inkless pen to the center axis of the end cylindrical pin are equal.

[0013] Furthermore, the method for adjusting the drawing radius of the ellipse drawing mechanism is as follows:

[0014] S1. Determine the size of the major semi-axis a and the minor semi-axis b of the ellipse to be drawn, and then mark the origin, minor axis point and major axis point on the same straight line on the paper, where the minor axis point and the major axis point are on the same side of the origin, the distance from the minor axis point to the origin is b, and the distance from the major axis point to the origin is a;

[0015] S2. Loosen the first nut and the second nut to allow the second connecting rod to rotate, so that the two first scissor arms can rotate, align the central axis of the central gear with the origin, pull the inkless pen and the ink pen so that the tip of the inkless pen is aligned with the short axis point and the tip of the ink pen is aligned with the long axis point. The angle between the two connecting rods changes adaptively with the pulling of the pen holder, and the distance from the central axis of the end gear to the central axis of the central gear is automatically adjusted to Note that L1, the distance from the ink pen tip to the center axis of the end gear is automatically adjusted to Denoted as L2;

[0016] S3. Tighten the first nut and the second nut to lock the size of L1 and L2. During the process of drawing the ellipse, ensure that the distance from the center axis of the end gear to the center axis of the center gear and the distance from the ink pen tip to the center axis of the end gear remain unchanged.

[0017] Furthermore, in the above step S2, the method of aligning the central axis of the central gear with the origin includes but is not limited to:

[0018] First, a freely retractable positioning rod is installed on the bottom surface of the central gear base, and the positioning rod is coaxial with the central gear. When the bottom end of the positioning rod coincides with the origin, the central axis of the central gear is aligned with the origin;

[0019] Secondly, the center gear base is in the shape of a truncated cone, which is coaxial with the center gear. A circle is drawn on paper with the origin as the center and the radius of the center gear base as the radius. When the bottom surface of the center gear base coincides with the drawn circle, the central axis of the center gear is aligned with the origin.

[0020] Furthermore, the method for drawing an ellipse by the ellipse drawing mechanism is:

[0021] Use the thumb of one hand to press the center gear so that the base of the center gear is firmly against the drawing plane and no sliding is allowed. The other fingers touch the hinged ends of the two connecting rods and turn the V-shaped connecting rod mechanism to rotate around the central axis of the center gear. The V-shaped connecting rod mechanism drives the transmission gear, the end gear and the pen holder to rotate around the central axis of the center gear. The transmission gear revolves around the central axis of the center gear, and the transmission gear rotates on its own. The end gear revolves around the central axis of the center gear, and the end gear rotates on its own. The pen holder and the inkless pen and ink pen installed on it rotate with the end gear. The trajectory drawn by the ink pen when it rotates one circle on the drawing plane is an ellipse with the major semi-axis a and the minor semi-axis b.

[0022] It can be seen from the above technical solution that the variable radius gear-type ellipse drawing mechanism based on the Fourier series concept provided by the present invention has the following beneficial effects:

[0023] 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, the fixing restriction of the two connecting rods on the pin shaft by the locking piece is released, so that the two connecting rods can rotate around the pin shaft under the action of external force to change the angle between the two. By manually turning the end gear, the central axis of the inkless pen and the central axis of the ink pen can be rotated to be coplanar with the central axis of the center gear. Based on the pen holder being a telescopic frame structure with adjustable length, the length from the center of the pen holder to its two end faces can be adjusted. The distance from the tip of the inkless pen to the central axis of the center gear can be adjusted to length a, and the distance from the tip of the ink pen to the central axis of the center gear can be adjusted to length b. The angle between the two connecting rods can be adjusted accordingly. At this time, the distance from the central axis of the end gear to the central axis of the center gear is Note that L1, the distance from the ink pen tip to the center axis of the end gear is Denoted as L2, after the drawing radius is adjusted in place, the locking piece can be tightened to keep the angle between the two connecting rods unchanged, which can ensure that the transmission gear and the end gear always keep L1 and L2 unchanged during the process of drawing an ellipse. When drawing an ellipse, press and fix the central gear with your fingers, and use your fingers to turn the V-shaped connecting rod mechanism around the central axis of the central gear. The V-shaped connecting rod mechanism can drive the transmission gear, the end gear and the pen holder to rotate around the central axis of the central gear. Based on the meshing relationship between the transmission gear and the central gear, the transmission gear can revolve around the central gear, and the transmission gear can rotate at the same time. Based on the meshing relationship between the end gear and the transmission gear, the end gear can rotate around the transmission gear, thereby driving the pen holder to rotate, and the ink pen and the inkless pen rotate with the pen holder. The ink pen draws an ellipse by rotating one circle; based on the different major semi-axis a and the different minor semi-axis b of the ellipse, L1 and L2 can be adjusted accordingly, so that ellipses of different sizes can be drawn. The ink pen fixing structure of the ellipse drawing mechanism is stable, which can help improve the accuracy of ellipse drawing. The ellipse drawing mechanism can be operated with one hand to draw an ellipse. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] 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.

[0025] Figure 1 It is a three-dimensional structural schematic diagram of the ellipse drawing mechanism of the present invention;

[0026] Figure 2 A three-dimensional bottom view of the ellipse drawing mechanism of the present invention;

[0027] Figure 3 It is a front view of the ellipse drawing mechanism of the present invention;

[0028] Figure 4 A schematic diagram of a coordinate system for adjusting the drawing radius of an ellipse drawing mechanism of the present invention;

[0029] Figure 5 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 figure: 1. connecting rod, 2. pin shaft, 3. first nut, 4. transmission gear, 5. center gear, 6. center cylindrical pin, 7. pen without ink, 8. end gear, 9. pen holder, 9.1. first scissors arm, 9.2. second scissors arm, 10. pen with ink, 11. end cylindrical pin, 12. center gear base, 13. second nut. 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 gear-type ellipse drawing mechanism based on the Fourier series idea, such as Figures 1 to 3 As shown, it is mainly composed of a V-shaped connecting rod mechanism, a central gear 5, a transmission gear 4, a terminal gear 8, a central gear base 12, a pen holder 9, an ink pen 10 and an inkless pen 7;

[0035] The V-shaped connecting rod mechanism is formed by two connecting rods 1 hinged by a pin shaft 2. A locking piece for limiting the free rotation of the two connecting rods 1 on the pin shaft 2 is provided on the pin shaft 2 between the two connecting rods 1. The locking piece is a first nut 3 threadedly connected to the top of the pin shaft 2 for pressing and fixing the two connecting rods 1. Tightening the first nut 3 can press and fix the two connecting rods 1 so that the two connecting rods 1 are fixed on the pin shaft 2. When the first nut 3 is loosened, the lock of the two connecting rods 1 is released, and the two connecting rods 1 can be rotated by hand to change the angle between the two connecting rods 1, and the distance between the center axis of the terminal gear 8 and the center axis of the center gear 5 can be adjusted. The spacing between them; in addition, the locking member can also be replaced by a bolt parallel to the pin shaft 2, which is threadedly connected to the end of the connecting rod 1 on the upper layer at the pin shaft 2. When the bolt is tightened downward, the bottom end of the bolt presses against the connecting rod 1 on the lower layer to keep the two connecting rods 1 relatively fixed. When the bolt is loosened upward, the bolt releases the restriction on the connecting rod 1, so that the two connecting rods 1 can rotate relative to each other; the locking member can also be a rubber sleeve sleeved on the pin shaft 2, and the two connecting rods 1 and the rubber sleeve have an interference fit to form a damping shaft structure. A certain external force needs to be applied to rotate the connecting rod 1. When drawing an ellipse, it can also ensure that the two connecting rods 1 do not rotate relative to each other;

[0036] The central gear 5 and the terminal gear 8 are respectively rotatably connected to the other ends of the two connecting rods 1, and the terminal gear 8 is rotatably connected to the pin shaft 2 between the two connecting rods 1, and the central gear 5 and the terminal gear 8 are both meshed with the transmission gear 4, and the number of teeth of the central gear 5 is twice the number of teeth of the terminal gear 8. The central gear 5, the terminal gear 8 and the transmission gear 4 can rotate relative to the V-shaped connecting rod mechanism, and the transmission gear 4 transmits power between the central gear 5 and the terminal gear 8. After pressing and fixing the central gear 5, rotating the transmission gear 4 by hand can make the transmission gear 4 and the terminal gear 8 revolve around the central axis of the central gear 5, and at the same time, the transmission gear 4 and the terminal gear 8 can rotate;

[0037] The center of the center gear 5 is fixed with a center cylindrical pin 6, the bottom of the center cylindrical pin 6 is fixed on the center gear base 12, and the top of the center cylindrical pin 6 is rotatably connected to the connecting rod 1; the center gear base 12 can support and fix the center gear 5 and the center cylindrical pin 6. When drawing an ellipse, the center gear 5 can be pressed with the thumb to fix the center gear base 12 on the drawing plane, so that the center gear base 12 can be firmly attached to the drawing plane without sliding. The center gear 5, the center cylindrical pin 6 and the center gear base 12 are all stationary relative to the earth coordinate system;

[0038] The pen holder 9 is a length-adjustable scissor frame structure, which includes two first scissor arms 9.1; a terminal cylindrical pin 11 is fixed to the center of the circle of the terminal gear 8, the top of the terminal cylindrical pin 11 is rotatably connected to the connecting rod 1, the middle parts of the two first scissor arms 9.1 are rotatably connected to the bottom of the terminal cylindrical pin 11, and the two first scissor arms 9.1 are crossed in an X shape, and the bottom of the terminal cylindrical pin 11 is threadedly connected with a second nut 13 for pressing and fixing the two first scissor arms 9.1 on the terminal cylindrical pin 11, and the two ends of each first scissor arm 9.1 are rotatably connected to the second scissor arms 9.2, which The ends of the two second scissor arms 9.2 located on the same side are rotatably connected to the top of the inkless pen 7, and the ends of the other two second scissor arms 9.2 located on the same side are rotatably connected to the top of the ink pen 10; after loosening the second nut 13, the restriction of the second nut 13 on the two first scissor arms 9.1 is released, and the two first scissor arms 9.1 can be manually moved to rotate relative to each other to adjust the length of the pen holder 9, thereby adjusting the spacing between the ink pen 10 and the inkless pen 7. Based on the scissor frame structure, the distances from the pen tips of the ink pen 10 and the inkless pen 7 to the center axis of the end cylindrical pin 11 are equal.

[0039] In addition, the pen holder 9 can also be a telescopic rod structure, which includes an intermediate rod and two sleeves sleeved on both ends of the intermediate rod. The ink pen 10 and the ink-free pen 7 are respectively fixed at the outer ends of the two sleeves, wherein there is friction resistance between the sleeve and the intermediate rod (an anti-slip rubber ring can be arranged inside the sleeve), and a certain external force needs to be applied to make the sleeve slide on the intermediate rod. Both ends of the intermediate rod are marked with scale lines, so that when the two sleeves slide on the intermediate rod, they can slide equal distances with reference to the scale lines, ensuring that the distances from the tips of the ink pen 10 and the ink-free pen 7 to the center axis of the end cylindrical pin 11 are equal.

[0040] Example 2

[0041] A variable radius gear-type ellipse drawing mechanism based on the Fourier series concept, the method for adjusting the drawing radius of the ellipse drawing mechanism is:

[0042] S1. Determine the size of the major semi-axis a and the minor semi-axis b of the ellipse to be drawn, and then mark the origin, minor axis point, and major axis point on the same straight line on the paper, where the minor axis point and the major axis point are on the same side of the origin, the distance from the minor axis point to the origin is b, and the distance from the major axis point to the origin is a;

[0043] S2, loosen the first nut 3 and the second nut 13, so that the second connecting rod 1 can rotate, so that the two first scissor arms 9.1 can rotate, align the central axis of the central gear 5 with the origin, pull the inkless pen 7 and the ink pen 10 so that the tip of the inkless pen 7 is aligned with the short axis point, and the tip of the ink pen 10 is aligned with the long axis point, the angle between the two connecting rods 1 changes adaptively with the pulling of the pen holder 9, and the distance from the central axis of the end gear 8 to the central axis of the central gear 5 is automatically adjusted to Note that L1, the distance from the tip of the ink pen 10 to the center axis of the end gear 8 is automatically adjusted to It is denoted as L2; ​​it should be noted that the center of the final gear 8 is on its axis, and the center of the central gear 5 is on its axis. Therefore, the distance from the center of the final gear 8 to the center of the central gear 5 is also Note it as L1; the above distances all refer to vertical distances;

[0044] S3. Tighten the first nut 3 and the second nut 13 to lock the size of L1 and L2. During the process of drawing an ellipse, ensure that the distance from the center axis of the end gear 8 to the center axis of the center gear 5 and the distance from the tip of the ink pen 10 to the center axis of the end gear 8 remain unchanged.

[0045] The drawing radius adjustment principle of the ellipse drawing mechanism is as follows:

[0046] 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 shape of an ellipse can be formed by superimposing two circles with different radii and opposite rotation angles;

[0047] like Figure 4 As shown, in the plane rectangular coordinate system, the coordinate origin is the center point of the ellipse and the projection point of the center point of the central gear 5, the major semi-axis of the ellipse is a and the minor semi-axis is b, the projection point of the tip of the inkless pen 7 is located at the minor axis point A, the projection point of the tip of the ink pen 10 is located at the major axis point G, and the pen holder 9 is a scissor frame structure. Figure 4 Point C is the projection point of the center of the final gear 8, BD and FE represent two first scissor frames, AB, AF, GE and GD represent four second scissor frames, and based on the quadrilateral ABCF being equal to GDCE, AC=CG, so A0+AG=A0+2·AC=b+2·AC=a, so and then Therefore, the distance between the center of the central gear 5 (coordinate point 0) and the center of the final gear 8 (coordinate point C) is Note that L1, the distance between the center of the final gear 8 (coordinate point C) and the tip of the ink pen 10 (coordinate point G) is Denoted as L2;

[0048] When adjusting the drawing radius of the ellipse drawing mechanism, first determine the sizes of the major semi-axis a and the minor semi-axis b of the ellipse to be drawn, and then adjust the distance from the center axis of the end gear 8 to the center axis of the center gear 5 and the distance from the tip of the ink pen 10 to the center axis of the end gear 8 on the same straight line to determine the sizes of L1 and L2. After tightening the first nut 3 and the second nut 13 to lock them, the ellipse drawing mechanism can be used to draw an ellipse.

[0049] Preferably, in the present embodiment, in the above step S2, the method for aligning the central axis of the central gear 5 with the origin is as follows: the central gear base 12 is in the shape of a truncated cone, which is coaxial with the central gear 5, and a circle with the origin as the center and the radius of the central gear base 12 as the radius is drawn on paper, and when the bottom surface of the central gear base 12 coincides with the drawn circle, the central axis of the central gear 5 is aligned with the origin;

[0050] In addition, a method that can also be used is: a freely retractable positioning rod is installed on the bottom surface of the center gear base 12, and the positioning rod is coaxial with the center gear 5. When the bottom end of the positioning rod coincides with the origin, the central axis of the center gear 5 is aligned with the origin. Specifically, the bottom end of the positioning rod is a pointed cone to facilitate alignment with the origin; when drawing an ellipse, the bottom surface of the center gear base 12 fits the drawing plane, and the freely retractable positioning rod can be pushed into the interior of the center gear base 12.

[0051] Example 3

[0052] A variable radius gear-type ellipse drawing mechanism based on the Fourier series concept, the method of drawing an ellipse by the ellipse drawing mechanism is as follows:

[0053] Adjust the drawing radius of the ellipse drawing mechanism according to the method described in Example 2, then press the center gear 5 with the thumb of one hand so that the center gear base 12 is firmly attached to the drawing plane and no sliding is allowed to occur. The other fingers touch the hinged ends of the two connecting rods 1 and turn the V-shaped connecting rod mechanism to rotate around the central axis of the center gear 5. The V-shaped connecting rod mechanism drives the transmission gear 4, the end gear 8 and the pen holder 9 to rotate around the central axis of the center gear 5. The transmission gear 4 revolves around the central axis of the center gear 5, and the transmission gear 4 rotates on its own. The end gear 8 revolves around the central axis of the center gear 5, and the end gear 8 rotates on its own. The pen holder 9 and the inkless pen 7 and the ink pen 10 installed thereon all rotate with the end gear 8. The trajectory drawn by the ink pen 10 when it rotates one circle on the drawing plane is an ellipse with a major semi-axis a and a minor semi-axis b.

[0054] In this embodiment, the number of teeth of the central gear 5 is 140, the number of teeth of the transmission gear 4 is 140, and the number of teeth of the terminal gear 8 is 70. Figure 5 As shown, in the plane rectangular coordinate system, L1 is the distance from the center axis of the end gear 8 to the center axis of the center gear 5, and L2 is the distance from the tip of the ink pen 10 to the center axis of the end gear 8;

[0055] The line connecting the center of the central gear 5 and the center of the transmission gear 4 is defined as the x-axis of the dynamic system 1, the line connecting the center of the transmission gear 4 and the center of the final gear 8 is defined as the x-axis of the dynamic system 2, the y-axes of the dynamic system 1 and the dynamic system 2 are straight lines perpendicular to the x-axis and leading the x-axis by 90°, the x-axes and y-axes of the dynamic system 1 and the x-axes and y-axes of the dynamic system 2 constitute the dynamic system 1 and the dynamic system 2 respectively;

[0056] When the transmission gear 4 revolves counterclockwise around the central axis of the center gear 5 by an angle of θ1, since the number of teeth between the two is 140, the transmission ratio is 1:1. At this time, the transmission gear 4 also rotates counterclockwise by an angle of θ1 relative to the static system 1. Since the static system 1 and the static system 2 do not rotate relative to each other, and the gear ratio between the transmission gear 4 and the final gear 8 is 2:1, the final gear 8 rotates clockwise by an angle of 2θ1 relative to the static system 2. Since the center of the final gear 8 rotates clockwise by an angle of θ1, the final gear 8 rotates counterclockwise by an angle of θ1 relative to the earth coordinate system, that is, it rotates clockwise by an angle of -θ1, thereby satisfying that the radius L1 of the first circle rotates by an angle of θ1, and the radius L2 of the second circle rotates by an angle of -θ1.

[0057] Furthermore, when the transmission gear 4 revolves counterclockwise around the central axis of the central gear 5 by an angle of θ2, since the number of teeth between the two is 140, the transmission ratio is 1:1. At this time, the transmission gear 4 also rotates counterclockwise by an angle of θ2 relative to the static system 1. Since the static system 1 and the static system 2 do not rotate relative to each other, and the gear ratio between the transmission gear 4 and the final gear 8 is 2:1, the final gear 8 rotates clockwise by an angle of 2θ2 relative to the static system 2. Since the center of the final gear 8 rotates clockwise by an angle of θ2, the final gear 8 rotates counterclockwise by an angle of θ2 relative to the geodetic coordinate system, that is, it rotates clockwise by an angle of -θ2, thereby satisfying that the radius L1 of the first circle rotates by an angle of θ2, and the radius L2 of the second circle rotates by an angle of -θ2.

[0058] When the ink pen 10 rotates around the coordinate origin on the paper, the trajectory it draws is an ellipse with a major semi-axis a and a minor semi-axis b.

[0059] 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. The transmission is realized through the meshing relationship of three gears. The ratio of the number of teeth of the center gear 5 to the number of teeth of the terminal gear 8 is 2 to 1. They mesh with each other through the transmission gear 4 to transmit the power of continuous motion, which improves the accuracy and efficiency of power transmission and helps to improve the accuracy of the drawn ellipse. By aligning the tip of the inkless pen 7 with the minor axis point and the tip of the ink pen 10 with the major axis point, the V-shaped connecting rod mechanism of the ellipse drawing mechanism releases the restriction and automatically adjusts the radius of the first rotating circle to The radius of the second rotating circle is This can automatically satisfy the Fourier decomposition of the ellipse.

[0060] 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 gear-type ellipse drawing mechanism based on the Fourier series concept, comprising two connecting rods (1), one end of the two connecting rods (1) being hinged to form a V-shaped connecting rod mechanism through a pin (2), characterized in that: A locking member for limiting the free rotation of the two connecting rods (1) is provided on the pin shaft (2) between the two connecting rods (1); The invention comprises a central gear (5), a transmission gear (4) and a terminal gear (8), wherein the central gear (5) and the terminal gear (8) are respectively rotatably connected to the other ends of the two connecting rods (1), and the terminal gear (8) is rotatably connected to a pin shaft (2) between the two connecting rods (1), and the central gear (5) and the terminal gear (8) are both meshed with the transmission gear (4), and the number of teeth of the central gear (5) is twice the number of teeth of the terminal gear (8); The invention comprises a pen holder (9), wherein the pen holder (9) is a telescopic frame structure with adjustable length, wherein the middle part is mounted on the bottom surface of the end gear (8), and an inkless pen (7) and an ink pen (10) are mounted on both ends of the pen holder (9), respectively. The length from the center of the pen holder (9) to the two end surfaces thereof is adjustable for adjusting the distance between the inkless pen (7) and the ink pen (10), and the central axis of the inkless pen (7) and the central axis of the ink pen (10) are parallel to the central axis of the end gear (8) and the distances are equal.

2. The variable radius gear type ellipse drawing mechanism based on the Fourier series concept according to claim 1 is characterized in that: The locking member comprises a first nut (3) threadedly connected to the top of the pin shaft (2) for pressing and fixing the two connecting rods (1).

3. The variable radius gear type ellipse drawing mechanism based on the Fourier series concept according to claim 2 is characterized in that: The ellipse drawing mechanism also includes a central gear base (12), a central cylindrical pin (6) is fixed at the center of the central gear (5), the bottom of the central cylindrical pin (6) is fixed on the central gear base (12), and the top of the central cylindrical pin (6) is rotatably connected to the connecting rod (1).

4. The variable radius gear type ellipse drawing mechanism based on the Fourier series concept according to claim 2 or 3, characterized in that: The pen holder (9) is a scissor frame structure with adjustable length, comprising two first scissor arms (9.1); a terminal cylindrical pin (11) is fixed at the center of the circle of the terminal gear (8); the top of the terminal cylindrical pin (11) is rotatably connected to the connecting rod (1); the middle parts of the two first scissor arms (9.1) are rotatably connected to the bottom of the terminal cylindrical pin (11), and the two first scissor arms (9.1) cross in an X shape; the bottom of the terminal cylindrical pin (11) is threadedly connected to a second nut (13) for pressing and fixing the two first scissor arms (9.1) on the terminal cylindrical pin (11); both ends of each first scissor arm (9.1) are rotatably connected to a second scissor arm (9.2); the ends of two second scissor arms (9.2) located on the same side are rotatably connected to the top of a pen without ink (7); and the ends of the other two second scissor arms (9.2) located on the same side are rotatably connected to the top of a pen with ink (10).

5. The variable radius gear type ellipse drawing mechanism based on the Fourier series concept according to claim 4 is 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, and then mark the origin, minor axis point and major axis point on the same straight line on the paper, where the minor axis point and the major axis point are on the same side of the origin, the distance from the minor axis point to the origin is b, and the distance from the major axis point to the origin is a; S2, loosen the first nut (3) and the second nut (13), align the central axis of the central gear (5) with the origin, pull the inkless pen (7) and the ink pen (10) so that the tip of the inkless pen (7) is aligned with the short axis point and the tip of the ink pen (10) is aligned with the long axis point, the angle between the two connecting rods (1) changes adaptively with the pulling of the pen holder (9), and the distance from the central axis of the end gear (8) to the central axis of the central gear (5) is automatically adjusted to Note that L1, the distance from the tip of the ink pen (10) to the center axis of the end gear (8) is automatically adjusted to Denoted as L2; S3, tighten the first nut (3) and the second nut (13) to lock the size of L1 and L2.

6. The variable radius gear type ellipse drawing mechanism based on the Fourier series concept according to claim 5 is characterized in that: In step S2, the method of aligning the central axis of the central gear (5) with the origin includes but is not limited to: Firstly, a freely retractable positioning rod is installed on the bottom surface of the central gear base (12), and the positioning rod is coaxial with the central gear (5). When the bottom end of the positioning rod coincides with the origin, the central axis of the central gear (5) is aligned with the origin; Secondly, the center gear base (12) is in the shape of a truncated cone and is coaxial with the center gear (5). A circle is drawn on paper with the origin as the center and the radius of the center gear base (12) as the radius. When the bottom surface of the center gear base (12) coincides with the drawn circle, the center axis of the center gear (5) is aligned with the origin.

7. The variable radius gear type ellipse drawing mechanism based on the Fourier series concept according to claim 5 or 6, characterized in that: The method for drawing an ellipse by the ellipse drawing mechanism is: The center gear (5) is pressed with the thumb of one hand so that the center gear base (12) is firmly fixed on the drawing plane, and the other fingers contact the hinged ends of the two connecting rods (1) and move the V-shaped connecting rod mechanism to rotate around the central axis of the center gear (5). The V-shaped connecting rod mechanism drives the transmission gear (4), the end gear (8) and the pen holder (9) to rotate around the central axis of the center gear (5). The transmission gear (4) revolves around the central axis of the center gear (5), and the transmission gear (4) rotates on its own. The end gear (8) revolves around the central axis of the center gear (5), and the end gear (8) rotates on its own. The pen holder (9) and the inkless pen (7) and the ink pen (10) installed thereon all rotate with the end gear (8). The trajectory drawn by the ink pen (10) 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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