# US 5,075,865 A · Method and apparatus for involute interpolation

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- Number: US 5,075,865 A
- Document ID: US5075865A
- Status: Granted
- Kind: A
- Application number: 07/397,462
- Filed: 1989-08-22
- Granted: 1991-12-24
- Earliest claimed: 1988-01-08
- Assignees: Fanuc Corporation
- Inventors: Hideaki Kawamura; Kentaro Fujibayashi; Masafumi Sano
- Web page: https://patentgrep.com/patent/US5075865A

## 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 a computerized numerical control apparatus having a rotational axis and a linear axis is effected by giving commands for a direction in which an involute curve (IC) rotates, the position of the center of a base circle (BC), and the radius (R) of the base circle, and interpolating the involute curve (IC) according to the commands. Interpolated distances are converted to those along the rotational axis and the linear axis for the control of a machine tool (9).

## Claims

### Claim 1

An involute interpolation method for a computerized numerical control apparatus having a rotational axis and a linear axis, comprising the steps of:
giving commands for a direction in which an involute curve rotate, a position of the center of a base circle, and a radius (R) of the base circle;
interpolating the involute curve and a distance along a Z-axis according to the commands; and
controlling the rotational axis and the linear axis of a machine in response to said interpolating step.

### Claim 2 (depends on 1)

An involute interpolation method according to claim 1, wherein said step of giving commands comprises giving commands in an orthogonal coordinate system, and wherein said interpolating step comprises interpolating the commands in orthogonal coordinates, further comprising the step of:
converting an interpolated distance in the orthogonal coordinate system to a distance of movement in a polar coordinate system after said interpolating step.

### Claim 3

An involute interpolation apparatus for a computerized numerical control apparatus having a rotational axis and a linear axis, comprising:
means for providing commands which define a two-dimensional involute curve, the commands comprising a direction in which an involute curve rotates, a position of a center of a base circle for locating the involute curve in a two-dimensional plane, and a radius (R) of the base circle which defines a size of the involute curve in the two-dimensional plane;
means for interpolating the involute curve according to the commands; and
means for controlling the rotational axis and the linear axis according to the involute curve.

### Claim 4 (depends on 3)

An involute interpolation apparatus according to claim 3, wherein said means for providing commands comprises means for providing commands in an orthogonal coordinate system, and wherein said means for interpolating comprises means for interpolating the involute curve in orthogonal coordinates, further comprising a means for converting the interpolated curve in orthogonal coordinates to an involute curve in a polar coordinate system.

### Claim 5

An involute interpolation method for a computerized numerical control apparatus having a rotational axis and a linear axis, comprising the steps of:
giving commands which define an involute curve;
interpolating the involute curve in X and Y dimensions according to said commands to provide interpolated values;
converting the interpolated values in the X and Y dimensions into R and C dimensions to provide converted interpolated values; and
controlling said rotational axis and said linear axis according to said transformed interpolated values.