Curve interpolation method

Details Curve interpolation method Curve interpolation method

2003-07-23

2004-11-23

Paladini, Albert W. (Department: 2125)

Data processing: generic control systems or specific application

Specific application, apparatus or process

Product assembly or manufacturing

C700S181000

Reexamination Certificate

active

06823234

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a curve interpolation method for obtaining a smooth curve based on data of a sequence of command points and performing interpolation on the smooth curve in machining a workpiece along a curved surface using a numerical controller.
2. Description of Related Art
In machining a workpiece along a curved surface of an object such as a mold by a numerical controlled machine tool, etc. according to data of a sequence of command points which are created by a CAD/CAM device or a profiler device, a curve interpolation is performed based on the data of the sequence of command points. For example, there is disclosed a method of creating an approximate spline curve based on the data of the sequence of command points and performing the curve interpolation on the created approximate spline curve in JP 2-113305A.
In JP 10-240328A, there is described an interpolation method in which vectors of line segments between adjacent twos of command points are obtained and a modification amount for each command point is obtained such that the sum of squares of differential vectors between the obtained vectors of the line segments is the least so as to modify each command point. In this document, it is described to set an evaluation range in a sequence of the command points and create an approximate curve for successive points in the evaluation range, so that the command points are modified based on differences between the approximate curve and the respective command points in the evaluation range.
In the CAD/CAM device, a tolerance is set for a target curve created by the CAD device and a plurality of line segments are created by the CAM device within the tolerance to obtain data of end points of the respective line
 
f
(
t
)
x
=A
x
t
3
+B
x
t
2
+C
x
t+D
x
f
(
t
)
y
=A
y
t
3
+B
y
t
2
+C
y
t+D
y
f
(
t
)
z
=A
z
t
3
+B
z
t
2
+C
z
t+D
z
Thus obtained curve Ce is shown in FIG.
20
.
Then, interpolation is performed on the defined curve Ce with a unit not greater than a set unit in preparing the sequence of command points (Step S
16
).
In the foregoing embodiment, at the start of the procedure, all of the command points P
0
, P
1
, P
2
, . . . , Pn−1, Pn are read at Step S
1
. Alternatively, only the necessary command points may be read and the procedure may be carried out on the read points, so that the approximate curve is successively created while reading the data of the command points to expedite the procedure.
In obtaining interpolation points, i.e. shape-defining points, respective two points are interpolated between adjacent twos of the command points in the foregoing embodiment, respective points more than two may be interpolated between adjacent twos of the command points. Further, in creating the approximate curve Cm, the shape-defining points not greater than two are selected before and after the shape-defining point Qi. The shape-defining points greater than two may be selected. Furthermore, one or more of the command points P
0
, P
1
, P
2
, . . . , Pn−1, Pn may be used as the shape-defining points with the interpolation points Q
1
, Q
2
, . . . , Q
2
n.
If a line segment connecting adjacent two of the command points P
0
, P
1
, P
2
, . . . , Pn−1, Pn is shorter than a reference value, an interpolated point Pj′, such as a middle point between such adjacent command points Pj, Pj+1 may be regarded as a substitute command point for the adjacent command points Pj, Pj+1 which are to be deleted. In this case, it is determined whether or not a distance between the adjacent command points Pi and Pi+1 is not greater than the predetermined at Step S
2
, and if the distance is not greater than the predetermined value, the above procedure is performed to define a substitute command point for obtaining the interpolation points. segments as a sequence of command points to be outputted to the numerical controller.
As shown in
FIG. 1
, line segments L
0
, L
1
, L
2
, . . . are created by the CAM device within a tolerance width “2w” set by a tolerance amount “w” on both sides of an original target curve Cs which are created by the CAD device, and data of points P
0
, P
1
, P
2
, . . . at both ends of respective line segment L
0
, L
1
, L
2
, . . . are outputted to a numerical controller as data of a sequence of command points. Since a curve Ce for the curve interpolation is defined based on the position data of the sequence of command points, the curve Ce may exceed the tolerance width 2w set to the original curve Cs.
According to the method disclosed in JP10-240328A, the positions of the command points are modified but there is a possibility of creating the curve Ce same as that in
FIG. 1
based on the modified command points, and it is not assured that the curve Ce is created within the tolerance width 2w set for the original curve Cs.
It is probable that the sequence of command points are positioned near ends of a band of the tolerance width 2w set to the original curve Cs. Therefore, if the curve Ce is defined based solely on the sequence of command points, the curve Ce may be positioned considerably remote from the original curve Cs. For instance, in the case where the original curve Cs is a circular arc, as shown in
FIG. 2
, the command points P
0
, P
1
, P
2
, . . . defined by the line segments L
0
, L
1
, L
2
, . . . within the tolerance width 2w are positioned remote from the original curve Cs by an mount approximately equal to the tolerance amount w. In this case, two points Q
1
and Q
2
interpolated on each of the line segments L
0
, L
1
, L
2
, . . . at a ratio of approximately 0.15:0.7:0.15 are positioned on the original curve Cs, as shown in FIG.
3
.
The above circumstance is the same in the case where the positions of the command points are modified. For example, in the case where the original curve is a circular arc, since a sequence of command points are aligned along a circular arc, if a curve approximating the command points is created, the sequence of command points are not substantially modified. Thus, the modified sequence of command points are positioned remote form the original curve Cs by the tolerance amount w.
Since the curve Ce is defined to pass the sequence of command points P
0
, P
1
, P
2
, . . . , if there is an error in calculation for obtaining the sequence of command points P
0
, P
1
, P
2
, . . . or in approximation by a set unit in the CAD/CAM device, the error influences the definition of the curve Ce to lower machining precision and cause a vibration of the machine. Thus, the definition of the curve Ce to pass the sequence of command points may cause deterioration of the precision of the machined surface.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a curve interpolation method capable of obtaining a curve approximating an original target curve within a tolerance set for the original target curve based on a sequence of command points, and performing interpolation on the obtained curve.
As describe, the command points P
0
, P
1
, P
2
, . . . are positioned within the tolerance width 2w and the line segments L
0
, L
1
, L
2
, . . . connecting the adjacent twos of the command points (P
0
, P
1
), (P
1
, P
2
), . . . are positioned within the tolerance width 2w, as shown in FIG.
5
. Therefore, points Q
1
, Q
2
, Q
3
, . . . interpolated on the respective line segments L
0
, L
1
, L
2
, . . . are positioned within the tolerance width 2w. According to the present invention, a smooth curve Ce approximating an original curve Cs is defined using the interpolated points Q
1
, Q
2
, Q
3
, . . . , and a curve interpolation for machining a workpiece is performed on the smooth curve Ce by a procedure comprising the following steps (1)-(7).
(1) Interpolation points Q
1
, Q
2
, Q
3
,. . . are defined between adjacent twos of the command points (P
0
, P
1
), (P
1
, P
2
), . . . , as shape-defining points. The shape-defining points Q
1
, Q
2
, Q
3
, . . . are po

Affiliated with

Also associated with

Rating

Curve interpolation method does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with Curve interpolation method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Curve interpolation method will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFUS-PAI-O-3340702