CN101570100B - Trisection gauge of plane angle - Google Patents
Trisection gauge of plane angle Download PDFInfo
- Publication number
- CN101570100B CN101570100B CN 200910099286 CN200910099286A CN101570100B CN 101570100 B CN101570100 B CN 101570100B CN 200910099286 CN200910099286 CN 200910099286 CN 200910099286 A CN200910099286 A CN 200910099286A CN 101570100 B CN101570100 B CN 101570100B
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- CN
- China
- Prior art keywords
- riveting axle
- lath
- riveting
- angle square
- axle
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Abstract
The invention relates to a trisection gauge for any angle, which comprises a holding rack and an angle square assembly; wherein, the holding rack consists of two plate strips which are respectively provided with a longitudinal rail groove. One end of every plate strip is connected by a riveting shaft. The angle square assembly consists of a scribing angle square and a reference angle square, wherein, the scribing angle square is composed of a plate strip 3 and a plate strip 4 which are crossed with each, and the reference angle square is composed of a plate strip 5 and a plate strip 6 or the plate strip 4. A riveting shaft 5 and a riveting shaft 6 respectively slide along the rail grooves, and simultaneously respectively change the angles between the two plate strips of the holding rack, the two plate strips of the scribing angle square and the two plate strips of the reference angle square. A riveting shaft 4 penetrates through one end of every plate strip of the reference angle square and the crossing point of the scribing angle square to connect the riveting shafts of the four plate strips. The riveting shafts 1, 2, 3 and 4 respectively form four vertexes of an equal-edge quadrilateral. In the invention, a compasses and a ruler are used for dividing a plane angle into three equal parts, and the ruler is designed by a drawing principle to perform odd equal division such as trisection on plane angle. The trisection gauge has the characteristics of accurate equal division, simple structure, wide application, convenient use and the like, and provides a drawing tool which can directly divide angle into three equal parts for teaching, scientific researching and engineering design.
Description
Technical field
The invention belongs to and draw or survey tool particularly a kind of rule or chi of drawing the trisection of an angle.
Background technology
In teaching, scientific research and engineering design, only use compasses and the ruler often can not be, and the trisection of an angle, duplication of the cube body and quadrature of a circle close and claim Three Difficult Issues how much with plane angle trisection or odd number five equilibrium.A famous mathematician just once said: " is impossible as walking is landed on the moon just with any angle of compasses ruler trisection "; On market, do not have always can be directly with the drawing instrument of plane angle trisection; Usually adopt aid to survey and draw, the degree of accuracy is undesirable.
Summary of the invention
The trisection gauge drawing instrument that the purpose of this invention is to provide a kind of plane angle can be directly with the plane angle trisection, and the degree of accuracy is higher relatively.
The trisection gauge of plane angle; It is characterized in that this ruler is by holding frame and the angle square assembly is formed; Holding frame is made up of the lath that has vertical rail groove one, lath two; One end of two laths is connected by riveting axle one, and making two laths is that fulcrum rotates each other with riveting axle one, and this fulcrum is positioned on the extended line of rail groove longitudinal midline; The angle square assembly is made up of straightedge rule and benchmark angle square; Wherein straightedge rule is made up of lath three, lath four intersections; The end in the same way of this two lath is connected by riveting axle three, riveting axle two with the two lath plate bodies of holding frame respectively, and this riveting axle two and riveting axle three lay respectively at two and hold on the extended line of longitudinal midline of frame rail groove and holding the frame rail groove and holding between the frame riveting axle one; The benchmark angle square is made up of lath five, lath six; Riveting axle five and riveting axle six run through respectively the benchmark angle square lath five, lath six the plate body and hold vertical rail groove of frame, make riveting axle five and riveting axle six respectively along the rail groove slide and change respectively simultaneously hold between frame two laths, angle between straightedge rule two laths, between benchmark angle square two laths; Riveting axle four runs through an end of benchmark angle square two laths and the crosspoint of straightedge rule connects four laminate bar riveting axles; Distance between distance between riveting axle three, the riveting axle six and riveting axle two, the riveting axle five constitutes two bases of two isosceles triangles respectively, and riveting axle one, two, three, four constitutes equilateral tetragonal four summits respectively.
Said riveting axle two, riveting axle four and riveting axle three, riveting axle four lay respectively at two line of straightedge rule along on the straight line that forms; Two angulations that riveting axle four, riveting axle six and riveting axle four, riveting axle five lay respectively at the benchmark angle square are along on the straight line that forms, and riveting axle five and riveting axle six also lay respectively on the extended line of longitudinal midline of the rail groove of holding frame.
Said frame and the straightedge rule held also can constitute by the lath that has vertical rail groove, and riveting axle four is positioned on the extended line of rail groove longitudinal midline of straightedge rule, and this two rails groove constitutes setting-out groove.
The lath of holding frame and angle square assembly of the trisection gauge of said plane angle is processed by metal or plastics.
But said six laths holding frame and angle square assembly constitute stepped construction by the effect of each riveting axle, and two laths wherein holding frame are positioned at outermost layer, and it connects riveting axle one outer axle sleeve that is with, and the height of this axle sleeve cooperates with four range upon range of thickness of lath of centre.
The present invention can also process following structure:
A kind of trisection gauge of plane angle; It is characterized in that this ruler is by holding frame and the angle square assembly is formed; Holding frame is made up of lath one, connecting plate one; One end of two laths is connected by riveting axle one, and its middle plate strip one upwards has vertical rail groove at a segment distance that leaves riveting axle one, and riveting axle one is positioned on the extended line of longitudinal midline of this rail groove; Riveting axle five is riveted on and runs through behind connecting plate three upper ends and be snug fit at vertical rail groove of holding frame plate bar one, connecting plate two lower ends near the position of holding frame plate bar one vertical rail groove lower end by two connections of riveting axle; The angle square assembly is made up of straightedge rule and benchmark angle square; Wherein straightedge rule is made up of lath three and lath four intersections; The benchmark angle square is made up of the lath four of connecting plate three and straightedge rule, and plate palette body bottom has vertical rail groove, and riveting axle one runs through and be snug fit at vertical rail groove of lath four; Three on riveting axle is plate one upper end and lath three lower ends repeatedly; The crosspoint that riveting axle four runs through connecting plate three lower ends, connecting plate two upper ends, straightedge rule connects four laminate bar riveting axles, riveting axle five and riveting axle one respectively along lath one hold frame rail groove and lath four rail grooves slide and change respectively simultaneously hold between frame plate bar one and the connecting plate one, angle between straightedge rule lath three and the lath four, between benchmark angle square connecting plate three and the straightedge rule lath four; Connecting plate two and connecting plate three constitute two isosceles limits of isosceles triangle respectively, and riveting axle one, two, three, four constitutes equilateral tetragonal four summits respectively.
Said riveting axle three and riveting axle four are positioned at the line of lath three of straightedge rule along on the straight line that forms; Riveting axle one and riveting axle four are positioned at the line of lath four along on the straight line that forms with lath four rail groove longitudinal midline extended lines overlap, and riveting axle one, riveting axle two and riveting axle four are positioned on the longitudinal midline extended line of vertical rail groove of holding frame plate bar one.
The said lath of holding frame and angle square assembly is processed by metal or plastics.
But said five laths holding frame and angle square assembly constitute stepped construction by the effect of each riveting axle, and its middle plate strip one is positioned at outermost layer with lath four, and it connects riveting axle one outer axle sleeve that is with, and the height of this axle sleeve cooperates with three range upon range of thickness of lath of centre.
The applicant is owing to solved with compasses and the ruler technique of painting with the plane angle trisection; And utilize this technique of painting principle design to go out the present invention; Can solve the technique of painting of plane angle trisection; Compare with the existing technique of painting, have characteristics such as five equilibrium is accurate, simple in structure, of many uses, easy to use. for teaching, scientific research and engineering design provide a kind of can be directly with the drawing instrument of plane angle trisection.
Description of drawings
Fig. 1 is a kind of structural front view of the present invention.
Fig. 2 is an A-A partial cross section enlarged drawing among Fig. 1.
Fig. 3, Fig. 4 are for compasses and the ruler technique of painting schematic diagram with the plane angle trisection.
Fig. 5 another kind of structural front view of the present invention.
Fig. 6 is the rearview of Fig. 5.
Fig. 7 is the front view of the another kind of shape of Fig. 1 structure.
Fig. 8 is the range upon range of state front view of Fig. 7.
The specific embodiment
With compasses and ruler with the technique of painting principle of plane angle trisection with reference to Fig. 3, Fig. 4:
Known: ∠ AOB, ask with compasses and ruler and to do trisection of an angle.
The mapping process:
(1) being the center of circle with O, is radius with OA, draws circle, hands over OB in the B point.
(2) make straight line ON, hand over AMB arc mid point M, and make MN=OM.
(3) make radius OQ, make ∠ QOM=45 °; With Q is the center of circle, is that radius is drawn arc friendship MN in the P point with OQ; Equal the compasses of radius with A/F, last tiptoe drops on the Q point, and following tiptoe drops on the P point.
(4) with a ruler, upper end-face edge is overlapped with A, the lower end slowly by disturbing compasses, is promoting to go up tiptoe, makes it prolong circumferential bottom right and moves, and descends tiptoe also prolonging MN moving down slowly simultaneously.When two tiptoes touched ruler simultaneously, A, D, three points of C were point-blank.Make straight line AC, hand over circumference in the D point, hand over MN in the C point, straight line ADC has just come out, and last tiptoe is the D point, and following tiptoe is the C point.
(5) make radius OD, then the OD=DC=radius.
(6) be symmetry axis with ON, make symmetrical figure, connect BC, hand over circle, make radius OG in G.
(7) ∵ OA=OB=radius, ∠ AOC=∠ BOC, OC is a common edge.
∴ΔAOC≌ΔBOC，∠1＝∠2，AC＝BC ……①
(8) ∵ OA=OB=OD=OG=radius, ∴ Δ AOD and Δ BOG are isosceles triangles.
(9) two base angles of ∵ isosceles triangle equate, ∠ 1=∠ 2, and ∴ ∠ 3=∠ 4, ∠ 5=∠ 6 simultaneously.
∴ΔAOD≌ΔBOD，AD＝BG ……②
(10)①-②AC-AD＝DC，BC-BG＝GC，∴DC＝GC。
∵ OD=DC=GC=OG, ∴ quadrangle ODCG are rhombuses, and four limits equate that opposite side is put down shape.
(11) prolong OD and hand over circle, prolong OG, hand over circle in E in F.
(12) OF, OE are exactly the trisection line of ∠ AOB, ∠ AOE=∠ EOF=∠ FOB.
Proof:
∵ AD//EG, FD//BG, (extended line of parallel lines is also parallel)
∠ AOE=∠ DOG, ∠ FOB=∠ DOG, two folded arcs of parallel lines (string) equate, its right central angle also equate.
∵ ∠ EOF=∠ DOG again, (vertical angles)
∴∠AOE＝∠EOF＝∠FOB。
Map successfully.
When making straight line ADC, last tiptoe must move on circumference, and following tiptoe must be at the MN rectilinear motion.3 of A, D, C must be rule in will be on the ruler edge again, otherwise cause error easily.
The trisection gauge of the plane angle of making according to above-mentioned mapping principle, like Fig. 1, shown in Figure 2, this ruler is held frame and is used to hold structure angle square assembly, by having vertical rail groove C by holding frame and the angle square assembly is formed
11Lath C
1, have vertical rail groove C
21Lath C
2Form, the lower end of two laths is connected by riveting axle 1, makes two lath C
1, C
2With riveting axle 1 is that fulcrum rotates each other, and the axle center of riveting axle 1 is positioned at above-mentioned two rail groove C
11, C
21On the extended line of longitudinal midline.The angle square assembly is made up of straightedge rule and benchmark angle square, and wherein straightedge rule is used for 1/3rd jiaos in picture, by lath B
1, lath B
2The scissors intersection constitutes lath B
1The lower end with hold frame plate bar C
2The plate body is connected by riveting axle 2, and this riveting axle is positioned at holds frame rail groove C
21And hold and hold frame rail groove C between the frame riveting axle 1
21The extended line of longitudinal midline on, and near holding frame rail groove C
21The lower edge; Lath B
2The lower end with hold frame plate bar C
1The plate body is connected by riveting axle 3, and this riveting axle is positioned at holds frame rail groove C
11And hold and hold frame rail groove C between the frame riveting axle 1
11The extended line of longitudinal midline on, and near holding frame rail groove C
11The lower edge.The benchmark angle square is used to aim at the plane angle by five equilibrium, by lath A
2, lath A
1Form, riveting axle 5 runs through lath A
2The plate body with hold vertical rail groove C of frame
21, riveting axle 6 runs through lath A
1The plate body with hold vertical rail groove C of frame
11, when riveting axle 5,6 respectively along rail groove C
21, C
11During slip, also promptly change lath A
2, A
1Between angle the time, drive to change simultaneously and hold frame plate bar C
1, lath C
2Between angle, and then drive straightedge rule lath B
1, B
2Between angle.Riveting axle 4 runs through benchmark angle square two lath A
2, A
1An end and straightedge rule lath B
1, B
2The crosspoint this four laminates bar riveting axle is connected, thereby constitute the linkage structure of above-mentioned six laths.
During making; Distance between distance between requirement riveting axle 3, the riveting axle 6 and riveting axle 2, the riveting axle 5 constitutes two bases of two congruent isosceles triangles respectively; Riveting axle 1,2,3,4 constitutes equilateral tetragonal four summits respectively, also requires riveting axle 2, riveting axle 4 and riveting axle 3, riveting axle 4 to lay respectively at two of straightedge rule and rules along B
11, B
21On the straight line that forms, riveting axle 4, riveting axle 6 and riveting axle 4, riveting axle 5 lay respectively at two angulations of benchmark angle square along A
11, A
21On the straight line that forms, riveting axle 5 also lays respectively at the rail groove C that holds frame with riveting axle 6
21, C
11The extended line of longitudinal midline on.
The above-mentioned lath of holding frame and angle square assembly is according to using specification requirement to be processed by metal or plastics, such as stainless steel or polystyrene.Because the effect of each riveting axle; But six laths holding frame and angle square assembly constitute stepped construction; Two lath C1, C2 wherein holding frame are positioned at outermost layer; Be with axle sleeve 7 outside the riveting axle 1 of its connection, the height of this axle sleeve cooperates with four range upon range of thickness of lath of middle angle square assembly, with unsettled between the junction of avoiding lath C1, C2.
The trisection gauge of said plane angle can also be processed other shape, constitutes by the lath that has vertical rail groove such as holding frame and straightedge rule, and as shown in Figure 7, riveting axle 2,3 is positioned at straightedge rule lath B
1, B
2Rail groove B
12, B
22On the extended line of longitudinal midline, this two rails groove constitutes the setting-out groove, needs only during setting-out nib is stretched into rail groove B
12, B
22Get final product.Certainly, also can be with the lath A of benchmark angle square
2, lath A
1Also process like straightedge rule lath B
1, B
2Have the lath shape of vertical rail groove.
The trisection gauge of Fig. 1 and plane angle shown in Figure 7, can similar folding fan structure range upon range of in time spent not, represent like Fig. 8, but require each riveting axle and the heavy hole of lath countersunk head to cooperate, like Fig. 2 institute illustration.
More accurate for the five equilibrium setting-out, can adopt the riveting axle 4 of hollow structure, as shown in Figure 7, be inserted in the axis hole of the riveting axle 4 that the aperture cooperates with the drawing pin diameter with a drawing pin during setting-out, the nail point is aimed at by the drift angle of the plane angle of five equilibrium.
The trisection gauge of the plane angle of making according to above-mentioned mapping principle can also be processed like Fig. 5,2 structures embodiment illustrated in fig. 6, and this ruler is held frame by lath C by holding frame and the angle square assembly is formed
1, connecting plate D forms, the lower end of two laths connects its middle plate strip C by riveting axle 1
1Upwards have vertical rail groove C leaving riveting axle 1 one segment distances
11, riveting axle 1 is positioned on the extended line of longitudinal midline of this rail groove, and riveting axle 5 is riveted on connecting plate A
1Run through and be snug fit at behind the upper end and hold frame plate bar C
1Vertical rail groove C
11, connecting plate C
2The lower end is near holding frame plate bar C
1Vertical rail groove C
11The position of lower end is connected by riveting axle 2; The angle square assembly is made up of straightedge rule and benchmark angle square, and wherein straightedge rule is by lath B
2With lath B
1Intersect and form, the benchmark angle square is by connecting plate A
1Lath B with straightedge rule
1Form, i.e. lath B
1Have line and station meter effect concurrently, can omit a slice lath, its plate body bottom has vertical rail groove B
12, riveting axle 1 runs through and is snug fit at vertical rail groove B of this lath
123 on riveting axle is the upper end and line lath B of plate D repeatedly
2The lower end, riveting axle 4 runs through connecting plate A
1Lower end, connecting plate C
2Upper end, straightedge rule B
2And B
1The crosspoint, four laminate bar riveting axles are connected; Riveting axle 5 and riveting axle 1 are respectively along lath C
1Hold frame rail groove C
11With lath B
1Rail groove B
12Slide, can change respectively simultaneously and hold frame plate bar C
1And between the connecting plate D, straightedge rule lath B
2With lath B
1Between, benchmark angle square connecting plate A
1With straightedge rule lath B
1Between angle; Connecting plate C
2With connecting plate A
1Constitute two isosceles limits of isosceles triangle respectively, riveting axle 1,2,3,4 constitutes equilateral tetragonal four summits respectively.
Riveting axle 3 and riveting axle 4 are positioned at the lath B of straightedge rule
2Line along B
21On the straight line that forms, riveting axle 1 is positioned at lath B with riveting axle 4
1Line along B
11Form with lath B
1Rail groove B
12On the straight line that the longitudinal midline extended line overlaps, riveting axle 1, riveting axle 2 and riveting axle 5 are positioned at holds frame plate bar C
1Vertical rail groove C
11The longitudinal midline extended line on.
Similar with embodiment 1, hold the lath of frame and angle square assembly and can process, but hold the effect formation stepped construction of five laths of frame and angle square assembly owing to each riveting axle, its middle plate strip C by stainless steel or plastics
1With lath B
1Be positioned at outermost layer, it connects the riveting axle 1 outer axle sleeve 7 that is with, and the height of this axle sleeve cooperates with three middle range upon range of thickness of lath.
Claims (5)
1. the trisection gauge of plane angle is characterized in that this ruler by holding frame and the angle square assembly is formed, holds frame by having vertical rail groove (C
11, C
21) lath one (C
1), lath two (C
2) form, an end of two laths is connected by riveting axle one (1), makes two lath (C
1, C
2) be that fulcrum rotates each other with riveting axle one (1), this fulcrum is positioned at rail groove (C
11, C
21) on the extended line of longitudinal midline; The angle square assembly is made up of straightedge rule and benchmark angle square, and wherein straightedge rule is by lath three (B
1), lath four (B
2) intersect and form this two lath (B
1, B
2) in the same way the end respectively with the two lath (C that hold frame
1, C
2) the plate body is by riveting axle three (3), two (2) connections of riveting axle, this riveting axle two lays respectively at two with riveting axle three and holds frame rail groove (C
11, C
21) the extended line of longitudinal midline on and be positioned at and hold frame rail groove (C
11, C
21) and hold between the frame riveting axle one (1); The benchmark angle square is by lath five (A
2), lath six (A
1) form, riveting axle five (5) and riveting axle six (6) run through the lath five (A of benchmark angle square respectively
2), lath six (A
1) the plate body with hold vertical rail groove (C of frame
21, C
11), make riveting axle five (5) and riveting axle six (6) respectively along rail groove (C
21, C
11) slide and change respectively simultaneously hold between frame two laths, between straightedge rule two laths, the angle between benchmark angle square two laths; Riveting axle four (4) runs through an end of benchmark angle square two laths and the crosspoint of straightedge rule connects four laminate bar riveting axles; Distance between distance between riveting axle three (3), the riveting axle six (6) and riveting axle two (2), the riveting axle five (5) constitutes two bases of two isosceles triangles respectively, and riveting axle one, two, three, four constitutes equilateral tetragonal four summits respectively.
2. according to the trisection gauge of the said plane angle of claim 1, it is characterized in that riveting axle two (2), riveting axle four (4) and riveting axle three (3), riveting axle four (4) lay respectively at two line edge (B of straightedge rule
11, B
21) on the straight line that forms, riveting axle four (4), riveting axle six (6) and riveting axle four (4), riveting axle five (5) lay respectively at the two angulations edge (A of benchmark angle square
11, A
21) on the straight line that forms, riveting axle five (5) and riveting axle six (6) also lay respectively at the rail groove (C that holds frame
21, C
11) the extended line of longitudinal midline on.
3. according to the trisection gauge of claim 1 or 2 said plane angles, it is characterized in that holding frame and straightedge rule by the lath formation that has vertical rail groove, riveting axle four (4) is positioned at the rail groove (B of straightedge rule
12, B
22) on the extended line of longitudinal midline, this two rails groove constitutes setting-out groove.
4. according to the trisection gauge of claim 1 or 2 said plane angles, it is characterized in that the lath of holding frame and angle square assembly processes by metal or plastics.
5. according to the trisection gauge of claim 1 or 2 said plane angles, but it is characterized in that said six laths holding frame and angle square assembly constitute stepped construction by the effect of each riveting axle, wherein hold two lath (C of frame
1, C
2) being positioned at outermost layer, it connects riveting axle one (1) the outer axle sleeve (7) that is with, and the height of this axle sleeve cooperates with four middle range upon range of thickness of lath.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 200910099286 CN101570100B (en) | 2009-06-01 | 2009-06-01 | Trisection gauge of plane angle |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 200910099286 CN101570100B (en) | 2009-06-01 | 2009-06-01 | Trisection gauge of plane angle |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN101570100A CN101570100A (en) | 2009-11-04 |
| CN101570100B true CN101570100B (en) | 2012-12-05 |
Family
ID=41229631
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN 200910099286 Expired - Fee Related CN101570100B (en) | 2009-06-01 | 2009-06-01 | Trisection gauge of plane angle |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN101570100B (en) |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN2574911Y (en) * | 2002-11-04 | 2003-09-24 | 胡流洁 | Vacuum dust-absorbing blackboard eraser |
| CN2770995Y (en) * | 2005-01-18 | 2006-04-12 | 李志平 | Trisection angle resolver |
| CN201229686Y (en) * | 2008-06-11 | 2009-04-29 | 上海市南汇区宣桥学校 | A three equality angle dividing instrument |
| CN201410832Y (en) * | 2009-06-01 | 2010-02-24 | 徐特灿 | Trisection ruler for arbitrary angles |
-
2009
- 2009-06-01 CN CN 200910099286 patent/CN101570100B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN2574911Y (en) * | 2002-11-04 | 2003-09-24 | 胡流洁 | Vacuum dust-absorbing blackboard eraser |
| CN2770995Y (en) * | 2005-01-18 | 2006-04-12 | 李志平 | Trisection angle resolver |
| CN201229686Y (en) * | 2008-06-11 | 2009-04-29 | 上海市南汇区宣桥学校 | A three equality angle dividing instrument |
| CN201410832Y (en) * | 2009-06-01 | 2010-02-24 | 徐特灿 | Trisection ruler for arbitrary angles |
Also Published As
| Publication number | Publication date |
|---|---|
| CN101570100A (en) | 2009-11-04 |
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Granted publication date: 20121205 Termination date: 20180601 |