CN106128232A - A kind of variable element circle fan annular demonstration and arc length area measuring device - Google Patents

Abstract

The invention discloses a variable parameter circular fan ring demonstration and arc length area measuring device, which comprises a disc bracket, a fan-shaped disc cover, a protection gate, a radial connecting rod, elastic slats, a rectangular bracket and a vernier ruler. The protective gate and the radial connecting rod are respectively arranged on the disc bracket, and the protective gate is perpendicular to the radial connecting rod, the elastic slats are placed on the disc bracket in an arc shape, and the two ends of the elastic slats They are respectively connected with the protection gate and the radial connecting rod, the fan-shaped disc cover is set on the elastic slat, the rectangular bracket is set on the disc bracket, and the two adjacent right-angled sides of the rectangular bracket are respectively connected with the protection gate and the radial The connecting rods touch each other, the vernier ruler is set on the rectangular bracket, and the radial connecting rod pushes and pulls the elastic slats to convert the circular arc and the straight line between the disc bracket and the rectangular bracket, and then realize the circle from the circular fan to the triangle or trapezoidal presentation and area measurement. The invention is simple in operation, strong in applicability, low in cost and convenient to carry.

Description

A variable parameter circular fan ring demonstration and arc length area measurement device

Technical field:

The invention relates to a variable parameter circular fan ring demonstration and arc length area measuring device.

Background technique:

The knowledge of graphics such as circles, fans, fan rings, and bows formed by arcs is one of the important contents that primary and secondary schools must learn. It is also the most commonly used graphics in all walks of life and daily life. Because arcs are not like straight lines Intuitively, teachers lack suitable teaching aids when teaching, and it is difficult to express such problems. It is difficult for students to understand during the learning process. It is easy to confuse the formulas for arc length and area in memory. Teachers urgently need some more scientific teaching aids or measuring tools to assist teaching. Students also need some tools that are easy to learn, and engineers and technicians need convenient measuring tools.

In order to solve the above problems, a small number of devices related to the circular sector have also appeared in the recent stage. For example, the document with the patent application number 201110273519.3 provides "a circular area demonstrator". Opening method, dividing the arc surface of an odd number of fan-shaped blocks with patches of equal size into upper and lower sides and bonding them to two side strips to form a complete disc, separating the two semi-circular sectors and crossing them correspondingly to form a The approximate rectangle of the curved edge, the area of the circle is represented by the area of the rectangle, and the area formula of the circle is obtained. Since the number of blocks of the sector is divided less, the side of the rectangle is not a straight line, the demonstration effect is not accurate, especially the related problems of any sector ring cannot be solved; The document with the patent application number of 201510189586.5 provides a "circle area size illusion demonstrator", which can clearly demonstrate and is conducive to illusion resolution, and cannot solve the problems of arc length and graphic area formed by arcs. .

Therefore, it is necessary to improve the prior art to solve the deficiencies of the prior art.

Invention content:

The present invention provides a variable parameter circular fan ring demonstration and arc length area measurement device in order to solve the problems in the prior art.

The technical solutions adopted in the present invention are: a variable parameter circular fan ring demonstration and arc length area measurement device, including a disc bracket, a fan-shaped disc cover, a protective gate, a radial connecting rod, elastic slats, a rectangular bracket and The vernier ruler, the protection gate and the radial connecting rod are respectively arranged on the disc bracket, and the protection gate is perpendicular to the radial connecting rod, and the elastic slats are placed on the disc bracket in an arc shape, and the elastic The two ends of the slats are respectively connected with the protection gate and the radial connecting rod, the fan-shaped disc cover is set on the elastic slats, the rectangular bracket is set on the disc bracket, and the two adjacent right-angled sides of the rectangular bracket are respectively connected to the The protection gate is in contact with the radial connecting rod, the vernier ruler is set on the rectangular bracket, and the radial connecting rod pushes and pulls the elastic slats to perform arc and straight line conversion between the disc bracket and the rectangular bracket, and then realizes Demonstration and area measurement of circular sector rings to triangles or trapezoids.

Further, the disk bracket includes a disk, a pulley bracket, a fixed pulley, a vertical shaft, spokes, radial rollers, a clamp bracket and a spring clip, the pulley bracket is fixed on the disk, and several fixed pulleys Circumferential rotation is connected to the disc, and the fixed pulley is located inside the pulley bracket, the vertical shaft is placed at the center of the disc, seven spokes are arranged between the pulley bracket and the vertical shaft along the circumferential direction of the disc, and the fixture bracket is fixed on a On the spokes, the spring clips are fixed on the fixture bracket, and the six radial rollers are rotated on the other six spokes; the protection gate and the radial connecting rod are respectively placed at the two spokes perpendicular to each other, and the elastic plate The strips are overlapped and placed on the tangential rollers in an arc shape, and the fan-shaped disc cover is covered on the elastic laths.

Further, the fan-shaped disk cover includes a transparent cover plate, a vertical shaft hole is opened in the center of the transparent cover plate, an arc groove is arranged on the transparent cover plate, and an arc scale is arranged along the inner edge of the arc groove. The transparent cover Linear scales are provided on both sides of the board.

Further, the protective gate includes a rectangular bottom plate, a door frame, a third gate and a door lock groove, the door frame is fixed on the rectangular bottom plate, and a rectangular door opening is provided on the door frame, above the door frame and facing the door opening There is a third gate slot at the center, and the third gate is arranged in the third gate slot, and a door lock groove is opened on the rectangular bottom plate directly below the third gate.

Further, the radial connecting rod includes a rectangular connecting rod, a notch gate, a push rod, a fourth roller, a handle and a collar, the rectangular connecting rod is provided with a fourth gate groove, and the notch gate is arranged on the fourth In the gate slot, the push rod is fixedly connected to the rectangular connecting rod, and the lower end of the push rod passes through the rectangular connecting rod and is connected with the fourth roller, the handle is fixed on the top of the push rod, and the collar is fixed on the side wall of the rectangular connecting rod superior.

Further, the elastic slats include a rectangular slat body, a push-pull plate, a guide leg, an indicator light and a ball post, and the push-pull plate, guide legs, indicator lights and ball post are all connected to the rectangular slat body.

Further, the rectangular bracket includes a rectangular base plate, a left slideway, a right slideway, a front riser and a rear riser, and the left slideway, the right slideway, the front riser and the rear riser are respectively arranged on rectangular On the four sides of the base plate, several linear grooves are arranged on the rectangular base plate, an aisle is opened at the lower part of the left slideway, and a sixth pin hole is arranged at the edge of the rectangular base plate.

Further, the vernier ruler includes a ruler plate, a vernier, a left slider and a right slider, the left slider and the right slider are respectively fixedly connected to both sides of the ruler plate, and the vernier is arranged on the ruler plate; Both the left slider and the right slider are provided with T-shaped grooves.

The present invention has following beneficial effect:

The invention is easy to operate, and the demonstration and numerical measurement can be completed by simply pushing the handle after the assembly is completed; the applicability is strong: the equal-area demonstration, arc length measurement and area simple calculation of various graphics can be completed by selecting different radii and central angles; The cost is low, and it is easy to carry, and can be placed in a pencil case.

Description of drawings:

Fig. 1 is a structural schematic diagram of the present invention.

Fig. 2 is a structural schematic diagram of the disc bracket in the present invention.

Fig. 3 is a schematic structural view of the fan-shaped disk cover in the present invention.

Fig. 4 is a structural schematic diagram of the protective gate in the present invention.

Fig. 5 is a structural schematic diagram of the radial connecting rod in the present invention.

Fig. 6 is a schematic structural view of the elastic slats in the present invention.

Fig. 7 is a schematic structural diagram of a rectangular bracket in the present invention.

Fig. 8 is a schematic structural view of a vernier ruler in the present invention.

detailed description:

The present invention will be further described below in conjunction with the accompanying drawings.

As shown in Fig. 1, a kind of parameter-variable circular fan circular demonstration and arc length area measuring device of the present invention comprises a disc bracket 1, a fan-shaped disc cover 2, a protective gate 3, a radial connecting rod 4, an elastic slat 5, and a rectangular support Frame 6 and vernier ruler 7, protective gate 3 and radial connecting rod 4 are respectively arranged on the disc bracket 1, and protective gate 3 is perpendicular to radial connecting rod 4, and elastic slats 5 are placed in an arc shape. On the disc bracket 1, and the two ends of the elastic slats 5 are respectively connected with the protection gate 3 and the radial connecting rod 4, the fan-shaped disc cover 2 is set on the elastic slats 5, and the rectangular bracket 6 is set on the disc support on the frame 1, and the two adjacent right-angled sides of the rectangular bracket 6 are respectively in contact with the protection gate 3 and the radial connecting rod 4, and two vernier rulers 7 are set on the rectangular bracket 6, and the radial connecting rod 4 is pushed and pulled The elastic slats 5 perform circular arc and straight line conversion between the disk bracket 1 and the rectangular bracket 6, and then realize the demonstration and area measurement of the circular fan ring into a triangle or trapezoid.

As shown in Fig. 2, the disc bracket 1 among the present invention comprises disc 11, is provided with pulley support 12 on disc 11, fixed pulley 13 is housed in pulley support 12 inside, is provided with cylinder at the center of disc 11 The vertical shaft 14 is provided with seven spokes 15 between the vertical shaft 14 and the pulley bracket 12, and a clamp support 19 is fixed outside one of the spokes 15, and a plurality of spring clamps 110 are arranged on the clamp support 19. Take the spoke 15 fixed with the clamp bracket 19 as the first spoke, and then clockwise on the remaining second to seventh spokes 15, all are provided with tangential rollers 16 . Below the outer edge of the disc 11, a lower facade 17 is provided, a first pin 18 is provided at the first quadrant of the disc, and a first fixing hole 111 is provided at the second to fourth quadrant edges of the disc. The protective gate 3 and the radial connecting rod 4 are respectively placed on the first and seventh spokes 15 of the disc bracket 1, the elastic slats 5 are placed on the tangential roller 16 in an arc shape, and the fan-shaped disc cover 2 covers Above the elastic slats 5 , a rectangular bracket 6 is fixed on the disc bracket 1 at the first quadrant and adjacent to the protective gate 3 and the radial link 4 . The vernier ruler 7 is placed on the rectangular bracket 6 . The radial connecting rod 4 pushes and pulls the elastic slats 5 to perform circular arc and straight line conversion between the disc bracket 1 and the rectangular bracket 6, thereby realizing the demonstration and area measurement functions of circular fan rings to triangles or trapezoids.

As shown in Fig. 3, the fan-shaped disc cover 2 includes a transparent cover plate 21 and an outer facade 22, a vertical shaft hole 24 is opened at the arc center of the transparent cover plate 21, and an arc groove 23 is opened at the arc edge of the transparent cover plate 21, An arc scale 25 is arranged along the inner edge of the arc groove 23 , and a linear scale 26 is arranged on both straight sides of the transparent cover plate 21 , and a second fixing hole 27 is opened on the outer edge of the arc groove 23 . The fan-shaped disc cover 2 is fixed to the vertical shaft 14 and the first fixing hole 111 on the disc bracket 1 through the vertical shaft hole 24 and the second fixing hole 27 on the transparent cover plate 21, and the outer facade 22 is wrapped on the lower facade 17 outside.

As shown in Figure 4, the protection gate 3 comprises a rectangular bottom plate 31, a door frame 32 and a third gate 35, the door frame 32 is fixed on the rectangular bottom plate 31, and the front end of the door frame 32 has a recessed rectangular door opening 33, on the door frame 32 Fangzheng has a third gate slot 34 opposite the door opening 33, and a third gate 35 is installed in the third gate slot 34. On the rectangular bottom plate 31, there is a door lock groove 36 directly below the third gate 35. On the rectangular bottom plate Both ends of 31 are provided with screw holes 37 . The protection gate 3 is fixed on the seventh spoke 15 of the disc bracket 1 through screw holes 37 .

As shown in Figure 5, the radial connecting rod 4 comprises a rectangular connecting rod 41, a gap gate 44, a push rod 45 and a fourth roller 46, and a gate hole 42 is arranged in front of the rectangular connecting rod 41, and the first gate hole 42 is arranged above the gate hole 42. Four gate slots 43, a gap gate 44 is housed in the fourth gate slot 43, a push rod 45 is arranged on the rectangular connecting rod 41, a fourth roller 46 is installed on the lower end of the push rod 45, and a handle 47 is connected to the upper end of the push rod 45 , The rectangular connecting rod 41 is provided with a collar 48 . The radial connecting rod 4 is sleeved on the vertical shaft 14 of the disk carrier 1 through a collar 48 .

As shown in Figure 6, the elastic slat 5 includes a rectangular slat body 51, a push-pull plate 52, a guide leg 53, an indicator light 58 and a ball post 510, and the surfaces of the rectangular slat body 51 are respectively a front elevation 54 and a rear elevation 55 , the upper section 56, the lower section 57, the left elevation 59 and the right elevation 511, the front and rear elevations are smooth and flat, and are not deformed when they form arcs. The left end of the upper section 56 is provided with a push-pull plate 52, and the right end is provided with an indicator lights 58. The right end of the lower section 57 is provided with a guide foot 53 , and a ball post 510 is provided on the left elevation 59 . The lower section 57 of the elastic slat 5 is placed on the radial roller 16, the push-pull plate 52 is placed in the gate hole 42 of the radial connecting rod 4, and the guide leg 53 is placed in the gate hole 33 of the protection gate 3.

As shown in Figure 7, the rectangular bracket 6 includes a rectangular base plate 61, a linear groove 62, a left slideway 63, a right slideway 64, a front vertical plate 65 and a rear vertical plate 66, and a plurality of parallel plates are opened on the upper surface of the rectangular base plate 61. The linear groove 62 of the left slideway 63, the right slideway 64, the front vertical plate 65, and the rear vertical plate 66 are vertically fixed on the four sides of the rectangular base plate 61 successively, and there is an aisle 67 in the left slideway 63 bottom, and the rectangular A sixth pin hole 68 is formed on the edge of the base plate 61 . The rectangular bracket 6 is fixed to the first pin hole 18 on the disk bracket 1 through the sixth pin hole 68 , and the aisle 67 is connected to the door opening 33 of the protection gate 3 .

As shown in Figure 8, the vernier ruler 7 comprises a ruler plate 71, a vernier 73, a left slider 74 and a right slider 75, the ruler plate 71 is a straight hard board with a length scale 72 above, and the vernier 73 is stuck on the ruler On the plate 71, the left and right ends of the ruler plate 71 are respectively fixed on the left slider 74 and the right slider 7), and a "T" shaped groove 76 is provided under the left slider 74 and the right slider 75, The vernier ruler 7 is connected on the left slideway 63 right slideway 64 of the rectangular bracket 6 by the groove 76 on the left slide block 74 right slide block 75.

The working principle of the present invention is, according to the curvature of the arc and the straight line is constant, the arc that rotates around the center of the circle is converted into the equal length tangent of a certain point on the arc, and the equal area of the circular sector covered by the arc of continuous radius becomes A right triangle covered by a line segment.

The present invention has the function of demonstration and measurement, and can demonstrate the relationship between the arc change of different parameters and the area change of the circle sector and calculate its value. The operation steps are:

1) Assembly: put the side of the disc bracket with the pulley bracket facing up, fix the protective gate at the seventh spoke, lift the third gate to open the door opening, and lift the push-pull plate of the elastic slat upward from the door opening Go through the protection gate on the right, push the elastic slats counterclockwise to move along the fixed pulley, and clamp the ball column in the spring clip of the disc bracket. When the guide feet stay in the third gate, press the third gate, and all The elastic slats are arranged in order of length from outside to inside to form a circular sector. Put the collar of the radial connecting rod on the central vertical shaft of the disc bracket, press the push-pull plate of the elastic slat on the rectangular connecting rod, pass the fan-shaped disc cover through the push rod of the radial connecting rod and cover it on the The top of the disc bracket is fixed, and the straight line groove of the rectangular bracket is aligned with the guide feet of the elastic slats in the third gate and fixed. Clamp the sliders of the two vernier rulers on the left and right slideways of the rectangular bracket respectively.

2) Initial state adjustment: Adjust the two ends of all elastic slats to be on a straight line, and the radial connecting rod to be at 0 degrees on the fan-shaped disk cover. To demonstrate (or measure) the arc radius of the graph is The central angle is ( is radian), press down on the radial connecting rod at Those gap gates that are within range, and with the gap stuck on the ball post, lift the For those gap gates, find the scale point at the protection gate , press at of those third gates, brought Those third gates within the range, and open the indicator light on the elastic slats, adjust a vernier ruler on the rectangular bracket with the The circle tangent at is consistent, and slide the cursor to 0 scale.

3) Demonstration: Grasp the main body of the measuring device with one hand and hold the handle of the push rod with the other hand, and slowly push the radial connecting rod clockwise. The indicator lights of the elastic slats in the range are spread out in a straight line along the straight groove of the rectangular bracket, The front end of the elastic slat at the position pushes the cursor forward, and at the arrival angle of the radial connecting rod stop pushing and turning, and the cursor stops at the place, The reading at is the radius of The central angle is arc length , resting on the upper section of the elastic slat portion of the rectangular bracket arranged in a right triangle ( is the center point of the disc), the indicator lights are all on up, right triangle the area of is the radius of The central angle is The area of the circular sector of ;

4) End: push the radial connecting rod counterclockwise back to 0 radians, press it to For those third gates, adjust the vernier ruler on the rectangular bracket close to the frame.

The present invention can demonstrate the variation relationship of circular fan annular area with different parameters and measure the quick calculation area value. The operation steps are:

a) Assembly: Same as step 1) above;

b) Initial state adjustment: To demonstrate or measure the radius by arrive The central angle is ( is the fan ring in radians, press down on the radial connecting rod at Those gap gates that are within range, and with the gap stuck on the ball post, lift the For those gap gates, find the scale point at the protection gate , , press at of those third gates, brought Those third gates within the range, and turn on the indicator lights on the elastic slats, adjust the two vernier rulers on the rectangular bracket to correspond to the , The circle tangents at are consistent, and slide the cursors to 0 scale;

c) Demonstration: Grasp the main body of the measuring device with one hand and hold the handle of the push rod with the other hand, and slowly push the radial connecting rod clockwise. The indicator lights of the elastic slats in the range are spread out in a straight line along the straight groove of the rectangular bracket, , The front end of the elastic slat at the position pushes the vernier I and the vernier II forward (for the convenience of distinguishing the verniers in the two vernier rulers 7, the vernier in the two vernier rulers 7 are respectively distinguished by the vernier I and the vernier II), Arrival angle in radial link Stop pushing and turning, and cursor Ⅰ is at the position of the vernier ruler. , cursor II stops at , the upper section of the elastic slat part of the rectangular bracket forms a right-angled isosceles trapezoid , the area of is the area of the circular sector .

d) End: Same as step 4) above.

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, some improvements can also be made without departing from the principle of the present invention, and these improvements should also be regarded as the invention. protected range.

Claims (8)

1. a variable element circle fan annular demonstration and arc length area measuring device, it is characterised in that: include disk bracket (1), fan Shape disk cover (2), protection gate (3), radial link (4), elastic slat (5), rectangular bracket (6) and vernier ruler (7), described Protection gate (3) and radial link (4) are respectively arranged on disk bracket (1), and protection gate (3) is hung down mutually with radial link (4) Directly, elastic slat (5) is placed in arc-shaped on disk bracket (1), and the two ends of elastic slat (5) respectively with protection gate (3) Being connected with radial link (4), fan-shaped disk cover (2) is covered on elastic slat (5), and rectangular bracket (6) is located at disk bracket (1) On, and adjacent two right-angle sides of rectangular bracket (6) touch mutually with protection gate (3) and radial link (4) respectively, vernier ruler (7) being located on rectangular bracket (6), radial link (4) push-and-pull elastic slat (5) is between disk bracket (1) and rectangular bracket (6) Carry out the conversion of circular arc and straight line, then realize circle fan annular and arrive triangle or trapezoidal demonstration and area measurement.

2. variable element circle fan annular demonstration as claimed in claim 1 and arc length area measuring device, it is characterised in that: described circle Disc holder (1) include disk (11), pulley bracket (12), fixed pulley (13), vertical shaft (14), spoke (15), footpath way roller (16), Fixture mount (19) and alligator clamp (110), described pulley bracket (12) is fixed on disk (11), some fixed pulleys (13) edge The circumferencial direction of disk (11) is rotationally connected with on disk (11), and fixed pulley (13) is positioned at the inner side of pulley bracket (12), vertical Axle (14) is placed in the center of disk (11), seven spokes (15) along the circumferencial direction of disk (11) be located at pulley bracket (12) with Between vertical shaft (14), fixture mount (19) is fixed on spoke described in (15), and alligator clamp (110) is fixed on fixture mount (19) On, six roots of sensation footpath way roller (16) rotates and is located on spoke (15) described in the other six roots of sensation；Described protection gate (3) and radial link (4) being respectively placed in orthogonal described two spokes (15) place, elastic slat (5) is placed in tangential roller (16) in arc-shaped overlap On, fan-shaped disk cover (2) covers the top in elastic slat (5).

3. variable element circle fan annular demonstration as claimed in claim 1 and arc length area measuring device, it is characterised in that: described fan Shape disk cover (2) includes a transparent cover plate (21), has vertical shaft hole (24) at the center of transparent cover plate (21), on transparent cover plate (21) Being provided with arc groove (23), the inward flange along arc groove (23) is provided with circular arc scale (25), and the dual-side of transparent cover plate (21) sets There is slide-rule dial (26).

4. variable element circle fan annular demonstration as claimed in claim 1 and arc length area measuring device, it is characterised in that: described guarantor Protecting gate (3) and include rectangular base plate (31), door frame (32), the 3rd gate (35) and door lock ditch (36), described door frame (32) is solid In rectangular base plate (31), door frame (32) is provided with rectangular-shaped door opening (33), in door frame (32) top and just to door opening (33) place has the 3rd gate slot (34), and the 3rd gate (35) is located in the 3rd gate slot (34), in rectangular base plate (31) And the underface being positioned at the 3rd gate (35) has door lock ditch (36).

5. variable element circle fan annular demonstration as claimed in claim 1 and arc length area measuring device, it is characterised in that: described footpath Rectangle connecting rod (41), gap gate (44), push rod (45), the 4th roller (46), handle (47) and the collar is included to connecting rod (4) (48), described rectangle connecting rod (41) is provided with the 4th gate slot (43), and gap gate (44) is located in the 4th gate slot (43), Push rod (45) is fixedly connected on rectangle connecting rod (41), and the lower end of push rod (45) through rectangle connecting rod (41) and with the 4th roller (46) being connected, handle (47) is fixed on the top of push rod (45), and the collar (48) is fixed on the sidewall of rectangle connecting rod (41).

6. variable element circle fan annular demonstration as claimed in claim 1 and arc length area measuring device, it is characterised in that: described bullet Property lath (5) include rectangular strip body (51), draw back plate (52), guide leg (53), display lamp (58) and goalpost (510), Described draw back plate (52), guiding leg (53), display lamp (58) and goalpost (510) are all connected on rectangular strip body (51).

7. variable element circle fan annular demonstration as claimed in claim 1 and arc length area measuring device, it is characterised in that: described square Shape bracket (6) includes rectangular substrate (61), left slideway (63), right slideway (64), front vertical plate (65) and back vertical plate (66), a described left side Slideway (63), right slideway (64), front vertical plate (65) and back vertical plate (66) are correspondingly arranged at four sides of rectangular substrate (61) respectively Bian Shang, is provided with some straight line grooves (62) in rectangular substrate (61), has passageway (67) in left slideway (63) bottom, at square The edge of shape substrate (61) is provided with the 6th pin hole (68).

8. variable element circle fan annular demonstration as claimed in claim 1 and arc length area measuring device, it is characterised in that: described trip Mark ruler (7) includes ruler plate (71), vernier (73), left slider (74) and right slide block (75), left slider (74) and right slide block (75) being respectively fixedly connected with in the both sides of ruler plate (71), vernier (73) is located on ruler plate (71)；At left slider (74) with right T-shaped groove (76) it is equipped with on slide block (75).