JPH056442A - Circular arc generating method - Google Patents

Abstract

PURPOSE:To easily generate a circular arc for production of a fillet curved surface where two curved surfaces are smoothly connected together in a designated radius by deciding first the 1st and 2nd surfaces and a plane which crosses these two surfaces. CONSTITUTION:A plane 8 passing through a point set on a line 7 piercing through the surfaces 1 and 2 is obtained together with the lines 9 and 10 crossing both surfaces 1 and 2. Then the lines 9 and 10 are moved by the same extent within the plane 8 and an intersecting point 13 is defined as the center of a circular arc. Thus a circular arc is obtained on both lines 9 and 10. In the same way, the circular arcs are generated with other points on the line 7. A fillet curved surface is obtained when those circular arcs are connected together. This generating procedure can be simply carried out by a computer.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for smoothly connecting two curved surfaces with a specified radius to generate an arc suitable for generating a fillet curved surface.

[0002]

2. Description of the Related Art Conventionally, a fillet curved surface to be added between two free curved surfaces cannot be represented by data, and therefore cannot be machined by a numerically controlled machine tool. For that reason, there was no choice but to rely on copying or electric discharge machining.

[0003]

However, this conventional technique has problems that the machining accuracy is poor and the number of machining steps is large.

It is desirable to easily generate a curved surface (fillet curved surface) in contact with two surfaces by a computer in order to smoothly connect the two surfaces. An object of the present invention is to provide a method of generating an arc suitable for generating a fillet curved surface.

[0005]

In the method of generating an arc according to the present invention, a first plane and a second plane and one plane intersecting them are determined, and a pair of the plane and the first plane is formed. From the intersection line of, the pair of offset lines obtained by offsetting the pair of intersection lines so that the points on each intersection line move in the plane in the normal direction of the intersection line. A line is obtained, an intersection of a pair of these offset intersections is obtained, and an arc that is in the plane with the obtained intersection as the center and that is in contact with the plane and the pair of intersections before the offset is generated.

[0006]

Since the arc is generated after defining one surface, the arc can be easily generated.

[0007]

EXAMPLE An example of the present invention will be described below as first, second, third,
This will be described with reference to FIGS.

FIG. 1 shows the overall structure, which is cpu3.
As input data of, two curved surface data to which a fillet curved surface is added is given. This curved surface data is given as S ₁ (x, y, z) = o and S ₂ (x, y, z) = o in the case of an analytical curved surface, and as shown in FIG. 2 in the case of a free curved surface. The surface parameters u and v are given by u and v lattice points where integer values are taken, for example, position coordinates x, y and z at 6 and tangent vectors in the directions of u and v. In cpu3, fillet curved surface data is obtained based on the curved surface data 1 and 2 by the processing flow shown in FIG. The fillet curved surface data has the same format as in FIG. Next, in order to drive the numerically controlled machine tool (hereinafter abbreviated as NC) 4 based on the fillet curved surface data,
Data 5 that controls the movement of the NC cutter in cpu3
Sweep out to NC4.

The above is the overall configuration. Next, a method for obtaining fillet curved surface data will be described with reference to FIGS.

Incidentally, FIG. 4 is a view seen from the back side of the curved surfaces 1 and 2 for the sake of easy understanding.

First, an equation of a plane (cutting plane) 8 perpendicular to 7 is obtained at a point 18 on the intersection line 7 of the curved surfaces 1 and 2. Cut surface 8
The production interval is determined according to the change in curvature of 7, and the production position is sequentially determined from the start point 16 to the end point 17 (or the opposite direction) 16, 24, 25 ... On the intersection line 7. Next, the intersection lines 9 and 10 between 7 and the curved surfaces 1 and 2 are offset in the normal direction of the intersection lines 9 and 10 on the cut surface 7. In the following, the symbols with the subscript v represent vector quantities.

In the offset equation, the intersection line 9 is C _{v, 1} (t),
10 is C _{v, 2} (t), the offset amount R, and the unit normal vector on the cutting plane at the point on C _{v, 1} (t), C _{v, 2} (t) corresponding to the parameter t is N _v, Letting ₁ (t) and N _{v, 2} (t) be C _{v, 1} (t) and C _{v, 2} (t) respectively offset curves C _{v, 1} , _m (t), C _{v, 2} , _m (t) is C _{v, j, m} (t)
= C _{v, j} (t) + R · N _{v, j} (t) (j = 1, 2)
Given in. The offset amount R is the radius of the fillet curved surface determined by the position of the cut surface 7.

[0013] Now, at the beginning 16 of the radius on the phase transmural line 7 of the designated fillet R _1, the radius of the fillet curved in 18 point in the interpenetrating line When R ₂ at the end 17 R = R ₁ + f ( l) where l is the length of the curve of intersection from start point 16 to point 18, f
(L) is a function that satisfies f (o) = o and f (L) = R ₂ −R ₁ where the total phase line length L between the start point 16 and the end point 17 is L.

[0014] You can give a function.

The intersection 13 of the offset curves 11 and 12 is the center position of the arc generated. Since the points 14 and 15 on the intersecting lines 9 and 10 corresponding to the intersecting point 13 are both end points of the arc, the equation of the arc is uniquely determined.

By repeating the above procedure for a plurality of cut surfaces having different positions, as shown in FIG.
B-spline curves that connect the arc end point sequences 26, 27, 28, ... On the second side so that they are in contact with the curved surface 1 and the curved surface 2, respectively.
We get 22 expressions.

Another boundary curve of the fillet curved surface is a circular arc. The boundary curves 19, 20, 21, and 22 are represented by C _{v, 1} (u),
When C _{v, 2} (v), C _{v, 3} (u), and C _{v, 4} (v),
The fillet surface expression S (u, v) is the well-known Co
The ons formula is given by the following formula.

S (u, v) = C _{v, 1} (u) {1-φ (v)} +
C _{v, 2} (v) {1-φ (u)} + C _{v, 3} (u) φ (u) + C _{v, 4} (v) φ (u) −P _{v, A} {1-φ (u)} {1-φ (v)}- _{Pv, B} φ (u) {1-φ (v)}- _{Pv, C} φ (u) {1-φ (v)}- _{Pv, D} {1- φ (u)} φ (v) where P _{v, A} = C _{v, 1} (o) = C _{v, 2} (o) P _{v, B} = C _{v, 1} (1) = C _{v, 4} (o ) P _{v, C} = C _{v, 3} (1) = C _{v, 4} (1) P _{v, D} = C _{v, 2} (1) = C _{v, 3} (o) φ (x) is a blending function .

S (u, v) is obtained by x, y, z coordinate values.

A method for obtaining control data for machining with a numerically controlled machine tool based on the fillet curved surface formula thus obtained will be described with reference to FIG.

To move the cutter in the u direction to cut the curved surface, u = u from the position of the point P corresponding to u = u ₁ and v = v _1.
This is possible by moving the cutter to the point Q corresponding to ₁ + Δu, v = v ₁ . Since the position coordinate values x, y, z when u and v are given are obtained from the Coons equation, the point Q (x ₂ , y ₂ , z ₂ ) is changed from the point P (x ₁ , y ₁ , z ₁ ). The cutter position is controlled by sweeping the deviations Δx = x ₂ −x ₁ , Δy = y ₂ −y ₁ , and Δz = z ₂ −z ₁ to the numerically controlled machine tool. Similarly, u is changed by Δu, and v = v ₁
The fillet curved surface is cut by moving the cutter on the curve, and then changing v by Δv, and moving the cutter on the v = v ₁ + Δv curve.

As described above, according to this embodiment, it is possible to generate a fillet curved surface having a predetermined radius with respect to the designated self-curved surface shape. Furthermore, by using the method of the present invention, it has become possible to perform the die machining of the outer shape of a home electric appliance, which has been frequently used for the fillet curved surface, which has been conventionally used for the copying, by using a numerically controlled machine tool.

Further, by doing so, the design restrictions resulting from the processing restrictions are eliminated, and the mold manufacturing period is 15 to
40% reduction, processing accuracy improved by one digit, material cost 20-35
There is a% savings effect.

As is apparent from the above embodiment, in this embodiment, the fillet curved surface is located in any one of a plurality of planes intersecting the first and second surfaces, and , Using the plurality of arcs that are in contact with the line of intersection of the one plane on which each is located and the first and second surfaces, and that use the plurality of arcs whose endpoints are the points of contact with these lines of intersection, A curved surface (fillet curved surface) that is in contact with the second surfaces to smoothly connect them is generated by an electronic computer.

Therefore, the fillet curved surface can be generated easily and accurately.

[0026]

According to the arc generating method of the present invention, the first and second surfaces and one plane intersecting them are determined,
From this pair of intersecting lines of the first and second surfaces, a pair of intersecting lines of the intersecting lines so that points on the intersecting lines move in the plane in the normal direction of each intersecting line by a certain amount. Obtain a pair of offset lines of intersection obtained by offsetting, find the intersection point of these offset pair of intersection lines, centered on the obtained intersection point, in the plane, that plane and the pair of Generates an arc that touches the intersection line before the offset. These procedures can be easily done by a computer. Therefore, the arc suitable for generating the fillet curved surface is
It can be easily generated by a computer.

[Brief description of drawings]

FIG. 1 is an overall configuration diagram of an apparatus to which the present invention is applied.

FIG. 2 is an explanatory diagram of a method of expressing a curved surface.

FIG. 3 is a flowchart of processing of a method for creating a fillet curved surface.

FIG. 4 is a schematic diagram of a method for creating a fillet curved surface.

FIG. 5 is an explanatory diagram of an arc generation method on a cut surface.

FIG. 6 is an explanatory diagram of connection of generated arc end points.

FIG. 7 is an explanatory diagram of a numerical representation method of a fillet curved surface.

FIG. 8 is an explanatory diagram of a method for processing a fillet curved surface.

[Explanation of symbols]

1, 2 ... Filled curved surface, 3 ... cpu,
4 ... Numerically controlled machine tool, 5 ... Data for controlling 4, 6 ...
Lattice points of curved surface parameters u and v, 7 ... Penetration line of curved surfaces 1 and 2, 8 ... Cutting plane, 9, 10 ... Penetration line of curved surface 1 and cutting plane, 11 ... Intersection line 9 are offset Curve, 12 ... Curve obtained by offsetting the intersection line 10, 13 ... Intersection point of the offset curves 11 and 12, 14, 15 ... Curved surface 1 of generated arc
End point on the side, 16 ... Start point of the intersection line 7, 17 ... End point of the intersection line 18, 18 ... Point on the intersection line 7 through which the cutting plane 8 passes, 19 ... Boundary curve C _{v, 1} (of fillet curved surface) u), 20 ... Boundary curve C _{v, 2} (v) of fillet curved surface, 21 ... Boundary curve C _{v, 3} (u) of 22 fillet curved surface, 22 ... Boundary curve C _{v, 4} (v) of 23 fillet curved surface, 23 ... Arc, 24, 25 ... Penetration line 7
Upper cut plane creation point, 26, 27, 28 ... Arc end point sequence.

Claims (2)

[Claims] 1. A method for generating a circular arc in contact with first and second surfaces located in a three-dimensional space by a computer, comprising:
One plane intersecting with the second plane is determined, and a pair of lines of intersection between the first and second planes and the plane are defined, and points on the respective lines of intersection are normals of the lines of intersection within the plane. Obtain a pair of engagements that are offset by the same amount in the direction, find the intersection of these offset pairs of intersections, center on the intersections obtained, and in the plane of the intersection A method of generating arcs that generate touching arcs. 2. When the arc is generated, a pair of points corresponding to the intersections on each of the pair of intersections is obtained, and the intersection is centered, and the distance from the intersection to the pair of points. The method of generating an arc according to claim 1, wherein an arc having a radius of is generated on the plane.