Oscillating figure

Abstract

An oscillating body, and a method of manufacturing an oscillating body using a mold having a mold cavity with a curved surface. The method involves inserting a predetermined amount of a hardenable mixture in the mold cavity and allowing the hardenable mixture to harden to produce a body that is a negative of at least a portion of the mold cavity, including a curved surface that is a negative of the curved surface of the mold. A ballast is connected to the body portion such that the ballast remains stationary relative to the body portion. An oscillating body is made in part or in whole from the body portion with the ballast, wherein the oscillating body is adapted to roll on the curved surface in an oscillating manner after being subjected to a displacement.

Description

This application claims the benefit of U.S. provisional application No. 60/512,768, filed Oct. 21, 2003, which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

Oscillating toys and oscillating figures are well known in the art, and have been used both to amuse and to attract attention. For example, roly-poly devices have been provided to children (and adults) for amusement and visual stimulation, as well as to develop the sensory nervous system (such as, for example, sight and/or hearing). However, the prior art oscillating toys/figures are typically crudely made and their movements are not well understood. Indeed, a survey of the art suggests that the movements of the produced toys/figures is unpredictable and sometimes even irritating. There is a need to provide superior oscillating figures that will be more esthetically pleasing and desirable to the users. Still further there is a need to improve the various methods of manufacture of these oscillating figures over current manufacturing methods.

SUMMARY OF THE INVENTION

One aspect of the invention concerns a method of manufacturing an oscillating body utilizing a mold having a mold cavity with a curved surface. The method comprises inserting a predetermined amount of a hardenable mixture in the mold cavity and allowing the hardenable mixture to harden to produce a body that conforms to at least a portion of the mold cavity, the body having a curved surface that is a negative of the curved surface of the mold. A ballast is connected to the interior of the body such that the ballast remains stationary relative to the body. The oscillating body is made in part or in whole from the body with the ballast, wherein the oscillating body is adapted to roll on the curved surface in an oscillating manner after being subjected to a displacement.

The mold can be a flexible mold, and the hardenable mixture can be a resin, or a mixture of polystyrene and CaCO₃.

The method preferably involves determining a coefficient of oscillation of the oscillating body, making the mold in accordance with the coefficient of oscillation, and making the oscillating body so that it has substantially that coefficient of oscillation.

The coefficient of oscillation preferably is greater than about 0.05 and less than about 1. The frequency of oscillation of the body preferably is about 0.5 hertz to about 3 hertz.

Another aspect of the invention concerns an oscillating body comprising a body including a curved surface adapted to enable the oscillating body to be in rolling contact with a support surface, the body having a center of mass located substantially directly below the center of curvature of the curved surface when the oscillating body is in an at rest position on the support surface and free to roll. The curved surface has a curve of contact extending at least about 10 degrees in at least one direction away from a point at which the curved surface contacts the support surface in the at rest position. The curvature of the curved surface, when evaluated along the curve of contact within about 10 degrees from the point at which the curved surface contacts the support surface at the at rest position, results in stable center of mass travel. The coefficient of oscillation of the body is greater than about 0.05 and less than about 1.

The curved surface of the oscillating body may have a portion that extends over at least a hemisphere, and may be elliptical, cylindrical or spherical.

The frequency of oscillation of the oscillating body preferably is about 0.5 hertz to about 3 hertz.

The curve of contact of the curved surface of the oscillating body preferably extends at least about 45 degrees—preferably uninterrupted—in at least two directions away from each other and away from the point at which the curved surface contacts the support surface at the at rest position.

A second curve of contact of the curved surface may extend uninterrupted at least about 45 degrees in at least two additional directions away from each other and away from the point at which the curved surface contacts the support surface at the at rest position, the two additional directions being substantially orthogonal to the two directions.

The oscillating body may have protrusions extending past the curved surface.

The oscillating body may have at least two portions of substantially different densities. The portion having a higher density preferably is located substantially at the bottom of the oscillating body.

The oscillating body may comprise a solid mixture of polystyrene and CaCO₃. The shell of the oscillating body may comprise a solid mixture of polystyrene and CaCO₃, and an interior portion of the oscillating body may comprise CaCO₃ and/or a mixture of polystyrene and CaCO₃.

The oscillating body preferably has a shell and a ballast, the ballast being located at the bottom of the shell and fixed to the shell. The ballast may comprise CaCO₃.

Yet another aspect of the invention concerns an oscillating body comprising a body including a curved surface adapted to enable the oscillating body to be in rolling contact with a support surface, the body being adapted to have a frequency of oscillation for an initial angular displacement having a value selected between the range of about 1 degree to about 20 degrees given by a particular equation set forth herein; and the coefficient of oscillation of the body is greater than about 0.05 and less than 1.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments that incorporate the best mode for carrying out the invention are described in detail below, purely by way of example, with reference to the accompanying drawing, in which:

FIG. 1 is a vertical sectional view of an oscillating body according to a first embodiment of the present invention.

FIG. 2 is a vertical sectional view of an oscillating body according to a second embodiment of the present invention.

FIG. 3 is a schematic illustration of an oscillating body according to a third embodiment of the present invention.

FIG. 4 is a schematic illustration of an oscillating body according to a fourth embodiment of the present invention.

FIG. 5 is a schematic illustration of an body according to a fifth embodiment of the present invention.

FIG. 6 is a schematic illustration of an oscillating body according to a FIG. 5.

FIG. 7 schematically illustrates a contact curve of the first embodiment of the present invention.

FIG. 8 is a schematic illustration of an oscillating body according to a sixth embodiment of the present invention.

FIG. 9 is a vertical sectional view of an oscillating body according to a seventh embodiment of the present invention.

FIG. 10 schematically illustrates a method of making an oscillating body.

FIG. 11 schematically illustrates another method of making an oscillating body.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the first embodiment of the present invention, as shown in FIG. 1, there is an oscillating body 10 having a curved surface 15 configured to support the body 10 on a base portion 20 that is connected to head portion 30. In the embodiment shown in FIG. 1, the base portion 20 of the oscillating body 10 is made of a thin walled material having a thickness T₂₀. The head portion 30 of the oscillating body 10 is likewise made from a material having a thickness T₃₀, which in the first embodiment, is about the same thickness as the thickness T₂₀ of the base portion 20. Collectively, these portions form a shell 11 of the body 10. The shell 11 may be made via a swirl molding technique utilizing resins, as will be discussed in greater detail below. The oscillating body 10 further has a ballast 40 located at the bottom of the oscillating body 10 in the base portion 20 of the oscillating body 10. Still further, the oscillating body 10 has a center of mass 100 located in the base 20 (although in other embodiments the center of mass 100 may be located in the head portion 30). In the first embodiment of the present invention, the center of mass 100 is located with respect to the other elements of the oscillating body 10 such that it has a tendency to remain substantially upright in an at rest position when only acted upon by gravity and to return to the upright position if displaced. The particular features of the oscillating body 10 will now be described in greater detail.

As can be seen from FIG. 1, the oscillating body 10 has a curved surface 15 at its base. This curved surface 15 enables oscillation of the oscillating body 10 by permitting the body 10 to “roll” back and forth (also referred to as “rotate” and/or “angular displacements” herein). This curved surface 15 permits the oscillating body 10 to roll, by way of example, on a flat surface 1000 (see, e.g., FIG. 3) such as a table top, when it is displaced and as it oscillates back and forth as a result of the displacement. In this embodiment of the invention, this curved surface 15 takes the form of a substantially complete hemisphere. As such, the curved surface 15 at the base of the base 20 may be round and has a substantially uniform radius of curvature r along its outside surface. Thus, the center of curvature 200 remains at a substantially fixed point relative to the oscillating body 10. It is noted that in some embodiments of the present invention, instead of a spherical or substantially spherical base 20, the base 20 may be formed of a hemisphere at, for example, its bottom, as shown in FIG. 3, above which the oscillating body 10 may not be curved and/or may have a different radius of curvature r. Still further, other embodiments of the present invention may utilize a truncated hemisphere (that is, a hemisphere that is cut off at a location below the “equator” and parallel to the equator). In yet other embodiments of the present invention, any surface 15 having a surface that would follow a surface of a portion of a sphere can be utilized to practice the invention.

At this point, it is noted that while the embodiments shown in some of the figures display an oscillating body 10 that does not extend past hypothetical boundaries extending vertically and located at the ends of the curved surface 15, other embodiments of the present invention may be practiced with components that do extend past the curved surface 15, such as that shown in FIG. 4. Still further, it is noted that while in some embodiments of the present invention, the oscillating body 10 may have a base portion 20 and a head portion 30 which are discrete sections of the body 10, other embodiments of the present invention may be practiced with more or fewer sections and/or without discrete sections. Indeed, some embodiments of the present invention may be practiced with a body 10 made only of a substantially perfect sphere (on the outside surface) as long as the center of mass 100 is located appropriately, as will be discussed in greater detail below. Thus, the exterior geometry of the oscillating body 10 is not a limitation of the present invention unless otherwise specified (such as, by way of example, a shape limitation).

In a first embodiment of the invention, the center of mass 100 is located relative to the body 10 such that it maintains a substantially upright orientation at its at rest position (e.g., where the center of mass 100 is at its lowest location as compared to the various positions of the oscillating body 10 as it oscillates). Thus, as it can be seen from FIG. 1, the center of mass 100 is located below the center of curvature 200 of the curved surface 15 as determined from the point at which the body 10 contacts the support 1000, as shown in FIG. 3. In the first embodiment of the invention, the center of curvature 200, as determined along the curved surface 15 (see FIG. 3) remains substantially at the same location relative to the oscillating body 10 because the curved surface 15 substantially conforms to a surface of a sphere. (It is noted, of course, that when referring to the curved surface 15, it is referred to as the surface on which the oscillating body 10 “rolls” as it oscillates.) However, in other embodiments of the present invention, the center of curvature 200 may vary along the curved surface 15 because the radius of curvature of discrete portions of the curved surface 15 on which the oscillating body 10 rolls varies. By way of example and not by way of limitation, the curved surface 15 may be an elliptical surface, such as is shown in FIG. 5. Thus, because the radius of curvature changes at various locations on the elliptical curved surface 15, the center of curvature 200 will likewise change along the curved surface 15. It is noted at this time that any surface that will permit the oscillating body 10 to oscillate according to the present invention may be utilized.

FIGS. 5 and 6 represent a view of an oscillating body 10 according to the present invention at a given instant. FIG. 5 further shows a displacement vector that represents the direction that the oscillating body 10 is initially displaced to begin the oscillations.

A horizontal location(s) of the center of mass 100 according to the present invention may be described based on a hypothetical line 500 that is normal to a plane that is tangent to the point 12 on the surface 15 that contacts the support surface 1000 as shown, for example, in FIGS. 3, 5 and 6. That is, as the oscillating body 10 “rolls” away from its at rest position, the center of mass 100 may be located on a side of this hypothetical line 500 that is opposite to the side that the body 10 rolls towards, as is shown in FIG. 5. Conversely, as the oscillating body 10 rolls towards its at rest position, the center of mass 100 may be located on the same side of the hypothetical line 500 that the oscillating body 10 rolls towards, as is shown in FIG. 6. This will be referred to herein as stable center of mass travel. That is, the horizontal location of the center of mass 100 with respect to the surface 15, in some embodiments, may be as follows: as the oscillating body 10 rolls in a direction away from its “at rest position,” the horizontal position 500 of the center of curvature 200 should be located between the horizontal position of the center of mass 100 and a point 18 on the curved surface 15 immediately adjacent to the point 12 that contacts the surface 1000 that will next come into contact with the curved surface 1000, as shown in FIG. 5. Conversely, when the oscillating body 10 is rolling in a direction towards its at rest position, the point 18 at which the surface 15 will next contact the support surface 1000 should be in-between the horizontal position of the center of curvature 200 and the horizontal position of the center of mass 100 as shown in FIG. 6.

In some embodiments of the present invention, as noted above, the center of mass 100 may be located substantially directly below the center of curvature when the oscillating body 10 is at rest. It is further, as is shown in FIG. 1. Explained in other terms, the center of mass 100 will be located between the center of curvature and the point at which the body 10 contacts the surface 1000 when the body 10 is at is at rest position.

Stable center of mass travel may be described in yet other terms. For example, if the oscillating body 10 of FIG. 5 is rolling towards the left of the Figure (i.e., counterclockwise), and thus away from its at rest position, the center of mass 100 will be to the right of the horizontal position of the center of curvature 200 and thus to the right of the horizontal position of the hypothetical line 500. Conversely, if the oscillating body 10 shown in FIG. 6 is rolling towards the right (i.e., in a clockwise direction), the location of the center of mass 100 will be located to the right of the horizontal position of the center of curvature and thus to the right of the hypothetical line 500.

In some embodiments of the invention, locating the center of mass 100 with respect to the center of curvature 200 and/or the hypothetical line 500 as described above will enable the oscillating body 10 to be substantially stable. That is, a displacement in one direction or another direction may result in the oscillating body 10 oscillating back and forth until friction forces completely dampen the oscillation, thus substantially returning the body 10 to its at rest position. The oscillating mass 10 of some embodiments of the present invention may be configured such that the stability exists along only a portion of the curved surface 15. That is, some embodiments of the present invention may be practiced with a complex surface 15 that has a varying radius of curvature r such that at some given displacement, the oscillating body 10 could be unbalanced, become unstable and thus “fall” on its side and remain there (unless it bounces back or is again acted on by an additional force.) Thus, in such an embodiment, only limited displacements may result in harmonic oscillation of the oscillating body 10. Still, in yet other embodiments of the present invention, the configuration of the oscillating body 10 may be such that the oscillating body 10 will always return to its upright at rest position regardless of how much displacement is applied to the body 10. By way of example and not by way of limitation, the oscillating body shown in FIG. 1 may be such a configuration, such that regardless of the orientation of the body 10 (except, perhaps for a perfectly balanced upside down oscillating body 10 of FIG. 1), the body 10 will return to its at rest position after frictional forces dampen the oscillations.

It is noted that the movements and geometry of the oscillating body 10 are being described herein in terms of two dimensions, as will be readily apparent from most of the figures, such as FIG. 1. Thus, the terms of oscillation will be described in terms of oscillation with respect to a plane that passes through the displacement vector and or the plane in which the body 10 is angularly displaced. That is, for the purposes of describing the embodiments shown in the figures, oscillation is described in terms of two dimensional oscillation. Thus, by way of example, for a perfectly balanced body 10, having a perfectly spherical curved surface 15, the plane will lie on the displacement vector of the force imparted onto the body 10 to initiate oscillation as well as the point 12 on the surface 15 that contacts the support surface 1000, and therefore, the contact points between the curved surface 15 and the support surface 1000 will fall on this plane as the body rolls, thus resulting in a curve of contact 600 along curved surface 15 as shown in FIG. 7. It is noted that this curve of contact 600 may be present in embodiments that are not perfectly balanced and/or do not have a perfectly spherical curved surface 15. For example, an elliptical curved surface 15 may also have a curve of contact 600. Thus, the curve of contact 600 represents the points on the curved surface 15 that come into contact with the support surface 1000 as the oscillating body 10 rolls back and forth. In the case of an oscillating body that has a cylindrical curved surface 15 (i.e., contact of the curved surface 15 results in line contact (as opposed to point contact) with the support surface 1000), the curve of contact 600 may be utilized to represent contact between the curved surface 15 and the support surface 1000 as well. This leads to yet another point: while some embodiments of the present invention may be practiced with curved surfaces 15 that are sphere like (e.g., they result in point contact with the support surface 1000), other embodiments of the invention may be practiced with cylinder like surfaces 15 that result in line contact with the support surface 1000. In yet other embodiments, a plurality of curved surfaces 15 may be utilized. In such embodiments, the plurality of surfaces may be aligned and/or substantially identical to result in a substantially uniform oscillation of the oscillating body 1000.

Still, it is noted that the present invention may be practiced with embodiments that oscillate in three-dimensions (which, in actuality, is how the oscillating body 10 will oscillate, albeit that the oscillations in the third dimension may be minor), because the body 10 will never be perfectly balanced and/or a torque may be imparted to the body by the initial displacement, etc. Thus, the present invention is not limited to an oscillating body 10 that oscillates only in two dimensions unless otherwise specified. However, such embodiments may be described and/or analyzed in terms of two dimensional oscillation.

It is noted that in some embodiments in the present invention, the oscillating body 10 may have a substantially symmetrical surface geometry about its longitudinal (i.e. lengthwise) axis, for example, as shown in FIG. 1. However, it is noted that in other embodiments of the present invention, the body 10 may have an asymmetrical surface geometry. That is, the body may be lopsided, as shown in FIG. 8, which represents an asymmetrical oscillating body 10 at the at rest position. It is noted that in such a configuration, the center of gravity 100 may still be horizontally aligned with the center of curvature 200, as shown in FIG. 8, when the body 10 is at the at rest position. Thus, according to the embodiment of FIG. 8, when at the at rest position, a portion of the body 10 will appear to be leaning backwards (or forwards or to the side depending on the viewer's frame of reference). When the body of FIG. 8 is oscillated, it may, for example, appear to oscillate to an upright position and then to a position where the body leans very far backwards, and then continue oscillating until frictional forces reduce the oscillations to zero, at which point the body 10 will be at rest and the body will again be seen as leaning to the left.

FIG. 8 also shows that some embodiments of the present invention may utilize an oscillation stop 50. The oscillation stop 50, which may be a protrusion or other physical structure, may be configured so that it will stop or otherwise interrupt the oscillating body 10 as it rolls on the curved surface 15. By way of example, when the oscillating body 10 shown in FIG. 8 rolls in a counterclockwise fashion (that is, rolls to the left), at some point, the stop 50 may hit the support surface 1000, at which point the oscillating body 10 may reverse direction or bounce a bit or maybe tip over or maybe tip around point 55, and/or then reverse direction of rolling towards the right. That is, the stop 50 may result in an interruption and/or change in the oscillations. It is noted that the present invention may be practiced with any configuration that may result in an interruption in the oscillations and/or cause an abnormal oscillation of the body 10. It is further noted that in the embodiment of FIG. 8, for small displacements initiating the oscillation of the body 10, the stop 50 may not come into contact with surface 1000. In such a scenario, the body 10 may oscillate as if the stop 50 was not present.

In some embodiments of the present invention, the stop 50 may enable the body 10 to spin or jump or hop or otherwise have an abnormal movement, as may be desirable and pleasing to a user. It is noted that while the embodiment of FIG. 8 shows a stop only on the right side, other embodiments of the present invention may utilize more stops or the stops may be located at any location. It is further noted that while the embodiment shown in FIG. 8 has just been described in terms of rolling to the left and thus hitting the stop, but if a displacement is imparted on the body 10 in the forward or backward direction (as viewed from the orientation shown in FIG. 7), the stop 50 may not come into contact with the surface 1000 for even large displacements because the curve of contact 600 on the surface 15 with the support surface 1000 does not pass by and/or pass through and/or is not aligned stop surface 50. That is, the plane that passes through the curve of contact 600 does not pass through the stop 50. For example, a stop surface 50 that extends approximately over a 10 degree arc around a circumference of the body 10 may leave 350 degrees of rolling direction that may avoid contact with the stop 50. Conversely, if the stop 50 extends all around the circumference (a full 360 degrees) every direction of rolling may result in contact with the stop 50 by the surface 1000 if the displacement is large enough.

As noted above, when the oscillating body 10 is at the at rest position, the center of mass 100 may be substantially horizontally aligned with the horizontal location of the center of curvature 200 of the curved surface 15, as evaluated from the point that the curved surface 15 contacts the support surface 1000. The horizontal distance from the center of curvature 200 and the center of mass 100 at the at rest position will be referred to as the setoff distance. As noted above, the radius of curvature r of the body 10 may be substantially constant for a surface 15 that is indicative of a surface of a perfect sphere or substantially indicative of a surface on a perfect sphere, and thus the distance between the center of curvature 200 and the center of mass 100 does not change when measured along the curvature of contact of the surface 15. Thus, a coefficient of oscillation, c₀, may be formulated, which is equal to the set off distance divided by the radius of curvature r at the point of contact 12 that the curved surface 15 contacts the support surface 1000 at the at rest position, and may be used to determine the frequency of oscillation of the body 10, as will be discussed in greater detail below. However, in other embodiments of the present invention that have a non-spherical surface 15 (e.g., an elliptical surface), the distance between the center of mass 100 and the center of curvature 200 may vary, as evaluated along the curve of contact 600, because the center of curvature 200 may change because the radius of curvature r changes along the surface 15. Thus, for non-spherical type surfaces 15, the coefficient of oscillation c₀ may be utilized for very small displacement angles of the body 10. That is, displacement angles that result in substantially only contact of the surface 15 with the support surface 1000 at a portion of the curved surface 15 that continuously has a radius of curvature r that is the same as or substantially the same as the radius of curvature r at the point 12 on which the oscillating body 10 contacts the support surface 1000 at the at rest position.

It is noted that in other embodiments of the present invention, a variable coefficient of oscillation may be used to determine the frequency of oscillation. This variable coefficient of oscillation may be determined based on a ratio of the vertical distance between the center of curvature 200 and the center of mass 100 and the radius of curvature r as evaluated at finite displacement angles where the surface 15 contacts the support surface 1000. Thus, for non-spherical type surfaces 15, the variable coefficient of oscillation may be considered in terms of c_oθ, where θ is the angle measured from an arbitrary reference line and/or a horizontal line passing through the center of mass 100 at the at rest position (however, in this latter case, the angle may include negative angles to account for oscillation to the left and to the right). Still further, for evaluating oscillations in three dimensions, the variable coefficient of oscillation may be considered in terms of c_oθβ where θ is the angle measured from an arbitrary reference plane which may lie on a horizontal line passing through the center of mass 100 at the at rest position and ψ is the angle measured from an arbitrary reference plane which may lie on a horizontal line passing through the center of mass 100 at the at rest position and is orthogonal to the plane on which θ is measured. Still further, coefficients of oscillations may be defined in terms of spherical coordinates and/or polar coordinates and/or Cartesian coordinates as may be applicable. It is noted that variable coefficients of oscillations may be used for spherical surfaces 15 as well. Thus, the variable coefficients may be determined over the total range of angular displacements expected for the oscillating body 10 and recorded, thus, as will be described below, “instantaneous” frequencies may calculated which may be utilized to characterize the overall frequency at which the body 10 oscillates.

In some embodiments of the present invention, it may be desirable to make an oscillating body 10 that has a predetermined or pre-estimated frequency of oscillation. That is, it may be desirable to determine, before making the oscillating body 10, how long it will take for the oscillating body 10 to complete one oscillation (e.g., roll back and forth). More particularly, when manufacturing the oscillating body 10, it may be desirable to manufacture the body so that it will have a predetermined oscillation frequency. An equation has been formulated that provides a way to do this utilizing the coefficient of oscillation co. As shown below, a frequency equation (1) may be used to determine the frequency and thus provides a way to estimate and/or to determine the dimensions and mass of the oscillating body 10 that may result in the desired frequency of oscillation: $\begin{array}{cc}\mathrm{freq}=0.5\frac{{\mathrm{meters}}^{\frac{1}{2}}}{\mathrm{seconds}}\sqrt{\frac{c_o\left(r\right)}{\left(\frac{I}{M}\right)+r^2+c_o^2{r}^2-2r^2{c}_o}}& \left(1\right)\end{array}$
where,

• • I=Moment of Inertia of the body 10,
  • M=mass of the body,
  • r=the radius of curvature, and
  • c_o=the coefficient of oscillation.
    By solving equation (1), the frequency at which the body 10 may oscillate based on the coefficient of oscillation co and the radius of curvature r of the surface 15 at the point 12 where the surface 15 contacts the support surface 1000 may be determined if the moment of inertia and the mass of the body is known and/or estimated. The following equations may be useful in determining the moment of inertia of the body 10:
    I_x=∫(y²+z²)dm  (2)
    I_y=∫(x²+z²)dm  (3)
    I_z=∫(x²+y²)dm  (4).
    It is noted that the constant 0.5 meters^1/2/second represents a derived rounded acceleration constant which is utilized with the coefficient of oscillation c₀. It is further noted that a more accurate value of the derived acceleration constant may be determined by taking the square root of the gravitational acceleration value at sea level at the equator of the Earth and dividing by 2 pi.

The above frequency equation (1) may be utilized to estimate or otherwise determine the frequency of oscillation of the oscillating body 10 for a small angular oscillation about the at rest position. That is, the frequency equation (1) yields a value that most closely comports with the actual frequency of the oscillating body (10) for small angular oscillations of the body 10. However, it is noted that this value may vary slightly. For larger angular oscillations about the at rest position of the body 10, the actual frequency of oscillation of the body 10 and the calculated frequency from equation (1) may vary slightly or more than slightly. It is further noted that the frequency equation may be utilized to calculate the natural frequency of the body 10 by multiplying equation (1) by 2 pie.

Still further, it is noted that equation (1) may be written in terms of a variable coefficient of oscillation as shown below, $\begin{array}{cc}\begin{array}{c}\mathrm{freqf}\left(\theta \right)=0.5\frac{{\mathrm{meters}}^{\frac{1}{2}}}{\mathrm{seconds}}\\ \sqrt{\frac{c_{o\theta }\left(r\right)}{\left(\frac{I}{M}\right)+r^2+c_{o\theta }^2{r}^2-2r^2{c}_{o\theta }}}+\\ \mathrm{freqf}\left(\mathrm{prior}\theta \right)\end{array}& \left(5\right)\end{array}$
where c_oθ is the coefficient of oscillation measured at a present displacement angle θ and freqf(prior θ) is a modifying frequency based on the frequency at which the oscillating body 10 oscillated at the displacement angle θ immediately before the oscillation at the previous displacement angle θ. Equation (5) might be solved utilizing a numerical method, which may include summing various frequencies, etc, and/or a computer, and thus, the overall frequency of oscillation might be determined on a per oscillation basis, as the overall frequency of oscillation for each oscillation may differ because portions of the surface 15 that previously contacted the support surface 1000 no longer come into contact with the support surface 1000 as friction forces dampen the oscillations.

However, once the concept of oscillations in two dimensions is applied to the body 10 of the present invention, three dimensional oscillation may be evaluated utilizing similar concepts. Thus, the frequency equation may be written in terms of a variable coefficient of oscillation in three dimensions, as shown below: $\begin{array}{cc}\begin{array}{c}\mathrm{freqf}\left(\theta ,\beta \right)=0.5\frac{{\mathrm{meters}}^{\frac{1}{2}}}{\mathrm{seconds}}\\ \sqrt{\frac{c_{o\mathrm{\theta \beta }}\left(r\right)}{\left(\frac{I}{M}\right)+r^2+c_{o\mathrm{\theta \beta }}^2{r}^2-2r^2{c}_{o\mathrm{\theta \beta }}}}+\\ \mathrm{freqf}\left(\mathrm{prior}\theta ,\beta \right)\end{array}& \left(5\right)\end{array}$
where c_oθβ is the coefficient of oscillation measured at a present displacement angle θ, β and freqf(prior θ, β) is a modifying frequency based on the frequency at which the oscillating body 10 oscillated at the displacement angle θ, β immediately before the oscillation at the previous displacement angle θ, β. Equation (6) might be solved utilizing a numerical method, which may include summing various frequencies, etc, and/or a computer, and thus, the overall frequency of oscillation might be determined on a per oscillation basis, as the overall frequency of oscillation for each oscillation may differ because portions of the surface 15 that previously contacted the support surface 1000 no longer come into contact with the support surface 1000 as friction forces dampen the oscillations. It is further noted that the above equations might be solved utilizing an iterative technique.

It should be noted that other embodiments of the present invention may use other equations utilizing the coefficient of oscillation to determine the frequency at which the oscillating body 10 according to the present invention oscillates, and thus the above equations may represent just one embodiment of the present invention.

In the first embodiment of the present invention, the oscillating body 10 may be made from a hardenable mixture such as a resin which includes calcium carbonate (CaCO₃) and polystyrene. In the first embodiment of the invention, the resin is about a 50-50 mix, by weight and/or by volume of the just mentioned materials. However, in other embodiments of the present invention, it is about a 60-40 mix (60% polystyrene, 40% CaCO₃), while in yet other embodiments, it is about a 70-30 mix, while in other embodiments, it is about a 40-60 mix (40% polystyrene and 60% CaCO₃), and in other embodiments it is about a 30-70 mix (30% polystyrene, 70% CaCO₃). It is noted that in yet other embodiments, the combination of the polystyrene and CaCO₃ may be in any percentage that will permit the oscillating body 10 to be practiced according to the present invention. In yet other embodiments of the invention, other materials may be included in the resin make-up as well. It is further noted that other embodiments of the present invention may utilize any mixture of polystyrene and calcium carbonate CaCO₃ that may be used to form a body that will be sufficiently strong enough to practice the various aspects of the present invention. In some embodiments of the invention, the body 10 may be strong enough to withstand minor impacts such as those resulting from the body being dropped on a hardwood floor and/or onto a concrete floor or other hard surface from a height. In yet other embodiments of the invention, the shell 11 and/or the entire body 10 may be made from PVC.

In some embodiments of the present invention, the material used to manufacture the shell 11 of the body 10 is conducive to the adherence of paints, coloring inks and/or other coloring substances to the shell 11.

In some embodiments of the present invention, the entire body 10 is made of the resin. However in other embodiments of the present invention, the body 10 includes other materials. By way of example and not by way of limitation, the ballast 40 may include iron or lead or other materials. In such an embodiment, the shell 11 of the body 10 may be made from the resin and the ballast 40 might be made from other materials, such as by way of example, again, iron, lead, etc.

In one embodiment of the present invention, the shell 11 making up portions 20 and 30 of the body 10 may be made entirely from the resin described above. Thus, in one embodiment, the resin is a 50-50 mixture by weight and/or by volume of polystyrene and calcium carbonate. The ballast portion 40 may be likewise made from the same resin formulation as well. In some embodiments of the present invention, the ballast 40 is made from CaCO₃ rocks/pellets/particles, which in some embodiments, are pure CaCO₃. The resin material may be utilized to hold the calcium carbonate rocks/pellets/particles in place.

An implementation of this embodiment shall now be described with reference to FIG. 9. In one embodiment of the invention the shell 11 of the body 10 is formed in a mold so that the shell (this will be described in greater detail below) is hollow. One or more holes 750 in the shell are then drilled or otherwise bored through the shell (or perhaps formed during the molding process) so that the CaCO₃ rocks/pellets/particles 770 may be inserted into the interior of the shell 11 through the holes, as shown in FIG. 9. In some embodiments, these rocks are of pellet form while in other embodiments these rocks are a powder or in substantially powder form and thus may be poured into the interior of the shell 11. It is noted that in other embodiments of the invention, iron or lead pellets or other materials may be inserted into the shell instead of or in addition to the CaCO₃. That is, any material of sufficient density that will result in a center of mass 100 location of the body 10 to be positioned so that the present invention may be practiced can be utilized to practice the invention. Then, a resin and/or other form of binder is poured through the holes and allowed to cure such that the inserted rocks form ballast 40. As noted above, the resin could be the same resin formulation that is utilized to formulate the shell 11 and could be a different formulation as well. Any formulation that will bind the ballast 40 to the shell 11 may be used to practice the invention.

In other embodiments of the present invention, the ballast 40 is pre-formed prior to insertion into the shell of the body 10, as shown in FIG. 10. By way of example and not by way of limitation, the shell of the body 10 may be formed in two parts utilizing a flexible mold (as will be discussed in greater detail below) utilizing two different molds. A top part of the body might include, for example, the upper hemisphere 20′ of the base portion 20 and the upper body 30. The bottom part might include a hemisphere of the base 20″. The ballast 40 may be formed in another mold and then may then be inserted into one of the shell parts (for example the lower hemisphere shell 20″ of the base 20), after which the lower hemisphere of the base 20 may be connected to the upper hemisphere of the lower base 20, and welded or otherwise joined together, thus sealing the shell 11 of the body 10 and sealing the ballast 40 inside the body 10. In some embodiments of the present invention, the pre-formed ballast 40 is formed to substantially contour to the inside surface of a portion of the shell of the body. In some embodiments of the present invention, the ballast 40 could be friction fit into the shell 11 and/or otherwise positively retain inside the shell by interfering components. In yet other embodiments of the present invention, the ballast 40 could connected by utilizing a resin etc.

A specific method of manufacturing the shell 11 of the body 10 according to the present invention will now be discussed. In the first embodiment of the invention, a clay template is made that represents the geometry of the production configuration of the body 10. In a first embodiment, the clay template may have the likeness of a well-known person and/or a well-known structure or article of manufacture, etc. By way of example and not by way of limitation, the clay template might have a spherical base portion to which is connected a head of a professional athlete, etc. Further by way of example, the clay template may have feet and/or hands and/or clothing as well. This clay template may then be placed in a flexible mold solution, the solution allowed to cure, thus forming a flexible mold around the clay template. However, in other embodiments of the invention, a rigid mold may be formed around the clay template. The clay template removed by cutting a hole or slit into the flexible mold so that the clay template may be removed. In the case of rigid molds, the mold may be split into two or more sections and separated so that the template may be removed. A predetermined amount of pre-cured resin may then be placed into the cavity of the flexible mold (or the cavity of the mold parts when the mold is placed together). The resin is then deposited on the interior surfaces of the mold cavity via a swirl or rotational molding method and permitted to harden.

In other embodiments of the invention, an injection molding technique may be used by injecting resin into a sectional mold to make the shell or a portion of the shell.

In the first embodiment of the invention, the thickness of the resin deposited onto the surface of the cavity is substantially constant, although in other embodiments of the present invention, swirl molding may be practiced so that the thicknesses are variable as with the embodiment shown in FIG. 2, where wall portions 25 are thicker than the other wall portions 22 of the shell 11. Once the resin has hardened sufficiently, the shell of the body 11 may then removed. In some embodiments of the present invention, this may result in a hollow shell that is completely closed, as is shown in FIG. 11. As noted above, however, in other embodiments of the present invention, the shell 11 of the body 10 is made of two or more parts. Thus, this process would be repeated two or more times for each part with respective molds. In such an embodiment (2 or more parts) there may be openings. Thus, in a first embodiment, the manufactured shell 11 (and thus the oscillating mass 10) may have the likeness of a well-known person and/or a well-known structure or article of manufacture, etc. By way of example and not by way of limitation, the shell 11 might have a spherical base portion to which is connected a head of a professional athlete, etc. Further by way of example, the shell 11 may have feet and/or hands and/or clothing. Thus, in one embodiment of the present invention, the oscillating body 10 may have a rendition of a head of a person connected to a spherical body such that when displaced, the body will roll along its surface 15 and thus the head will oscillate.

Some embodiments of the body 10 may be practiced with portions extending outward past the curved surface 15 and/or extending inward past the curved surface 15. By way of example, some embodiments of the invention may have arms and/or legs and/or feet extending past the curved surface 15. Thus, embodiments of the present invention may be practiced with a variety of modeled human appendages and/or other body parts extending from the body 10. It is further noted that embodiments of the present invention may be practiced with oscillating bodies 10 of various sizes. By way of example, oscillating bodies 10 may be about 0.5 inches in height or smaller, about 1 inch in height, about 1.5 inches in height, about 2 inches in height, about 2.5 inches in height, about 3 inches in height, about 3.5 inches in height, about 4 inches in height, about 4.5 inches in height, about 5 inches in height, about 5.5 inches in height, about 6 inches in height, about 6.5 inches in height, about 7 inches in height, about 7.5 inches in height, about 8 inches in height, or about 8.5 inches in height or larger. Thus, bodies 10 according to the present invention may be practiced having heights anywhere in the range from about 0.25 inches to about 12 inches in increments of about 0.1 inches. Indeed, smaller and larger bodies 10 may be practiced as well. Thus, some embodiments of the invention may have life size heights of, by way of example, about 2, 3, 4, 5, 6 and 7 feet. Still further, oscillating bodies 10 having a radius of curvature r anywhere in the range of about 0.1 inches to about 15 inches in increments of about 0.01 inches may be used to practice the present invention. By way of example, bodies 10 having a radius of curvature of about 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75, 3 and/or 3.25 inches may be used to practice the present invention. Still further, some embodiments of the present invention may be practiced having masses of about 0.05 kg or less, about 0.1 kg, about 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0 kgs, and/or about 1.05 kgs or more. Indeed, some embodiments may be practiced with any appropriate mass in the range from about 0.05 kg to about 3 kg in about 0.005 kg increments. Likewise, some embodiments of the invention may be practiced with a coefficient of oscillation of about 0.1 or less, about 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95 or more and in any range therebetween in increments of about 0.01. Still further, the oscillating body according to the present invention may be configured to oscillate at about 0.1 hertz, about 0.2 hertz, about 0.3 hertz, 0.4 hertz, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0, and/or about 3.1 hertz or more. Some embodiments may oscillate at a frequency anywhere within the range of about 0.1 hertz to about 5 hertz in increments of 0.05 hertz.

It will be understood that any method of molding that will result in a shell 11 for a body 10 according to the present invention and/or a completed body 10 according to the present invention may be utilized to practice the present invention.

In some embodiments of the invention, the oscillating body 10 may be displaced to a given angular displacement and held at that angle for a period of time, after which it is released to being oscillating. In some embodiments of the invention, the oscillating body 10 may be formed to have a surface 15 configured to first slide across the support surface 1000 and then begin to oscillate, while in other embodiments the present invention, the body 10 may be configured to slide while oscillating. In other embodiments, the oscillating body 10 may not slide and/or not substantially slide during and/or before oscillation.

Given the disclosure of the present invention, one versed in the art would appreciate that there may be other embodiments and modifications within the scope and spirit of the present invention. Accordingly, all modifications attainable by one versed in the art from the present disclosure are within the scope and spirit of the present invention are to be included as further embodiments of the present invention.

Claims

1. A method of manufacturing an oscillating body utilizing a mold having a mold cavity, the mold cavity having a curved surface, the method comprising:

inserting a predetermined amount of a hardenable mixture in the flexible mold cavity and allowing the hardenable mixture to harden to produce a body that conforms to at least a portion of the mold cavity, wherein the body has a curved surface that is a negative of the curved surface of the mold;

connecting a ballast to the interior of the body such that the ballast remains stationary relative to the body; and

forming an oscillating body made in part or in whole from the body with the ballast, wherein the oscillating body is adapted to roll on the curved surface in an oscillating manner after being subjected to a displacement.

2. A method according to claim 1, further comprising fabricating a template piece having a curved surface and forming the mold cavity based at least on the curved surface, wherein at least a portion of the mold cavity is a substantial negative of at least a portion of the template piece.

3. A method according to claim 1, wherein the template piece has the likeness of a human face.

4. A method according to claim 1, wherein the mold is a flexible mold.

5. A method according to claim 4, wherein the hardenable mixture comprises a resin.

6. A method according to claim 4, wherein the hardenable mixture is a mixture of polystyrene and CaCO3.

7. A method according to claim 1, further comprising determining a coefficient of oscillation of the oscillating body, making the mold in accordance with the coefficient of oscillation, and making the oscillating body so that it has the coefficient of oscillation.

8. A method according to claim 7, wherein the coefficient of oscillation is greater than about 0.05 and less than about 1.

9. A method according to claim 8, wherein the coefficient of oscillation is greater than about 0.2 and less than about 0.8.

10. A method according to claim 8, wherein the coefficient of oscillation is about 0.15.

11. A method according to claim 8, wherein the coefficient of oscillation is about 0.10.

12. A method according to claim 8, wherein the frequency of oscillation of the body is about 0.5 hertz to about 3 hertz.

13. A method according to claim 9, wherein the frequency of oscillation of the body is about 0.5 hertz to about 3 hertz.

14. A method according to claim 8, wherein the coefficient of oscillation of the body is about 0.10 to about 0.25, and the frequency of oscillation of the body is about 0.5 hertz to about 3 hertz.

15. A method according to claim 1, wherein the frequency of oscillation of the body is about 0.7 hertz.

16. An oscillating body, comprising:

a body including a curved surface adapted to enable the oscillating body to be in rolling contact with a support surface; wherein

the oscillating body has a center of mass located substantially directly below the center of curvature of the curved surface when the oscillating body is in an at rest position on the support surface and free to roll; wherein

the curved surface has a curve of contact extending at least about 10 degrees in at least one direction away from a point at which the curved surface contacts the support surface in the at rest position; wherein

the curvature of the curved surface, when evaluated along the curve of contact within about 10 degrees from the point at which the curved surface contacts the support surface at the at rest position, results in stable center of mass travel; and wherein

the coefficient of oscillation of the body is greater than about 0.05 and less than about 1.

17. An oscillating body according to claim 16, wherein the curved surface has a portion that extends over at least a hemisphere.

18. An oscillating body according to claim 17, wherein the portion that extends over at least a hemisphere is selected from the group consisting of an elliptical surface and a spherical surface.

19. An oscillating body according to claim 16, wherein the curved surface is substantially spherical.

20. An oscillating body according to claim 16, wherein the coefficient of oscillation is greater than about 0.2 and less than about 0.8.

21. An oscillating body according to claim 16, wherein the coefficient of oscillation is about 0.15.

22. An oscillating body according to claim 16, wherein the coefficient of oscillation is about 0.10.

23. An oscillating body according to claim 16, wherein the frequency of oscillation of the body is about 0.5 hertz to about 3 hertz.

24. An oscillating body according to claim 20, wherein the frequency of oscillation is about 0.5 hertz to about 3 hertz.

25. An oscillating body according to claim 16, wherein the coefficient of oscillation is about 0.10 to about 0.25 and the frequency of oscillation is about 0.5 hertz to about 3 hertz.

26. An oscillating body according to claim 16, wherein the frequency of oscillation is about 0.7 hertz.

27. An oscillating body according to claim 16, wherein the curve of contact of the curved surface extends at least about 45 degrees in at least two directions away from each other and away from the point at which the curved surface contacts the support surface at the at rest position.

28. An oscillating body according to claim 27, wherein the curve of contact of the curved surface extends uninterrupted at least about 45 degrees in at least two directions away from each other and away from the point at which the curved surface contacts the support surface at the at rest position.

29. An oscillating body according to claim 27, wherein the curvature of the curved surface, when evaluated along the curve of contact in the two directions within about 40 degrees from the point at which the curved surface contacts the support surface at the at rest position, results in stable center of mass travel.

30. An oscillating body according to claim 27, wherein a second curve of contact of the curved surface extends uninterrupted at least about 45 degrees in at least two additional directions away from each other and away from the point at which the curved surface contacts the support surface at the at rest position, and wherein the two additional directions are substantially orthogonal to the two directions.

31. An oscillating body according to claim 30, wherein the curvature of the curved surface, when evaluated along the curve of contact in the two additional directions within about 40 degrees from the point at which the curved surface contacts the support surface at the at rest position, results in stable center of mass travel.

32. An oscillating body according to claim 16, wherein the curved surface is a substantially cylindrical surface.

33. An oscillating body according to claim 32, wherein the cylindrical surface is selected from the group consisting of an elliptical surface and a spherical surface.

34. An oscillating body according to claim 16, further comprising protrusions extending past the curved surface.

35. An oscillating body according to claim 16, wherein the oscillating body comprises at least two portions having substantially different densities.

36. An oscillating body according to claim 35, wherein the portion having a higher density is located substantially at the bottom of the oscillating body.

37. An oscillating body according to claim 16, wherein the oscillating body comprises a solid mixture of polystyrene and CaCO3.

38. An oscillating body according to claim 16, wherein a shell of the oscillating body comprises a solid mixture of polystyrene and CaCO3, and an interior portion of the oscillating body comprises at least one of CaCO3 and a mixture of polystyrene and CaCO3.

39. An oscillating body according to claim 16, wherein the oscillating body comprises a shell and a ballast, and wherein the ballast located at the bottom of the shell and fixed to the shell.

40. An oscillating body according to claim 39, wherein the ballast comprises CaCO3.

41. An oscillating body, comprising:

a body including a curved surface adapted to enable the oscillating body to be in rolling contact with a support surface, the body being adapted to have a frequency of oscillation for an initial angular displacement having a value selected between the range of about 1 degree to about 20 degrees given by the equation:

freq = 0.5 ⁢ meters 1 2 seconds ⁢ c o ⁡ ( r ) ( I M ) + r 2 + c o 2 ⁢ r 2 - 2 ⁢ r 2 ⁢ c o

where

I=a moment of inertia of the body,

M=a mass of the body,

r=a radius of curvature of the curved

surface that contacts the flat support

surface during the angular displacement, and

co=a coefficient of oscillation of the body;

wherein the coefficient of oscillation is greater than about 0.05 and less than about 1.

42. An oscillating body according to claim 41, wherein the coefficient of oscillation is greater than about 0.2 and less than about 0.8.

43. An oscillating body according to claim 41, wherein the frequency of oscillation is about 0.5 hertz to about 3 hertz.