# US 4,935,681 A · Involute interpolation method

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- Number: US 4,935,681 A
- Document ID: US4935681A
- Status: Granted
- Kind: A
- Application number: 07/335,666
- Filed: 1989-03-29
- Granted: 1990-06-19
- Earliest claimed: 1987-08-27
- Assignees: Fanuc Corporation
- Inventors: Hideaki Kawamura; Takao Sasaki; Kentaro Fujibayashi; Kunihiko Murakami; Masafumi Sano
- Web page: https://patentgrep.com/patent/US4935681A

## CPC

- G05B 19/4103: Digital interpolation
- 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 is provided for machining operations in a numerical control apparatus, in which a rotational direction of an involute curve, a center position of a base circle (C), and a radius (R) of the base circle (C) are instructed, and an interpolation is performed with respect to an involute curve having a start point (P.sub.s) on a first involute curve (IC1) and an end point (P.sub.e) on a second involute curve (IC2). According to such a method, machining operations can be done by the use of a specifically configured involute curve which is distinct from the two involute curves.

## Claims

### Claim 1

An involute interpolation method for use in machining operations by a numerical control apparatus, which comprises the steps of:
instructing a rotational angle of an involute curve, a center position of a base circle, and a radius (R) of said base circle;
further instructing a curve start point of a first involute curve resulting from said base circle and a curve start point of a second involute curve resulting from said base circle; and
wherein an interpolation is performed with respect to said involute curve having a start point on said first involute curve and an end point on said second involute curve.

### Claim 2 (depends on 1)

An involute interpolation method according to claim 1, further comprising the steps of: computing a coordinate (X.sub.o, Y.sub.o) of said base circle, an angle (.theta..sub.s) of said start point, an angle of said end point (.theta..sub.e) and an angle of said involute curve start point (.theta..sub.o) based upon said instructions and a coordinates of said start points;
in accordance with equations representing an arbitrary point on said involute curve,
X=R {cos .theta.+(.theta.-.theta..sub.o) sin .theta.}+X.sub.o
Y=R {sin .theta.-(.theta.-.theta..sub.o) cos .theta.}+Y.sub.o
obtaining points on said involute curve while incrementing .theta. in the range of .theta..sub.s to .theta..sub.e by a predetermined value, wherein .theta..sub.o is set to .theta..sub.o =.theta..sub.1 at said start point of the involute interpolation, .theta..sub.o is set to .theta..sub.o =.theta..sub.o +(D/NR) during the interpolation of said involute curve, and .theta..sub.o is set to .theta..sub.o =.theta..sub.2 at said end point of said involute interpolation.