# US 4,899,096 A · Involute interpolation speed controlling method

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- Number: US 4,899,096 A
- Document ID: US4899096A
- Status: Granted
- Kind: A
- Application number: 07/309,669
- Filed: 1989-02-07
- Granted: 1990-02-06
- Earliest claimed: 1987-06-24
- Assignees: Fanuc LTC
- Inventors: Hideaki Kawamura; Kentaro Fujibayashi; Toshiaki Otsuki
- Web page: https://patentgrep.com/patent/US4899096A

## CPC

- G05B 19/41: characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path (G05B19/25, G05B19/31, G05B19/37, G05B19/39, G05B19/40 take precedence)
- G05B 2219/34144: Involute, evolute
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)

## Abstract

An involute interpolation method for use in machining by a numerical control apparatus. A rotational direction (G03.1) of an involute curve, coordinates of an end point (Xe, Ye), a center position (I, J) of a base circle as viewed from a start point, and a radius (R) of the base circle are instructed, from two equations representing the involute curve sequence of points are obtained, and interpolation of the involute curve is performed while interpolating those points in a range of the angle .theta. corresponding to the start point on the involute curve to the end point thereon. The increment of .theta. is decremented in proportion to the increment of the angle owing to the factor K/ (R.multidot..theta.), so that the interpolation is performed in such a manner that the speed in the tangential direction is made at constant, whereby a machining speed of the involute curve is maintained at constant.

## Claims

### Claim 1

In an involute interpolation speed controlling method for use in machining by a numerical control apparatus, an involute interpolation method for interpolating an involute curve comprising the steps of: instructing a rotational direction of the involute curve, coordinates of an end point, a center position of a base circle as viewed from a start point, a radius (R) of the base circle, and a speed;
obtaining coordinates (X.sub.0, Y.sub.0) of the center of the base circle of the involute curve, an angle (.theta.2) of the start point, an angle (.theta.3) of the end point and a curve start angle (.theta.1) on the basis of the instructions and coordinates (Xs, Ys) of the start point; and
with respect to an involute curve represented by
X=R{cos (.theta.+.theta.1)+.theta. sin (.theta.+.theta.1)+X.sub.0
Y=R{sin (.theta.+.theta.1)-.theta. cos (.theta.+.theta.1)}+Y.sub.0
increasing .theta. in a range from .theta.=(.theta.2-.theta.1) to .theta.=(.theta.3-.theta.1) according to a relation defined by
.theta..sub.n+1 =.theta..sub.n +K/(R.multidot..theta.)
to thereby obtain corresponding points X.sub.n+1, Y.sub.n+1 from the above equation.

### Claim 2 (depends on 1)

An involute interpolation method according to claim 1, further comprising the step of instructing a designation of a plane.