Patent Application
20090241875
1. Field of the Invention
The present inventions relate to internal combustion engines, and, more particularly, to apparatus and methods for phase shifting a driver gear and a driven gear connected by a timing belt.
2. Description of the Related Art
Various phase shift devices have been developed to alter the phase relationship between a driver gear such as a crankshaft gear and a driven gear such as a driven gear in mechanical communication by a timing belt in an internal combustion engine. Some phase shift devices may be mechanically complex. Other phase shift devices may vary the timing belt path length of the timing belt, which could limit the range over which the phase relationship may be altered, cause the device to bind, cause over-tensioning of the timing belt thereby causing the timing belt to fail, or otherwise function ineffectively. Accordingly, a need exists for improved apparatus and methods for regulating the phase relationship between a driver gear and a driven gear in communication by timing belt.
A phase shift apparatus and methods in accordance with the present inventions may resolve many of the needs and shortcomings discussed above and will provide additional improvements and advantages that may be recognized by those of ordinary skill in the art upon study of the present disclosure.
The phase shift apparatus in various aspects includes a movable base continuously positionable between at least a base first position and a base second position. The phase shift apparatus in various aspects includes a first idler which defines a first idler axis of rotation and is disposed about the movable base and adapted to engage a first timing belt segment of a timing belt. The phase shift apparatus includes a second idler, which defines a second idler axis of rotation and is disposed about the movable base a fixed idler center-to-center distance from the first idler, with the second idler adapted to engage a second timing belt segment of the timing belt, in various aspects. The phase shift apparatus may include a path traversed by the first idler axis of rotation and the second idler axis of rotation as the movable base is positioned between at least the base first position and the base second position; the path configured such that a first segment path length of the first timing belt segment changes continuously in substantial correspondence to continuous changes in a second segment path length of the second timing belt segment to maintain a substantially constant timing belt path length.
The methods, in various aspects, include defining a path and altering the phase relationship between a driver gear and a driven gear connected by a timing belt by traversing a first idler engaging the timing belt and a second idler engaging the timing belt continuously along the path between at least a first position and a second position thereby maintaining the timing belt at a substantially constant length.
Other features and advantages of the present inventions will become apparent from the following detailed description and from the claims.
The Figures are adapted to facilitate explanation of the present inventions. The extensions of the Figures with respect to number, position, relationship and dimensions of the parts to form the embodiment will be explained or will be within the skill of the art after the following description has been read and understood. Further, the dimensions and dimensional proportions to conform to specific force, weight, strength, flow and similar requirements will likewise be within the skill of the art after the following description has been read and understood.
Where used in the Figures, the same numerals designate the same or similar parts. Furthermore, when the terms “top,” “bottom,” “right,” “left,” “forward,” “rear,” “first,” “second,” “inside,” “outside,” and similar terms are used, the terms should be understood to reference only the structure shown in the drawings and utilized only to facilitate describing the illustrated embodiments.
A phase shift apparatus for use in an internal combustion engine is presented herein. The phase shift apparatus, in various aspects, is adapted to be continuously positionable between at least a first position and a second position in order to alter continuously the phase relationship between a driver gear and a driven gear connected by a timing belt. The phase shift apparatus includes a first idler and a second idler configured to engage the timing belt. As the phase shift apparatus is positioned between at least the first position and the second position, the first idler and the second idler are traversed in fixed relation to one another along a path wherein the path is configured to maintain a substantially constant timing belt path length of the timing belt.
Methods for positioning the first idler and the second idler in fixed relation to one another, describing the path, designing the phase shift apparatus, and calculating the resulting maximum phase shift between the driver gear and the driven gear are also presented herein.
The Figures generally illustrate various exemplary embodiments of the phase shift apparatus and methods. The particular exemplary embodiments illustrated in the Figures have been chosen for ease of explanation and understanding. These illustrated embodiments are not meant to limit the scope of coverage, but, instead, to assist in understanding the context of the language used in this specification and in the claims. Accordingly, variations of the phase shift apparatus and methods that differ from the illustrated embodiments may be encompassed by the appended claims.
With general reference to the Figures in the following, in various aspects, the internal combustion engine 400 includes a driver shaft 22 carrying a driver gear 20 and a driven shaft 32 carrying a driven gear 30. The driver shaft 22, in various aspects, may be a crankshaft, or other such shaft driven by pistons or other source of power, and the driven shaft 32, in various aspects, may be a camshaft, or other shaft as would be recognized by those of ordinary skill in the art upon study of this disclosure. The driver gear 20 and the driven gear 30 may be, for example, spur gears, sprockets, pulleys, toothed pulleys, or similar and combinations thereof, and the driver gear 20 and the driven gear 30 may be composed of steel, various metals and metal alloys and other materials, as would be recognized by those of ordinary skill in the art upon study of this disclosure.
The driver gear 20, in various aspects, bears a fixed rotational relationship with the driver shaft 22 upon which it is fixedly mounted, and, thus, the operation and position of the driver gear 20 may be directly related to, for example, piston position through the driver shaft 22. Likewise, in various aspects, the driven gear 30 bears a fixed rotational relationship with the driven shaft 22 upon which it is fixedly mounted, and, thus, the operation and position of the driven gear 30 may be directly related, for example, to valve position. The driven gear 30, in many aspects, is about twice the circumference of the driver gear 20.
The timing belt 40, in various aspects, connects the driver gear 20 and the driven gear 30 such that rotation of driver shaft 22 causes the simultaneous rotation of driven shaft 32. The timing belt 40 defines an internal periphery 46 and an external periphery 44, and, in various aspects, engages the driver gear 20 and the driven gear 30 with the internal periphery 46 as it passes about the driver gear 20 and the driven gear 30. The timing belt 40 may be a belt, a toothed belt with teeth disposed about the internal periphery 46, a chain, or otherwise configured to engage mechanically the driver gear 20 and the driven gear 30, as would be recognized by those of ordinary skill in the art upon study of this disclosure. In various aspects, the timing belt 40 may be composed of metal, rubber, various flexible synthetic materials, composite materials, and other materials and combinations of materials as would be recognized by those of ordinary skill in the art upon study of this disclosure.
In various aspects, the phase shift apparatus 10 includes the first idler 50, the second idler 60. The phase shift apparatus 10, in various aspects, is located intermediate of driver gear 20 and driven gear 30 at least partially within the internal periphery 46 of the timing belt 40 to allow the first idler 50 and the second idler 60 to engage mechanically the timing belt 40 along the internal periphery 46 in order to alter the phase relationship between the driver gear 20 and the driven gear 30. Accordingly, the first idler 50 and the second idler 60 may be sprocket gears, pulleys, toothed pulleys, or suchlike configured to engage mechanically the timing belt 40, and the first idler 50, the second idler 60, and may be made of metals or other materials or combinations of materials, as would be recognized by those of ordinary skill in the art upon study of this disclosure. The first idler 50 and the second idler 60 may be of similar geometry, i.e. same diameter, same number of teeth, and so forth in some aspects, while, in other aspects, the first idler 50 and the second idler 60 may have differing geometry.
The first idler 50, in various aspects, is rotatably secured about a first axle 52 to allow the first idler 50 to rotate as it engages the timing belt 40. The first idler 50 defines a first idler axis of rotation 142 about which the first idler 50 rotates, and, in various aspects, the first idler axis of rotation 142 corresponds to the centerline of the first axle 52. Similarly, in various aspects, the second idler 60 is rotatably secured about a second axle 62 to allow the second idler 60 to rotate as it engages the timing belt 40. The second idler 60 defines a second idler axis of rotation 144 about which the second idler 60 rotates, and, in various aspects, the second idler axis of rotation 144 corresponds to the centerline of the second axle 62.
The phase shift apparatus 10 maintains the first idler 50 and the second idler 60 in a substantially fixed geometric relationship with the first idler axis of rotation 142 set a substantially fixed idler center-to-center distance 132 apart from the second idler axis of rotation 144. As the phase shift apparatus 10 is positioned continuously between at least the first position 110 and the second position 120, the first idler 50 and the second idler 60 are traversed along path 100 in fixed geometric relation to one another to alter the phase relationship between the driver gear 20 and the driven gear 30. Accordingly, the first idler 50 and the second idler 60 are positioned in a unitary manner along the path 100 as the phase shift apparatus 10 is positioned between at least the first position 110 and the second position 120. In various aspects, the phase shift apparatus 10 may be positioned continuously between at least the first position 110 and the second position 120 so that the first idler 50 and the second idler 60 traverse the path 100 continuously and continuously alter the phase relationship between the driver gear 20 and the driven gear 30.
In some aspects, the phase shift apparatus 10 may be configured to cooperate with one or more positioning gears, actuator(s), armatures, or similar that may be provided to position the phase shift apparatus 10 and, hence, the first idler 50 and the second idler 60, as would be recognized by those of ordinary skill in the art upon study of this disclosure, in order to modulate the phase relationship between the driver gear 20 and the driven gear 30, and, hence, for example, between pistons and valves in response to various engine controls. For example, the phase relationship between pistons and valves may be modulated, in various aspects, in response to load on the engine, engine speed, fuel type, fuel-air mixture, and so forth. In some aspects, the phase relationship between the driver gear 20 and the driven gear 30 may be modulated as the thermodynamic cycle of the engine is altered between, for example, the Diesel cycle and the Otto cycle.
In various aspects, the phase shift apparatus 10 includes a movable base 70 with the first idler 50 and the second idler 60 secured thereto. In order to position the phase shift apparatus 10 between at least the first position 110 and the second position 120, the movable base 70 may be positioned between at least base first position 710 and a base second position 720. The first axle 52 and the second axle 62 are mounted fixedly to the movable base 70 so that the first idler 50 and the second idler 60 are oppositely disposed about the movable base 70 in various aspects. The first idler 50 and the second idler 60 remain in fixed geometric relation to one another as the movable base 70 is positioned continuously between at least the first base position 710 and the second base position 720 to traverse the first idler 50 and the second idler 60 along the path 100. In various aspects, the movable base 70 may be configured as a plate, bar, or suchlike with essentially unitary construction such that the first idler 50 and the second idler 60 are maintained in fixed relationship to one another. The movable base 70 may be made of metal such as steel or aluminum or other materials or combinations of materials, as would be recognized by those of ordinary skill in the art upon study of this disclosure.
The movable base 70, in various aspects, is movably secured about the engine block 410 or otherwise adapted to be continuously positionable between at least the first base position 710 and the second base position 720. Accordingly, the phase shift apparatus 10 is positioned between at least the first position 110 and the second position 120 by positioning the movable base 70 between at least the base first position 710 and the base second position 720, which traverses the first idler 50 and the second idler 60 along path 100.
In various aspects, portions of the movable base 70 are slidably retained within a slot 73 configured about the engine block 410. Posts 77 may be affixed to the engine block 410. The movable base 70 may be slid about posts 77 engaged within the slot 73 between at least the base first position 710 and the base second position 720 to position the phase shift apparatus 10 between at least the first position 110 and the second position 120. As the movable base 70 is slid between the base first position 710 and the base second position 720, the first idler 50 and the second idler 60 are traversed along path 100. In various aspects, the movable base 70 rotates about a movable base shaft 72, which is secured to the engine block 410, and the phase shift apparatus 10 may be positioned between at least the first position 110 and the second position 120 by rotation of the movable base 70 about the movable base shaft 72 between at least the base first position 710 and the base second position 720. Rotation of the movable base 70 between the base first position 710 and the base second position 720 traverses the first idler 50 and the second idler 60 along path 100. The movable base 70 may, in various other aspects, be configured and secured to the engine block 410 in other ways that would be recognized by those of ordinary skill in the art upon study of the present disclosure to traverse the first idler 50 and the second idler 60 continuously along the path 100 as the phase shift apparatus 10 is positioned continuously between at least the first position 110 and the second position 120.
In various aspects, the phase relationship between the driver gear 20 and the driven gear 30 is determined by the position of the movable base 70. For example, when the movable base 70 is positioned in the base first position 710 the distance between the first idler 50 and the driver gear 20 is decreased and the distance between second idler 60 and the driver gear 20 is increased. Accordingly, the phase relationship is shifted relatively, for example, to one in which driven gear 30 is advanced ahead of driver gear 20. In certain aspects, this alters the closing of the exhaust valves with respect to the position of the pistons. Similarly, when the movable base 70 is positioned in the base second position 720 to increase the distance between the first idler 50 and the driver gear 20 and to decrease the distance between second idler 60 and the driver gear 20, the phase relationship is shifted relatively, for example, to one in which driven gear 30 is retarded behind the driver gear 20. In certain aspects, this alters the closing of the exhaust valves with respect to the position of the pistons.
The first idler axis of rotation 142 and the second idler axis of rotation 144 traverse the path 100 as the phase shift apparatus 10 is positioned continuously between at least the first position 110 and the second position 120. In some aspects, the phase shift apparatus 10 may be positioned continuously between the first position 110 and the second position 120 through intermediate positions 115 bounded by the first position 110 and the second position 120 to traverse the first idler 50 and the second idler 60 continuously along the path 100. In some aspects, the path 100 may be an arc, but, in various aspects, the path 100 may have other non-linear (curved) shapes. The path 100 may be determined, and the phase shift apparatus 10 adapted to traverse the first idler axis of rotation 142 and the second idler axis of rotation 144 along the path 100.
In various aspects, the timing belt 40 defines a timing belt path length 45 which is the length of the path followed by the timing belt 40 as the timing belt 40 passes about the driver gear 20, the first idler 50, the driven gear 30, and the second idler 60. The timing belt 40 may be subdivided into a first timing belt segment 47 and a second timing belt segment 49. The first timing belt segment 47 is the portion of the timing belt 40 that passes generally from a driver gear medial point 29, which is generally the midpoint of the arc along which the timing belt 40 engages the driver gear 20, about the first idler 50, and thence to a driven gear medial point 39, which is generally the midpoint of the arc along which the timing belt 40 engages the driven gear 30 in various aspects. The first timing belt segment 47 defines a first segment path length 147, which is the length of the path followed by the first timing belt segment 47. The second timing belt segment 49 is the portion of the timing belt 40 that passes generally from the driven gear medial point 39, about the second idler 60, and thence to the driver gear medial point 29 in various aspects. The second timing belt segment 49 defines a second segment path length 149, which is the length of the path followed by the second timing belt segment 49. The sum of the first segment path length 147 and the second segment path length 149 would be equal to the timing belt path length 45 in various aspects. In various aspects, the timing belt path length 45, the first segment path length 147, and the second segment path length 149 may be defined as the pitch length along the belt pitch centerline or in other ways as would be recognized by those of ordinary skill in the art upon study of this disclosure.
In various aspects, the path 100 is defined such that the first segment length 147 of the first timing belt segment 47 changes in substantial correspondence to the second segment length 149 of the second timing belt segment 49 to maintain a substantially constant timing belt path length 45 of the timing belt 40 as phase shift apparatus 10 is positioned between at least the first position 110 and the second position 120. Because the timing belt length 45 is substantially constant as the phase shift apparatus 10 is positioned between at least the first position 110 and the second position 120, the timing belt 40 is not stretched substantially, and, accordingly, the tension in the timing belt 40 is not altered substantially. Although the interplay of the driver gear 20 and the driven gear 30 may induce changes in tension in the timing belt 40, the tension in the timing belt 40 may be said to be constant in that the phase shift apparatus 10 generally does not alter the tension in the timing belt 40 as the phase shift apparatus 10 is positioned between at least the first position 110 and the second position 120.
The timing belt path length 45 is substantially constant as the phase shift apparatus 10 is positioned continuously between at least the first position 110 and the second position 120 in various aspects. As the phase shift apparatus 10 is positioned at intermediate positions 115 between the first position 110 and the second position 120 in some aspects, the first idler 50 and the second idler 60 are traversed along path 100. In various aspects, the path 100 is adapted such that the first segment length 147 of the first timing belt segment 47 changes in substantial correspondence to the second segment length 149 of the second timing belt segment 49 as the first idler 50 and the second idler 60 engage the timing belt 40 to maintain a substantially constant timing belt path length 45 of the timing belt 40. Accordingly, the timing belt path length 45 of the timing belt 40 is substantially maintained throughout the range of intermediate positions 115 between the first position 110 and the second position 120, so that the phase relationship between the driver gear 20 and the driven gear 30 may be modulated continuously by the phase shift apparatus 10 over a range that may include varying amounts of positive and negative phase relationships.
Various illustrative implementations of the phase shift apparatus 10 and associated methods are illustrated in the Figures.
The driver gear 20 may define a driver gear axis 24 about which it rotates, and the driven gear 30 may define a driven gear axis 34 about which it rotates. In the embodiment of
An elevation line 158 may be defined to pass from the idler pivot point 134 and perpendicularly bisect the idler line 131 defined by the first idler axis of rotation 142 and the second idler axis of rotation 144 as illustrated in
The line 154 may pass through the driver gear 20 and the driven gear 30 to define a driver gear left hemisphere 27, a driver gear right hemisphere 28, a driven gear left hemisphere 37, a driven gear right hemisphere 38, as illustrated in
As illustrated in
The path 100 and other geometric characteristics of the phase shift apparatus 10 that include, in various embodiments, the idler center-to-center distance 132, the distance of the idler pivot point 134 from driven gear axis 34 on the line 154, the pivot radius 136, and the maximum off-symmetry angle 162, are chosen such that the increase in the first segment path length 147 of the first timing belt segment 47 substantially corresponds to the decrease in the second segment path length 149 of the second timing belt segment 49 and visa versa, as illustrated in
In
In
Methods, in various aspects, may include continuously altering the phase relationship between a driver gear 20 and a driven gear 30 by traversing the first idler 50 and the second idler 60 along the path 100, the first idler 50 and the second idler 60 engaging the timing belt 40, and changing linearly the first segment path length 147 of the first timing belt segment 47 in a continuous manner in substantial correspondence with linear change in the second segment path length 149 of the second timing belt segment 49 such that the timing belt path length 45 of the timing belt 40 remains substantially constant. The methods may include traversing the first idler 50 and the second idler 60 along path 100 by positioning the phase shift apparatus 10 between the first position 110 and the second position 120 and maintaining the first idler 50 in fixed geometric relation with the second idler 60. In various aspects, increasing the first segment path length 147 of the first timing belt segment 47 and correspondingly decreasing the second segment path length 149 of the second timing belt segment 49 in a continuous manner by traversing the first idler 50 and the second idler 60 continuously along path 100 may be included in the methods. In various aspects, decreasing the first segment path length 147 of the first timing belt segment 47 and correspondingly increasing the second segment path length 149 of the second timing belt segment 49 in a continuous manner by traversing the first idler 50 and the second idler 60 along path 100 may be included in the methods.
In various aspects, methods may be provided for defining the path 100. The methods may include adapting the phase shift apparatus 10 to traverse the first idler 50 and the second idler 60 along the path 100. The methods may include specifying the configurations of the timing belt 40, the driver gear 20, the driven gear 30, the first idler 50, and the second idler 60 and determining the idler center-to-center distance 132, the distance of the idler pivot point 134 from driven gear axis 34 on the line 154, the pivot radius 136, and the maximum off-symmetry angle 162. In some aspects, an optimization method may be used to determine the idler center-to-center distance 132, the distance of the idler pivot point 134 from driven gear axis 34 on the line 154, the pivot radius 136, and the maximum off-symmetry angle 162. The path 100 may be defined, at least in part, by arcing the pivot radius 136 about the pivot point 134.
A further understanding may be obtained by reference to certain specific examples, which are provided herein for the purpose of illustration only and are not intended to be limiting unless otherwise specified. Note that at least some of the values given in these examples are computationally derived, and may be rounded, truncated or otherwise refined to engineering tolerances in physical implementations, as would be readily recognized by those of ordinary skill in the art upon study of this disclosure.
In Example 1, the configuration of the timing belt 40 was specified as indicated in Table 1-1 and the driver gear 20, the driven gear 30, the first idler 50 and the second idler 60, and the driven gear axis to driver gear axis distance 166 were specified as indicated in Table 1-2. As indicated in Table 1-3, initial values that describe the geometry of the phase shift apparatus 10 were chosen, and these values were refined by iteration subject to the constraints given in Table 1-4. The geometric parameters include the idler center-to-center distance 132, distance of the idler pivot point from driver gear axis 168, the pivot radius 136, and the maximum off-symmetry angle 162. The distance of the idler pivot point from the driver gear axis 168 and the distance of idler pivot point from driven gear axis 169 are illustrated in
An exemplary Microsoft Excel® spreadsheet for calculation of the design optimization parameters, which may include the idler center-to-center distance 132, the distance of the idler pivot point 134 from driven gear axis 34, the distance between idler pivot point 134 and idler axes 142,144, and the maximum off-symmetry angle 162, and the resulting maximum phase shift between the driver gear 20 and the driven gear 30 is given in Table A-1, Table A-2, and Table A-3 in the Appendix Table A-1 illustrates the spreadsheet, and the corresponding formulae for the various cells within the spreadsheet are given in Table A-2. The design optimization parameters in Table 1-3, which include the idler center-to-center distance 132, the distance of the idler pivot point 134 from driven gear axis 34, the distance between idler pivot point 134 and idler axis, and the maximum off-symmetry angle 162, were entered into cells B19, B20, B21, and B22, respectively. [See Table A-1—note that the values in Table A-1 are the initial non-optimized values] The solution was found by non-linear optimization of the idler center-to-center distance 132, the distance of the idler pivot point 134 from driven gear axis 34, the distance between idler pivot point 134 and idler axes 142, 144, and the maximum off-symmetry angle 162 subject to the constraints given in Table A-3. A non-linear optimization technique was used to compute the optimized values. This optimization technique employed a conjugate gradient method using centered difference approximations to the derivatives and quadratic estimates. Because of the non-linear nature of the problem, other solutions may exist that satisfy the constraints. As will be readily recognized by those of ordinary skill in the art upon study of this disclosure, other methods of solution may be utilized, and the methods of solution may be implemented using other computational means including symbolic algebra programs, computer codes such as C and FORTRAN, and various other spreadsheets.
Some results of the computation are presented in Table 1-5, Table 1-6, and Table 1-7. Table 1-5, lists the optimal idler center-to-center distance 132, the distance of the idler pivot point 134 above the driver gear axis 24 along line 154, the distance between the idler axis and the idler pivot point 134, and the maximum off-symmetry angle 162, the pivot point angle 164, and the distance of the idler pivot point 134 from the driven gear axis 34.
The path 100 is described in Table 1-6 which lists the x-y coordinates of the loci of the first idler axis of rotation 142 and the second idler axis of rotation 142 over the range of off-symmetry angles 162 between zero and the maximum off-symmetry angle 162. The x and y coordinates originate at the driver gear axis 24, with the positive x direction and the positive y directions as indicated in
Table 1-7 gives the length of the first timing belt segment 47 and the length of the second timing belt segment 49 as well as the total length of the timing belt 40 for various off-symmetry angles 162. In Example 1, the length of the first timing belt segment 47 changes in correspondence to the length of the second timing belt segment 49 so that the total length of the timing belt 40 varies by less than 1/10,000 of an inch as per the specified constraint in this example. The phase relationship results are also given in Table 1-6. In Example 1, the maximum phase angle rotational skew between the driver gear 20 and the driven gear is 5.7247°.
The results of the computation are presented graphically in
In Example 2, the timing belt 40 configuration was specified as indicated in Table 2-1, and the driver gear, the driven gear 30, the first idler 50 and the second idler 60 were specified as indicated in Table 2-2. As indicated in Table 2-3, initial values that describe the geometry of the phase shift apparatus 10 were chosen, and these values were refined by iteration subject to the constraints given in Table 2-4.
Some results of the computation are presented in Table 2-5, Table 2-6, and Table 2-7. Table 2-5, lists the optimal center-to-center distance between the first idler axis and the second idler axis, the distance of the idler pivot point 134 with respect to the driver gear axis 24, the distance between the idler axis and the idler pivot point 134, and the maximum off-symmetry angle 162, the pivot point angle 164, and the distance of the idler pivot point 134 from the driven gear axis 34.
The path 100 is described in Table 2-6, which gives the loci of the first idler axis of rotation 142 and the second idler axis of rotation 142. The x and y coordinates are measured from the driver axis of rotation.
Table 2-7 gives the length of the first timing belt segment 47 and the length of the second timing belt segment 49 as well as the total length of the timing belt 40 for various off-symmetry angles 162. In Example 2, the length of the first timing belt segment 47 changes in correspondence to the length of the second timing belt segment 49 so that the total length of the timing belt 40 varies by less than 1/10,000 of an inch as per the specified constraint in this example. The phase relationship results are also given in Table 2-6. In Example 2, the maximum phase angle rotational skew between the driver gear 20 and the driven gear 30 is 5.41704°.
The results of the computation are presented graphically in
The foregoing discussion and the Appendix disclose and describe merely exemplary implementations. Upon study of the specification, one of ordinary skill in the art will readily recognize from such discussion, and from the accompanying figures and claims, that various changes, modifications and variations can be made therein without departing from the spirit and scope of the inventions as defined in the following claims.
