Trochoid, Polar or Conic Section Spoke for Wheels

Abstract

The invention is for a single spoke for an entire wheel that connects the hub to the rim in the shape of a trochoid graph, polar graph, or series of connected conic sections. It is impossible to determine where the spoke begins or terminates as it's one continuous piece of material.

Claims

1. The trochoid, polar or conic spoke can absorb and distribute forces from bumps, potholes, and other irregularities in the road more efficiently than previously designed spokes.

2. The trochoid, polar or conic spoke can use less materials for the same strength, thus making the wheel less expensive to produce and any vehicle using this spoke would require less energy to propel the vehicle and less stopping distance due to inertia than previously designed spokes.

3. A rim made with the trochoid, polar or conic spoke would take less time to manufacture, because one could make a rim with a single spoke.

4. The trochoid, polar or conic spoke creates infinitely more opportunities for creative variations in design than previously designed spokes.

5. The trochoid, polar or conic spoke creates infinitely more opportunities for uses than previously designed spokes because one could increase strength by increases the thickness of the material, and/or the number of petals in the spoke.

6. The trochoid, polar or conic spoke creates more plains of resistance than previously designed spokes, thus allowing any vehicle using it to corner or handle better than a vehicle with previously designed spokes.

7. The trochoid, polar or conic spoke utilizes the same hubs and rims as previously designed spokes and can be placed in service without modifying current rims and hubs unless the user wants to.

8. Especially in the case of the Hypotrochoid spoke, the spoke is positioned in the same direction as centripetal force instead of perpendicular to the centripetal force, thus making the transfer of energy more efficient and the strain on the spoke less.

9. The trochoid, polar or conic spoke can be made with unidirectional carbon fiber because its natural shape achieves 360 degrees of strength. The advantage being unidirectional carbon fiber is less expensive and easier to work with than multidirectional carbon fiber.

10. The trochoid, polar or conic spoke can be made with any of the modern or traditional materials, as it's the shape that's the improvement. Some materials would better take advantage of the design than others, but that would depend largely upon the use.

11. Since there are an infinite number of values that could be placed into variables for the trochoid, polar or conic spoke, such as size of wheel, speed, weight, g-forces, number of wheels, and working conditions, it is impossible to show which design is best for which purpose. Testing would have to be performed on many designs before the user would find the optimal choice for the spoke.

12. The end user of the trochoid, polar or conic spoke may choose to employ more than one trochoid, polar or conic spoke in a wheel for a myriad of reasons including but not limited to strength, safety, aesthetic etc. The benefits of the design would still be realized regardless of the number of the trochoid, polar or conic spokes used on a wheel.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0034] The purpose of many of these figures are to show hypotrochoids and epitrochoid spokes fit into 15-17 car rims or in bicycle wheels with larger diameters. With these formulas the hypotrochoid and epitrochoid spokes have an infinite number of sizes and petals, both of which can be adjusted based on application. The thickness and choice of material used to create the spoke will also depend on the application of the spoke. Attaching the spoke to the hub or the rim will be dependent on the hub or rim to which its being applied and can be adjusted as needed.

[0035] A full and enabling disclosure of the present invention, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which: These and other systems, methods, objects, features, and advantages of the present disclosure will be apparent to those skilled in the art from the following detailed description of the other embodiment and the drawings. All documents mentioned herein are hereby incorporated in their entirety by reference.

[0036] The foregoing features and elements may be combined in various combinations without exclusivity, unless expressly indicated otherwise. These features and elements as well as the operation thereof will become more apparent considering the following description and the accompanying drawings. It should be understood, however, the following description and drawings are intended to be exemplary in nature and non-limiting.

[0037] FIGS. 1-5 Hypotrochoid5 Petal Spoke

[0038] Formula:

[00001]$x\left(t\right)=\left(8-4.8\right)\cos t+5.7\cos \frac{8-4.8}{4.8}ty\left(t\right)=\left(8-4.8\right)\sin t-3\sin \frac{8-4.8}{4.8}t$

[0039] FIG. 1 5 Petal Hypotrochoid SpokeFront view

[0040] Label #1Rim [0041] 2Hub [0042] 3Lugs [0043] 45 Petal Hypotrochoid Spoke

[0044] FIG. 2 5 Petal Hypotrochoid Spoke 1.sup.st 2 acrossFront view [0045] Displaying how the material would be laid if the spoke were not made by casting.

[0046] Label #55 Petal Hypotrochoid Spoke 2 across

[0047] FIG. 3 5 Petal Hypotrochoid Spoke 1.sup.st 4 acrossFront view [0048] Displaying how the material would be laid if the spoke were not made by casting.

[0049] Label #65 Petal Hypotrochoid Spoke 4 across

[0050] FIG. 4 5 Petal Hypotrochoid SpokeOffset 3D View

[0051] FIGS. 5-9 Hypotrochoid9 Petal Spoke

[0052] Formula:

[00002]$x\left(t\right)=\left(13.5-9.5\right)\cos t+3.5\cos \frac{13.5-9.5}{9.5}ty\left(t\right)=\left(13.5-9.5\right)\sin t-3.5\sin \frac{13.5-9.5}{9.5}t$

[0053] FIG. 5 9 Petal Hypotrochoid SpokeFront view

[0054] Label #79 Petal Hypotrochoid Spoke

[0055] FIG. 6 9 Petal Hypotrochoid Spoke 1.sup.st 2 acrossFront view

[0056] Displaying how the material would be laid if the spoke were not made by casting.

[0057] Label #89 Petal Hypotrochoid Spoke 1.sup.st 2 across

[0058] FIG. 7 9 Petal Hypotrochoid Spoke 1.sup.st 4 acrossFront view

[0059] Displaying how the material would be laid if the spoke were not made by casting.

[0060] Label #99 Petal Hypotrochoid Spoke 1.sup.st 4 across

[0061] FIG. 8 9 Petal Hypotrochoid Spoke 1.sup.st 6 acrossFront view

[0062] Displaying how the material would be laid if the spoke were not made by casting.

[0063] Label #109 Petal Hypotrochoid Spoke 1.sup.st 6 across

[0064] FIG. 9 9 Petal Hypotrochoid Spoke Offset 3D View

[0065] FIGS. 10-13 6 Petal Epitrochoid Spoke

[0066] Formula:

[00003]$x\left(t\right)=\left(3+2.5\right)\cos t-3\cos \frac{3+2.5}{2.5}ty\left(t\right)=\left(3+2\right)\sin t-3\sin \frac{3+2.5}{2.5}t$

[0067] FIG. 10 6 Petal Epitrochoid SpokeFront view

[0068] Label #116 Petal Epitrochoid Spoke

[0069] FIG. 11 6 Petal Epitrochoid Spoke 1.sup.st 1% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0070] Label #126 Petal Epitrochoid Spoke 1.sup.st 1% loops

[0071] FIG. 12 6 Petal Epitrochoid Spoke 1.sup.st 2% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0072] Label #136 Petal Epitrochoid Spoke 1.sup.st 2% loops

[0073] FIG. 13 6 Petal Epitrochoid Spoke 1.sup.st 3% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0074] Label #146 Petal Epitrochoid Spoke 1.sup.st 3% loops

[0075] FIGS. 14-17 7 Petal Epitrochoid Spoke

[0076] Formula:

[00004]$x\left(t\right)=\left(3.5+2\right)\cos t-3\cos \frac{3.5+2}{2}ty\left(t\right)=\left(3.5+2\right)\sin t-3\sin \frac{3.5+2}{2}t$

[0077] FIG. 14 7 Petal Epitrochoid SpokeFront view

[0078] Label #157 Petal Epitrochoid Spoke

[0079] FIG. 15 7 Petal Epitrochoid Spoke 1.sup.st 1% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0080] Label #167 Petal Epitrochoid Spoke 1.sup.st 1? loops

[0081] FIG. 16 7 Petal Epitrochoid Spoke 1.sup.st 2% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0082] Label #177 Petal Epitrochoid Spoke 1.sup.st 2% loops

[0083] FIG. 17 7 Petal Epitrochoid Spoke 1.sup.st 3% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0084] Label #187 Petal Epitrochoid Spoke 1.sup.st 3% loops

[0085] FIGS. 18-21 8 Petal Epitrochoid Spoke

[0086] Formula:

[00005]$x\left(t\right)=\left(4+1.5\right)\cos t-3\cos \frac{4+1.5}{1.5}ty\left(t\right)=\left(4+1.5\right)\sin t-3\sin \frac{4+1.5}{1.5}t$

[0087] FIG. 18 8 Petal Epitrochoid SpokeFront view

[0088] Label #198 Petal Epitrochoid Spoke

[0089] FIG. 19 8 Petal Epitrochoid Spoke 1.sup.st 1% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0090] Label #208 Petal Epitrochoid Spoke 1.sup.st 1% loops

[0091] FIG. 20 8 Petal Epitrochoid Spoke 1.sup.st 2% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0092] Label #218 Petal Epitrochoid Spoke 1.sup.st 2% loops

[0093] FIG. 21 8 Petal Epitrochoid Spoke 1.sup.st 3% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0094] Label #228 Petal Epitrochoid Spoke 1.sup.st 3% loops

[0095] FIGS. 22-25 8 Petal Orbital Epitrochoid Spoke

[0096] Formula:

x(t)=5.5 cos t+3 cos 9t

y(t)=5.5 sin t+3 sin 9t

[0097] FIG. 22 8 Petal Orbital Epitrochoid SpokeFront view

[0098] Label #238 Petal Orbital Epitrochoid Spoke

[0099] FIG. 23 8 Petal Orbital Epitrochoid Spoke 1.sup.st loopFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0100] Label #248 Petal Orbital Epitrochoid Spoke 1.sup.st loop

[0101] FIG. 24 8 Petal Orbital Epitrochoid Spoke 1.sup.st 2 loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0102] Label #258 Petal Orbital Epitrochoid Spoke 1.sup.st 2 loops

[0103] FIG. 25 8 Petal Orbital Epitrochoid Spoke 1.sup.st 3 loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0104] Label #268 Petal Orbital Epitrochoid Spoke 1.sup.st 3 loops

[0105] FIGS. 26-29 10 Petal Big Loop Epitrochoid Spoke

[0106] Formula:

[00006]$x\left(t\right)=\left(10+3\right)\cos t-5.5\cos \frac{10+3}{3}ty\left(t\right)=\left(10+3\right)\sin t-5.5\sin \frac{10+3}{3}t$

[0107] FIG. 26 10 Petal Big Loop Epitrochoid SpokeFront view

[0108] Label #2710 Petal Big Loop Epitrochoid Spoke

[0109] FIG. 27 10 Petal Big Loop Epitrochoid Spoke In 1% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0110] Label #2810 Petal Big Loop Epitrochoid Spoke 1.sup.st 1% loops

[0111] FIG. 28 10 Petal Big Loop Epitrochoid Spoke 1.sup.st 2% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0112] Label #2910 Petal Big Loop Epitrochoid Spoke 1.sup.st 2% loops

[0113] FIG. 29 10 Petal Big Loop Epitrochoid Spoke 1.sup.st 3% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0114] Label #3010 Petal Big Loop Epitrochoid Spoke 1.sup.st 3% loops

[0115] FIGS. 30-33 12 Petal Polar Bicycle Wheel Spoke

[0116] Formula:

r=10 cos(6?)

[0117] FIG. 30 12 Petal Polar Bicycle Wheel SpokeFront view

[0118] Label #3112 Petal Polar Bicycle Wheel Spoke

[0119] FIG. 31 12 Petal Polar Bicycle Wheel Spoke 1.sup.st 2 acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0120] Label #3212 Petal Polar Bicycle Wheel Spoke 1.sup.st 2 across

[0121] FIG. 32 12 Petal Polar Bicycle Wheel Spoke 1.sup.st 4 acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0122] Label #3312 Petal Polar Bicycle Wheel Spoke 1.sup.st 4 across

[0123] FIG. 33 12 Petal Polar Bicycle Wheel Spoke 1.sup.st 6 acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0124] Label #3412 Petal Polar Bicycle Wheel Spoke 1.sup.st 6 across

[0125] FIGS. 34-37 39 Petal Epitrochoid Spoke

[0126] Formula:

[00007]$x\left(t\right)=\left(3.9+1.6\right)\cos t-3.2\cos \frac{3.9+1.6}{1.6}ty\left(t\right)=\left(3.9+1.6\right)\sin t-3.2\sin \frac{3.9+1.6}{1.6}t$

[0127] FIG. 34 39 Petal Epitrochoid SpokeFront view

[0128] Label #3539 Petal Epitrochoid Spoke

[0129] FIG. 35 39 Petal Epitrochoid Spoke 1.sup.st 1% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0130] Label #3639 Petal Epitrochoid Spoke 1.sup.st 1% loops

[0131] FIG. 36 39 Petal Epitrochoid Spoke 1.sup.st 2% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0132] Label #3739 Petal Epitrochoid Spoke 1.sup.st 2% loops

[0133] FIG. 37 39 Petal Epitrochoid Spoke 1.sup.st 3% loopsFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0134] Label #3839 Petal Epitrochoid Spoke 1.sup.st 3% loops

[0135] FIGS. 38-41 40 Petal Hypotrochoid Spoke

[0136] Formula:

[00008]$x\left(t\right)=\left(8-4.6\right)\cos t+6\cos \frac{8-4.6}{4.6}ty\left(t\right)=\left(8-4.6\right)\sin t-6\sin \frac{8-4.6}{4.6}t$

[0137] FIG. 38 40 Petal Hypotrochoid SpokeFront view

[0138] Label #3940 Petal Hypotrochoid Spoke

[0139] FIG. 39 40 Petal Hypotrochoid Spoke 1.sup.st 2 acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0140] Label #4040 Petal Hypotrochoid Spoke 1.sup.st 2 across

[0141] FIG. 40 40 Petal Hypotrochoid Spoke 1.sup.st 4 acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0142] Label #4140 Petal Hypotrochoid Spoke 1.sup.st 4 across

[0143] FIG. 41 40 Petal Hypotrochoid Spoke 1.sup.st 6 acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0144] Label #4240 Petal Hypotrochoid Spoke 1.sup.st 6 across

[0145] FIGS. 42-45 1000 Loop Epitrochoid Spoke

[0146] Formula:

[00009]$x\left(t\right)=\left(-\text{.8}-6.3\right)\cos t-3\cos \frac{8-4.6}{6.3}ty\left(t\right)=\left(-\text{.8}-6.3\right)\sin t-6\sin \frac{-\text{.8}-6.3}{6.3}t$

[0147] FIG. 42 1000 Loop EpitrochoidFront view

[0148] Label #431000 Loop Epitrochoid Spoke

[0149] FIG. 43 1000 Loop Epitrochoid Spoke 1.sup.st Loop acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0150] Label #441000 Loop Epitrochoid Spoke 1.sup.st Loop across

[0151] FIG. 44 1000 Loop Epitrochoid Spoke 1.sup.st Loop acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0152] Label #451000 Loop Epitrochoid Spoke 1.sup.st Loop across

[0153] FIG. 45 1000 Loop Epitrochoid Spoke 1.sup.st Loop acrossFront view. Displaying how the material would be laid if the spoke were not made by casting.

[0154] Label #461000 Loop Epitrochoid Spoke 1.sup.st Loop across

DETAILED DESCRIPTION OF THE INVENTION

[0155] The key to this new design in the spoke is to identify curves that are rotationally symmetrical to the origin of a circle, meet the hub and/or rim in the shape of an arc, and begin where they end. These graphs include Polar roses, hypotrochoids, epitrochoids, amongst other geometric roulettes. Polar graphs in the form r=a sin n? and r=a cos n? are called roses. In these equations, the value of a, controls the size. Negative values of a give the same graph as the positive values of a except they are reflected through the origin. The value of n determines the number of petals. For both equations, when n is odd n equals the number of petals, and when n is even the number of petals equals 2n, given n is a natural number. As the value of a, the amplitude in the trigonometric functions, increased, the distance between the peak and trough of the sine and cosine graphs increased, in essence creating taller waves. In a similar way, as the value of a in the roses increased, so did the length of the petals. Therefor a would be equal to the radius of the rim. The value of n in the roses is positioned in the same way as the frequency in the trigonometric graphs, the b value. Quintessentially, increasing the frequency in the trigonometric function increases the number of waves in the same interval, just like increasing the value of n in the roses increases the quantity of petals.

Epitrochoids

[0156] [00010]$x\left(t\right)=\left(R+r\right)\cos t-p\cos \frac{R+r}{r}ty\left(t\right)=\left(R+r\right)\sin t-p\sin \frac{R+r}{r}t$

Hypotrochoids

[0157] [00011]$x\left(t\right)=\left(R-r\right)\cos t+p\cos \frac{R-r}{r}ty\left(t\right)=\left(R-r\right)\sin t-p\sin \frac{R-r}{r}t$

[0158] Hypotrochoids are roulettes formed by a fixed point in a circle that rolls within a larger circle.

[0159] Epitrochaids are raulettes formed by a fixed point in a circle that rails outside a circle.

[0160] Most hypotrochoids and epitrocoids, whether in polar or parametric form, are born from the graphs of sine and cosine.

[0161] Where C.sub.o is the fixed outer circle, R is the radius of the outer circle, C.sub.i is the inner circle, r is the radius of the inner circle (r<R), p is a point within the inner, and t is the independent variable. In reality

Mathematically Speaking:

[0162] [00012]$C_1\left(\mathrm{Circumference}\mathrm{of}\mathrm{the}\mathrm{outer}\mathrm{circle}\right)=96=2?r,r_1=\frac{48}{?}{C}_2\left(\mathrm{Circumference}\mathrm{of}\mathrm{the}\mathrm{inner}\mathrm{circle}\right)=52=2?r,r_2=\frac{26}{?}\mathrm{Therefore},r_1:r_2=\frac{48}{?}:\frac{26}{?}=48:26=96:52$

[0163] The key to making roulettes with a specific number of petals is starting with circles that have rational circumferences.

[0164] When I rotate the smaller circle within the larger circle after two full rotations of the smaller circle inside the larger circle, the smaller circle clicks 104 units. If I chose a starting point on both the smaller circle and the larger circle, after two full rotations the starting point on the smaller circle will be eight units past the starting point of the outer circle. It would take 24 complete rotations of the inner circle for the two starting points to align again. To calculate the number of petals in the spiral, first I need to find the GCF of the two circles. Next, I would divide the Circumference on the outer circle by the GCF of the two circles to calculate the number of petals. If the number of units in the inner circle didn't contain a GCF greater than one with the outer circle than the number of petals would equal the number of units on the outer circle. Therefore, the maximum number of petals that can be achieved using a hypotrochoid would equal the number of units on the outer circle. More petals could be achieved when graphing on a calculator because the number of units could be irrational, but that is physically impossible. In this case, the prime factorization of 96 is 2.sup.5.Math.3, so if the inner circle had a circumference (number of teeth) that was any prime number greater than three and less than 96, then there would be 96 petals on the subsequent spiral.

[0165] This summarizes the mathematical relationships between the variables in the roulettes. The user would have test different variations to find the optimum design for the user's purpose. As has been previously stated in this application, it is impossible to detail every variation in use, size, weight, speed etc. Therefor the application is for the general shape of the spoke. This shape will allow for the creation of wheels that are far superior to currently designed wheels.