US2673401A - Generating geometric surface - Google Patents

Description

March 30, 1954 BRADNER 2,673,401

GENERATING GEOMETRIC SURFACE Filed Aug. 14, 1946 4 Sheets-Sheet l fiENTOR.

14 A4 ATTORNEYS.

March 30, 1954 BRADNER 2,673,401 GENERATING GEOMETRIC SURFACE Filed Aug. 14, 1946 4 Sheets-Sheet 2 INVENTOR March 30, 1954 J. A. BRADNER 2,673,401

GENERATING GEOMETRIC SURFACE Filed Aug. 14, 1946 4 Sheets-Sheet 3 IN V EN TOR.

March 30, 1954 BR 2,673,401 GENERATING GEOMETRIC SURFACE Filed Aug. 14, 1946 4 Sheets-Sheet 4 i r 1' I+i= 4 L"=E s.l

| l J in I I l l l l I l i l a 2 A'B INVENTOR.

Patented Mar. 30, 1954 GENERATING GEOMETRIC SURFACE John A. Bradner, Shaker Heights, Ohio, to The Lees-Bradner Company,

assignor Cleveland,

Ohio, a corporation of Ohio Application August 14, 1946, Serial N 0. 690,354 13 Claims. (Cl. 33-1795) This invention relates to surfaces.

An object of the invention is to provide an improved means for accurately generating certain geometric surfaces.

Another object of the invention is to provide an improved means of describing involute curves.

Another object of the invention is to provide an improved apparatus which will accurately describe involute curves from an infinite number of base circles.

Another object of the invention is to provide an improved apparatus which may be easily and accurately adjusted to describe involute curves from any of an infinite number of base circles.

Another object of the invention is to provide an improved apparatus which will generate involute curves from a single circular or arcuate member and a single rectilinearly moving element.

Another object of the invention is to provide an improved apparatus which may be easily and economically manufactured.

Another object of the invention is to provide an improved apparatus which will be small and compact.

Another object of the invention is to provide an improved apparatus which will be easy to perate and read.

Another object of the invention is to provide an improved apparatus which will be composed of few and simple parts.

Another object of the invention is to provide an improved method of generating involute curves.

Other objects will hereinafter appear.

The invention will be better understood from the description of one practical embodiment generating geometric thereof, illustrated in the accompanying drawings, in which:

Figure 1 is a diagrammatic view showing the relationship of various involute curves to their respective base circles and lines and to each other;

Figure 2 is a plan view of an apparatus for measuring the involute face of gear teeth;

Figure 3 is a longitudinal section view of the apparatus taken on the line IIIIII of Figure 2; and

Figure 4 is a front elevational view of the apparatus of Figures 2 and 3.

The involute now is one of the most popular forms for gear tooth design, because of the many and peculiar advantages possessed by this tooth form, including the possibility of producing a tooth by a generative action. Numerous machines have been developed for generatively forming such teeth as by bobbing, grinding, and the like, and, as a basis for this generative action, such devices have relied upon the base circle of the gear to be generated, using a master drum of precisely the diameter of this base circle, a master gear and rack having, the same base circular diameter, or other equivalent mechanism to obtain the generative motion of the gear relative the tool.

This, of course, has necessitated the extremely accurate making of the basic drum, master gear, or the like, and its associated parts, for each base circle diameter to which gear teeth are. to be generated, and likewise has required the accurate adjustment of these parts whenever a tool is changed to operate on a gear of a different base circle diameter.

The present invention contemplates the easy and rapid adjustment from any base circle diameter to any other (within the range of the apparatus) without interchange of any parts whatsoever.

In the diagram of Figure 1, the center for a plurality of circles is indicated at O. R indicates the radius of a circular arc AB. The radius of a smaller circular arc ab concentric therewith is indicated by r.

Assuming a line CD tangent to are AB at E, which line may roll without slipping upon the arc AB, point E of this line will trace the true involute EF.

The lines C -D C D G -D and C -D all indicate successive positions of the line CD in rolling on the arc AB, and the points E E E and E are corresponding positions of the point E along the involute EF.

R, R R R and R indicate the radii of the arc AB to the respective points of tangency of the lines C D C D O -D and C -D If now we consider the line cd, tangent to are ab at the intersection of this arc with radius R (and also radius r) it will be noted that line cd is parallel to line CD, both being perpendicular to radius R.

Similarly line 0 -01 is parallel to C -D both being perpendicular to radii R T and so likewise c d 0 -12 and c d are parallel to C D C D and C D respectively, and the point e traces the involute ef, being that developed from base circle ab.

Similarly, any other line rolling on any other base circle with its center at 0 will trace the involute derived from this base circle; as for instance the line Cg-Dg, rolling on the arc of circle Ag-Bg, which is the base circle of the gear G shown as placed concentric with arcs ab and AB. may have. a point Eg used to trace the involute gear tooth face EgFg.

The only requirement is that the lines CgDg, ed and CD remain always parallel, and that each remain at it fixed radiusv distance from center 0.

If, now, instead of holding the circles stationary, we consider line CD as moving lengthwise and are AB as rotating about center so that the tangent portion of the line and are are moving at the same velocity, it will be apparent that lines cd and Cg-Dg can also move lengthwise in directions parallel to line CD at rates such that the tangent portions of these lines move at the same velocity as their respective arcs Ag-Bg ab and the points e and Eg will trace the involutes ef and Eg-Fg.

The velocities of points Eg, e, E thus will be seen to be directly proportional to the radii By, T and R, respectively.

If the motion of line CD is uniform, it will be apparent that the motion of lines cd and CgDg will also be uniform and proportional to their respective radial distances from point 0, and that the angular velocities of points E, e and Ey will be identical.

Thus it is only necessary to make line CD move in a lengthwise direction and arc AB remain tangent to it and move, at the point of tangency, at the same speed as line CD, and then to cause lines at (and/or Cg-Dg) to move in a direction parallel to line CD at such a rate that points Eg, e and E all remain on the same radial line passing through center 0, to insure all three of these points tracing their respective involute curves; and when these conditions are met arcs Ag-Bg and ab may exist only as geometrical abstractions and need have no physical embodiment.

The apparatus shown in the remaining figures is based upon this principle.

This apparatus is shown as a device for measuring the face of gear teeth. It consists of a base i, which is shown as a hollow casting having a depending front 2 and side 3 flanges and a top 4.

Extending vertically upward from the top 5 is a shaft or spindlefi, to which is fixed a sector or arm 6 having arcuate end 6A6B, corresponding to the arc AB of the first figure.

Mounted in guideways 1 and 8, the former of which is formed in the upper surface of top 6 and the latter of which is adjustably secured in place by screws 9, is a transversely movable slide The projecting end of the shaft is formed into a square 24, to which may be applied a handle, knob, or wheel for rotating the shaft 23 to adjust the position of the carriage on the base.-

The upper surface of bridge IE is provided with fixed guideways 25 and adjustable guideways 26, the latter of which is secured in position by machine screws 21, and in these guideways is transversely movable slide 28, having a straight inner edge 28c-28d, corresponding to either line cd or Cg-Dg of the first figure.

It will be understood that the guideways l and 8 are at all times parallel to guideways 25 and 26, so that, irrespective of the adjustment of screw 20, slides l0 and 28 must move parallel to each other.

Pivoted upon the shaft 5 is a hub 29, provided with an arm 30 having a straight side to the left (as shown in Figure 2) which lies in a vertical plane including the axis of shaft 5.

Abutting this straight edge of the arm is an abutment, shown as a knife edge 3!, fixed to slide In directly over line IBC-l GD.

A spring 32 presses the arm 30 against the abutment 3 I.

A similar abutment 33 projects upwardly from 7 carriage 28 directly above line 28c28d and likewise abuts the left hand edge of arm 33, while a spring, similar to 32, is shown at 34, abutting the right hand edge of this bar and holding the knife edge tightly thereagainst.

Projecting upwardly from carriage 28 are two lugs 35, to which is secured, as by a bolt 33, an indicator 31, the contacting part 38 of the spindle of the indicator being so arranged as to be directly over the edge of abutment 33.

A gear G is shown as clamped on spindle shaft 5 by a nut 39 threaded on the reduced end 4|] of the spindle.

In comparing the plan View of Figure 2 with the diagrammatic view of Figure 1, it will be seen that the knife edge 3| is, in effect, the point I0 having a vertical flat surface IOC-IOD adjacent the arcuate surface (SA-6B of a sector, this flat surface corresponding to line CD of the first figure.

To obviate any possibility of slippage between the end of sector 6 and the slide 1 I], crossed tapes H and [2 of relatively unstretchable material, such as thin steel bands are provided, the ends of these being secured to the sector and slide as by machine screws I3. One end of tape II is secured to the sector at 6A and its other end to the slide at HiD, while the ends of tape [2 are secured to the slide at IDC and to the sector at 6B. The top 4 of the base is formed with a large rectangular central opening, the side edges of which I l form, with the top and bottom of this base, guideways engaged by a bridgelike carriage having vertical side portions l5 and a bridge or top It extending over the narrower portion of sector 6.

The side portions of the carriage slide upon the upper surface of top 4, while on the bottom surface is a transverse plate or yoke l1, secured to the side pieces 15 by machine screws l8.

The yoke has depending central boss l9 into which is threaded an adjusting screw 20, having a flange 2! lying against the front I of the base and a collar 22 abutting the opposite side of this front and shown as held in place on the screw by tapered pin 23. l

E while the knife edge 33 and the overlying indicator contact 38 is, in effect, the point e or Eg of Figure l.

The sector 6 rolls without slipping on slide l0,

' corresponding to are AB rolling on line CD, and

the point E (or 3|) traces the involute EF.

As it traces this involute, it causes line 280-2811 of slide 28 to reciprocate parallel to line MiG-48D at a rate which causes point 38 (or Eg) to describe the involute Eg-Fg, so that the indicator generates a true involute curve, the base circle of which is the distance from the axis of shaft 5 to line 28c--28d.

The radius of this base circle, of course, may be easily varied by rotation of threaded shaft 20, to any one of the infinite radii possible within the range of adjustment of the apparatus.

It will 'be seen that therelative linear velocity of line lGC-l0D is equal to the circumferential velocity of arc 6A-6B. In other words, if we let LV=the linear velocity of line IBC- 3D AV=the angular velocity of arc 6A-6B R=the radius of arc 6A6B Lg=the linear velocity of line 28c--2Bd rg=the radius of the base circle of gear G=the distance of surface 28c-28d from axis 0 erg-. 2 a *0 aerator While the mechanism shown and described is designed for the measuring of gear tooth surfaces, it will be apparent that, with little or no modification, it can be used for the production of such surfaces.

For example, it is only necessary to substitute for the contact 38 of the indicator a cutting or forming tool, such as a shaper or milling cutter, a grinding wheel, lap, burnisher or the like and, of course, the tooth spacing of the gear may be arrived at by mounting any suitable dividing head or indexing mechanism upon or in the spindle 5.

While bands I I and I2 have been shown to preclude slippage between arc 6A6B and straight surface IOClD, it will be obvious that with very light loads, such as produced by the indicator shown, friction alone may be sufiicient to cause these surfaces to roll upon each other without slipping.

While I have described the illustrated embodiment of my invention in some particularity, it will be apparent that many variations and modifications thereof may be made by those skilled in the art, and I therefore do not limit myself to the precise details herein shown and described, but claim as my invention all variations, modifications and embodiments coming within the scope of the appended claims.

I claim:

1. A generating apparatus comprising two elements relatively movable about an axis, two parallel elements carried by one of said first mentioned elements and movable in guide means in parallel lines at fixed distances from said axis, connections between the second of the two first mentioned elements and both parallel elements, said connections both lying in the same plane including the axis.

2. A generating apparatus comprising two elements relatively movable about an axis, two parallel elements carried by one of said first mentioned elements and movable in guide means in parallel lines in a plane normal to the axis at fixed distances from said axis, connections between the second of the two first mentioned elements and both parallel elements, said connections both lying in the same plane including the axis.

3. A curve generating device comprising two pivotally connected supports, article clamping means carried by one support, a movable tool holding means carried by the second support and movable in guide means along a line adjustably spaced from the axis of the pivot, a movable member carried by said second mentioned support movable in guide means along a line parallel to the line of motion of the tool holding means and at a, fixed distance from said axis, a connection between the first mentioned support and the last mentioned linearly movable member causing said second mentioned linearly movable member to move at a constant rate in relation to the relative angular movement of the supports, a connection between said first mentioned support and said tool carrying member, both connections lying in a plane including the axis of the pivot.

4. A curve generating mechanism comprising a base, a holder pivotally mounted thereon, parallel guide-ways carried by the base at difierent distances from the pivotal axis of the holder, slides in said guide-ways, a driving member connected to the holder and having positive rolling contact with one of the slides, a member-pivotally mounted co-axial to said holder and having 6 positive driving connections between fixed points on each of said slides, said fixed points lying in a plane including the pivotal axis.

5. A curve generating mechanism comprising a base, a holder pivotally mounted thereon, parallel guide-ways carried by the base at different distances from the pivotal axis of the holder, one of said guide-ways being adjustable toward and from the pivotal axis, slides in said guide-ways, a driving member connected to the holder and having positive rolling contact with one of the slides, a member pivotally mounted to rotate about the same axis as said holder and having positive driving connections between fixed points on each of said slides, said fixed points lying in a plane including the pivotal axis.

6. A curve generating apparatus comprising a base, a vertical spindle mounted thereon, parallel horizontal guideways carried by the base, slides movable in said guideways, an extension on said spindle having an arcuate end in driving engagement with one of said slides, an arm pivoted on said spindle, and connections between said arm and both said slides, said connections lying in a single plane including the axis of the spindle.

7. A curve generating apparatus comprising a base, a vertical holder spindle mounted thereon, two parallel horizontal guideways carried by the base, slides movable in both said guideways, an extension on said spindle having an arcuate end in driving engagement with one of said slides, an arm pivoted on said spindle, and connections between said arm and both said slides, said connections lying in a single plane including the axis of the spindle.

8. A curve generating apparatus comprising a base, a vertical holder spindle mounted thereon, horizontal guideways carried by the base, a carriage movable upon said base, guideways on the carriage parallel to the guideways on the base, slide movable in both said guideways, an eX- tension on said spindle having an arcuate end in driving engagement with one of said slides,

. an arm pivoted on said spindle, and connections between said arm and both said slides, said connections lying in a single plane including the axis of the spindle.

9. A curve generating apparatus comprising a base, a vertical holder spindle mounted thereon, horizontal guideways carried by the base, a carriage movable upon said base and adjustable toward and from said spindle, guideways on the carriage parallel to the guideways on the base, a slide movable in said guideways on the base, a second slide movable in the guideways on the carriage, an extension on said spindle having an arcuate end in driving engagement with one of said slides, an arm pivoted on said spindle, and connections between said arm and both said slides, said connections lying in a single plane including the axis of the spindle.

10. A curve generating device comprising, a base, a vertical spindle pivotally mounted thereon, a horizontal guideway on said base, a slide movable along said guideway, horizontal guideways on the base angularly disposed with respect to said first mentioned guideway, a carriage movable along said second mentioned guideways, moving means for moving said carriage along said guideways, guideways carried by said carriage parallel to the first mentioned guideways on the base, a slide movable in said guideways on the carriage, an arm fixed to said spindle and having an arcuate end in driving engagement With the first mentioned slide, an arm pivotally mounted on said spindle and having positive driving connections with both said slides, both driving connections lying in the same radial plane including the axis of the spindle, a tool connected to said second mentioned slide and clamping means for clamping an article to said spindle.

11. A curve generating device comprising a base, a vertical spindle pivotally mounted thereon, a horizontal guideway on said base extending along a line spaced from the spindle, a slide movable along said guideway, horizontal guideways on the base angularly disposed with respect to said first mentioned guideway, a carriage movable along said second mentioned guideways, moving means for moving said carriage along said guideways, guideways on said carriage parallel to the first mentioned guideways on the base, a second slide movable in said guideways on the carriage, an arm fixed to said spindle and having an arcuate end in driving engagement with the first mentioned slide, an arm pivotally mounted on said spindle and having positive driving connections with both said slides, both driving connections lying in the same radial plane including the axis of the spindle, a tool connected to said second mentioned slide and clamping means for clamping an article to said spindle.

12. A curve generating device comprising a base, a vertical spindle pivotally mounted thereon, a horizontal guideway on said base extending along a line spaced from the spindle, a slide movable along said guideway, horizontal guideways on the base angularly disposed with respect to said first mentioned guideway, a carriage movable along said second mentioned guideways, a, lead screw for moving said carriage along said guideways, guideways on said carriage parallel to the first mentioned guideways on the base, a second slide movable in said guideways on the carriage, an arm fixed to said spindle and having an arcuate end in driving engagement with the first mentioned slide, an arm pivotally mounted on said spindle and having positive driving connections with both said slides, both driving connections lying in the same radial plane including the axis of the spindle, a tool connected to said second mentioned slide and clamping means for clamping an article to said spindle.

13. A curve generating device comprising a base, a vertical spindle pivotally mounted thereon, a horizontal guideway on said base, a slide movable along said guideway, horizontal guide- Ways on the base angularly disposed with respect to said first mentioned guideway, a carriage movable along said second mentioned guideways, moving means for moving said carriage along said guideways, guideways on said carriage parallel to the first mentioned guideways on the base, a second slide movable in said guideways on the carriage, an arm fixed to said spindle and having an arcuate end in driving engagement with the first mentioned slide, an arm pivotally mount-v ed on said spindle, rigid radially disposed abutments between one side of said arm and both said slides, the contacting sides of said abutments lying in the same plane including the axis of the spindle, resilient means maintaining the contact with said abutments, a tool connected to said second mentioned slide, and clamping means for clamping an article to said spindle.

J. A. BRADNER.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 1,564,589 Laessker Dec. 8, 1925 2,013,365 Snarry Sept. 3, 1935 2,176,924 Olson Oct. 24, 1939 FOREIGN PATENTS Number Country Date 637,563 Germany Oct. 30, 1936 OTHER REFERENCES Involute Gears, W. Steeds, Longmans, Green and Co., 1948, pages 103 and 104. (Copy in Sci,- entific Library.)

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