US2855678A - Apparatus for generating involutes - Google Patents

Apparatus for generating involutes Download PDF

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US2855678A
US2855678A US476801A US47680154A US2855678A US 2855678 A US2855678 A US 2855678A US 476801 A US476801 A US 476801A US 47680154 A US47680154 A US 47680154A US 2855678 A US2855678 A US 2855678A
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disc
board
tangent
carriage
pin
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US476801A
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Hofer Hermann
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ZF Friedrichshafen AG
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ZF Friedrichshafen AG
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B43WRITING OR DRAWING IMPLEMENTS; BUREAU ACCESSORIES
    • B43LARTICLES FOR WRITING OR DRAWING UPON; WRITING OR DRAWING AIDS; ACCESSORIES FOR WRITING OR DRAWING
    • B43L11/00Non-circular-curve-drawing instruments
    • B43L11/08Non-circular-curve-drawing instruments for drawing involutes

Description

Oct. 14, 1958 Filed Dec. 21, 1954 H. HOFER 2,855,678

APPARATUS FOR GENERATING INVOLUTES 3 Sheets-Sheet 1 Oct. 14, 1958. H. HOFER APPARATUS FOR GENERATING INVOLUTES Filed Dec. 21, 1954 5 Sheets-Sheet 2 ATTORNEKS Oct. 14, 1958 I HOFER 2,855,678

7 v APPARATUS FOR GENERATING INVOLUTES Filed Dec. 21, 1954 5 Sheets-Sheet 3 7 7 I ILfiIIIIIIE-U 1555355555515 INVENTOR I .E j I ATTORNEY United States Patent O APPARATUS FOR GENERATING INVOLUTES Hermann Hofer, Friedrichshafen, Germany, assignor to Zahnradfabrik Friedrichshafen, Friedrichshafen A. B., Germany Application December 21, 1954, Serial No. 476,801

Claims priority, application Germany December 23, 1953 12 Claims. (Cl. 33--27) The present invention relates generally to mechanisms for generating geometric curves and more particularly to a mechanism for the direct generating of involute curves.

The object of the invention is to provide an inexpensive mechanism which is simple in construction and containing a minimum number of parts by which involute curves may be accurately and quickly generated upon a working surface.

Another object of the invention is the provision of adjustable elements in the mechanism whereby involute curves corresponding to various diameter base circles may be accurately generated with a simple movement on a working surface using only a single roller arc.

Other objects and advantages, in part, will be obvious, and :in part pointed out hereinafter during the course of the following description:

The invention accordingly resides in the combination of elements, features of construction and arrangement of parts. The scope of the invention will be more fully set forth in the claims at the end of this specification.

For a more ready comprehension of this invention, reference is had to the accompanying drawings, wherein:

Fig. l is a plan view of the invention.

Fig. 2 is a side view of the invention, viewed substantially in direction 22 of Fig. 1.

Fig. 3 is a sectional View taken substantially along line 3-3 of Fig. l with an accompanying side view of the drawing board.

Fig. 4 is a sectional view taken substantially along line 4-4 of Fig. 1 with the carriage in its zero position where the involute angle equals zero.

Fig. 5 is an enlarged sectional view taken substan tially along line 5-5 of Fig. 4 showing the mounting of the graduated rule.

Fig. 6 is a sectional longitudinal view of a modification of the invention embodying a movable drawing board.

Fig. 7 is a sectional view of the modification of the invention taken substantially along line 7-7 of Fig. 6.

Fig. 8 is a sectional view similar to Fig. 7 of the modification of the invention with some of the parts removed to show the invention in an adjusted position.

Like reference characters refer to like parts throughout the several views of the drawing.

As conducive to a clearer understanding of certain features of the invention, it may be noted at this point that an involute curve is defined as being the path of any point on a tangent to a curve that rolls without sliding around the curve. In the past the involute curve has found widespread application in design work. One example of such an application is in the design of gears where the gear teeth are of involute curvature. The involute curvature of gear teeth has a circular generating curve. In practice the base circle of the gear is used as the generating curve upon which a tangent is in efiect 'rotated without sliding.

The usual well known methods for constructing inyollltc curves such as the point by point layout method,

ice

the use of templates, or the unwinding or winding of a taut string from or on the surface of a cylinder require lengthy and involved operations, and any of these methods are subject to errors. Various instruments have been proposed to generate involute curves but they have been complicated and expensive and also not particularly beneficial from the standpoint of accuracy.

It is therefore the outstanding object of this invention to provide an involute generating mechanism both light and simple and characterized by a high degree of accuracy that will produce with a single rolling arc an involute curve from an infinite number of various diameter base circles within its range of operation.

As specifically illustrative of the practice of this invention, Fig. 1 illustrates an involute curve generating mechanism inscribing an involute curve. There is utilized a stationary semi-circular drawing board or disc 10 which has a center point designated by a pin 11. Adjacent the board 10 there is arranged a straight rail or tangent element 12 which is adapted to roll around the outer periphery of the board 10 without sliding. The rolling movement of the rail 12 is secured by two bands or strips 13 and 13 located around the outer periphery of the board 10 and secured to it by means of screws 14 and 14 respectively. The opposite ends of the strips 13 and 13' are fixed to the rail 12 by means of screws 15 and 15 respectively. The strips or bands may be of any flexible material such as metal or plastic in order that a smooth surface be provided. In order that the rail 12 rolls ofi perfectly on board 10 I provide recesses 16 and 16' at the upper and lower portion of the board edge as shown in Fig. 3. The bands 13 and 13 fit within these recesses and have a thickness less than the depth of the recesses to insure continuous tangential contact between the board and rail. The rail 12 is provided with an extension or side rail 17 connected thereto in a fixed manner which laps over the upper surface of the board 10 (see Fig. 3).

As shown in Fig. 1, there is provided a pivoted lever serving as a guide rail 18 containing a centrally located slot 19 constituting a longitudinal guideway. At the lower end of the slot, pin 11 is located, around which the rail pivots. On the straight rail 12 a stationary pin 20 is provided and projects through the slot 19 also and serves as a follower. When the rail is moved around the edge of the board the pin 2%) slides longitudinally within the slot 19 while the guide rail 18 pivots around pin 11. On the upper side of the extension 17 there is provided a shallow groove 21 as seen in Fig. 2 and Fig. 3 constituting a longitudinal guideway. This groove receives a pair of wheels 22, 22' which form parts of a carriage 23 and being supported in spaced relationship on extensions 24, 24' fixed to a rigid crossbar or connecting member 25. The crossbar 25 contains a central passage 26 arranged to receive a slide in the form of a graduated rule 27. This rule is adjustably positioned with respect to the carriage 23 and is rigidly maintained in the desired position by means of threaded screw 28 mounted in a housing 29 attached to the carriage. The housing 29 is recessed longitudinally at 30 to receive the rule 27. A plate 31 secured by means of screws 32, 32 to the housing retains the slide within the recess. When the screw 28 is screwed down its lower end contacts the rule 27 and secures it in fixed position.

At the end of the rule 27 there is located a curve describing instrument such as a downwardly depending scribing point 33 which rides in the slot 19 and inscribes the involute curve on the surface of the board as the guide rail 18 pivots.

In the operation of this mechanism the material or paper upon which the desired involute curve is to be reproduced is attached to the board 10. The basic circle around which my mechanism operates is the circle formed by the edge of the drawing board containing a radius Rg and a centerpoint defined by pin 11. An involute is described by themovement of pin 20 as the rail ll is rolled around the board 10 without sliding in continuous tangential contact. I The cusp of such an involute curve at the base circle is F It can be seen that the writing element 33 as it moves within the slot 19 will always lie on the same'radial line as the pin.20 and since the rule 27 is always maintained perpendicular to the tangential rail 12 a line through point 33 parallel to rail 12 willbe in continuous tangential relationship with a base circle having a diameter rg. This diameter therefore would depend on the distance (a) between the point 33 and the tangential rail 12. The involute therefore inscribed by writing element 33 would have a cusp (R) from its base circle. Itwill be noted that the mechanism can be operated in'either direction or rotation. Therefore an involute curve with a cusp (f on the base circle can be drawn in either a clockwise or counter-clockwise direction as shown by the arrows in Fig. 1.

The rule can be provided with a graduation scale in order to provide for a ready selection of the distance (a) and consequently the base circle diameter of the drawn involute curve. The operation of the mechanism is practically automatic as the operator need only grasp the rail 12 or 18 and with a single rotary movement the selected involute curve is reproduced.

If it is desired to obtain the involute angle an angle scale may be attached to the board 10. As shown in Fig. 1 the involute angle a would be the dilference between angle }8 and angle g0. Angle ,8 would be the angle formed by the two lines taken from pin 11, the base circle center, one to the point of tangential contact of bands 13 and 13' and the other through points of origin F and f of the involute curve. Angle 0 would be the angle formed by the two lines taken from pin 11, as shown on Fig. 1.

Figures 6, 7 and 8 illustrate a modification of the invention wherein a movable drawing board or base disc 50 in the form of a circular segment is utilized instead of a fixed drawing board. The drawing board is mounted on a base or ground plate 51 and rolls ofi without sliding with its arcuate edge on a solid rolling line fixed to the base plate.

The rolling oif movement can be secured through a wire having ends 52, 52' and a back section 53 tensioned over two fixed rollers or plugs 54 and 54. One end 52' of the wire lies against the arcuate surface of board 50 as shown in Fig. 6 and is fastened thereto by screw 55'.

The other extremeity 52 of the wire also runs along the arcuate edge of board 50 and is connected to the board by screw 55. The wire may be considered a stationary tangent element relative disk 50 although it has motion to drive a curve describing element.

In base plate 51 clamping pin 56 is located and the back section 53 of the wire passes through the pin shank. By means of a screw 57 7 carried by the pin the roll off wire can be fixed in the drawing position.

Within the base plate 51 a shallow guide groove 58 is provided in which a pin or bolt 59 fixed to board 50 slides. The lower end of the guide pin 59 is cylindrical and of somewhat smaller diameter than the width of the groove 58. Therefore when rolling oif the board 50 on a rolling line the center of the rolling circle formed by the board moves on a line parallel to the rolling line. The pin 59 serves simultaneously as a rotation pin for rail or lever 60.

' Mounted directly over the drawing board as shown in Fig.6 a guide rail 60 is provided having on its underside a rectangular groove 61 constituting a longitudinal guideway. A stirrup member 62 is fixed to one side of the baseplate 51 and contains an extension 63 on which a fixed pin or follower 64 is supported. This fixed .4 pin is arranged to slide freely in the rail groove 61 and lies above the rolling line formed by the wire ends 52, 52 as shown in Fig. 7.

The base plate 51 is provided with another groove 65 constituting a longitudinal guideway which runs parallel appropriately with inclined side walls. As shown in Fig. 6 a carriage 66 provided with a pair of rollers 67, 67" mounted within holes 68, 68 of the carriage moves by means of the rollers in the groove 65. The rolling surface of the rollers is conical and shaped to fit the form of the groove 65.

The carriage 66 is provided with an arm 69 or bar which carries a writing element 70. The writing element 70 is positioned in a guide or slide 71 which is a curve describing instrument and is fixed adjustably along the arm 69 by screw 72. In addition guide 71 has a guide pin 73 which slides in the rectangular groove 61 and lies on the sameaxis as writing element 70. Pin 64 and guide pin 73 are formed correspondingly conical and slide on the lower edges of the rectangular groove 61.

In order to equalize the weight of the carriage 66, the U-shaped portion of the carriage which lies to the right of the rollers 67, 67 in Fig. 6, is made of steel and the arm 69 is made of light metal. Therefore the writing element 70 presses equally and only lightly on the paper in all positions.

In the operation of the device pin 59 is pushed against and guided along the surface of groove 58 facing the rolling ofi side of the board 50. In this longitudinal movement the drawing board 50 with its arcuate surface rolls off on the rolling line of wire 52, 52'. During this operation rail 60 rotates around pin 59 and is guided at its face end by means of the fixed pin 64 in groove '61. At the same time carriage 66 is moved sidewise by means of the pin 73 and rolls in groove 65. Pin 73 of the guide 71 is guided in groove 61 and writing element 70 draws the involutes indicated in Fig. 7 at e e and e;;.

It will be noted that the plumb line as shown in Fig. 7 which is created on the rolling line by fixed point 64 is also the symmetrical axis of the drawing board 50. The base points of the involutes e e and eg, etc., drawn in this position of the drawing'board lie also-on the center axis of the board. The involutes can be drawnin either direction from the base points depending on the direction of movement of pin 59. a

If it is desired the screw 57 can be loosened and the wire 52, 52' 53 can be displaced by rotating board 50 around pin 59-which is held fast. The screw '57 is subsequently tightened again. The plumb line established on the rolling line through the fixed pin 64 is now displaced by the angle AE form the symmetrical axis of the board 50 as shown in Fig. 8. Therefore another plurality of involutes e e e etc., can be drawn, the base points of which lie on a new zero axis.

Along the wire section 53 adjacent the groove 65 a longitudinal scale 74 is printed on the base plate 51. Along the wire 53 above the scale a mark 75' is attached which indicates the desired amount of displacement of the wire. This scale can be calibrated in units of the center angle. The mark 75 is opposite the zero point of the scale when the axis of symmetry of the board 50 lies on the plumb line through the pin 64.

If it is desired a perfect operation of the rolling off device can be obtained by eliminating the wire 52, 52', 53 and groove 58. Instead a simple, smooth, tangential rule is fixed on the base plate 51 in place of the wire against which the arcuate edge of the drawing-board 50 rolls off without further auxiliary means merely by pressing against the tangential rule. The necessarycourse of the rolling 0E movement (without sliding) is obtained here by the contact friction of the two rolling surfaces against each other.

As will be readily seen, I provide a simple and inexpensive mechanism by which a wide variety of involute curves maybe quickly and-accurately generatedby effecting a simple adjustment and previously developed involute curves may be readily checked. Furthermore the desired involute may be generated in one direction or the other with respect to the base circle without modification or adjustment of the apparatus. I

It is apparent from the foregoing that once the broad aspects of the invention are disclosed, many embodiments thereof and many modes of application all falling within the scope thereof, will readily occur to those skilled in the art. Moreover, many modifications of the particular embodiment herein disclosed will likewise suggest themselves. Accordingly, the invention is intended to be limited only by the scope of the following claims and the foregoing disclosure is made solely by way of illustration.

I claim:

1, A mechanism for generating involutes comprising a circular base disc, a rotatable lever pivoted at the center of said disc, a tangent element rolling tangentially without slipping on said disc, a follower connected to said tangent element, said follower engaging said lever and movable along said lever, a carriage slidably connected to said tangent element for longitudinal movement therealong, a slide adjustably positioned on said carriage and extending perpendicular to the direction of movement of said carriage, said slide containing a point engaging said lever and slidable along said lever to generate involute curves of various base circle diameters according to position of said slide, when said tangent element is rolled on said disc.

2. A mechanism for generating involutes comprising a circular base disc, a rotatable lever pivoted at the center of said disc, a tangent element rolling tangentially without slipping on said disc, a follower on said tangent element engaging said lever and movable longitudinally along said lever, a carriage slidably connected to said tangent element for longitudinal movement therealong, a slide adjustably positioned on said carriage and perpendicular to the direction of motion thereof, said slide containing a point engaging said lever and slidable along said lever to generate both branches of involute curves of various base circle diameters in either direction of rolling of said tangent element on said disc.

3. A mechanism for generating involutes comprising a circular base disc, a rotatable lever containing a central longitudinal slot and pivoted at the center of said disc, a tangent element movable tangentially on the periphery of said disc without slipping, a follower on said tangent element slidable within said lever slot, a carriage slidaby connected to said tangent element for longitudinal movement therealong, a slide adjustably positioned on said carriage and perpendicular to the direction of motion thereof, said slide containing a point also slidable within said lever slot to generate both branches of involute curves of various base circle diameters according to position of said slide when said tangent element is rolled in either direction on said disc.

4. A mechanism for generating involutes comprising a circular base disc, a rotatable lever pivoted at the center of said disc, a tangent element rolling tangentially relative to said disc without slipping, and containing a follower engaging said lever and movable along said lever, a carriage slidably connected to said tangent element for longitudinal movement therealong, a bar fixed on said carriage and extending perpendicular to the direction of motion of said carriage, a slide adjustably positioned on said bar and containing a point also slidable along said lever to generate both branches of involute curves of various base circle diameters according to the position of said slide, when said tangent element is rolled in either direction on said circular disc.

5. A mechanism for generating involutes comprising a circular base disc, a rotatable lever containing a central longitudinal groove and pivoted at the center of said disc, a stationary tangent element, said circular base disc rolling on said tangent element, a follower incorporated in said tangent element and engaging said groove of said lever, a carriage slidably connected to said tangent element for longitudinal movement therealong, a bar fixed on said carriage and extending perpendicular to the direction of movement of said carriage, a slide adjustably positioned on said bar and containing a point also slidable within the groove of said lever to generate both branches of involute curves of various base circular diameters according to the position of said slide, when said disc is rolled in ,either direction on said tangent element.

6. A mechanism for generating involutes comprising a circular base disc, a rotatable lever having a longitudinal slot and pivoted at the center of said disc, a tangent element movable tangentially without sliding relative to the periphery of said disc, and having a longitudinal groove, a follower on said tangent element slidable along said lever slot, a carriage supported by a pair of rollers maintained in spaced apart relationship, a connecting member for maintaining said relationships, said rollers rolling within said groove, a slide adjustably positioned on said connecting member for adjustment perpendicular thereto, said slide containing an element also slidable along said lever slot to generate both branches of involute curves of various base circles when said tangent element is rolled in either direction on said disc.

7. A mechanism for generating involutes, comprising a circular base disc, a rotatable lever containing a central longitudinal groove and pivoted at center of said disc, a ground plate carrying said disc, two plugs secured to said plate, a wire stretched around said plugs, the opposite end pieces of said wire crossing each other and embracing said disc and said wire extending linearly in opposite directions from the crossover point, and the ends of said wire secured to said disc, a groove provided in said ground plate and parallel to the centerline of said plugs, a bolt at the center of said disc engaging said groove in said ground plate and adapted to be guided manually in said groove, said disc being adapted to roll on the linear length of said wire in either direction from said crossover point, a follower incorporated in said ground plate, the vertical axis of said follower being in the plane of said center-line, said follower engaging said groove of said lever, a carriage slidably connected to said ground plate for movement parallel to said centerline, a bar fixed on said carriage and extending perpendicular to said center-line, a slide adjustably positioned on said bar and containing a point also slidable within said groove of said lever and adapted to generate both branches of involute curves of various base circle diameters according to position of said slide, when said bolt at center of said disc is guided in either direction within said groove in said ground plate.

8. The apparatus according to claim 7 in which the bar of said carriage is provided with graduations by which the base circle diameter of the generated involute curve can be selectively predetermined.

9. The apparatus according to claim 1 in which the circular base disc contains an angle scale by which the involute angle may be determined.

10. The apparatus according to claim 7, in which said wire is adjustable along said center-line.

11. The apparatus according to claim 7, in which the ground plate is provided with graduations, said wire carrying a mark sliding along said graduations in order that the position of the wire along its center-line may be selectively predetermined.

12. A mechanism for generating involutes comprising a segment of a circular disc, a rotatable lever having a longitudinal guideway, and pivoted at the center of said disc segment, a tangent element movable tangentially without sliding relative the segment periphery and having a longitudinal guide means, a follower on said tangent element slidable along said lever guide means, carriage means guided in the direction of said longitudinal guideway of said tangent element, a curve describing element, means for supporting said element for translation with said carriage in the direction of said guide means of 7 said tangent element, means for adjusting said element References Cited in'the file of this patent reletive said carriage alonga line normal to the direction UNITED STATES PATENTS of travel of said carriage, means on said element slidable 1 606 0 Fellows Nov 9 1926 along the ay of said rotatable lever whereby said 401 Bradner 1954 element cribes an involute when said tangent element and' said segment of the disc are moved relative each FOREIGN PATENTS other. 534,650 France Jan. 9, 1922

US476801A 1953-12-23 1954-12-21 Apparatus for generating involutes Expired - Lifetime US2855678A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3233331A (en) * 1962-11-29 1966-02-08 Nat Broach & Mach Universal involute checker

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE1219696B (en) * 1963-05-10 1966-06-23 Manfred Maske Device for the construction and drawing of alignment sequences formed from clothotids and circular arcs
US3315265A (en) * 1963-07-26 1967-04-18 Us Rubber Co Instrument and method for profile generation

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR534650A (en) * 1921-04-27 1922-03-29 Method and device for plotting involutes of circles
US1606520A (en) * 1926-11-09 Involute-measuring
US2673401A (en) * 1946-08-14 1954-03-30 Lees Bradner Co Generating geometric surface

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1606520A (en) * 1926-11-09 Involute-measuring
FR534650A (en) * 1921-04-27 1922-03-29 Method and device for plotting involutes of circles
US2673401A (en) * 1946-08-14 1954-03-30 Lees Bradner Co Generating geometric surface

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3233331A (en) * 1962-11-29 1966-02-08 Nat Broach & Mach Universal involute checker

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GB758905A (en) 1956-10-10

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