WO1983002986A1

WO1983002986A1 - A transmission mechanism

Info

Publication number: WO1983002986A1
Application number: PCT/DK1983/000016
Authority: WO
Inventors: Jens Kugle Aps Licensselskabet
Original assignee: Kugle, Jens
Priority date: 1982-02-18
Filing date: 1983-02-17
Publication date: 1983-09-01
Also published as: AU1222883A; SU1209042A3; DK71082A; JPS59500234A; EP0101461A1

Abstract

A steplessly variable ball gear has two co-axial rings of balls (A and B), which are so supported by two inner and two outer rolling paths (19-22) formed on moulding rings (12-15) that each ball in one ring touches two rolling paths and two balls in the other ring. The inner and outer rings are axially shiftable with respect to each other. As the distance between both the inner and the outer rings is constant and the rolling paths have concave-curved, preferably circular arc-shaped cross-sections, it can be ensured that the contacts of tangency, required for transmission of torque, between the balls and between the balls and the rolling paths are maintained over a wide variation range.

Description

A transmission mechanism

The invention relates to a transmission mechanism of the type defined in the introductory portion of claim 1. The axial shiftings of one or the other set of rolling paths must result in such changes of the mutual positions of the balls and the rolling paths that the transmission ratio of the mechanism continuously changes with the shiftings.

The US Patent Specification 2862407 discloses a transmission mechanism of the present type in various embodi ments, which share the feature that one set of rolling paths has rectilinear generatrices, while a single one has convex generatrices. For the balls in such a construction to maintain the four contacts of tangency with a changed transmission ratio, it is necessary that either the two inner or the two outer rolling paths are axially shiftable with respect to each other, and that the shiftable rolling path is under the action of a spring force. As the tangential forces forming part of the torques transmitted by friction roll gears are the normal force multiplied by the coefficient of friction, the normal forces must be of a size ten times the force which multiplied by the power arm constitutes the moment transferred.

Moreover, with the generatrix geometry of the rolling paths used in this known friction roll gear only a very limited variation range can be obtained, and consequently most practical uses will require multiplication of the transmission ratio, e.g. by combining the gear with a planet gear, as is also shown in the patent specification.

The invention consists in the finding that the establish ment of a constant axial distance between both the inner and the outer rolling paths makes it possible, on the basis of simple considerations and desired data, to calculate such dimensions and shapes of the constituent elements as will allow the contacts of tangency required for transmission of torque to be maintained within a variation range which makes the transmission mechanism generally applicable for the performance of transmission tasks in practice.

When the mechanism is constructed as stated in claim 2 both the rotation of the balls about their individual axis of rotation and their rotation about the main axis are utilized for transmission. The circumstance that the individual axes of rotation always intersect the rolling paths or imaginary inwardly extending extensions of them within the ball points of tangency ensures that the balls will not assume a position in which they only rotate about fixed individual axes of rotation.

There are many curve shapes which can satisfy the necessary conditions, but it is preferred in practice to use rolling paths having substantially circular arcshaped generatrices, as stated in claim 3, because such rolling paths are relatively easy to manufacture and can meet all normal requirements of transmission ratios and variation widths.

When all the balls are of the same size, the rolling paths in the transmission mechanism of the invention have generatrices which are symmetrical in pairs, as stated in claim 4. The greatest variation width can be obtained when the four rolling paths have double-symmetrical generatrices, as stated in claim 5.

The invention will be explained in greater detail below with reference to the drawing, in which

figs. 1 and 2 show an axial section of an embodiment of the ball gear of the invention in a neutral position and an extreme position, respectively,

fig. 3 shows the balls in such a gear, as seen in the direction of the gear axis,

figs. 4 and 5 are geometrical figures serving to explain the operation of the gear,

fig. 6 is a horizontal section through the centres of the two lower balls in fig. 3,

figs. 7-13 show geometrical figures serving to explain the operation of the gear,

fig. 14 is a schematic axial section of the upper half of a gear like the one shown in fig. 1,

fig. 15 show symbols used in fig. 16,

figs. 16a and b are a survey of various gear types of the invention,

fig. 17 is an axial section like the one shown in fig. 2, but with the gear in the opposite extreme position,

figs. 18 and 19 are spatial views serving to illustrate the radii used in the calculation of the transmission ratio of the gear,

fig. 20 schematically shows a development of a part of the ball gear and serves to illustrate directions of rotation, figs. 21-27 are geometrical figures used in the calculation of the transmission ratio,

figs. 28 and 29 show the two ball rings in a gear of the invention in a limit position as seen from the side and in the direction of the gear axis, respectively,

figs. 30-52 are geometrical figures serving to illustrate certain limits of gears of the invention, and

figs. 33-38 are schematic axial sections of various variants, or parts of them, of the ball gear of the invention.

The transmission mechanism shown in figs. 1 and 2 has an input shaft 10 which receives power marked by an arrow 11 and mounts two moulding rings 12 and 13. Two other moulding rings 14 and 15 are mounted around and coaxially with the rings 12 and 13 and are spaced from these in a radial direction by ring-shaped spaces 16; one 14 is stationary as shown by hatched areas 17, while the other 15, spaced from the first one in an axial direction by a space 23, is freely rotatable but not slidable axially and forms the output element from which the power marked by two half-arrows 18 is taken. The four moulding rings 12, 13, 14 and 15 are formed with rolling paths 19, 20, 21 and 22, respectively, which face toward each other and have circular arc-shaped cross-sections in the embodiment shown. Two ball rings are so mounted between the rolling paths that each ball A in one ring touches the inner rolling path 20, the outer rolling path 21 and two balls B in the other ring, and similarly each of these balls B touches the inner rolling path 19, the outer rolling path 22 and two balls A in the first ring.

The frictional contacts, as caused by the rotation of the input shaft 10, between the rolling paths and the ball and between the balls will make the balls rotate about their own individual axes O_A and O_B and about the gear axis x of the entire mechanism. The rotation of the ball ring about this axis takes place in the opposite direction of that of the input shaft. The axes of rotation O_A and O_B of the balls intersect each other on the gear axis x.

In fig. 1 there is plotted an axis y which is at right angles to the axis x and is an axis of symmetry for the two axially fixed. outer rolling paths 21 and 22.

Axial shifting of the inner moulding rings 12 and 13, as shown in fig. 2, changes the quantities which determine the ratio of the rotary speed of the input shaft 10 to that of the output element 15, i.e. the gear ratio of the transmission mechanism. During such shifting the contacts of tangency between the rolling paths and the balls and between the balls must be maintained, and it will be explained below what conditions are to be met in order for this to be possible.

Fig. 3 shows two ball rings each having three balls A and B, as seen in the direction of the gear axis. In addition to the y axis an axis z is plotted in fig. 3 which is at right angles to both axes x and y. Moreover, equiangular lines P are plotted, representing planes which intersect each other in the x axis and in which the ball centres move with relative axial movements of the ball rings. One of the lines P coincides with the z axis. The angle between two adjacent planes P, hereinafter called the centre angle, is designated β and depends upon the number n of balls:

β - (i)

If the balls in one ring are shifted towards the x axis, the balls in the other ring will move away from the x axis, as shown by broken lines. The projection of a line or an imaginary rod S between the centres of two balls touching each other on a line perpendicular to the bisector plane of the centre angle remains constant, as readily appears from the two congruent triangles resulting from the projection of the broken line S on the solid line S. As the balls must constantly touch each other, the direct distance, as represented by the length of the rod S, between the ball centres must constantly be equal to 2 R_k, where R_k is the radius of the balls.

If the two planes P in which the ball centres can move had been parallel with a distance of less than 2 R_k , the possibilities of motion for the ball centres while maintaining contact of tangency between the balls might be represented by two circles Cy of the same size, fig. 4, which are so disposed in their respective ones of the two planes as to form end faces of an imaginary cylinder Cy, whose axis is perpendicular to the planes and in which the imaginary rod S will extend between an arbitrary point on one circle and the diametrically opposite point on the other circle. The point of tangency of the balls will be the centroid of this cylinder.

In reality, however, the two planes in which two adjacent ball centres move are not parallel, but form the angle β with each other. In fig. 5 the imaginary cylinder Cy and rod S are plotted in three different positions between two planes P. The position shown by solid lines is the neutral position in which the two ball centres are equidistantly spaced from the x axis, and the position shown by broken lines is an extreme position in which the difference between the distances of the ball centres from the x axis are as great as possible. The position shown by broken lines is an intermediate position. Above the cylinder are shown the projections of the rod on the z axis in three positions. It will be seen that relative movements of the ball centres are reflected by axial movements of the cylinder Cy, and that the paths in which the ball centres can move in the planes P are the ellipses in which the cylinder face intersects the planes. One of these ellipses is shown at E in fig. 5 together with a circle Ci representing the cylinder, as seen from the end. Half the minor axis of the ellipse which is equal to the radius in the circle, is designated a and half its major axis is designated b.

In fig. 3 two adjacent balls A and B are hatched. Suppose a section is made through the centres of these balls in parallel with the xz plane, and the result will be a view like the one shown in fig. 6 where the two ball radii R_k disposed in elongation of each other represent the imaginary rod, which forms an angle α with a line which is parallel with the z axis and extends through the centre of the ball A and which represents an outer generatrix of the imaginary cylinder, as seen in the direction of the x axis. The end face of the cylinder is represented by a line of the length 2a which extends through the centre of the ball B and is parallel with the x axis. The angle α depends upon the "density" of the balls in the neutral position. It will be seen from figs. 5 and 6 that the axes of the ellipse can be expressed by

a = R_k ^. sin α (2) ^{3 =} (3)

In practice, the shifting of the balls is produced by axial shifting of one set of moulding rings with respect to the other set. This implies that the imaginary cylinder Cy is shifted in a direction perpendicular to its axis and in parallel with the gear axis x. Thus the ball centres perform a composite movement with a radial and an axial component along a resulting path which defines the cross-section of the rolling paths in planes containing the gear axis. Theoretically, an infinite number of curve shapes may be used; but only one curve shape satisfies the demand that for the achievement of the greatest possible variation of the force arms determined by the location of the points of tangency of the balls with the rolling paths, there must be symmetrical movement both radially and axially of these points of tangency. In view of the double-symmetrical movement of the points of tangency of the balls with the rolling paths, the relation between the oppositely directed radial shifting and common axial shifting of two ball centres must necessarily be so that the shifting paths of the ball centres are likewise symmetrical.

The required conditions of symmetry are met by the cycloid. A cycloid produced by rolling a circle having a radius a on a straight line is shown in fig. 7. The oppositely directed movements of the ball centres along the edges of the imaginary cylinder and their common axial shifting together with the cylinder can be depicted by two half cycloids in the bisector plane of the centre angle, as shown in fig. 8, where the axis parallel with the x axis and perpendicular to t cylinder axis is designated x'. In the range a

y

-a, where y is taken from the x' axis, the curves can be expressed by the equation x .

The ball centres can be fixed on these uniform curves symmetrical about the y axis by means of identical curves, which are symmetrical with the first ones with respect to the x' axis, by shifting one pair of curves in relation to the other pair along the x' axis, as shown by broken lines in fig. 9. These double-symmetrical curves establish the geometrical basis for the rolling path profiles. However, the curves are plotted on a plane forming an angle of half the centre angle β with the planes P in which the ball centres can move. The curves must therefore be projected on one of these planes for them to form a basis for the desired profiles. The y co-ordinates of the curves must therefore be divided by the cosine to half the centre angl resulting in the view shown in fig. 10. In the range c

y

-c, where c is the selected value of the maximum shifting in a radial direction, i.e. in the direction of the y axis, the curves can now be expressed by

x =

As will appear from the following, the gearing range of the transmission mechanism is determined by the maximum difference obtainable between the radii from the gear axis to the points of tangency between the balls and the rolling paths and the radii from the individual axes of rotation of the balls to the same points of tangency as well as between the radii from the latter axes to the mutual point of tangency of the balls, by shifting of the balls of the ball rings. As the maximum differences in radii are determined not only by the number of balls, the angle α and the value of c, but also by the travel radius r of the fundamental cycloid, the radius r may be used in the adaption of the gearing range, as desired. The travel radius of the cycloid is defined by

r =

where m is the y value corresponding to x' = -c, so the generalized formula of e ifting curve of the ball centres in the range c

y -c will be:

x =

Fig. 11 shows an example of a travel radius r smaller than the radius a of the imaginary cylinder.

The curve shapes found here lead to rolling path profiles which are rather difficult to manufacture; but the curve segments which are needed as a basis for the profiles are very approximate to circular arcs which lead to profiles that lend themselves to manufacture. It can be calculated that the maximum deviation is an order less than the inaccuracy which is usually incident to the balls. To this should be added that the effects of the curve inaccuracies on two touching balls virtually neutralize each other because of the curve symmetry.

Fig. 12 shows a view corresponding to fig. 10, where the ball centre paths are circular arcs Ci₁ and Ci₂ with radius R and with their respective centres C₁ and C₂ at the same distance y_c from the minor axis or the x' axis and at the same distance x_c from and at their respective sides of the y axis, which coincides with the major axis in the solid ellipse E representing the imaginary cylinder in its neutral position. Moreover, the simplification has been made in fig. 11 that the broken ellipse representing an extreme position of the imaginary cylinder intersects the y axis at the points y = + c. In the neutral position the projection on the x' axis of the imaginary rod S forms the minor axis of the ellipse. The projection of the rod on the x' axis in the extreme position of the cylinder is designated d.

If the shifting takes place to the left instead of to the right in fig. 12, the ball centres will follow extensions of the circular arcs, viz. in respect of the arc Ci₁ down to the line y = -c which it intersects on the y axis, and in respect of the arc Ci₂ up to the line y = c.

If the right ball centre, fig. 12, during shifting of the ellipse to the right, moves downwardly instead of upwardly as shown and in case of shifting to the left moves upwardly, two other arc-shaped paths Ci₃ and Ci₄ result, forming a mirror picture of the arcs Ci₁ and Ci₂, as shown in fig. 13. During relative movements one set of arcs is shifted in the direction of the x' axis with respect to the other. The ball centres will constantly lie in their respective intersections between the upper and the lower arc paths. It will be seen from fig. 13 that the maximum relative shifting of the set of arcs is equal to d. On the basis of the ellipse formula d can be expressed by the ellipse axes and the quantity c:

d =

The following three equations with the three unknown quantities R, x_c and y_c may be deduced from fig . 12.

R² = (y_c + c)² + ^χ _c ²

R² = y_c ² + (χ_c + a)²

R² = (y_c - c)² + (χ_c + d)²

Hence the coordinates of the ball centre C₁ and the radius of the circular arc Ci₁

x_c = ² - ² - d² (4)

. y_c = 4c (5)

When the rings are formed with a track radius

R_i = R + R_k (7)

as shown in fig. 14, shifting of the inner and outer moulding rings with respect to each other will produce the desired elliptical path movement of the ball centres and thus ensure that the contact of tangency between the balls and the rolling paths and between the balls is maintained.

In fig. 14 is marked the radius R_y of the gear bearing, as is the case with fig. 5, too. Half the length of the projection of the imaginary rod shown by a solid line in fig. 3 is R_k ^. cos α, and hence ^Ry ⁼ (8)

All dimensions of the transmission mechanism can be calculated from the foregoing equations.

Ball gear types

In the embodiment of the transmission mechanism of the invention shown in figs. 1 and 2 the moulding ring 14 is, as mentioned, fixed, while the input power is fed to the moulding rings 12 and 13 , and the output power is taken from the moulding ring 15. The use of four moulding rings. however, may be combined in many other ways to provide various transmissions and variation ranges. Some types may also be used as a differential. Figs. 16a and 16b are symbolic views of a plurality of different combinations with type designations, and fig. 15 shows the symbols used in these views. In fig. 15, 1, 2, 3 and 4 represent the four moulding rings, and in the type designations the figure before the hyphen represents the moulding ring or rings coupled to the input shaft, while the figure after the hyphen represents the moulding ring or rings coupled to the output shaft. The two types which have a slanted stroke in the type designation are differential structures, and the two figures separated by the slanted stroke represent the rings coupled to their respective output shafts.

Calculation of gear ratio

Fig. 17 shows a ball gear of type 14-3 in an extreme position corresponding to a shifting d of the moulding rings 1 and 4, or - with the designations used in figs. 1 and 2 - 12 and 13. In this position the radii A_c and B_c of the centre paths of the ball rings are A_c = R_y-c (9)

B_c = R_y+c (10)

A comparison between figs. 14 and 17 moreover shows that the radii in the circular paths in which the ball rings touch the rolling paths are

A_i = A_c - R_k ^. Y ( 11)

B_i = B_c - R_k ^. (12)

A_y = 2 R_y - B_i (13)

B_y = 2 R_y - A_i (14)

A general idea of the meaning of the designations now introduced can be obtained by consideration of the spatial view shown in fig. 18. This figure additionally comprises the new designations a_i and a for the perpendicular distances from the points of tangency of the ball A with the rolling paths to the axis of rotation O_A of the ball, and b_i and b_y for the corresponding distances for the ball B. Also introduced are the designations a_k and b_k for the perpendicular distances from the common point of tangency of the balls to their respective axes of rotation.

Fig. 19 illustrates the same as fig. 18, but differently, because instead of the two balls it shows the planes P in which the ball centres can move. In fig. 19 are marked the regulating length d of the ball gear and the distance x from the centre of the double ball ring to the point where the axes of rotation of the balls intersect the x axis. The two axes of rotation must necessarily intersect each other on the x axis, as there must be no slipping between the balls or between the balls and the rolling paths.

To calculate the gear ratio of a gear it is necessary to know all the quantities shown in fig. 19. The transmission possibilities of a gear can be determined on the basis of the conditions in the extreme positions between which it can be varied in stepless manner.

As mentioned before, the combinations shown in fig. 16 give various possibilities of transmission. For an arbitrarily selected combination it is possible to set up just as many equations as there are unknown radii on the basis of the geometrical conditions applying to the radii in the planes shown in fig. 19, and the gear ratio can thus be calculated. Here, there is selected the combination shown in fig. 17 with the two inner moulding rings 1 and 4, fig. 15, secured to the input shaft, one 2 of the outer moulding rings stationary and- the other outer moulding ring 3 secured to the output shaft. This combination has the type designation 14-3. Fig. 1 shows the same gear in a neutral position, which is neutral gear, it being readily apparent for reasons of symmetry that the outer moulding ring must stand still just like .the fixed moulding ring. It will be seen from fig. 20 that in operation the balls in the two rings always rotate oppositely each other irrespective of gear ratios. Both in figs. 17 and 19, the inner and the outer moulding rings are shifted the maximum distance d in one direction with respect to each other, corresponding to maximum transmission ratio.

On the basis of fig. 18 it is possible to set up a mutual dependence between some of the radii. Suppose the moulding ring 1 has rotated precisely one revolution, a point on the ball A will have moved the distance 2.π.A₁, which in turn means that it has rotated

times about its own axis of rotation. i_i

This rotation of the ball A has caused the point of tangency with the ball B to have moved the distance

As the moulding ring 4 is secured to the moulding ring 1, this ring will likewise have moved one revolution, and the same considerations can now be made in respect of the ball B. On the ball B the point of tangency with the ball A must have moved the distance

As the two distances must be of the same length, we have

(15)

As mentioned, selection of another combination of fixed and rotating rings will involve another dependence between the radii than (15).

The task is now to find a distance x, fig. 19, which satisfies this equation. A_i and B_i are known from the equations (11) and (12) and what remains is thus to find a_i, a_k, b_i and b_k . These quantities can be found by geometrical considerations of figs. 18 and 19. a_i can be calculated by consideration of the plane shown in fig. 21 and containing the x axis and the axis of rotation A of the ball A. On the basis of this figure, and with 1_A being the distance along the axis O_a betwen its intersection with the x axis and the centre of the ball A, we have

1_A A (16)

v = - c-_R i) - (₁ (17)

a_i = (18)

It will be seen that all that is needed for a₁ to be calculated is knowledge of x.

Similarly, a set of equations may be set up for the calculation of b_i on the basis of fig. 22, where the distance along the axis of rotation of the ball B from its intersection with the x axis to the centre of the ball is designated 1_B:

1_B = (19)

v = ^{- -} (20)

b_i = . (21)

b_i can now be calculated if x is known.

It will be seen from fig. 19 that the perpendicular distance S₁ from the x axis to the mutual point of tangency of the balls can be calculated from fig. 23:

S₁ ^{2 2 2 .} (22)

Then, the length T, as indicated in figs. 19 and 20, from the mutual point of tangency of the balls to the intersection of the axes O_A and O_B with the x axis can be calculated: T = (23)

Finally, the plane of fig. 25 is considered, containing the axes of rotation of the two balls. From this figure are obtained

a_k = T ^. sin ( (24)

b_k = T ^. sin (25)

A set of equations has now been formed which makes it possible to calculate x. These calculations are admittedly rather difficult, but can be made relatively easily by means of an electronic calculating machine.

When x has been found, the values of a_i, b_i, a_k and b_k can be found. What remains is then the calculation of A_y, a_y, B _y and b _y before all the radii of the gear are known. With x being now known, these calculations can be made from figs. 26 and 27:

v = 90 - sin^{- -} (26)

a_y = R_ksin(v) (27)

v = 90 - sin^{- -} (28)

b _y = R_k sin(v) (29)

As all radii in the extreme position of a selected combination are now known, it is possible to calculate the maximum gear ratio of the gear.

Suppose that the ball ring A, figs. 17 and 18, has moved precisely one revolution about the gear axis, the point of tangency with the moulding ring 2 will have moved the distance 2.π A _y, and the ball will thus have moved

= times about its own axis of rotation as

moulding ring 2 is fixed.

A similar consideration shows that the moulding ring 1 must have moved

- 1 times about its own axis of rotation, which is

the gear axis; here one revolution which the ball ring has moved in the opposite direction must be subtracted.

The ball row B must similarly have moved one revolution. It appears from fig. 18 that a ball in this ring must have moved

times about its own axis of rotation, and hence

moulding ring 3 must have moved

- 1 times about its own axis of rotation which is

the gear axis. Here too, one revolution which the ball ring B has moved in the opposite direction must be subtracted.

It is known how many revolutions the moulding rings 1 and 4 (the input shaft) and the moulding ring 3 (the output shaft) move when the ball rings rotate just once about the gear axis. When the number of revolutions of the output shaft is 1, the number of revolutions of the input shaft can be calculated as

Rewritten, the gear ratio of the gear can be expressed as

(30)

As appears from the position in which the gear bearing is shown in figs. 17 and 18, and likewise from the foregoing, this gear ratio corresponds to reverse gear and is therefore a negative figure. If the number of revol utions in the reverse gear is called -k, (30) may be written as

1 : -k (reverse) (31)

Upon regulation to the opposite extreme position of the gear (as shown in fig. 2), the gear ratio passes through neutral gear to forward gear. A similar calculation of the maximum gear ratio in this extreme position can now be made. Such a calculation will show that the maximum gear ratio for the forward gear will be k + 1, i.e. the gear ratio will be

1 : k + 1 (forward) (32)

To the forward gear ratio one revolution of the input shaft is to be added when the output shaft, in case of forward as well as reverse, is supposed to make one revolution, because the ball rings always rotate oppositely the rotary direction of the input shaft and thus gives the reverse gear the improved gearing range.

Generalization of the geometry of the transmission mechanism

On the basis of an analysis, which will not be repeated here, of the capacity of the transmission mechanism of transmitting power and torque it can be shown that the conditions mentioned in the foregoing do not allow optimum use of the permissible surface pressure between the balls when the quantities n, R_k , α and c are selected so as to provide a great gearing width. If optimum use of the permissible surface pressure between the balls and a great gearing width are to be obtained at the same time, the condition that the circular arc-shaped shifting paths of the ball centres intersect each other on the major axis of the imaginary ellipse, as shown in fig. 12, must be abandoned. The reason is that optimum use of the permissible surface pressure occurs at such a great value of the angle α that the balls in one ball ring touch each other in the marginal gearing position, as shown in figs. 28 and 29. However, if a great α value is selected and the shifting paths of the ball centres intersect each other on the major axis of the ellipse, the width of the gearing range will be limited because the inward shifting of the balls must not entail that their points of tangency with the rolling paths exceed the x' axis.

However, the condition relating to the intersection of the ball centre paths just represents a borderline case, where the distance between the major axis of the imaginary ellipse and one extremity of the shifting path of the ball centres is equal to zero. This distance, called m, may, however, be between zero and the distance marked x" in fig. 30. Thus, if a suitable value of the quantity m is allowed, optimum use of the surface pressure between the balls and great gearing width can be obtained at the same time.

In a sense it is possible to calculate a gear in which the present ball gear principle is fully utilized both in respect of forces and gearing width. However, this requires that the calculation procedure is changed on one point more. The addition of the margin m does not guarantee that the quantity c is selected so that the greatest gearing width occurs at optimum use of the surface pressure between the balls. To ensure this, the formulae must be amended so that the ball point of tangency with the moulding ring at the marginal gearing position lies in the intersection of the x' axis, as shown in fig. 31. This provides the greatest variation of the involved radii and thus the greatest gearing width.

However, these two improvements of the geometry are possible only in theory. In practice, it cannot be justified either that the balls in one and the same ball ring touch each other, or that the ball points of tangency with the moulding rings lie in the x' axis; but the closer this theoretical ideal can be approached in practice, the better. Both improvements are determined by the axial shifting of the balls, so the interblocking of the balls as well as the transgression of the actual extent of the rolling paths can be prevented by adding a security margin t on the axial shifting c, as shown in fig. 32.

In the event that a greater gearing width is desired than the one made possible by the above-mentioned amendments of the calculation procedure, a smaller value of the angle α than calculated is selected. But an increase in the gearing width obtained in this manner will be at the expense of the optimum use of the surface pressure between the balls.

Variants

The geometrical principle in the regulation of the ball gear can be applied in several different ways. Four such variants are schematically shown in figs. 33-36. However, these do not represent any improvement in relation to the arrangement of the rolling paths where they are symmetrical in pairs and have balls of the same size in both ball rings, but just changes in the characteristic relating to the regulation of the gear ratios.

The individual variants of the gear can, in addition to the use on the ten different types, be varied in a special manner, the aim of which is to shift the gearing range. Figs. 37 and 38 schematically show such a special arrangement of a gear type 14-3 in one and the other extreme position, respectively. As will be seen from the figures, neutral gear, like before, is obtained when the ball centres are disposed in the x' axis; but owing to the different circular arc-shaped cross-sections of the ring tracks neutral is here in one marginal gearing position. On the other hand, the regulation extends further to the other side so that an increase in the gearing width to that side corresponds to the restriction to the other. In other words, the gearing range can in this manner be shifted to one or the other side of the gear ratio scale. Thus, different ball gear types can be manufactured, each of which covers various sections of the gear ratio scale.

Claims

P a t e nt C l a i m s

1. A transmission mechanism containing two sets of balls which form co-axial rings and are so supported by a pair of inner and a pair of outer ring-shaped rolling paths co-axial with the ball rings that each ball in one ring touches two balls in the other ring, and vice versa, and that the ball rings can rotate about the common main axis upon relative rotation of the rolling paths, and each ball can additionally rotate about its own individual axis through its centre, the inner and outer rolling paths being axially shiftable with respect to each other within predetermined limits, c h a r a c t e r i z e d in that the axial distance between the inner as well as the outer rolling paths is constant.

2. A transmission mechanism according to claim 1, c h a r a c t e r i z e d in that the rolling paths have such concave-curved generatrices that, in all relative positions of the inner and outer rolling paths within said limits, the individual axes of rotation of the balls intersect the corresponding outer and inner rolling- paths or imaginary, inwardly extending extensions thereof at points within the points of tangency of the balls with the rolling path in question, and that the distances of each outer or inner point of tangency from the main axis and the individual axes of rotation vary oppositely upon relative shifting of the rolling path pairs, and that the ratio of these distances is always greater for the outer rolling paths than for the inner ones.

3. A transmission mechanism according to claim 2, c h a r a c t e r i z e d in that the rolling paths have substantially circular arc-shaped generatrices.

4. A transmission mechanism according to claim 2 or 3, in which the balls in the two sets are of the same size, c har a c t e r i z e d in that each pair of opposite rolling paths has symmetrical generatrices.

5. A transmission mechanism according to claim 4, char a c t e r i z e d in that the four rolling paths have double-symmetrical generatrices.