FIELD OF THE INVENTION

The invention relates to involute gear types and its potential uses. In more detail, the present invention relates to a multi ratio gear, an intermeshing set of gears including said multi ratio gear, a transmission including a set of multi-ratio gears and a main gear for said transmission.

BACKGROUND OF THE INVENTION

Transmissions are used in many mechanical devices to convert the available rotational speed and torque into the required one. Sometimes the required range is simply too large for a single ratio transmission to deliver and a transmission with more than one gear ratio is used.

Basically two types exist. Fully geared versions that are very efficient and can handle large torque, but which only have a very limited number of possible gear ratios so the engine will often be running at an inefficient speed. And CVT versions that are not fully geared, and which within a range have an infinite number of gear ratios so the engine can run at the most efficient speed, but which are themselves inefficient and most often can't handle large torque. So currently either the engine is most often not running at its most efficient speed or else the transmission itself is inefficient. Fully geared transmissions with a large number of possible gear ratios would presumably contain a large cascade of gears, which would naturally result in a cone like shape. And there are examples of such transmissions in the literature.

US9027427B2 shows a system in which a part of all the gears in the main gear are shifted one gear up or down so that an intermeshing gear can start in one gear, then shift to another gear together with the intermeshing gear, and then continue at the other gear. The underlying problem here is that the radius from the shifting gear part does not change so intermeshing is only possible with a lot of backlash. Another problem is that the whole main gear is on a moving platform sandwiched between two intermeshing gears in order to solve the problem of the distance between the axes changing. In all the system is quite complex and not suitable for high speed or huge torque. Also the number of possible gear ratios is not that big as the two intermeshing gears are not independent of each other. W02004059190 (Al) relies on the very brief moment in the rotational cycle, when the teeth in the stack of gears all line up, to enable a gear change. This means that gear changes can only be done at very low speed or during standstill. The type of gear used is not clear and intermeshing is likely to be a problem as each possible gear type has limitations and these do not appear to be to have been met for any of them. US6321613 (Bl) has similar problems to the previous one except here the pinion can move at any time and the gears in the main gear are spring loaded in order to move a bit. These will likely cause additional problems with a variable torque range. US5653143 (A) either uses spur gears cut into a conical shape or else conical involute gears (not clear from the text, tapered gears (conical involute gears are sometimes called tapered gears) are mentioned in the summery). If spur gears were meant then this would result in the contact surface being very small during part of a tooth's rotation. Elsewise if conical involute gears were meant then intermeshing them with a spur gear will result in a non-continuous rotational speed due to misalignment of the axes. Furthermore, a spring connected to the main gear is thought to solve the phase and sync problem, which does not seem realistic as the main gear will act very much as a flywheel. US3826152 (A) The fundamental problem here is that when the teeth of the intermeshing gear point away from its rotational axis, the teeth on the other intermeshing gear should also point away from its own rotational axis at the same angle. This condition is not met in this case. Furthermore, gear changes can only be done at the two points in the rotational cycle when all the gears line up, so gear changes can only be done at very low speed or during standstill. JP2000240738A, JP2009092080A will not have a continuous rotational speed. WO2011065926 (Al) uses flexible cogwheels instead of gears. DE3319178 (Al) shows a single figure with gear lines that out of sight (at the back) will cut into each other making it unviable. Summarising all the discussed solutions we can say that none of them are practical solutions and it is not surprising that to our knowledge none of them have gone into production. SUMMARY OF THE INVENTION

Against this background, the objective of the invention is to propose a type of fully geared transmission that is very efficient, can handle large torque and that has so many gear ratios that the engine can always run close to the most efficient speed.

A fundamental problem of changing gear in a geared transmission is that the intermeshing gears need to be in phase and in sync with each other. So changing gear by disengaging and then re engaging the intermeshing gears at random will cause problems. One object of the invention is to have a multi-ratio gear that cycles trough a fixed set of rotational speeds while it intermeshes with another gear that is rotating at a constant speed. So one could say that effectively the multi-ratio gear is within itself periodically changing gear without ever disengaging. This allows the multi-ratio gear(s) to act as an intermediary between the other gears in the transmission, providing that the switchovers are made in that part of the rotational cycle of the multi-ratio gear when the other gear is in phase and in sync with the multi-ratio gear. So the phase and sync problem encountered at the re-engaging part of changing gear, as described at the beginning of the paragraph, is avoided, as the gears are never disengaged to begin with.

This goal may be achieved by a multi-ratio gear according to claim 1, an intermeshing set of gears according to claim 7, a transmission according to claim 10 and a main gear according to claim 14. Embodiments may be found in the dependent claims, the following description and the accompanying drawings.

The present invention provides a multi-ratio gear comprising a rotational axis around which a plurality of circumferential gear sections from different circular involute gears are placed, whereby at least one is from a circular involute gear with a different amount of teeth as compared to the others. Each circumferential gear section therefore has its own amount of teeth per unit of rotation. So when the multi-ratio gear is intermeshing with another gear that is rotating at a constant speed, the multi-ratio gear will rotate at a plurality of different speeds. And the rotational speed at any given moment will depend on which one of its circumferential gear sections it is intermeshing with the other gear at that moment.

In one embodiment of the invention a multi-ratio gear may be provided, comprising a multi-ratio gear's rotational axis around which the multi-ratio gear rotates when intermeshing with another gear, and a plurality of circumferential gear sections that in regards to the teeth are arranged around the multi-ratio gear's rotational axis, wherein the shapes of the circumferential gear sections are in regards to the teeth substantially equivalent to the shapes of circumferential gear sections originating from a plurality of circular involute gears, and the shape of at least one individual circumferential gear section among the plurality of circumferential gear sections is in regards to the teeth substantially equivalent to the shape of a circumferential gear section originating from a circular involute gear with a different amount of teeth as compared to the other circumferential gear section(s).

Also in one embodiment the circumferential gear sections may functionally together make up 360 degrees around the multi-ratio gear's rotational axis.

Furthermore, in one embodiment the multi-ratio gear's rotational axis and all of the rotational axes of the circumferential gear sections may functionally be the same and/or may align with each other.

According to one embodiment, all the circumferential gear sections may contain a plurality of teeth.

Also in one embodiment the circumferential gear sections may be substantially equivalent in regards to the teeth to the shapes of circumferential gear sections that are defined within their respective originating circular involute gears by two straight lines both starting at the rotational axis and both in directions of substantially equal distance between opposing teeth. So basically the circumferential gear sections are cut/divided in such a way as to be in between opposing teeth. This is important, as an intermeshing gear going from one circumferential gear section to the next, must do so while in between teeth. Interference between gears is when two gears are intermeshing and a tooth of one gear cuts into the other gear. Normally gears rotate at a constant speed and this speed is just quickly enough for the gears to avoid the teeth of the other gear from cutting into them. All the circumferential gear sections of the multi ratio gear rotate at the same speed, but the ones originating from circular involute gears with fewer teeth require higher rotational speeds in order for them to move out of the way quickly enough to avoid interference. So with multi-ratio gears, just after the moment that the secondary gear has started to intermesh with a circumferential gear section that originated from a circular involute gear with more teeth than the former, there is a problem as the multi-ratio gear as a whole is now rotating too slowly for the former circumferential gear section that originated from a circular involute gear with fewer teeth, and interference will occur if nothing is done about it. Luckily the solution is simple and all that needs to be done is to enlarge the roots at the borders of the circumferential gear section that originated from a circular involute gear with fewer teeth.

So also in one embodiment individual roots belonging to an instance among the plurality of the circumferential gear sections may be enlarged if these roots are at a border with an instance among the plurality of the circumferential gear sections that originates from a circular involute gear with more teeth than the instance among the plurality of the circumferential gear sections respective to the root.

Gears cannot be well defined without also considering their function, as the prime variables defining a gear's shape are inter-depended on those of the gear with which it is intermeshing. So also in one embodiment an intermeshing set of gears, comprising the multi-ratio gear, a secondary gear being a circular involute gear, and a secondary gear's rotational axis around which the secondary gear rotates when intermeshing with another gear, wherein the multi-ratio gear and the secondary gear are intermeshing.

Also in one embodiment all the circumferential gear sections comprising the multi-ratio gear may substantially intermesh with the secondary gear without a substantial change in the distance between the multi-ratio gear's rotational axis and the secondary gear's rotational axis being required for an entire rotational cycle of the multi-ratio gear around the multi-ratio gear's rotational axis. In order for this to be possible the prime variables defining a gears shape need to be optimised for all the circumferential gear sections separately, as well as for the secondary gear (not excluding the possibility that some might be the same).

According to a further embodiment, the roots of the multi-ratio gear may be enlarged at the borders between the circumferential gear sections if interference with the secondary gear would otherwise occur at those borders. This deals with situations where the above mentioned optimisation cannot be done perfectly and a further enlargement of the roots at the border(s) is required.

We have now described the most important aspects of the multi ratio gear. A gear that continuously cycles between a plurality of rotational speeds while intermeshing with a secondary gear that is rotating a constant rotational speed. So this one gear provides a possible bases for a transmission where the phase and sync problem is no longer an issue. Of course other uses are also possible.

A further aspect of the present invention is directed to a transmission, comprising a set of the multi-ratio gear(s) functionally or otherwise formed from one or more part(s) moving as one within a cross section perpendicular to the multi-ratio gear's rotational axis. So for example, the multi-ratio gear might only be functionally formed during intermeshing with another gear. Meaning that it could for example be comprised of several parts from other gears that only together in cross- section function as a multi-ratio gear.

Also in one embodiment a set of circular involute gears may be functionally or otherwise formed from one or more part(s) moving as one within a cross section perpendicular to their rotational axis and we shall further refer to these circular involute gears as the "single-ratio gears", and a collection or a plurality of the secondary gear(s). So here we introduce the concept of the single-ratio gear. The single-ratio gear has a constant rotational speed while intermeshing with another gear that is rotating a constant rotational speed. So it is basically a normal gear and we only name it as the single-ratio gear in the context of multi-ratio gears. Like the multi-ratio gear, this single ratio gear might also be only functionally formed during the intermeshing with another gear.

Also in one embodiment a set of the collection or plurality of the secondary gear(s) may function as the input of the transmission and another set of the collection or plurality of the secondary gear(s) may function as the output of the transmission.

In a further embodiment the positioning of the set of the collection or plurality of the secondary gear(s) that functions as the input of the transmission may be substantially independent of the positioning of the set of the collection or plurality of the secondary gear(s) that functions as the output of the transmission.

Here we make use of the fact that a transmission with multi-ratio gears can be very efficient and that it can therefore be practically beneficial to create the equivalent of transmissions placed in series. So with the output of the one being the input of the other. Each independently setting it's own gear ratio. This set-up vastly increases the number of possible gear ratios for the system as a whole, creating a CVT like transmission.

In another aspect of the invention a main gear is provided, comprising a main gear's stack of conical gears comprising a stack of conical involute gears (defined in fig. 11-22), and a main gear's rotational axis around which the main gear rotates when intermeshing with other gear(s), wherein the rotational axes of all the conical gears in the main gear's stack of conical gears are substantially equal to the main gear's rotational axis, all the conical gears in the main gear's stack of conical gears have substantially the same conical gear's arrow direction (see the description explaining fig. 9), all the conical gears in the main gear's stack of conical gears have an even number of teeth, each next conical gear in the main gear's stack of conical gears has two more teeth than the latter, and the conical gears in the main gear's stack of conical gears partly extend into their neighbour's range along the main gear's rotational axis for a predetermined angular range, in particular about half a turn, around the main gear's rotational axis. Also in one embodiment the multi-ratio gear(s) may be functionally formed by the conical gears in the main gear's stack of conical gears in the cross-sections along the main gear's rotational axis in the range where they do indeed partly extend into their neighbour's range along the main gear's rotational axis for about half a turn around the main gear's rotational axis, and the single-ratio gear(s) may be functionally formed by the conical gears in the main gear's stack of conical gears in the cross-sections along the main gear's rotational axis in the range where they do not partly extend into their neighbour's range along the main gear's rotational axis for about half a turn around the main gear's rotational axis.

The two previous paragraphs together describe how a stack of conical involute gears can functionally comprise an alternating plurality of the single-ratio gears and the multi-ratio gears. All the conical involute gears in the stack have an even number of teeth and each next conical involute gear has two more teeth than the latter. They also all point in the same conical gear's arrow direction. The conical gears partly extend into their neighbour's range along the main gear's rotational axis for about half a turn around their common rotational axis. In this way the bottom 180 degree part of one conical gear in the stack combines with the top 180 degree part of the next conical gear in the stack, and thereby functionally forming the multi-ratio gear. The single ratio gears are functionally formed where the conical gears do not partly extend into their neighbour's range.

Also in one embodiment the collection or plurality of the secondary gear(s) may be conical involute gears, the collection of the secondary gear(s) comprises an input secondary gear with an input secondary gear's rotational axis around which the input secondary gear rotates when intermeshing with another gear, the input secondary gear's rotational axis is substantially parallel to the main gear's rotational axis, the input secondary gear's conical gear's arrow direction is substantially opposite to the conical gear's arrow direction of the conical gears in the main gear's stack of conical gears, the collection of the secondary gear(s) comprises an output secondary gear with an output secondary gear's rotational axis around which the output secondary gear rotates when intermeshing with another gear, the output secondary gear's rotational axis is substantially parallel to the main gear's rotational axis, and the output secondary gear's conical gear's arrow direction is substantially opposite to the conical gear's arrow direction of the conical gears in the main gear's stack of conical gears. So basically the input and output secondary gears are also conical involute gears, with their axes parallel to that of the main gear and with their conical gear's arrow direction in the opposite direction as compared to those in the stack of conical involute gears.

Also in one embodiment the input secondary gear may move over an input slider path and the input slider path enables the input secondary gear to reach along the input slider path the conical gears in the main gear's stack of conical gears and the input slider path also enables the input secondary gear to substantially intermesh with the conical gears in the main gear's stack of conical gears, and the output secondary gear may move over an output slider path and the output slider path enables the output secondary gear to reach along the output slider path the conical gears in the main gear's stack of conical gears and the output slider path also enables the output secondary gear to substantially intermesh with the conical gears in the main gear's stack of conical gears.

Also in one embodiment the input slider path may be substantially a straight or slightly curved line, and the output slider path may be substantially a straight or slightly curved line.

Here in the last two paragraphs we have described how the secondary gears can reach the gears in the stack of conical involute gears by moving over a straight or slightly curved line, which we have called a slider path. So named as the secondary gears can slide over the gears in the stack of conical involute gears along this path. The input and output secondary gears both have their own slider path.

Next we discuss the situations where a secondary gear is intermeshing with a single-ratio gear in the stack of conical gears while the transmission is not in the process of changing gear. These situations are important considerations for when designing a transmission.

Also in one embodiment the positions of the input secondary gear along the input slider path may be substantially equally spaced in regards to the instances where the input secondary gear intermeshes with one of the single-ratio gears in the main gear's stack of conical gears while the transmission is not in the process of changing gear, and the positions of the output secondary gear along the output slider path may be substantially equally spaced in regards to the instances where the output secondary gear intermeshes with one of the single-ratio gears in the main gear's stack of conical gears while the transmission is not in the process of changing gear.

Also in one embodiment a tangent angle (a general example of the tangent angle denoted as TA in fig. 10) may be substantially equal for a plurality of the single-ratio gears in the main gear's stack of conical gears in regards to the instances where the input secondary gear intermeshes with one of the single-ratio gears in the main gear's stack of conical gears while the transmission is not in the process of changing gear.

Also in one embodiment the tangent angle of the previous paragraph may be substantially equal to the inverse tangent of

0.5.

Also in one embodiment when the input secondary gear is intermeshing with one of the single-ratio gears in the main gear's stack of conical gear while the transmission is not in the process of changing gear then the distance between the input secondary gear's rotational axis and the main gear's rotational axis may be substantially equal to the sum of the radiuses of the reference circles of these two gears based on the pressure angle being the aforementioned tangent angle, and when the output secondary gear is intermeshing with one of the single-ratio gears in the main gear's stack of conical gears while the transmission is not in the process of changing gear then the distance between the output secondary gear's rotational axis and the main gear's rotational axis may be substantially equal to the sum of the radiuses of the reference circles of these two gears based on the pressure angle being the aforementioned tangent angle.

The novelty of this is based on its use in a transmission with multi-ratio gears. BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the present invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, in which:

Fig. 1 - General example representation of a two-dimensional cross-section of a circular involute donor gear with a plurality of identical tooth-root sections;

Fig. 2 - Close-up of fig. 1 showing a single instance from among the plurality of identical tooth-root sections, comprising one tooth and in-between two neighbouring lines that are equally spaced between opposing teeth;

Fig. 3 - The middle gear comprising a plurality of circumferential gear sections from two different circular involute donor gears, with at least one section from a gear with a different amount of teeth;

Fig. 4, 5 - The middle gear from fig. 3 here shown on the left, whereby its two circumferential gear sections both intermesh with a secondary gear at the same distance between the rotational axes of the two gears;

Fig. 6, 7 - An example embodiment of a multi-ratio gear formed from the gear on the left in fig. 4 by enlarging the roots on the border between the circumferential gear sections;

Fig. 8 - Example embodiment of a multi-ratio gear of the spur gear type;

Fig. 9 - Example embodiment of a multi-ratio gear of the conical involute gear type;

Fig. 10 - Introducing a general example of the tangent angle, the equivalent of the pressure angle in the new technology;

Fig. 11 - A triangle, the core of the conical involute gear;

Fig. 12 - Creating a second identical triangle; Fig. 13, 14 - Second triangle rolled into a cylinder and with the vertical line of the first triangle overlapping the cylinder;

Fig. 15 - Many copies of the first triangle: positioned alike the first triangle, but with the size of each copy adjusted to match the height of the cylinder at the copy's position around the cylinder;

Fig. 16, 17 - Many copies become infinite copies, creating the 3D involute shape that is the basis of involute gearing;

Fig. 18, 19, 20 - Most of the 3D involute shape removed, with the remaining outer surface becoming a tooth face;

Fig. 21 - The basic mathematical shape of a conical involute gear;

Fig. 22 - The end result, a conical involute gear;

Fig. 23 - Example embodiments of functional multi-ratio conical gears and example embodiments of functional single-ratio conical gears forming an example embodiment of a main gear;

Fig. 24 - An example embodiment of a stack of conical involute gears, with each gear having an even number of teeth, with each next gear having two more teeth than the later, and so cut as to functionally form the multi-ratio and single-ratio gears of the example embodiment of the main gear shown in fig. 23;

Fig. 25, 26 - An example embodiment of a transmission with the example embodiment of the main gear of fig. 23, 24 simultaneously intermeshing with an example embodiment of an input secondary gear and an example embodiment of an output secondary gear whereby both secondary gears can independently slide to any functional gear in the main gear without disengaging;

Fig. 27, 28, 29, 30, 31, 32 - An example sequence of changing gear ratio showing an example embodiment one of the secondary gears, intermeshing with the example embodiment of the main gear, sliding from one example embodiment of a single-ratio gear in the main gear to the next without disengaging; Fig. 33 - Orthographic schematic view focused on the example embodiment of the main gear intermeshing with the example embodiment of the input secondary gear and the example embodiment of the output secondary gear;

Fig. 34 - Orthographic schematic view focused on the example embodiments of conical gears in the example embodiment of the main gear;

Fig. 35 - Orthographic schematic view focused on the example embodiment of the functional multi-ratio gears and the example embodiment of the functional single-ratio gears in the example embodiment of the main gear; and

Fig. 36 - Orthographic schematic view focused on example embodiments of substantially equally spaced centre heights.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the present disclosure will now be explained with reference to the drawings. It will be apparent to those skilled in the field of gears and transmissions from this disclosure that the following description of the embodiments is provided for illustration only and not for the purpose of limiting the disclosure as defined by the appended claims. Features of the embodiments described below can also be used to further characterize the apparatus defined in the claims.

Modifications of features can be combined to form further embodiments. Features described in individual embodiments can be provided in a single embodiment if they are not incompatible. Likewise, features described in a single embodiment can be provided in several embodiments individually or in any suitable sub-combination. As used in the specification and the appended claims, the singular forms "a", "an", "the" and the like include plural referents unless the context clearly dictates otherwise.

The same reference numerals listed in different figures refer to identical, corresponding or functionally similar elements.

The inventor provides a new gear type that has a plurality, within one complete rotation, of different amounts of teeth per unit of rotation. Multiple versions and embodiments of this new gear type are possible. An example use of the new gear type is shown in an example embodiment of a transmission that is also based on conical involute gears. The present invention is described in enabling detail in the following examples, which may represent more than one embodiment of the present invention.

The invention is very much the product of the new technology we developed. So in order to explain the invention in all its detail we must also explain the new technology. This is why this section is more textbook like than one might otherwise expect from a patent application.

Fig. 1 - General example representation of a two-dimensional cross-section of a circular involute donor gear (DG fig. 1) with a plurality of identical tooth-root sections.

Here we see a general example representation of a two-dimensional cross-section of the circular involute donor gear (DG fig. 1). For this example the number of teeth, the exact shape, and even the type of the circular involute donor gear does not matter. We use this example to explain something about involute gears in general and to introduce the new terminology.

We see a circular involute donor gear's rotational axis (denoted as DR in fig. 2) indicated by the black circle in the middle around which the circular involute donor gear (DG fig. 1) rotates when it intermeshes with another gear. Each one of the dotted lines emanating from the circular involute donor gear's rotational axis (denoted as DR in fig. 2) in a direction of substantially equal distance between the two sides of the same tooth is an axial tooth line. And each one of the dotted lines emanating from the circular involute donor gear's rotational axis (denoted as DR in fig. 2) in a direction of substantially equal distance between opposing teeth is an axial root line. We also see a base circle (BC fig. 1,2) denoted by the dotted circle.

We also see a tooth-root section (TR fig. 1, 2), being a single instance from among the plurality of tooth-root sections that together make up the circular involute donor gear (DG fig. 1), which is located in-between two neighbouring axial root lines. The tooth-root section (TR fig. 1, 2) comprises one tooth and it rotates around the circular involute donor gear's rotational axis (denoted as DR in fig. 2) when it intermeshes with a gear. Fig. 2 - Close-up of fig. 1 showing the tooth-root section (TR fig. 1, 2), being a single instance from among the plurality of identical tooth-root sections that together make up the circular involute donor gear (denoted as DG in fig. 1), comprising one tooth and in-between two neighbouring lines that are equally spaced between opposing teeth.

Starting from the left we see the circular involute donor gear's rotational axis (DR fig. 2) around which the circular involute donor gear (denoted as DG in fig. 1) rotates when it intermeshes with another gear. The dotted line emanating horizontally from the circular involute donor gear's rotational axis (DR fig. 2) and going through the centre of the tooth is an axial tooth line (AT fig. 2). The outer borders of the tooth-root section (TR fig. 1, 2) are two neighbouring axial root lines, both emanating from the circular involute donor gear's rotational axis (DR fig. 2), from among the plurality of axial root lines. We see an axial root line 1 (AR1 fig. 2) at the top and we see an axial root line 2 (AR2 fig. 2) at the bottom. The dotted line on the right crossing the axial tooth line (AT fig. 2) vertically is the base circle (BC fig 1,2). On the base circle (BC fig 1,2) we see an involute starting point 1 (IP1 fig. 2) at the top and we see an involute starting point 2 (IP2 fig. 2) at the bottom. Involute starting points are the begin points of the involute curves, and these involute curves form the contact surfaces when a gear intermeshes with another gear. We see an involute curve (IC fig. 2). Note that it is actually the positions of the involute starting points that truly define a gear. So for example when we speak of the position of a tooth, we base this position on the involute starting points of that tooth. In general the section, of the base circle (BC fig 1,2) in-between the two involute starting points of the same tooth, in our example the involute starting point 1 (IP1 fig. 2) at the top and the involute starting point 2 (IP2 fig. 2) at the bottom, is known as a tooth section (TS fig. 2).

Now if we add-up the circumferences of all the tooth sections in a gear, and then divide this sum by the circumference of the base circle (BC fig 1,2) of that same gear, we get a fraction know as "the level of start angle shifting" of that gear. Also if we divide the circumference of a gear's base circle by the number of teeth in that gear we get the base circle modulus of that gear. This base circle modulus should always be the same between intermeshing gears.

When drawing gears it is best to start with half a root and then to draw the involute curve. So we need to know the angle between the axial root line 2 (AR2 fig. 2) and a line emanating from the circular involute donor gear's rotational axis (DR fig. 2) to the involute starting point 2 (IP2 fig. 2). We can calculate this angle from the level of start angle shifting. And fig. 2 shows a general example of such a start angle (SA fig. 2). Later we will present some formulas with which you can calculate start angles.

Note that the level of start angle shifting and the distance between the axes of intermeshing gears are interdependent. So one can vary the distance between the axes of intermeshing gears and then compensate by adapting the level of start angle shifting. This will prove very useful later on.

Most people skilled in the art of gearing will wonder why the term "profile shifting" wasn't mentioned just now, as that was clearly what was being described (as seen from within the context of the old terminology). This is because the terms "reference circle", "profile shifting and "pressure angle" are very confusing in the new technology, as they are interdependent of each other. Within the context of the old technology they make perfect sense, but it is unwise to use them within the context of new technology. Mathematically speaking, gears are based on the base circle and it is a good idea to keep that in mind. For this reason we also redefined the "modulus" of a gear to the "base circle modulus", as the "modulus" is based on the reference circle.

Fig. 3 - The middle gear comprising a plurality of circumferential gear sections from two different circular involute donor gears (shown on the left and right), with at least one section from a gear with a different amount of teeth.

Here to, like in fig.l and fig. 2, it is important to stress that we are discussing general example embodiments for the purpose of introducing the new terminology.

We see a circular involute donor gear with 10 teeth (DG10 fig. 3) on the left, and a circular involute donor gear with 12 teeth (DG12 fig. 3) on the right. The top part of the circular involute donor gear with 10 teeth (DG10 fig. 3) on the left (in solid line) is a circumferential gear section with 5 teeth (RS10 fig. 3-5). The bottom part of the circular involute donor gear with 12 teeth (DG12 fig. 3) on the left (in solid line) is a circumferential gear section with 6 teeth (RS12 fig. 3-5).

Notice that the solid top half of the gear on the left is comprised of exactly 5 tooth-root sections (5 teeth in 180 degrees => 1 section per 36 degrees), while the solid bottom half of the gear on the right is comprised of exactly 6 tooth-root sections (6 teeth in 180 degrees => 1 section per 30 degrees). Both these example embodiments of circumferential gear sections are 180 degrees around their rotational axes.

The middle gear from fig. 3 is comprised of these two circumferential gear sections placed on top of each other, so the circumferential gear section with 5 teeth (RS10 fig. 3-5) is placed at the top and the circumferential gear section with 6 teeth (RS12 fig. 3-5) is placed at the bottom, and with their rotational axes located at the same position.

We also see a base circle of the circumferential gear section with 5 teeth (BC10 fig. 3) and a base circle of the circumferential gear section with 6 teeth (BC12 fig. 3), and we notice that these two base circles have different radiuses.

Fig. 4, 5 - The middle gear from fig. 3 here shown on the left, whereby its two circumferential gear sections, being the circumferential gear section with 5 teeth (RS10 fig. 3-5) at the top and the circumferential gear section with 6 teeth (RS12 fig.

3-5) at the bottom, both intermesh with a secondary gear (EG fig.

4-7) at the same distance between the rotational axes of the two gears.

Fig. 5 shows a close-up of the intermeshing. As you can see both the top and bottom circumferential gear section, being the circumferential gear section with 5 teeth (RS10 fig. 3-5) at the top and the circumferential gear section with 6 teeth (RS12 fig. 3-5) at the bottom, of the middle gear from fig. 3 perfectly intermesh with the secondary gear (EG fig. 4-7). The levels of start angle shifting of both the circumferential gear sections , being the circumferential gear section with 5 teeth (RS10 fig. 3- 5) at the top and the circumferential gear section with 6 teeth (RS12 fig. 3-5) at the bottom, separately, as well as that of the secondary gear (EG fig. 4-7), were optimised to make this possible.

It is possible to use graphical software to draw the gear shapes and to then manually optimise all the different levels of start angle shifting. However, fig. 4 was actually created by using a few formulas that we will now present.

Note that the formulas use the "pressure angle" and the "centre pressure angle", the first term will be familiar to those skilled in the art, and the second term we invented. The term "pressure angle" can be highly confusing and we only need it for the formulas, so we avoid using it if possible. In 2-D the pressure angle is equal to a tangent angle (general example of a tangent angle denoted as TA in fig. 10), and in 3-D the centre pressure angle is the pressure angle at a gear's centre height and this centre pressure angle is also equal to the tangent angle (general example of a tangent angle denoted as TA in fig. 10). The term "active pressure angle" is sometimes used in the literature, but this doesn't solve the confusion.

Function StartAngle_calc(n, pa)

// This formula calculates the angle at which the involute curve starts (general example denoted as SA in fig. 2) on the base circle at the top of the 3D gear from the number of teeth and the

(active) pressure angle at the top of the gear.

Number of teeth = n

Pressure angle at the top = pa

Return = StartAngle = sa = (rί/2·h) + tan(pa) - pa

Function StartAngle_RefZero_calc(pAO, rT, rC)

// This formula calculates the angle at which the involute curve starts (general example denoted as SA in fig. 2) on the base circle at the top of the 3D gear from the radius at the top, the radius in the centre and the centre pressure angle.

Centre pressure angle = pAO

Radius in number of teeth at the top = rT

Radius in number of teeth at the centre = rC

Pressure angle 1 = pal = arccos(cos(pAO)·2·rC/(rC+rT)) Start angle 1 = sal = (pi/2rC) + tan(pal) - pal Start angle 2 = sa2 = (pi/2rC) + tan(paO) - paO Return = StartAngle RefZero = saO = 2·sal - sa2

Function MultiRatio_calc (rA, rX)

// This formula calculates a 2D multi-ratio gear.

Radius in number of teeth of the top half = rA

Radius in number of teeth of the secondary gear = rX

Radius in number of teeth of the bottom half = rB = rA + 2

Distance between the axes in number of teeth = d =

Sqrt(((Sqr(rA+rB)-(Sqr(rB)- Sqr(rA)))/ Sqr(rB)) + Sqr(rA+rX)) Pressure angle of the top half = pA = acos((rA + rX)/d)

Pressure angle of the bottom half = pB = acos((rB + rX)/d)

For calculating fig. 4 and fig. 5 use the previous functions with: n = number of teeth of the top half (of a whole gear) of the multi-ratio gear nX = number of teeth of the secondary gear For fig. 4 => n = nX = 10 d, pB = MultiRatio calc(n, nX)

Start angle of the top half = aA = StartAngle RefZero calc(pB, n, n + 2)

Start angle of the bottom half = aB = StartAngle calc(pB, n + 2) Start angle of the secondary gear = aX = StartAngle calc(pB, nX) Distance between the axes in number of teeth = d

Fig. 6, 7 - An example embodiment of a multi-ratio gear (RG fig.

6, 7) formed from the gear on the left in fig. 4 by enlarging the roots on the border between the circumferential gear sections.

Though both circumferential gear sections in fig. 4, 5, the circumferential gear section with 5 teeth (RS10 fig. 3-5) at the top and the circumferential gear section with 6 teeth (RS12 fig. 3-5) at the bottom, perfectly intermesh with the secondary gear (EG fig. 4-7). The gear comprising both segments as a whole does not intermesh over the full 360 degrees rotation. The problem is that at the borders between the two circumferential gear sections. At the point in the rotational cycle where the secondary gear (EG fig. 4-7) has just started to intermesh with the circumferential gear section with 6 teeth (RS12 fig. 3-5) that came from the circular involute donor gear with 12 teeth (denoted as DG12 in fig. 3). The intermeshing tooth of the secondary gear (EG fig. 4-7) cuts into the circumferential gear section with 5 teeth (RS10 fig. 3-5) of the gear that came from the circular involute donor gear with 10 teeth (denoted as DG10 in fig. 3). The cause of this is that at this point the rotational speed of the whole gear on the left is determined by the circumferential gear section with 6 teeth (RS12 fig. 3-5) that came from the circular involute donor gear with 12 teeth (denoted as DG12 in fig. 3). While the circumferential gear section with 5 teeth (RS10 fig. 3-5) requires the speed of the circular involute donor gear with 10 teeth (denoted as DG10 in fig. 3) in order to move out of the way quickly enough. So the circumferential gear section with 5 teeth (RS10 fig. 3-5) is simply not moving away quickly enough and a tooth of the secondary gear (EG fig. 4-7) cuts into it.

The solution is shown in fig. 6, with a close-up in fig. 7. These two figures are basically the same as fig. 4 and fig. 5 except that the roots in-between the teeth on the borderline have been enlarged, and more specifically in this example only the part of the root inside the circumferential gear section with less teeth per unit of rotation than the other was enlarged.

We see an example embodiment of such an enlarged multi-ratio gear root (RE fig. 7) in fig. 7. This prevents inter-cutting from taking place and the resulting gear can therefore intermesh with the secondary gear (EG fig. 4-7) for the full 360 degrees.

We call this type of gear, of which an example is shown in this embodiment (the multi-ratio gear (RG fig. 6, 7)), the multi-ratio gear type. And as you can see the two circumferential gear sections, being the circumferential gear section with 5 teeth (denoted as RS10 in fig. 3-5) at the top and the circumferential gear section with 6 teeth (denoted as RS12 in fig. 3-5) at the bottom, have different amounts of teeth per unit of rotation. This means that while the multi-ratio gear (RG fig. 6, 7) is intermeshing with the secondary gear (EG fig. 4-7) that is rotating at a constant speed, the multi-ratio gear (RG fig. 6, 7) will periodically switch between two different rotational speeds depending on which one of its two circumferential gear sections is at that moment intermeshing with the secondary gear (EG fig. 4-7). As stated before, the levels of start angle shifting of both circumferential gear sections separately, as well as that of the secondary gear (EG fig. 4-7), were optimised to make intermeshing possible.

In fig. 6 we also see a multi-ratio gear's rotational axis (RR fig. 6) and a secondary gear's rotational axis (ER fig. 6). The important thing to note here is that the distance between these two axes substantially remains constant during a full rotational cycle of the multi-ratio gear (RG fig. 6, 7). And this distance is therefore independent of whichever one of the two circumferential gear sections in this example embodiment is intermeshing with the secondary gear (EG fig. 4-7).

We have named the "multi-ratio" gear type the way we have is because, while it rotates, the resulting gear ratio continually switches between a plurality of gear ratios. So now we can also introduce a "single-ratio" gear type as a gear type where the resulting gear ratio remains constant. Though single-ratio gears are basically normal gears, the distinction is useful when discussing them in combination with multi-ratio gears.

There are many non-circular gears that have a varying rotational speed when intermeshing with another gear that is rotating at a constant speed, and it is even possible to create a pair of such gears where the distance between their axes remains constant. But these are not multi-ratio gears as the resulting output speed of the pair is still constant and nor do they switch instantly between a fixed set of ratios.

At this point it is good to remind ourselves that so far all this has been about two-dimensional cross-sections. But all gears in the real world are three-dimensional.

Fig. 8 - Example embodiment of a multi-ratio gear of the spur gear type (RGS fig. 8).

The spur gear version of the multi-ratio gear type is the same at every two-dimensional cross section perpendicular to its rotational axis. So in this case, at all two-dimensional cross- sections perpendicular to the multi-ratio gear's rotational axis, the levels of start angle shifting are not changing between the separate cross-sections. Fig. 9 - Example embodiment of a multi-ratio gear of the conical involute gear type (RGC fig. 9).

The conical involute gear version of the multi-ratio gear type is different at every two-dimensional cross section perpendicular to its rotational axis. So in this case, at all two-dimensional cross-sections perpendicular to the multi-ratio gear's rotational axis, the levels of start angle shifting are changing between the separate cross-sections. Another significant difference with spur gears is that although the involute curve still starts at the base circle, the roots can actually move outside of the base circle. We can see in fig. 9 that conical gears are like arrows pointing in a direction. In general we call this direction towards where a conical gear's conical shape ever more becomes a point, a "conical gear's arrow direction". And we can also see in fig. 9 that the conical gear's arrow directions of both intermeshing example gears are pointing in opposite directions as compared to each other. And we can also see that the rotational axes of both gears are parallel to each other.

Fig. 10 - Introducing a general example of the tangent angle (general example of a tangent angle denoted as TA in fig. 10), the equivalent of the pressure angle in the new technology.

We see an example embodiment of two conical involute gears (dotted lines) that are intermeshing. We will call the conical involute gear on the left a reference single-ratio gear (SGX fig. 10) and the conical involute gear on the right a reference secondary gear (EGY fig. 10). The solid lines are all in the same cross-section perpendicular to the rotational axes of both gears (the rotational axes are parallel to each other). The reference single-ratio gear (SGX fig. 10) has a reference single-ratio gear's base circle (BCX fig. 10) and a reference single-ratio gear's rotational axis (SRX fig. 10). The reference secondary gear (EGY fig. 10) has a reference secondary gear's base circle (BCY fig. 10) and a reference secondary gear's rotational axis (ERY fig. 10). We name a "line between the axes" (LA fig. 10) as a line between the reference single-ratio gear's rotational axis (SRX fig. 10) and the reference secondary gear's rotational axis (ERY fig. 10). We name a "diagonal tangent line" (DL fig. 10) as a tangent line shared by both the reference single-ratio gear's base circle (BCX fig. 10) and by the reference secondary gear's base circle (BCY fig. 10) and which also cuts trough the line between the axes (LA fig. 10) at a point in-between the reference single-ratio gear's rotational axis (SRX fig. 10) and the reference secondary gear's rotational axis (ERY fig. 10). We name a "perpendicular to the diagonal" (PL fig. 10) as a line that is perpendicular to the diagonal tangent line (DL fig. 10) and that also cuts trough the reference single-ratio gear's rotational axis (SRX fig. 10). We name the "tangent angle" (general example of a tangent angle denoted as TA in fig. 10) in this general example as the angle between the line between the axes (LA fig. 10) and the perpendicular to the diagonal (PL fig. 10).

For those familiar with the term "pressure angle" from the literature, and who are wondering in which way the pressure angle and tangent angle are different. The main reason we use the tangent angle is that it is very dangerous to mix up two- dimensional (the pressure angle) and three-dimensional terminology (the tangent angle). For example, the tangent angle is independent of the cross-section, while if we were to use the pressure angle when calculating the two-dimensional gear shape in all the different cross-sections it would require a different pressure angle (called active pressure angles in this case) for each cross-section. Simply put, it is about awareness. When working in 3D the pressure angle can quickly lead to complications that can easily be avoided by using the tangent angle instead, and if at some point the pressure angle is required then it more likely to be used in the correct way.

At this point the basics of the multi-ratio gear should be familiar to you. But you might wonder about what possible uses it might have. So imagine for example a multi-ratio gear sandwiched in-between two single-ratio gears. Then an intermeshing secondary gear could intermesh with one of the single-ratio gears and be fixed in that gear ratio. And then, while that single-ratio gear was in line with its identical part in the multi-ratio gear, the intermeshing secondary gear could slide over to the multi-ratio gear. And after the multi-ratio gear had then rotated enough for the other circumferential gear section to be intermeshing with the secondary gear, the same could happen in reverse and the intermeshing secondary gear could slide onto the other single ratio gear. Basically switching gear without ever disengaging. And thereby avoiding some of the fundamental problems normally associated with changing gear in fully geared multi-ratio transmissions. This is but one of the many of the possible uses of this new gear type.

Many different embodiments of transmission set-ups with cascading multi-ratio gears are possible, functionally formed in cross- sections and/or otherwise. For example, sets of connected secondary gears would only require at least one secondary gear not idling during operation for it to work. Also, one could have one set of secondary gears to function as the input of the transmission and another set for the output. This type of set-up creates a large number of available gear ratios due to the number of combinations of the independent positions that the input and the output secondary gears can take. It is impossible to discuss al possible embodiments in this application, so we will now discuss an example of our preferred embodiment. It has many of the elements we just discussed plus a few more.

Our preferred embodiment is based on the conical involute gear type, also know as the beveloid or tapered gear type. And here we immediately run into a problem. For this type of gear is not clearly defined in the literature. There is quite a bit of confusion about its exact nature. So in order to avoid having to write a dissertation on the subject, we will just present our definition based on a new mathematical shape that we named a 3D involute. Understanding this shape makes understanding involute gearing in general a lot easier. We will now go trough a step by step set of figures (fig. 11-22) that shows the creation of the 3D involute shape as well as how it relates to the conical involute gear type.

Fig. 11 - A triangle, the core of the conical involute gear. The triangle's horizontal line and the triangle's vertical line are at right angles to each other. For general use we name the diagonal line a "triangle's diagonal line" (TD fig. 11). Obvious, but important to state as some definitions of conical gears in the literature implicitly assume non-straight lines, the triangle's diagonal line (TD fig. 11) is a straight line. When conical involute gears intermesh with each other, with their axes parallel and their conical gear's arrow directions pointing in opposite directions, it are their triangle's diagonal lines that are the contact surfaces. With one single instance of the triangle's diagonal lines of each conical involute gear perfectly lining up against the other. Fig. 12 - Creating a second identical triangle. Here we see a further development of fig. 11 with a second triangle, identical to the first, and with the vertical lines of both triangles overlapping.

Fig. 13, 14 - Second triangle rolled into a cylinder and with the vertical line of the first triangle overlapping the cylinder. Fig. 13 shows a further development of fig. 12 whereby the second triangle has been rolled into a cylinder. This will later become the basis of the base circle. The vertical line of the first triangle overlaps this cylinder and the first triangle is within a tangent plane of the cylinder. Fig. 14 shows fig. 13 from another viewpoint point.

Fig. 15 - Many copies of the first triangle: positioned alike the first triangle, but with the size of each copy adjusted to match the height of the cylinder at the copy's position around the cylinder. Fig. 15 shows a further development of fig. 13. Many copies of the first triangle have been placed alongside the cylinder that was formed out of the second triangle. Each of these new triangles is also individually within a tangent plane of the cylinder. They only differ with the first triangle in that the their size is such that the their vertical line's height is equal the height of the cylinder at the point where they are just touching.

Fig. 16, 17 - Many copies become infinite copies, creating the 3D involute shape that is the basis of involute gearing. Fig. 16 shows a further development of fig. 15. The number of triangles is now infinite (we kept the diagonal lines of the last picture shining trough to better illustrate the shape). We call this shape the 3D involute. It is the underlying structure of all involute gears, both 2D and 3D. Every cross-section along the axis of the cylinder shows a two-dimensional involute curve emanating from a base circle. As you can see, understanding the involute curve is a lot easier in three dimensions than it is in two. Basically the 3D involute shape is nothing more than a straight line spiralling around and going up a cylinder at a constant speed. Fig. 17 shows fig. 16 from above and it should be no surprise that we see an involute curve emanating from a circle. Also note how all the copies of the first triangle's diagonal line are projected as tangents to this circle, while also being at right angles with the involute curve.

Fig. 18, 19, 20 - Most of the 3D involute shape removed, with the remaining outer surface becoming a tooth face. Fig. 18 shows a further development of fig. 16. Most of the 3D involute shape has been cut away (the dotted lines showing where it was) with only a small piece remaining. The remaining outer surface of the 3D involute will become a tooth face. Fig. 19 is a close-up of fig. 18 and fig. 20 shows fig. 19 from another viewpoint.

Fig. 21 - The basic mathematical shape of a conical involute gear. Fig. 21 shows a further development of fig. 18. Here what remained of the 3D involute shape has been mirrored onto itself and the result copied six times around the base circle. Here we see the basic mathematical shape of a conical involute gear with six teeth.

Fig. 22 - The end result, a conical involute gear (CG fig. 22). Fig. 22 shows a further development of fig. 21. Here the basic mathematical shape of the conical involute gear with six teeth has been changed into an actual example embodiment of the conical involute gear (CG fig. 22) in ways familiar to some one skilled in the art. Note that the tips were cut off along the line of the triangle's diagonal line at that position. This does not always need to be the case, as you will see later.

We have now defined the conical involute gear type, also know as the beveloid or tapered gear type, and we will mostly refer to it as a conical gear. It is this definition of a conical gear that is relevant to this application.

Fig. 23 - Example embodiments of functional multi-ratio conical gears and example embodiments of functional single-ratio conical gears forming an example embodiment of a main gear (MG fig. 23- 26, 33).

We see a cascading set of functional conical gears, that together form an example embodiment of the main gear (MG fig. 23-26, 33), whereby each next gear has one more tooth than the previous gear. Belonging to the main gear (MG fig. 23-26, 33) is a main gear's rotational axis (denoted as MR in fig. 33) around which the main gear rotates when intermeshing with other gears. All the gears that comprise the main gear (MG fig. 23-26, 33) have a rotational axis that is functionally equal to the main gear's rotational axis (denoted as MR in fig. 33). The gears with an even number of teeth are example embodiments of functional single-ratio conical gears, while the ones with an odd number of teeth are example embodiments of functional multi-ratio conical gears. Note that we show and define these gears in fig. 23 based on how they function in cross-sections along the main gear's rotational axis (denoted as MR in fig. 33) when intermeshing with another gear.

In fig. 23 we also indicate the location of some of the enlarged multi-ratio gear roots. And on the left we see two views of the main gear (MG fig. 23-26, 33), top left being a side view and bottom left being a top down view. On the right we see nine gears defined by how they function when the main gear (MG fig. 23-26, 33) intermeshes with another gear. We see: a functional single ratio gear with 8 teeth (SG8 fig. 23, 35), a functional multi ratio gear with 9 teeth (RG9 fig. 23, 35), a functional single ratio gear with 10 teeth (SG10 fig. 23, 35), a functional multi ratio gear with 11 teeth (RG11 fig. 23, 35), a functional single ratio gear with 12 teeth (SG12 fig. 23, 35), a functional multi ratio gear with 13 teeth (RG13 fig. 23, 35), a functional single ratio gear with 14 teeth (SG14 fig. 23, 35), a functional multi ratio gear with 15 teeth (RG15 fig. 23, 35), a functional single ratio gear with 16 teeth (SG16 fig. 23, 35), an enlarged multi ratio gear root of the functional multi-ratio gear with 9 teeth (RE9 fig. 23-25), an enlarged multi-ratio gear root of the functional multi-ratio gear with 11 teeth (RE11 fig. 23-25), an enlarged multi-ratio gear root of the functional multi-ratio gear with 13 teeth (RE13 fig. 23-25), and an enlarged multi-ratio gear root of the functional multi-ratio gear with 15 teeth (RE15 fig. 23-25).

Fig. 24 - An example embodiment of a stack of conical involute gears, with each gear having an even number of teeth, with each next gear having two more teeth than the later, and so cut as to functionally form the multi-ratio and single-ratio gears of the example embodiment of the main gear (MG fig. 23-26, 33) shown in fig. 23.

Note that in other embodiments of the invention the main gear (MG fig. 23-26, 33) might contain more than just the stack of conical involute gears. However, in the example embodiment of the invention we are discussing here we treat the stack of conical involute gears and the main gear (MG fig. 23-26, 33) as the same thing.

We see comprising the main gear (MG fig. 23-26, 33): a conical gear with 8 teeth (CG8 fig. 24-26, 34), a conical gear with 10 teeth (CG10 fig. 24-26, 34), a conical gear with 12 teeth (CG12 fig. 24-26, 34), a conical gear with 14 teeth (CG14 fig. 24-26, 34) and a conical gear with 16 teeth (CG16 fig. 24-26, 34).

If you compare fig. 23 with fig. 24 the reason for referring to the gears in fig. 23 as functional gears becomes clear. Different parts of the conical gears of fig. 24 form the functional gears of fig. 23. So: the top part of the conical gear with 8 teeth (CG8 fig. 24-26, 34) forms the functional single-ratio gear with 8 teeth (denoted as SG8 in fig. 23, 35), the bottom 180 degree part of the conical gear with 8 teeth (CG8 fig. 24-26, 34) forms the circumferential gear section with 4 teeth of the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35), the top 180 degree part of the conical gear with 10 teeth (CG10 fig. 24-26, 34) forms the circumferential gear section with 5 teeth of the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35), the middle part of the conical gear with 10 teeth (CG10 fig. 24-26, 34) forms the functional single-ratio gear with 10 teeth (denoted as SG10 in fig. 23, 35), the bottom 180 degree part of the conical gear with 10 teeth (CG10 fig. 24- 26, 34) forms the circumferential gear section with 5 teeth of the functional multi-ratio gear with 11 teeth (denoted as RG11 in fig. 23, 35), the top 180 degree part of the conical gear with 12 teeth (CG12 fig. 24-26, 34) forms the circumferential gear section with 6 teeth of the functional multi-ratio gear with 11 teeth (denoted as RG11 in fig. 23, 35), the middle part of the conical gear with 12 teeth (CG12 fig. 24-26, 34) forms the functional single-ratio gear with 12 teeth (denoted as SG12 in fig. 23, 35), the bottom 180 degree part of the conical gear with 12 teeth (CG12 fig. 24-26, 34) forms the circumferential gear section with 6 teeth of the functional multi-ratio gear with 13 teeth (denoted as RG13 in fig. 23, 35), the top 180 degree part of the conical gear with 14 teeth (CG14 fig. 24-26, 34) forms the circumferential gear section with 7 teeth of the functional multi-ratio gear with 13 teeth (denoted as RG13 in fig. 23, 35), the middle part of the conical gear with 14 teeth (CG14 fig. 24- 26, 34) forms the functional single-ratio gear with 14 teeth (denoted as SG14 in fig. 23, 35), the bottom 180 degree part of the conical gear with 14 teeth (CG14 fig. 24-26, 34) forms the circumferential gear section with 7 teeth of the functional multi-ratio gear with 15 teeth (denoted as RG15 in fig. 23, 35), the top 180 degree part of the conical gear with 16 teeth (CG16 fig. 24-26, 34) forms the circumferential gear section with 8 teeth of the functional multi-ratio gear with 15 teeth (denoted as RG15 in fig. 23, 35) and the bottom part of the conical gear with 16 teeth (CG16 fig. 24-26, 34) forms the functional single ratio gear with 16 teeth (denoted as SG16 in fig. 23, 35).

Also in fig. 24, like in fig. 23, we see: the enlarged multi ratio gear root of the functional multi-ratio gear with 9 teeth (RE9 fig. 23-25), the enlarged multi-ratio gear root of the functional multi-ratio gear with 11 teeth (RE11 fig. 23-25), the enlarged multi-ratio gear root of the functional multi-ratio gear with 13 teeth (RE13 fig. 23-25) and the enlarged multi-ratio gear root of the functional multi-ratio gear with 15 teeth (RE15 fig. 23-25).

Fig. 25, 26 - An example embodiment of a transmission with the example embodiment of the main gear (MG fig. 23-26, 33) of fig. 23, 24 simultaneously intermeshing with an example embodiment of an input secondary gear (EGI fig. 25, 26, 33) and an example embodiment of an output secondary gear (EGO fig. 25, 26, 33) whereby both secondary gears can independently slide to any functional gear in the main gear (MG fig. 23-26, 33) without disengaging.

Fig. 25 and fig. 26 are basically the same except that the main gear (MG fig. 23-26, 33) has been rotated for about 90 degrees and except that the two secondary gears are in different positions. We see the main gear (MG fig. 23-26, 33) of fig. 23 and fig. 24 with two secondary gears added to the system in fig. 25 and fig. 26. Both secondary gears can slide independently of each other up and down the main gear. One secondary gear functions as the input of the transmission, we call this the input secondary gear (EGI fig. 25, 26, 33). While the other one functions as the output, we call this the output secondary gear (EGO fig. 25, 26, 33). In this way both the position of the input secondary gear (EGI fig. 25, 26, 33), as well as the position the output secondary gear (EGO fig. 25, 26, 33), contribute independently to the gear ratio of the system as a whole. This combination of two independent secondary gear positions results in a great number of possible gear ratios for the transmission as a whole. Functionally this example embodiment of a transmission based on multi-ratio gears is therefore very much like a geared CVT. The reference signs: CG8, CG10, CG12, CG14, CG16, MG, RE9, RE11, RE13 and RE15 refer to the same things as in fig. 24.

Fig. 27, 28, 29, 30, 31, 32 - An example sequence of changing gear ratio showing an example embodiment one of the secondary gears (in this example either denoted as EGI in fig. 25, 26, 33 or denoted as EGO in fig. 25, 26, 33), intermeshing with the example embodiment of the main gear (denoted as MG in fig. 23-26, 33), sliding from one example embodiment of a single-ratio gear in the main gear (denoted as MG in fig. 23-26, 33) to the next without disengaging. The example embodiment of a transmission shown is the same as that of fig. 25 and fig. 26. We see the main gear (denoted as MG in fig. 23-26, 33) on the left intermeshing with one of the secondary gears (in this example either denoted as EGI in fig. 25, 26, 33 or denoted as EGO in fig. 25, 26, 33) on the right. As seen from above the secondary gear is turning clockwise.

Fig. 27 shows the secondary gear (in this example either denoted as EGI in fig. 25, 26, 33 or denoted as EGO in fig. 25, 26, 33) on the right intermeshing with the functional single-ratio gear with 8 teeth (denoted as SG8 in fig. 23, 35) at the top of the main gear (denoted as MG in fig. 23-26, 33) on the left. At this position of the secondary gear (ignoring the other secondary gear for a moment) the transmission is either not changing gear, or else is preparing to change gear or else has just changed gear. The gear ratio of the transmission at this point resulting in part from the conical gear with 8 teeth (denoted as CG8 in fig. 24-26, 34), while another part resulting from the other secondary gear likewise intermeshing with a conical gear in the main gear (denoted as MG in fig. 23-26, 33).

Fig. 28 is the sequel to fig. 27 and we see that the secondary gear is in the process of sliding down the main gear (denoted as MG in fig. 23-26, 33) along the teeth of the conical gear with 8 teeth (denoted as CG8 in fig. 24-26, 34). The tops of these teeth are part of the functional single-ratio gear with 8 teeth (denoted as SG8 in fig. 23, 35) and the bottoms of these teeth are part of the circumferential gear section with 4 teeth of the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35). So at this point the secondary gear is intermeshing simultaneously with both the functional single-ratio gear with 8 teeth (denoted as SG8 in fig. 23, 35) as well as the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35). The gear ratio of the transmission at this point resulting in part from the conical gear with 8 teeth (denoted as CG8 in fig. 24-26, 34), while another part resulting from the other secondary gear likewise intermeshing with a conical gear in the main gear (denoted as MG in fig. 23-26, 33).

Fig. 29 is the sequel to fig. 28 and we see that the secondary gear has now slid down all the way to the point where it is no longer intermeshing with the functional single-ratio gear with 8 teeth (denoted as SG8 in fig. 23, 35). But it is still intermeshing with the circumferential gear section with 4 teeth of the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35). So it is also still intermeshing with the conical gear with 8 teeth (denoted as CG8 in fig. 24-26, 34). At this point the secondary gear is just before the border between the two circumferential gear sections of the functional multi ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35), one segment with 4 teeth and the other segment with 5 teeth. The gear ratio of the transmission at this point resulting in part from the conical gear with 8 teeth (denoted as CG8 in fig. 24-26, 34), while another part resulting from the other secondary gear likewise intermeshing with a conical gear in the main gear (denoted as MG in fig. 23-26, 33).

Fig. 30 is the sequel to fig. 29 and the secondary gear has moved over the border from the circumferential gear section with 4 teeth of the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35) to the circumferential gear section with 5 teeth of the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35). So it has stopped intermeshing with the conical gear with 8 teeth (denoted as CG8 in fig. 24-26, 34) of the main gear (denoted as MG in fig. 23-26, 33) and it is now intermeshing with the conical gear with 10 teeth (denoted as CG10 in fig. 24-26, 34) of the main gear (denoted as MG in fig. 23-26, 33). The secondary gear at this point is only intermeshing with the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35). The gear ratio of the transmission at this point resulting in part from the conical gear with 10 teeth (denoted as CG10 in fig. 24-26, 34), while another part resulting from the other secondary gear likewise intermeshing with a conical gear in the main gear (denoted as MG in fig. 23-26, 33).

Fig. 31 is the sequel to fig. 30 and we see that the secondary gear is in the process of sliding down the main gear (denoted as MG in fig. 23-26, 33) along the teeth of the conical gear with 10 teeth (denoted as CG10 in fig. 24-26, 34). The tops of these teeth are part of the circumferential gear section with 5 teeth of the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35) and the middle of these teeth are part of the functional single-ratio gear with 10 teeth (denoted as SG10 in fig. 23, 35). So at this point the secondary gear is intermeshing simultaneously with both the functional multi-ratio gear with 9 teeth (denoted as RG9 in fig. 23, 35) as well as the functional single-ratio gear with 10 teeth (denoted as SG10 in fig. 23, 35). The gear ratio of the transmission at this point resulting in part from the conical gear with 10 teeth (denoted as CG10 in fig. 24-26, 34), while another part resulting from the other secondary gear likewise intermeshing with a conical gear in the main gear (denoted as MG in fig. 23-26, 33).

Fig. 32 is the sequel to fig. 31 and it shows the secondary gear intermeshing with the functional single-ratio gear with 10 teeth (denoted as SG10 in fig. 23, 35) of the main gear (denoted as MG in fig. 23-26, 33). At this position of the secondary gear (ignoring the other secondary gear for a moment) the transmission is either not changing gear, or else is preparing to change gear or else has just changed gear. The gear ratio of the transmission at this point resulting in part from the conical gear with 10 teeth (denoted as CG10 in fig. 24-26, 34), while another part resulting from the other secondary gear likewise intermeshing with a conical gear in the main gear (denoted as MG in fig. 23- 26, 33). So fig. 32 is very much like fig. 27 and it can be the start of another likewise sequence of changing gear ratio.

As you have seen, the transmission has gone from a gear ratio resulting in part from the conical gear with 8 teeth (denoted as CG8 in fig. 24-26, 34), to a gear ratio resulting in part from the conical gear with 10 teeth (denoted as CG10 in fig. 24-26, 34). And this was achieved without disengaging the secondary gear. Of course this is only one example of changing gear of only one example embodiment within the context of the invention, but the principle is clear. By using multi-ratio gears as intermediates, gear changes are possible that do not require the secondary gears to disengage. Furthermore, by using separate input- and output- secondary gears that can independently take positions on the main gear, the combination of these positions results in a great number of possible gear ratios for the transmission as a whole. Other embodiments within the context of the invention are also possible. If, for example, the conical gears of the main gear are cut like a "T" on its side rather than the step-shape depicted, then gear changes could go directly from one functional multi-ratio gear to the next functional multi ratio gear (with a quick move trough the range of the functional single-ratio gear in-between). This would result in quicker gear changes but would also require a higher speed from the system that slides de secondary gears into position.

Fig. 33, 34, 35, 36 - Here we see four figures (fig. 33, 34, 35,

36) that all show the same basic situation. Namely an orthographic schematic view of the example embodiment of the transmission that is also shown in fig. 25 and fig. 26. Each of the four figures (fig. 33, 34, 35, 36) focusing on a different aspect.

Fig. 33 - Orthographic schematic view of the example embodiment of the transmission that is also shown in fig. 25 and fig. 26, focused on the example embodiment of the main gear (MG fig. 23- 26, 33) intermeshing with the example embodiment of the input secondary gear (EGI fig. 25, 26, 33) and the example embodiment of the output secondary gear (EGO fig. 25, 26, 33).

Here we see the main gear (MG fig. 23-26, 33) in the middle rotating around the main gear's rotational axis (MR fig. 33). The main gear (MG fig. 23-26, 33) is simultaneously intermeshing with the input secondary gear (EGI fig. 25, 26, 33) and the output secondary gear (EGO fig. 25, 26, 33). The input secondary gear (EGI fig. 25, 26, 33) rotates around an input secondary gear's rotational axis (ERI fig. 33) and this rotational axis is parallel to the main gear's rotational axis (MR fig. 33). The input secondary gear (EGI fig. 25, 26, 33) can slide along the main gear (MG fig. 23-26, 33) over an input slider path (SPI fig.

33). This slider path is either a straight line or else is slightly curved. The output secondary gear (EGO fig. 25, 26, 33) rotates around an output secondary gear's rotational axis (ERO fig. 33) and this rotational axis is parallel to the main gear's rotational axis (MR fig. 33). The output secondary gear (EGO fig. 25, 26, 33) can slide along the main gear (MG fig. 23-26, 33) over an output slider path (SPO fig. 33). This slider path is either a straight line or else is slightly curved.

Fig. 34 - Orthographic schematic view of the example embodiment of the transmission that is also shown in fig. 25 and fig. 26, focused on the example embodiments of conical gears in the example embodiment of the main gear (denoted as MG in fig. 23-26, 33).

Here we see how the conical gears that make up the main gear (denoted as MG in fig. 23-26, 33) relate to the other orthographic schematic views in fig. 33, 35 and 36 as well as many of the previous figures. Note the step like shape of the conical gears in fig. 34. As previously mentioned, other possible embodiments of this invention might instead have a "T" like shape on its side. This would allow for quicker gear changes. The reference signs: CG8, CG10, CG12, CG14 and CG16 refer to the same things as in fig. 24.

Fig. 35 - Orthographic schematic view of the example embodiment of the transmission that is also shown in fig. 25 and fig. 26, focused on the example embodiment of the functional multi-ratio gears and the example embodiment of the functional single-ratio gears in the example embodiment of the main gear (denoted as MG in fig. 23-26, 33).

Here we see how the conical gears of fig. 34 are so cut as to functionally form the multi-ratio and single-ratio gears of the main gear (denoted as MG in fig. 23-26, 33). The reference signs:

SG8, RG9, SG10, RG11, SG12, RG13, SG14, RG15 and SG16 refer to the same things as in fig. 23.

Fig. 36 - Orthographic schematic view of the example embodiment of the transmission that is also shown in fig. 25 and fig. 26, focused on example embodiments of substantially equally spaced centre heights.

An underlying assumption in most gearing formulas in the literature is that the pressure angle is the same for both intermeshing gears. While when going through the cross-sections of a conical gear along its rotational axis the pressure angle seems to be changing (old 2D terminology: actually it is the active pressure angle that is changing, but as seen from within the cross-section it would be impossible to know the difference). So conical gears are three-dimensional in nature, while gearing formulas are two-dimensional in nature. In our example embodiment the conical gears intermesh upside down as compared to each other. So the pressure angles of the two intermeshing gears change in opposite directions and they are therefore only equal at one single centre cross-section along the parallel rotational axes of the two intermeshing gears. Cross-sections are two- dimensional in nature and at this cross-section the pressure angles are the same for both intermeshing gears, therefore in this cross-section we can use the two-dimensional formulas. The general name we use for the plane of this cross-section is the "centre height".

In fig. 36 we see the centre heights of the conical gears (equal to the centre heights of the functional single-ratio gears within them) of the example embodiment of the main gear (denoted as MG in fig. 23-26, 33). And as you can see the centre heights are substantially equally spaced in the direction along the main gear's rotational axis (denoted as MR in fig. 33). And you can also see that, while the transmission is not in the process of changing gear, the secondary gears intermesh with their centre heights in line with the centre heights of the functional single ratio gears in the main gear with which they are intermeshing.

We see: an input secondary gear's centre height (ECI fig. 36) of the input secondary gear (denoted as EGI in fig. 25, 26, 33), an output secondary gear's centre height (ECO fig. 36) of the output secondary gear (denoted as EGO in fig. 25, 26, 33), a centre height of the functional single-ratio gear with 8 teeth (SC8 fig. 36), a centre height of the functional single-ratio gear with 10 teeth (SC10 fig. 36), a centre height of the functional single ratio gear with 12 teeth (SC12 fig. 36), a centre height of the functional single-ratio gear with 14 teeth (SC14 fig. 36), and a centre height of the functional single-ratio gear with 16 teeth (SCI6 fig. 36).

When calculating conical gears it is a good idea to scale everything down to the unit of the number of teeth. Basically this means that we base the shape of the conical gears on the 3D involute shape of fig. 16 with a cylinder radius of the number of teeth. This way a gear with one tooth more in this unit will also result in a base circle radius of one tooth more in this unit. And down one tooth in this unit in height should also be scaled to result in a base circle equivalent of one tooth more in this unit. We used a height of 3 teeth for the conical gears in our example embodiment of the main gear (denoted as MG in fig. 23-26, 33). And the height of our example embodiments of the secondary gears is slightly less than 1 tooth in height to compensate for the inevitable slight imperfections in the real world. Note that after calculating the transmission in this simplified scale, we re-scaled it to meet requirements.

When drawing conical gears we need to start at the top (up being towards where the conical gear's conical shape ever more becomes a point). And we also need to use the formulas at the centre heights, so not the top. Fortunately we have a formula (Function StartAngle RefZero calc as discussed at fig. 4, 5) wherein we can use the pressure angle at the centre height to calculate the start angle (general example denoted as SA in fig. 2) at the top. At the centre height we can use the tangent angle (general example of a tangent angle denoted as TA in fig. 10) as a substitute for the pressure angle. We also found that for our example embodiment the best pressure angle to use for all the gears in the transmission was the inverse tangent of 0.5.

So for our example embodiment we used the following variables for the function StartAngle RefZero calc: pAO = arctan(l/2) rT = Number of Teeth rC = 1.5 + Number of Teeth // the height of the gear is 3 teeth, so 1.5 is the centre

Next we need to consider the angle at which to cut the tips of the teeth. It doesn't need to be a straight line as in our example embodiment, and the tip cuts of the conical gears in the main gear and of those of the secondary gears all can be different. But for our example embodiment for all the conical gears we simply choose an angle of 45 degrees before re-scaling.

And finally we need to calculate the distance between the axes of the intermeshing gears (we use this at the centre height). Function Reference_Circle_Radius(n, pa)

// For calculating the intermeshing distance use the sum of both gear's teeth numbers as n

// This formula calculates the reference circle radius from the number of teeth and the pressure angle. Note: This formula assumes base circle radius = number of teeth

Number of teeth = n

Pressure angle = pa

Return = n / cos(pa)

So far we have shown an example embodiment of a transmission with a gear ratio from 1:1 to 1:4 in great detail. But many other variants of this example embodiment are also possible. For example, transmissions based on multi-ratio gears, but not on conical gears, are of course also possible. Or for example, cascading transmissions based on multi-ratio gears, where each next transmission in the driveline adds many more possible gear ratios, are also interesting variants. Also lets not forget that a transmission based on multi-ration gears does not have the phase and sync problem, so it can be used to set the phase and sync correctly of another type of transmission. And then there are many other uses of the multi-ratio gear, outside the realm of transmissions that are obvious but that we did not mention. For example, the instant ratio change of the multi-ratio gear type for example is something new that can be exploited in many ways.

It will be apparent to one with skill in the art of gearing that the invention may be provided using some or all of the mentioned features and components without departing from the spirit and scope of the present invention. It will also be apparent to the skilled artisan that the embodiments described above are specific examples of a single broader invention which may have greater scope than any of the singular descriptions taught. There may be many alterations made in the descriptions without departing from the spirit and scope of the present invention.

REFERENCE SIGNS

AR1 axial root line 1 (fig. 2)

AR2 axial root line 2 (fig. 2)

AT axial tooth line (fig. 2)

BC base circle (fig. 1,2) BC10 base circle of the RS10 (fig. 3)

BC12 base circle of the RS12 (fig. 3)

BCX reference single-ratio gear's base circle (fig. 10)

BCY reference secondary gear's base circle (fig. 10)

CG conical involute gear (fig. 22)

CG8 conical gear with 8 teeth (fig. 24-26, 34)

CG10 conical gear with 10 teeth (fig. 24-26, 34)

CG12 conical gear with 12 teeth (fig. 24-26, 34)

CG14 conical gear with 14 teeth (fig. 24-26, 34)

CG16 conical gear with 16 teeth (fig. 24-26, 34)

DG circular involute donor gear (fig. 1)

DG10 circular involute donor gear with 10 teeth (fig. 3)

DG12 circular involute donor gear with 12 teeth (fig. 3)

DL diagonal tangent line (fig. 10)

DR circular involute donor gear's rotational axis (fig. 2)

ECI input secondary gear's centre height (fig. 36)

ECO output secondary gear's centre height (fig. 36)

EG secondary gear (fig. 4-7)

EGI input secondary gear (fig. 25, 26, 33)

EGO output secondary gear (fig. 25, 26, 33)

EGY reference secondary gear (fig. 10)

ER secondary gear's rotational axis (fig. 6)

ERI input secondary gear's rotational axis (fig. 33)

ERO output secondary gear's rotational axis (fig. 33)

ERY reference secondary gear's rotational axis (fig. 10)

IC involute curve (fig. 2)

IP1 involute starting point 1 (fig. 2)

IP2 involute starting point 2 (fig. 2)

LA line between the axes (fig. 10)

MG main gear (fig. 23-26, 33)

MR main gear's rotational axis (fig. 33)

PL perpendicular to the diagonal (fig. 10)

RE enlarged multi-ratio gear root (fig. 7)

RE9 enlarged multi-ratio gear root of the RG9 (fig. 23-25)

RE11 enlarged multi-ratio gear root of the RG11 (fig. 23-25)

RE13 enlarged multi-ratio gear root of the RG13 (fig. 23-25)

RE15 enlarged multi-ratio gear root of the RG15 (fig. 23-25)

RG multi-ratio gear (fig. 6, 7)

RG9 functional multi-ratio gear with 9 teeth (fig. 23, 35)

RG11 functional multi-ratio gear with 11 teeth (fig. 23, 35)

RG13 functional multi-ratio gear with 13 teeth (fig. 23, 35)

RG15 functional multi-ratio gear with 15 teeth (fig. 23, 35)

RGC multi-ratio gear of the conical involute gear type (fig. 9) RGS multi-ratio gear of the spur gear type (fig. 8)

RR multi-ratio gear's rotational axis (fig. 6)

RS10 circumferential gear section with 5 teeth (fig. 3-5)

RS12 circumferential gear section with 6 teeth (fig. 3-5)

SA start angle (fig. 2)

SC8 centre height of the SG8 (fig. 36)

SC10 centre height of the SG10 (fig. 36)

SC12 centre height of the SG12 (fig. 36)

SC14 centre height of the SG14 (fig. 36)

SC16 centre height of the SG16 (fig. 36)

SG8 functional single-ratio gear with 8 teeth (fig. 23, 35) SG10 functional single-ratio gear with 10 teeth (fig. 23, 35)

SG12 functional single-ratio gear with 12 teeth (fig. 23, 35)

SG14 functional single-ratio gear with 14 teeth (fig. 23, 35)

SG16 functional single-ratio gear with 16 teeth (fig. 23, 35)

SGX reference single-ratio gear (fig. 10)

SPI input slider path (fig. 33)

SPO output slider path (fig. 33)

SRX reference single-ratio gear's rotational axis (fig. 10) TA tangent angle (fig. 10)

TD triangle's diagonal line (fig. 11)

TR tooth-root section (fig. 1, 2)

TS tooth section (fig. 2)