JPH07104704B2 - Curve interpolation method in numerical control - Google Patents

Description

The present invention relates to a curve interpolation method in numerical control, and in particular,
The present invention relates to a curve interpolation method in a numerical control that connects two points with a smooth curve when given a position vector ▲ ▼ P ₂ and traveling direction vectors q ₁ and q _{2 at} two points P ₁ and P ₂ .

[Conventional technology]

Conventionally, the interpolation method in this type of numerical control has been a simple function expression, for example, an interpolation method for calculating coordinate points on a curve based on a straight line, a circle, an ellipse, a parabola, or the like.

[Problems to be solved by the invention]

The above-described conventional numerical control interpolation method has a drawback that when interpolating a free-form curve that does not follow a simple function, it requires a plurality of approximate pre-processing calculations for fitting to the functional expression.

[Means for solving problems]

In order to solve the above problems, two arbitrary points P ₁ of the present invention
A numerical control curve interpolation method that connects P ₂ with a smooth curve is based on the position vector at point P ₁ and the traveling direction vector at that point and the position vector at point P ₂ and the traveling direction vector at that point. Curvature at P ₁ 1 /
The curvature 1 / R ₂ at R ₁ and the point P ₂ is calculated, and the curvature between the two points is predetermined so as to be the curvature of an arc including the points P ₁ and P ₂ as points on the circumference. The feature is that the coordinate values of a plurality of interpolation loci are calculated by sequentially changing from curvature 1 / R ₁ to curvature 1 / R ₂ according to a function.

〔Example〕

Next, the present invention will be described with reference to the drawings. FIG. 1 shows an embodiment of the present invention, and FIG. 2 shows the principle of the interpolation method.

First, an embodiment of the present invention will be described with reference to FIG. First
The figure is a block diagram of one embodiment of the present invention. In the present invention, the data P ₁ , q ₁ , θ ₁ , P ₂ ,
Coordinate values (P _{(i) x} , P _{(i) y} ) on the interpolation locus are output to the output device 300 through q ₂ and θ ₂ through the interpolator 200.

The interpolator 200 includes a line segment divider 201 that divides a reference axis 1 that changes the curvature into n equal parts, and a curvature calculator 202 that obtains a curvature 1 / R _(i) for the i-th point that divides l into equal parts. And a coordinate value calculation for obtaining a coordinate value (P _{(i) x} , P _{(i) y} ) for the i-th point obtained by equally dividing l from the curvature 1 / R _(i) obtained by the curvature calculation unit 202 It is composed of a container 203.

Next, the interpolation method of the present invention will be described with reference to FIG. FIG. 2A shows a position vector ▲ ▼ at a point ▲ ▼ and a traveling direction vector ▲ ▼ and a point at that point.
The relationship between the position vector ▲ ▼ at P ₂ and the traveling direction vector ▲ ▼ at that point is shown. Hereinafter, calculated curvature 1 / R ₂ interpolation trajectory of curvature 1 / R ₁ and point P ₂ of the interpolation trajectory at point P _1,
A method of gradually changing the curvature between the points P ₁ and P ₂ and smoothly determining the interpolation locus between the two points will be described.

If shows a circle O ₁ in contact with the ▲ ▼ a circle passing through p ₁ and point P ₂ in FIG. 2 (b) and the curvature 1 / R ₁ of curvature of the circle O ₁ at the point P ₁ However, θ ₁ ; ▲ ▼ P ₂ (= ▲ ▼-▲ ▼) and ▲
It becomes the angle formed by ▼, and if we set | ▲ ▼ − ▲ ▼ | = l, the formula becomes 1 / R ₁ = 2sin θ ₁ / l ………. Similarly, the curvature 1 / R ₂ at point P ₂ is _{1 / R 2 = 2sinθ 2 /} l ......... However, theta _2; ▲ ▼ the angle between the P ₂ and ▲ ▼.

Therefore, as an example of the change in curvature between points P ₁ and P ₂ ,
Consider the case of changing the curve.

When the reference axis for changing the curvature is set on l, first, the line segment divider 201 divides l into n equal parts. Then, in the curvature calculator 202, when the curvature 1 / R _(i) at the i-th point obtained by dividing l into n is calculated, (See Figure 2 (c)) Focusing on the change in curvature 1 / R, it becomes as shown in Fig. 2 (d). When the point exists, the point becomes an inflection point of the interpolation locus between the points P ₁ and P ₂ .

A point on the interpolation locus for the i-th point obtained by dividing l into n equal parts
P _(i) is calculated by the coordinate value calculator 203 using the curvature obtained by the curve calculator 202 based on the following equation.
Here, the point P _(i) is a point on the line perpendicular to the i-th point on 1 perpendicular to l, and on the circle of radius of curvature R _(i) passing through the points P ₁ and P _2. . (FIG. 2 (e)) Further, the angle between the contact of this circle and the straight line l at the point P ₁ is θ _i, and the inclination of the straight line l is. Radius R _{(i) in} Fig. 2 (e ₎
Circle center coordinates for (O _x, O _y) to the equation of the circle ^{_{(x-O x) 2 +}} (y-O y) 2 = R 2 (i) ......... when the O _x = P _1x + R _{(i) sin} (θ _i +) ……… O _y = P _1y + R _{(i) cos} (θ _i +) ……… However, the coordinate value of ▲ ▼ (P _1x , P _1y ) The expression of a straight line passing through the i-th point on l and perpendicular to l is From the condition that it passes the point of P _i However (Where _{P 2x -P 1x = P 12x P} 2y -P 1y = P 12y and rear) Well _{Here, cos (θ i +) =} cosθ i cos ......... -sinθ i sin sin (θ i +) = sin θ _i cos ……… ＋ cos θ _i sin Substituting the expression into the expression and rearranging it using the expression (1 + A ² ) x−2F + G = 0 ……… However Also, if you solve the quadratic equation of l = | ▲ ▼ P ₂ | However, D is the same as the formula. Therefore, the coordinates of the point P (i) to be obtained are Becomes

As described above, the coordinate values on the interpolation locus are sequentially obtained on the basis of each point obtained by dividing n on n equally. That is, by repeatedly executing the curvature calculator 202 and the coordinate value calculator 203 while changing i from 1 to n, (P _{(i) x} ,
The coordinate value of 1 to n is calculated for j of P _{(i) y} ). A smooth interpolation locus can be obtained by connecting these coordinates in order. (See FIG. 2 (f)) Although the secondary plane has been described in this embodiment, the present invention is not limited to the secondary plane.

〔The invention's effect〕

Above-described manner, the present invention is a vector P ₁ position at the point P ₁ traveling direction of the vector at that point ▲ ▼ and the point P ₂
Position Vector ▲ ▼ and the point P ₁ a curvature between curves 1 / R ₁ and curvature at the point P ₂ 1 / R ₂ look 2 points in the travel direction of the vector ▲ ▼ points P ₁ than at that point a point in 1 / R ₁ to 1 / R ₂ so that the curvature of the arc includes P ₂ as a point on the circumference
Change sequentially between the two, calculate the coordinate values of multiple interpolation loci,
Since the respective coordinate values are connected in order, there is an effect that a smooth curve can be easily interpolated.

[Brief description of drawings]

FIG. 1 is a diagram showing an embodiment of the present invention. FIGS. 2A to 2F are views for explaining the principle of the interpolation method of the present invention. 100: Input device, 200: Interpolator, 201: Line segment divider, 202: Curve calculator, 203: Coordinate value calculator, ▲
▼ …… Vector of position of point P ₁ , ▲ ▼ …… Vector of traveling direction at point P ₁ , P ₂ …… Position vector of point P ₂ , q ₂ ……
Vector of travel direction at point P ₂ .

Continuation of front page (56) References JP-A-56-72704 (JP, A) JP-B-58-56895 (JP, B2)

Claims (1)

[Claims] 1. A numerical value-controlled curve interpolation method for connecting any two points P ₁ and P ₂ with a smooth curve, wherein a position vector at a point P ₁ , a traveling direction vector at that point, and a position vector at a point P ₂ and based on the traveling direction vector at that point, to calculate the curvature 1 / R ₂ in the curvature 1 / R ₁ and point P ₂ at point P _1, a curvature between two points, the point P ₁ and point P ₂ It is possible to calculate the coordinate values of multiple interpolation loci by sequentially changing from curvature 1 / R ₁ to curvature 1 / R ₂ according to a predetermined function so that the curvature of an arc included as a point on the circumference is obtained. Curve interpolation method in the characteristic numerical control.