Abstract:
A vibration isolation system for hand implements including sporting equipment and tools to substantially reduce impact forces from being delivered to the user&#39;s hands. Isolation elements provide low spring rates enabling the system to isolate bending vibration, recoil, and twist. An outer shell member substantially encircles the grip end of the hand implement and is spaced outwardly thereto allowing the grip end to freely deflect within the outer shell member.

Description:
This application claims priority under 35 U.S.C. §119(e) of U.S. provisional patent application Ser. Nos. 61/126,692 and 61/192,358 filed on May 7, 2008 and Sep. 9, 2008 respectively, and entitled “Baseball/softball bat and tool handle/grip shock/vibration isolator system” and “Baseball/Softball bat and tool handle/grip shock/Vibration isolator system” respectively, the disclosures of both of which are hereby incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The invention relates in general to hand implements used to impact objects. More specifically, the invention relates to a vibration isolation system for use on sporting equipment and tools to substantially reduce impact forces from being delivered to the user&#39;s hands. 
     BACKGROUND OF THE INVENTION 
     Hand implements used to impact objects generate vibrational forces that are transmitted to the user&#39;s hand(s). There have been numerous attempts to reduce the transmission of these forces to the user&#39;s hand(s). With respect to baseball bats, one approach is to establish a vibration within the bat that is 180 degrees out of phase with natural vibration of the bat. An example of this approach is found in U.S. Pat. No. 5,772,541 to Buiatti, where a vibration dampening member is allowed to vibrate within the knob of the bat to dampen unwanted lower frequency vibration of the bat. Another approach is to provide a two piece bat connected along an interface with a continuous elastomeric union, as is found in U.S. Pat. No. 5,593,158 to Filice, et al., to prevent vibration from the barrel of the bat from being transmitted to the grip end of the bat. It is believed such continuous elastomeric unions establish unnecessarily high spring rates for the system, which are averse to isolating the transmission of vibrational forces. What is needed is to establish a vibration isolation system that has a very low spring rate for the system, and thereby isolate the transmission of vibrational forces to the user&#39;s hand(s). 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides its benefits across a broad spectrum of hand implements. While the description which follows hereinafter pertaining to baseball bats and tennis rackets is meant to be representative of such applications, it is not exhaustive. It is intended that this specification and the claims appended hereto be accorded a breadth in keeping with the scope and spirit of the invention being disclosed despite what might appear to be limiting language imposed by the requirements of referring to the specific examples disclosed. 
     It is one aspect of the present invention to provide a vibration isolation system for hand implements that substantially reduces bending vibrational forces induced upon impact with an object from being transmitted to the user&#39;s hand(s). 
     It is another aspect of the present invention to provide a vibration isolation system for hand implements that minimizes the transmission of torsional forces induced upon impact with an object at a point offset from the centerline of the hand implement. 
     It is a feature of the present invention that an outer shell member is provided that substantially encircles and is spaced outwardly from the grip end of the hand implement. 
     It is another feature of the present invention that at least one isolation element is positioned between the grip end of the hand implement and the outer shell member. 
     It is still another feature of the present invention that the ratio of the fundamental bending natural frequency (ω) divided by the natural frequency of the vibration isolation system (ω o ) is greater than 1.5. 
     It is still yet another feature of the present invention that the ratio of the effective forcing frequency (ω f ) divided by the torsional natural frequency of the vibration isolation system (ω t ) is greater than 1.5 
     It is an advantage of the present invention that, by proper selection and location of isolation elements between the outer shell member and grip end, bending forces induced upon impact with an object are isolated from the user&#39;s hand. 
     It is another advantage of the present invention that, by proper selection and location of isolation elements between the outer shell member and grip end, torsional forces induced upon impact with an object at a point offset from the centerline of the hand implement are isolated from the users hand. 
     These and other aspects, features, and advantages are achieved/attained in the apparatus of the present invention that comprises a outer shell member having an inner surface substantially encircling and spaced outwardly from the grip end of a hand implement. The outer shell member sufficiently spaced outwardly from the grip end allowing the grip end to freely deflect within the outer shell member when the impact end of the hand implement impacts an object within an intended zone of contact. At least one isolation element is positioned between the grip end and the outer shell member and supporting the outer shell member about the grip end. The isolation element and outer shell member establish a spring rate (k) of the vibration isolation system when the system is affixed to the hand implement. The spring rate (k) and mass (m) of the hand implement define a natural frequency of the vibration isolation system (ω o ), wherein the ratio of the fundamental bending natural frequency (ω) divided by the natural frequency of the vibration isolation system (ω o ) is greater than 1.5 By selecting materials for the isolation element that are very soft, a low spring rate (k) is achieved, which in turn allows the ratio (ω/ω o ) to be greater than 1.5, and assures that bending vibrational forces are substantially isolated from the users hand(s). 
     For hand implements which may strike on object a point offset from the centerline of the implement, torsional forces are also isolated according to the present invention vibration isolation system. First, an effective forcing frequency (ω f ) based on the effective duration of impact with an object of the hand implement must be selected. With these values, and with the polar moment of inertia (J) of the hand implement about its centerline, a torsional spring rate (K t ) of the vibration isolation system affixed to the hand implement can be measured. A torsional natural frequency of the vibration isolation system (ω t ) can be determined and if the ratio of the effective forcing frequency (ω f ) divided by the torsional natural frequency of the vibration isolation system (ω t ) is greater than 1.5, the transmission of torsional forces to the users hands are substantially isolated. By the appropriate selection of material and configuration of the isolation element an optimal torsional spring rate (K t ) is achieved, which in turn allows the ratio (ω f /ω t ) to be greater than 1.5, and assures that torsional forces are substantially isolated from the user&#39;s hand(s). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The aspects, features and advantages of the present invention will become apparent upon consideration of the following detailed disclosure of the invention, especially when it is taken in conjunction with the accompanying drawings wherein: 
         FIG. 1  is a side view of a vibration isolation system of the present invention on a baseball bat. 
         FIG. 2  is a cross-sectional view of the vibration isolation system of  FIG. 1 . 
         FIG. 3  is a cross-sectional view of an alternative embodiment of the present invention vibration isolation system for a baseball bat. 
         FIG. 4  is a partial cross-sectional side view of the vibration isolation system on a tennis racket. 
         FIG. 5  is a cross-sectional view of the vibration isolation system of  FIG. 4 . 
         FIG. 6  is a cross-section view taken from  FIG. 5 . 
         FIG. 7  is a side view of an alternate embodiment of the vibration isolation system of the present invention for a tennis racket shown without the outer shell member, isolation elements, and dust shield. 
         FIG. 8  is a cross-section view taken from  FIG. 7  including the outer shell member, isolation elements, and dust shield. 
         FIG. 9  is a side view of the vibration isolation system of  FIG. 2  demonstrating the method of measuring the spring rate (k) of the system. 
         FIG. 10  is an isometric view of the vibration isolation system of  FIG. 4  demonstrating the method of measuring the torsional spring rate (K t ) of the system. 
     
    
    
     To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements or features common to the figures. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to  FIGS. 1 and 2 , a vibration isolation system is shown generally by numeral  10  affixed to a hand implement  12 . The hand implement  12 , in this embodiment, is an aluminum baseball bat having an impact end  14  and a grip end  16 . This embodiment illustrates the present invention in conjunction with hand implements which generally only strike objects at or near the centerline  32  of the implement. Such implements are subject predominately to bending vibrational forces. It is generally known that aluminum baseball bats have a mass (m) of around 16 ounces, and have a fundamental bending natural frequency (ω) of vibration of between about 200 to 600 Hz. Also shown in  FIG. 1  are the fundamental node locations  18 , of the first mode of vibration. At these locations there is essentially no deflection of the bat when it vibrates at the fundamental bending natural frequency (ω). When the batter hits a ball on the node location  18  on the impact end  14  of the bat, vibration of the bat is minimal. This is known as the “sweet spot,” where little of no vibration is transmitted to the batters hands. When the batter hits a ball away from the “sweet spot,” bending vibrational forces travel through the bat and are felt in the batters hands and the grip end  16  of the bat. The vibration isolation system  10  shown in  FIGS. 1-3  substantially eliminates these forces from being transmitted to the batters hands. 
     In reality there are numerous modes of vibration. For purposes of the present invention, only the first three modes are considered to determine vibrational deflection along the grip end  16  of the implement in a perpendicular direction from the centerline  32  of the implement  12 . The vibrational deflection for each of the first three modes are determined at various locations along the grip end  16 , and then added together to establish a vibration deflection profile along the grip end  16 . The following vibration deflection profile along the grip end  16  of a little league approved bat is shown in Table 1. Table 1 was produced based on a model YBCX13 Prodigy—13 bat, 29 inches long weighing 16 ounces, manufactured by Worth, Inc., of St. Louis, Mo. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 1 st  Mode 
                   
                 3 rd  Mode 
                   
               
               
                 Distance from 
                 deflection 
                 2 nd  Mode 
                 deflection 
                 Deflection sum 
               
               
                 knob of bat (x) 
                 (y 1 ) 
                 deflection (y 2 ) 
                 (y 3 ) 
                 (y 1  + y 2  + y 3 ) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0.0 
                 0.179 
                 0.015 
                 0.016 
                 0.211 
               
               
                 0.5 
                 0.159 
                 0.012 
                 0.012 
                 0.183 
               
               
                 1.0 
                 0.138 
                 0.009 
                 0.008 
                 0.156 
               
               
                 1.5 
                 0.118 
                 0.007 
                 0.003 
                 0.128 
               
               
                 2.0 
                 0.098 
                 0.004 
                 0.000 
                 0.102 
               
               
                 2.5 
                 0.078 
                 0.001 
                 −0.004 
                 0.076 
               
               
                 3.0 
                 0.059 
                 −0.001 
                 −0.007 
                 0.051 
               
               
                 3.5 
                 0.040 
                 −0.004 
                 −0.009 
                 0.027 
               
               
                 4.0 
                 0.021 
                 −0.006 
                 −0.010 
                 0.005 
               
               
                 4.5 
                 0.004 
                 −0.007 
                 −0.011 
                 −0.015 
               
               
                 5.0 
                 −0.013 
                 −0.009 
                 −0.011 
                 −0.033 
               
               
                 5.5 
                 −0.029 
                 −0.010 
                 −0.009 
                 −0.048 
               
               
                 6.0 
                 −0.044 
                 −0.010 
                 −0.007 
                 −0.062 
               
               
                 6.5 
                 −0.058 
                 −0.010 
                 −0.005 
                 −0.073 
               
               
                 7.0 
                 −0.070 
                 −0.010 
                 −0.002 
                 −0.082 
               
               
                 7.5 
                 −0.081 
                 −0.009 
                 0.001 
                 −0.089 
               
               
                 8.0 
                 −0.090 
                 −0.008 
                 0.004 
                 −0.094 
               
               
                 8.5 
                 −0.097 
                 −0.007 
                 0.007 
                 −0.097 
               
               
                 9.0 
                 −0.103 
                 −0.005 
                 0.009 
                 −0.099 
               
               
                 9.5 
                 −0.107 
                 −0.003 
                 0.010 
                 −0.099 
               
               
                 10.0 
                 −0.108 
                 −0.001 
                 0.011 
                 −0.099 
               
               
                 10.5 
                 −0.109 
                 0.001 
                 0.011 
                 −0.097 
               
               
                 11.0 
                 −0.107 
                 0.003 
                 0.010 
                 −0.094 
               
               
                   
               
             
          
         
       
     
     Referring to  FIG. 2 , the vibration isolation system  10  comprises an outer shell member  20  and isolation elements  22 . The outer shell member  20  has an inner surface  24  substantially encircling and spaced outward from the grip end  16  of the bat. Further, the outer shell member  20  is sufficiently spaced outwardly from the grip end  16  allowing the grip end  16  to freely deflect within the outer shell member  20  when the impact end  14  of the hand implement impacts an object within an intended zone of contact  52 . From the vibration deflection profile in Table 1, is was determined that a space or gap of about 0.090 inches is sufficient to allow the bat to vibrate without the grip end  16  contacting the outer shell member  20  for a little league approved aluminum bat. In the embodiment shown in  FIGS. 1-2 , the outer shell member  20  is a two piece shell that is adhesively bonded together about the bat, establishing an essentially rigid shell. The shell member  20  can be made from any substantially rigid material such as, for example, metal, plastic, hard rubber, and the like. A polycarbonate plastic tube having an internal diameter of 1.0 inch and a thickness of about 0.062 inches has shown to be satisfactory, with the two piece shell being bonded together with a urethane adhesive/sealant. 
     The isolation elements  22  have an inner mounting surface  26  and an outer mounting surface  28 . The inner mounting surface  26  is affixed to the grip end  16  and the outer mounting surface  28  is affixed to the outer shell member  20 . The isolation elements  22  may be adhesively affixed to the grip end  16  and outer shell member  20 , or held in place by friction. Alternatively the isolation elements  22  may be bonded on one side and allowed to slide or held by friction on the other. It is critical to the present invention to select a very soft material for the isolation elements  22 , so as to establish a low spring rate (k) of the vibration isolation system  10  as it is affixed to the bat. Materials such as elastomers, rubber, foam, plastic, and the like, may be used. Open cell ethylene vinyl acetate rubber 3 mm thick has proven to be a satisfactory material for the isolation elements  22 , such as the material sold as Darice® Foamies 3 mm thick by Darice, Inc. of Strongsville Ohio, being affixed to the outer shell member  20  and grip end  16  with double sided tape. In addition, the “footprint” of the isolation elements, the length of contact they have along the outer shell member  20 , must be relatively small compared to the length of the inner surface  24  along the outer shell member  20 . For the isolation elements  22  in  FIG. 2 , the “footprint” of each isolation element is a length of about 0.50 inches wide and the length of the inner surface  24  of the outer shell member  20  is between about 6 to 9 inches wide. This leaves a significant unsupported gap between the outer shell member  20  and the grip end  16  allowing the grip end to freely deflect. It is to be appreciated that, even with a very soft material for the isolation element  22 , if the “footprint” is too large, the extreme case the “footprint” being the entire length along the inner surface  24  of the outer shell member  20 , the overall spring rate (k) of the system  10  may be too great and significantly hinder the ability of the system  10  to isolate vibration. It is believed that the length of the outer shell member  20  be at least 2 times greater than the footprint length of the isolation elements  22  to allow the grip end  16  to freely deflect within the outer shell member  20 . 
     The isolation elements  22  cross-section may vary along its “footprint” length and also about the circumference of the element about the grip end. This may be done to optimize the vibration isolation system  10  by taking into account the vibration deflection profile for a given hand implement, and the node locations corresponding to the fundamental bending natural frequency (ω) of the hand implement, such as, for example, a golf club. It is to be appreciated that the cross-section of the isolation elements may vary depending on application, such as, for example, circular for a baseball bat, rectangular or octagonal for a tennis racket, or oval for a hammer. 
     Referring to  FIG. 9 , the embodiment shown in  FIGS. 1-2  is shown to illustrate how the spring rates (k) of the isolation elements  22  are measured. The outer shell member  20  is placed on scale  11  and a linear deflection (d) of the grip end  16  is measured under an evenly applied force (F) across the bat that is measured by scale  11 . In  FIG. 9 , the linear deflection (d) of the grip end  16  is shown by numeral  50 , and the sum of the evenly applied force (F) is provided at locations shown by numeral  38 . The forces provided at locations  38  must be applied so that the grip end  16  deflects linearly, that is, there is no angular rotation of the centerline  32  of the implement  12 . Preferably the spring rate (k) is measured along the direction in which the bat is intended to strike a ball. This also applies to any other hand implement that is intended to strike an object in a single direction, such as, for example, a wooden baseball bat, a tennis racket, a hammer, and the like. The spring rate (k) of the isolation elements  22  is determined by:
 
 k =( F÷d )/number of isolation elements in the system.
 
     In the embodiment shown, there are two isolation elements having the same “footprint” and the measured force divided by the deflection must be divided by 2. If there are three isolation elements, it would be divided by 3. According to the present invention, it is the spring rate of one isolation element that is to be determined for calculating the natural frequency of the vibration isolation system (ω o ). This can be accomplished by cutting the implement apart around one isolation element, and measuring the spring rate as shown in  FIG. 9 . 
     It is to be appreciated that the spring rate of each isolation element  22  may vary depending on the vibration deflection profile and node locations  18  of the hand implement  12 . For purposes of the present invention, the isolation element with the lowest spring rate (k) is to be considered in determining the natural frequency of the vibration isolation system (ω o ). It is also to be appreciated that the spring rate of each isolation element  22  may vary depending on the direction in which the spring rate is measured on the implement. For purposes of the present invention, the spring rate is to be measured in the direction in which the hand implement is designed to strike an object. 
     With the spring rate (k) determined and the mass (m) of the bat known, a natural frequency of the vibration isolation system (ω o ) is determined by:
 
ω o =( k÷m ) 1/2  
 
     With the fundamental bending natural frequency (ω) of the bat known, and with the natural frequency of the vibration isolation system (ω o ) determined, the ratio of the fundamental bending natural frequency (ω) divided by the natural frequency of the vibration isolation system (ω o ) is determined. According to the present invention, this ratio (ω/ω o ) must be greater than 1.5. If this ratio (ω/ω o ) is less than about 1.5, too much vibration will be transmitted to the batters hand(s). If the ratio (ω/ω o ) is too low, it can be increased by reconfiguring the isolation elements  22  to obtain a lower spring rate (k) of the isolation elements. The isolation elements can be reconfigured by changing to a softer material, and/or by changing their “footprint” to a smaller length. It is preferred to configure the isolation elements  22  in the system  10  to obtain a ratio (ω/ω o ) of 2.0 or above, yet a value of 1.5 or above is sufficient. The greater the ratio (ω/ω o ), the greater vibration is isolated from the batters hand(s). For the embodiment shown in  FIGS. 1-2 , Table 2 shows the values that were obtained for a little league aluminum bat for the first three fundamental bending natural frequency modes. 
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 ω 
                 M 
                 Impulse 
                 K 
                 ωo 
                   
               
               
                   
                 (rad/sec) 
                 (Ounces) 
                 (lbf-sec) 
                 (lbf/in) 
                 (rad/sec) 
                 (ω/ωo) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 1 st   
                 2640 
                 16 
                 2000 
                 280 
                 329 
                 8.0 
               
               
                 Mode 
               
               
                 2 nd   
                 7277 
                 16 
                 2000 
                 280 
                 329 
                 22.1 
               
               
                 Mode 
               
               
                 3 rd   
                 14268 
                 16 
                 2000 
                 280 
                 329 
                 43.4 
               
               
                 Mode 
               
               
                   
               
             
          
         
       
     
     When the ratio (ω/ω o ) (or forcing frequency/undamped natural frequency—as commonly known to those skilled in the art), increases beyond 1.5, absolute transmissibility (T A ) of vibration drops. The lower the absolute transmissibility, the less amount of vibration is transmitted through a damped or undamped system. Although the fraction of critical damping (ζ) of the system in conjunction with the ratio (ω/ω o ) determines the actual value of absolute transmissibility (T A ) of the system, absolute transmissibility (T A ) drops at a much greater rate in relation to the increase in the ratio (ω/ω o ). Hence, even without knowing the fraction of critical damping (ζ) of the system, when the ratio (ω/ω o ) is greater than 1.5, the absolute transmissibility (T A ) is sufficiently lowered for purposes of the present invention to minimize the transmission of vibration from a hand implement to the outer shell member  20  of the vibration isolation system  10 . Yet an isolation element  22  with a low fraction of critical damping (ζ) is desirable for a lower transmissibility (T A ). As can be seen in Table 2, the ratio (ω/ω o ) of the 1 st  fundamental mode of vibration is the lowest of the first three modes, and why, for purposes of the present invention, the fundamental bending natural frequency ratio (ω) of the 1 st  fundamental mode of vibration is used in determining the ratio (ω/ω o ). 
     Referring to  FIG. 3 , an alternative embodiment of the vibration isolation system  10  is shown. In this embodiment, the outer shell member  20  is integral with the knob  34  of the bat. This allows the system to be affixed to the grip end  16  as a single piece, in contrast to the two piece shell design of the embodiment shown in  FIGS. 1-2 . In both embodiments, dust shields  30  are provided that are affixed to the grip end  16  to prevent particulates from getting embedded between the outer shell member  20  and the grip end  16 . Such particulates would significantly alter the spring rate (k) of the system. Preferably these dust shields  30  are configured so as not to interfere with the movement between the shell member  20  and the grip end of the bat  16 , and therefore have no impact on the spring rate (k) of the system. 
     Referring to  FIGS. 4-6 , an alternative embodiment of the present invention vibration isolation system  10  is shown. This embodiment is intended for hand implements which often strike an object at a distance offset from the centerline  32  of the implement within an intended zone of contact  52 . For such implements, a torsional force is generated and transmitted to the users hand when an object is hit off center. For purposes of illustration, a tennis racket is used in this embodiment, in which the torsional forces generated from “off hit balls” results in what is commonly called “tennis elbow.” 
     The vibration isolation system  10  of  FIGS. 4-6  is similar to the previous embodiments, having an outer shell member  20 , isolation elements  22 , and dust shield  30 , but the outer shell member  20  is configured to mimic the shape of a conventional tennis racket handle, and has an end cap  36  to seal the system from contamination on the end. The system  10  is predominantly configured to isolate torsional forces being transmitted to the player&#39;s hand. Hence, the outer shell member  20  is sufficiently spaced outwardly from the grip end  16  to allow the grip end  16  to torsionally deflect within the outer shell member  20 . In order to configure the present invention vibration isolation system  10  for a tennis racket, the polar moment of inertia (J) about the centerline  32  of the racket, and an effective forcing frequency (ω f ) of the racket need to be determined. 
     To those skilled in the art, determining the polar moment of inertia (J) of the tennis racket about the centerline  32  of the racket is well known. Values of the polar moment of inertia (J) will vary somewhat depending on the type and make of racket. The vibration isolation system of the present invention may be configured for a specific racket thereby utilizing a specific polar moment of inertia (J) measured for a specific racket, or an average value of the polar moment of inertia (J) for a number of rackets may be used. The same applies to the other parameters that have to be selected/determined according to the present invention. 
     The effective forcing frequency (ω f ) of the tennis racket needs to be determined, a parameter related to the impulse (shock and vibration) received by the racket when impacting a tennis ball. For the baseball bat, the fundamental bending natural frequency (ω) was used, between about 200 Hz to 600 Hz. However, tennis racket frames have a first mode of vibration range of between about 90 Hz to 200 Hz, and for most rackets between about 120-130 Hz. Much of the shock is absorbed by the stretch of the rackets strings and the compression of the tennis ball. The total duration of impact (t) of a tennis ball on the strings of a racket is between about 5-6 milliseconds (compared to about 1 millisecond for a baseball and bat), yet the time for the shock wave of impact to reach a player&#39;s hands on a tennis racket is about 2.5 to 4 milliseconds. Hence, the shock wave reaches the player&#39;s hand before the ball leaves the strings of the racket. It is believed that the effective forcing frequency (ω f ) is best determined based on the pulse of the tennis ball impacting the strings of the racket. According to the present invention, the effective forcing frequency (ω f ) is determined by assuming the acceleration pulse of the tennis ball and strings of the racket is a versed sine acceleration pulse. The effective forcing frequency (ω f ) for a tennis racket was determined as follows: 
     (t) the total duration of pulse (period) t=5 milliseconds, 
     (t r ) the effective duration of impulse t r =(1/2) t=2.5 milliseconds, and 
     (ω f ) the effective forcing frequency ω f =(2π/t r )=2513 rad/sec 
     Next, the torsional spring rate (K t ) of the vibration isolation system  10  when affixed to the tennis racket is determined. Referring to  FIG. 10 , the vibration isolation system  10  of the embodiment in  FIGS. 4-6  is shown demonstrating how the torsional spring rate (K t ) is measured. The outer shell member  20  is held fixed, and a torque (T) is applied to the racket  46  about centerline  32 , and an angle of deflection (⊖) measured. The torque (T) is shown by numeral  40 , and the angle of deflection (⊖) is shown by numeral  44 . The torsional spring rate (K t ) is determined from the following equation:
 
 K   t   =T÷⊖ 
 
     It is important that the torsional spring rate (K t ) be measured under a very small angle of deflection (⊖), preferably no greater than between about 0.25 to 5.0 degrees, otherwise the measured value will be too high and will not be representative of the systems actual torsional spring rate for purposes of the present invention. It is believed that under a small angle of deflection, the spring rate will be generally linear, but at or near maximum deflection the spring rate will increase exponentially. Hence, the torsional spring rate (K t ) of the system  10  should be measured within a desired angular deflection range for the system, which for a tennis racket is believed to be between about 0.25 to about 3.0 degrees. One way of determining if the torsional spring rate (K t ) was measured correctly is to measure (K t ) at a number of different deflection points/angles within the desired angular deflection range for the system. The correct value for (K t ) will be the value where they are substantially similar. 
     With the torsional spring rate (K t ) measured, the torsional natural frequency of the vibration isolation system (ω t ) is determined from the following equation:
 
ω t =( K   t   ÷J ) 1/2  
 
     With the effective forcing frequency (ω f ) of the tennis racket, and with the torsional natural frequency of the vibration isolation system (ω t ), the ratio of the effective forcing frequency (ω f ) divided by the torsional natural frequency of the vibration isolation system (ω t ) is determined. This ratio (ω f /ω t ) must be greater than 1.5 in order for the system  10  to effectively isolate torsional forces from being transmitted to the player&#39;s hand(s). As with the previous embodiments, this ratio (ω f /ω t ) can also be adjusted by reconfiguring the isolation elements  22  to obtain a lower torsional spring rate (K t ) of the vibration isolation system. 
     For the embodiment shown in  FIGS. 4-6 , Table 3 shows the values that were determined for a tennis racket. 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                   
                 Off Center 
                   
                   
                 J 
                   
                   
                   
               
               
                 t 
                 tr 
                 ωf 
                 F 
                 Distance 
                 T 
                   
                 (lbm- 
                 Kt (in- 
                 ωt 
               
               
                 (sec) 
                 (sec) 
                 (rad/sec) 
                 (lbf) 
                 (inches) 
                 (in-lbf) 
                 Θ 
                 in 2 ) 
                 lbf/rad) 
                 (rad/sec) 
                 ωf/ωt 
               
               
                   
               
             
             
               
                 0.005 
                 0.0025 
                 2513 
                 100 
                 3 
                 300 
                 3° 
                 1.092 
                 5730 
                 1424 
                 1.76 
               
               
                   
               
             
          
         
       
     
     From value for the torsional spring rate (K t ) determined in Table 3, it is believed that, depending on player preferences, that the range of torsional spring rates (K t ) for various tennis rackets will be between about 3,300 and 40,200 in-lb f /rad. For most other hand implements, it is believed that the range of torsional spring rates (K t ) will be between about 1,140 and 70,000 in-lb f /rad. 
     Referring to  FIGS. 7-8 , an alternate embodiment of the vibration isolation system  10  for a tennis racket is shown. The grip end  16  of the racket  46  is provided with tabs  48 , and the outer shell  20  is provided with slots  42  on the inner surface  24 . Two isolation elements  22  are provided for each tab  48  and are affixed at their inner mounting surface  26  to a respective tab  48 , and at their outer mounting surface  28  to a respective slot  42 . As with the previous embodiments, the isolation elements  22  support the outer shell member  20  about the grip end  16 , and the outer shell member  20  is sufficiently spaced outwardly from the grip end  16  to allow the grip end  16  and grip end tabs  48  to torsionally deflect within the outer shell member  20  when the tennis racket impacts a tennis ball. In this embodiment, the isolation elements are loaded in tension and compression as the grip end  16  torsionally deflects within the outer shell  20 . It is believed this configuration can provide for greater control of the desired deflection range for the system  10 . This is accomplished by configuring the isolation elements  22  to provide a maximum torsional spring rate (K tmax ) for the system. This is achieved by first selecting values for the following parameters:
         (F) the maximum average impact force of the tennis racket when impacting a ball,   (d) the maximum off-center distance of the tennis racket, and   (φ) maximum allowable angle of rotation of the tennis racket when impacting a ball.       

     The maximum average impact force (F) of the tennis racket when impacting an object varies depending on the strength and skill level of the player. Generally, a player can generate an impact force of between about 60 to 120 lbs when striking a tennis ball during a groundstroke. In this embodiment, a maximum average impact force (F) was selected of 100 lbs. 
     The maximum off-center distance (d) of the tennis racket is the maximum distance away from the centerline  32  of the racket within the intended zone of contact of which the ball hits the strings. This is the furthest point from the centerline  32  on the racket that contact can be made while providing reasonable accuracy in the return of the ball. Referring to  FIGS. 4 and 7 , the maximum off-center distance (d) is shown by numeral  54 , and the off-center impact point is shown by numeral  56  at the maximum distance away from the centerline  32  of the racket within the intended zone of contact  52 . According to the present invention, the concern is to minimize torsional forces transmitted to the player&#39;s hands/elbow for off-center hits having a reasonable chance of returning in court to a location desired by the player. Hence an maximum off-center distance (d) for a typical tennis racket was determined to be 3 inches. 
     The maximum allowable angle of rotation (φ) of the hand implement when impacting an object is defined herein to be an acceptable maximum twist of the hand implement  12  within the vibration isolation system  10  due to maximum torsion forces transmitted to the system. It is necessary to select this angle as a constraint to maintain the accuracy of the tennis racket in directing the tennis ball to the location that the player desires. Because the tennis ball remains in contact with the strings of the racket while the isolation system  10  rotates, accuracy of the racket can be compromised if the allowable angle of rotation (φ) is too great, such as, for example, about 5 degrees or more. Hence, according to the present invention, the allowable angle of rotation (φ) for a tennis racket is selected to be 3 degrees. 
     The maximum torsional spring rate (K tmax ) is calculated as follows:
 
 K   tmax =( F·d )÷φ
 
     and the calculated (K tmax ) is then compared to an actual measurement of (K tmax ) following the method discussed in measuring (K t ) shown in  FIG. 10 . In contrast to measuring (K t ) under a small deflection angle, (K tmax ) is measured by increasing the force  40  until the deflection reaches the maximum allowable angle of rotation (φ) of 3 degrees. The isolation elements can then be reconfigured to get the measured (K tmax ) as close to the calculated (K tmax ) as desired. 
     It is to be appreciated that the measured (K tmax ) may be the same value, or nearly the same, as the measured (K t ) value. This would be the case if the torsional spring rate remains linear throughout the allowable angle of rotation range of the hand implement, as is believed to be the case in the embodiment shown in  FIGS. 4-6 . However, in the embodiment shown in  FIGS. 7-8 , (K tmax ) may be greater than (K t ) as the isolation elements may “bottom out” when loaded in compression due to maximum torque loads on the system. For purposes of the present invention, the measured value of (K tmax ) should not be used in determining the ratio (ω f /ω t ) unless it is identical to the value measured for (K t ). 
     The embodiments of the vibration isolation system  10  shown in  FIGS. 4-8  for a tennis racket not only isolate torsional forces from being transmitted to the player&#39;s hand(s), they also have the advantage of being able to increase racket control. The duration of time that a ball is in contact with the strings of a racket depends significantly on the tension in the strings of the racket. A tennis racket strung in high tension will have a smaller duration of time that the ball is in contact with the strings than a tennis racket strung with low tension. The duration of time that the ball is in contact with the strings, the racket rotates through a swing angle generated by the player. For a tennis racket strung in high tension, the swing angle will be less than a tennis racket strung in low tension. The higher the string tension, the lower the swing angle, and the greater the racket control is for the player. Unfortunately, the higher the string tension, the greater the recoil force is transmitted to the player. According to the present invention, the recoil force will angularly deflect the grip end  16  with respect to the outer shell member  20  thereby reducing the swing angle by this amount of deflection. Therefore, according to the present invention, racket control is increased for any given racket because the swing angle is reduced. 
     It is to be appreciated that the vibration isolation system  10  of the present invention can be tuned for different hand implements. The system can be tuned to account for bending vibration, as demonstrated with the bat, recoil, as demonstrated with the tennis racket, and twist, as also demonstrated with the tennis racket. Further, the system  10  can be tuned to account for all three; bending vibration, recoil, and twist. 
     What has been described are preferred embodiments of a vibration isolation system. Those skilled in the art will appreciate that numerous modifications are possible without materially departing from the novel teachings and advantages of the subject matter described herein. Other modifications, substitutions, changes, and omissions may be made in the design and arrangement of the preferred and other exemplary embodiments without departing from the spirit of the present invention.