Abstract:
An exemplary contour measuring method for measuring aspects of objects includes: (1) providing a measuring device including two contour measuring probes and a processor, the contour measuring probe having a tip extension and a displacement sensor used to sense a displacement of the tip extension, the processor being electrically connected to the displacement sensors; (2) driving two tip extensions to contact two opposite surfaces of an object respectively; (3) driving the two tip extensions to move and contacting the two opposite surfaces of the object respectively, while the displacement sensors sending the displacement information on the tip extensions to the processor; (4) computing a cross-section of the object by the processor according to the displacement information on the tip extensions; (5) repeating the step (3) and (4), the processor computing a plurality of cross-sections of the object, the cross-sections compiled to obtain aspects of object.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is related to nine co-pending U.S. patent applications, which are: application Ser. No. 11/611,724, filed on Dec. 15, 2006, and entitled “DISTANCE MEASURING PROBE WITH AIR DISCHARGE SYSTEM”, application Ser. No. 11/843,664, filed on Aug. 23, 2007, and entitled “CONTOUR MEASURING DEVICE WITH ERROR CORRECTING UNIT”, application Ser. No. 11/966,951, filed on Dec. 28, 2007, and entitled “CONTOUR MEASURING PROBE”, application Ser. No. 11/966,952, filed on Dec. 28, 2007, and entitled “CONTOUR MEASURING PROBE”, application Ser. No. 11/966,956, filed on Dec. 28, 2007, and entitled “CONTOUR MEASURING METHOD FOR MEASURING ASPECTS OF OBJECTS”, application Ser. No. 11/966,964, filed on Dec. 28, 2007, and entitled “MEASURING DEVICE FOR MEASURING ASPECTS OF OBJECTS”, application Ser. No. 11/966,961, filed on Dec. 28, 2007, and entitled “MEASURING DEVICE AND METHOD FOR USING THE SAME”, application Ser. No. 11/966,959, filed on Dec. 28, 2007, and entitled “BASE AND CONTOUR MEASURING SYSTEM USING THE SAME”, and application Ser. No. 11/966,954, filed on Dec. 28, 2007, and entitled “CONTOUR MEASURING PROBE FOR MEASURING ASPECTS OF OBJECTS”. In Ser. No. 11/611,724, Ser. No. 11/843,664, Ser. No. 11/966,951, and Ser. No. 11/966,956, the inventors are Qing Liu, Jun-Qi Li, and Takeo Nakagawa. In Ser. No. 11/966,961, Ser. No. 11/966,961, Ser. No. 11/966,964, Ser. No. 11/966,959, and Ser. No. 11/966,951, the inventors are Qing Liu and Jun-Qi Li. In Ser. No. 11/966,954, the inventors are Jian-bin Kong and Qing Liu. In Ser. No. 11/611,724 and Ser. No. 11/843,664, the assignee is Hon HAI PRECISION INDUSTRY CO. LTD and FINE TECH Corporation, and the assignee of other applications is HONG FU JIN PRECISION INDUSTRY (ShenZhen) CO., LTD and Hon HAI PRECISION INDUSTRY CO. LTD. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates generally to contour measuring methods for measuring aspects of objects, and more particularly to a contour measuring method for ultra precise measuring aspects of objects. 
   2. Discussion of the Related Art 
   A typical contour measuring method uses a contact probe as its measuring element. Referring to  FIG. 10 , the measuring device  90  includes a magnetic core  91 , a coil  92 , a fulcrum  93 , a level  94 , and a measuring tip  95 . A distal end of the measuring tip  95  always contacts with a surface of a workpiece  96 . The contour measuring method includes the following steps: (1) driving the workpiece  96  to move along an X-axis; (2) the measuring tip  95  moves along a Z-axis because the workpiece  96  has a curved surface, thus the level  94  rotates about the fulcrum  93 ; (3) the magnetic core  91  moves in the coil  92 , this movement of the magnetic core  91  induces a current in the coil  92 ; (4) The current flows into the managing circuit  97  and the managing circuit  97  amplifies and transforms the current into a digital value that is used as a signal to the computer  98 ; (5) the computer  98  calculates a displacement of the magnetic core  91  according to the digital signal, thus indirectly determining a displacement of the measuring tip  95 . 
   However, the above-described contour measuring method has the following disadvantages. Firstly, cumulative errors may generate and propagate from the coil  92 , and in each of the conversions, to the computer calculation of the displacement of the core  91 . Thus, a cumulative error is very large in the contour measuring method. Secondly, a non-linear error is generated when the coil  92  works in a non-linear region of the coil  92 . Thirdly, the measuring range is very small because of the non-linear region of the coil  92 . Finally, in order to measure the lower surface of the workpiece  96 , the workpiece  96  should be turned over. This turning over and repositioning of the workpiece  96  may result in the workpiece  96  being repositioned outside of the original position, thus the measuring precision further decreases. 
   Therefore, a contour measuring method for measuring aspects of objects which have high precision are desired. 
   SUMMARY 
   An exemplary contour measuring method for measuring aspects of objects includes: (1) providing a measuring device including two contour measuring probes and a processor, the contour measuring probe having a tip extension being slidable in a first direction, and a displacement sensor used to sense a displacement of the tip extension, the processor being electrically connected to the displacement sensors; (2) driving one tip extension to contact a first surface of an object, and driving the other tip extension to contact the second surface of the object opposite to a second surface; (3) driving the two tip extensions to move and maintain contact with the first surface and the second surface of the object respectively, while the displacement sensors sending the displacement information of the tip extensions to the processor; (4) computing a cross-section of the object by the processor according to the displacement information on the tip extensions; (5) repeating the step (3) and (4), the processor computing a plurality of cross-sections of the object, the cross-sections compiled to obtain aspects of object. 
   Other advantages and novel features will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The components in the drawings are not necessarily drawn to scale, the emphasis instead being placed upon clearly illustrating the principles of the present contour measuring method for measuring aspects of objects. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views, and all the views are schematic. 
       FIG. 1  is a schematic isometric view of a measuring device applied in a contour measuring method for measuring aspects of objects according to a first preferred embodiment of the present invention. 
       FIG. 2  is a top plan, cross-sectional view of a first contour measuring probe of the measuring device of  FIG. 1 . 
       FIG. 3  is a side, cross-sectional view of the first contour measuring probe of  FIG. 2 . 
       FIG. 4  is a schematic view of the measuring device of  FIG. 1  measuring aspects of an object. 
       FIG. 5  is a chart showing a process that a processor calculates values of a cross-section S 0  of the object of  FIG. 4 . 
       FIG. 6  is a top plan, cross-sectional view of a contour measuring probe applied in a contour measuring method for measuring aspects of objects in accordance with a second embodiment of the present invention. 
       FIG. 7  is a side, cross-sectional view of the contour measuring probe of  FIG. 6 . 
       FIG. 8  is a force analysis view of hollow tubes of the contour measuring probe of  FIG. 6 . 
       FIG. 9  is a top plan, cross-sectional view of a contour measuring probe applied in a contour measuring method for measuring aspects of objects in accordance with a third embodiment of the present invention. 
       FIG. 10  is a schematic view of a conventional measuring device. 
   

   DETAILED DESCRIPTION OF THE EMBODIMENTS 
   Reference will now be made to the drawings to describe preferred embodiments of the present contour measuring method, in detail. 
   Referring to  FIG. 1 , a measuring device  100  in accordance with a first embodiment is shown. The measuring device  100  includes a first contour measuring probe  10 , a second contour measuring probe  20 , and a processor  30 . The first and second contour measuring probes  10 ,  20  are electrically connected to the processor  30 . 
   Referring to  FIG. 2  and  FIG. 3 , the first contour measuring probe  10  includes a base  11 , a tube guide  12 , two hollow tubes  14 , a first tube frame  15 , the first tip extension  16 , a second tube frame  17 , a linear measuring scale  18 , a displacement sensor  19 , a pipe holder  110 , and two pipes  111 . The hollow tubes  14  and the first and second tube frames  15 ,  17  cooperatively form a movable rack (not labeled). 
   The base  11  is substantially a flat rectangular sheet. It should be understood that the base  11  may alternatively be any other suitable shapes. The tube guide  12  is securely mounted onto the base  11 . The tube guide  12  has a front end and a rear end. The tube guide  12  defines two tube chutes  13  each extending from the front end to the rear end. The tube chutes  13  are spaced apart from, and aligned parallel to each other. 
   Each of the hollow tubes  14  is a cylinder defining a cavity  142  that extends through the hollow tube  14  from a open rear end of the hollow tube  14  to a front cylinder base  140  of the hollow tube  14 . Each hollow tube  14  is received through a corresponding tube chute  13  of the tube guide  12 . The open rear ends of the hollow tubes  14  protrude out from the rear end of the tube guide  12  and are fixed onto the second tube frame  17 . The cylinder bases  140  of the hollow tubes  14  protrude out from the front end and are fixed onto the first tube frame  15 . An outer diameter of the hollow tubes  14  is configured to be smaller than a diameter of the tube chutes  13 , so that a gap (not labeled) is defined between each hollow tube  14  and the tube guide  12 . Air is continuously pumped into the gap between the hollow tubes  14  and the tube guide  12  at a predetermined rate. Thus, an air bearing (not labeled) is formed between each hollow tube  14  and the tube guide  12  when the gaps are filled with air. Therefore, frictional forces between the hollow tubes  14  and the tube guide  12  are minimal. As a result, the hollow tubes  14  are able to move smoothly in the tube chutes  13  correspondingly. 
   Each of the pipes  111  is partially inserted into the open end of a corresponding hollow tube  14 . An outer diameter of the pipes  111  is smaller than an inner diameter of the cavities  142  of the hollow tubes  14 , so that a gap  118  is defined between each pipe  111  and the corresponding hollow tube  14 . An air bearing (not labeled) is formed between each pipe  111  and the corresponding hollow tube  14  when air is pumped into the cavities  142  of the hollow tubes  14  via the pipes  111 . Therefore, frictional forces between the pipes  111  and the hollow tubes  14  is significantly small correspondingly. It should be understood that the gaps  118  may be omitted, and as an alternative, a lubricant can be applied between the pipes  111  and the hollow tubes  14  to reduce frictional forces. 
   The pipe holder  110  is fixed on the base  11 . The pipe holder  110  is configured to hold the pipes  111  in position. When air is pumped into the cavities  142  of the hollow tubes  14 , an air current inside the cavities  142  creates a pushing force that pushes the hollow tube  14  away from the pipes  111 , thereby driving the first tip extension  16  away from the second tube frame  17 . The air pumped into the cavities  142  of the hollow tubes  14  and the tube chutes  13  may also be any suitable kinds of gas such as oxygen, nitrogen, etc. 
   The first tip extension  16  is needle-shaped, and has a contact tip (not labeled) that touches a surface of an object when the first contour measuring probe  10  is used to measuring the object. The first tip extension  16  is fixed on the first tube frame  15  so that the first tip extension  16  is linearly movable together with the movable rack. The linear measuring scale  18  is fixed on the second tube frame  17  such that it moves (displaces) linearly when the movable rack moves. The displacement sensor  19  is mounted on the base  11  corresponding to the linear measuring scale  18 . The displacement sensor  19  is used for reading displacement values of the linear measuring scale  18 . Alternatively, the positions of the linear measuring scale  18  and the displacement sensor  19  may be exchanged. 
   Again referring to  FIG. 3 , the first contour measuring probe  10  further includes a cover  112  that engages with the base  11  and completely seals other various components of the first contour measuring probe  10  except the base  11  and a part of the first tip extension  16 . The cover  112  defines an opening (not labeled) for allowing an end portion including the contact tip of the first tip extension  16  to extend out from the opening. The air is pumped into the gaps between the tube guide  12  and the hollow tubes  14  to form the air bearing via a plurality of tubes  114  mounted to the cover  112 . 
   The first contour measuring probe  10  further includes an air discharge system  115 . The air discharge system  115  is configured to eject air out of the cavity  142  of each hollow tube  14 . The air discharge system  115  can be selected from one or more of a group of a first air eject hole (not shown) defined in a center of the cylinder base  140  of each hollow tube  14 ; a second air eject hole (not shown) defined in the cylinder base  140  of each hollow tube  14  and a plurality of peripheral air eject holes (not shown) defined in the cylinder base  140  and surrounding the second air eject hole; a plurality of third air eject holes (not shown) defined in the cylinder base  140  of each hollow tube  14 ; a plurality of cylindrical fourth air eject holes (not shown) defined in a sidewall of each hollow tube  14 ; and the gap  118  between each hollow tube  14  and the corresponding pipe  111 . That is, the air discharge system  115  is a channel communicating an outer of the hollow tube  14  and the cavity  142  of the hollow tube  14 . 
   In alternative embodiments, the first contour measuring probe  10  can include only one hollow tube  14  or more than two hollow tubes  14 . In such embodiments, there can correspondingly be only one pipe  111  or more than two pipes  111 . The tube guide  12  may define only one tube chute  13  or more than two tube chutes  13  corresponding to the number of the hollow tubes  14 . 
   In use, the first contour measuring probe  10  is placed near the object. The pipes  111  and the tubes  114  communicate with an air chamber (not shown), and air is pumped into the cavities  142  of the hollow tubes  14  and the gaps between the tube guide  12  and the hollow tubes  14 . When the contact tip of the first tip extension  16  touches the object, the movable rack together with the first tip extension  16  stops moving. When the first tip extension  16  and correspondingly the linear measuring scale  18  move from one position to another position, the displacement sensor  19  detects and reads a displacement of the linear measuring scale  18 . That is, a displacement of the first tip extension  16  is measured. The displacement sensor  19  connected to the processor  30  sends the displacement of the first tip extension  16  to the processor  30 . 
   When air is pumped into the cavities  142  of the hollow tubes  14 , air pressure in the cavities  142  pushes air out of the hollow tubes  14  via the air discharge systems  115 . That is, air is continuously pumped into the hollow tubes  14  via the pipes  111  and continuously ejected out of the hollow tubes  14  via the air discharge systems  115 . The air pumped into the hollow tubes  14  creates an air current that pushes the hollow tubes  14  to move in a direction that the hollow tubes  14  move out of the tube guide  12 . The air pressure pushing the hollow tubes  14  is relatively small and steady. That is, an overall measuring force that pushes the first tip extension  16  is relatively small and steady. As a result, the first tip extension  16  of the first contour measuring probe  10  is pushed so that the contact tip  162  gently touches the object. Thus, the contact tip of the first tip extension  16  and the object are not easily deformed or damaged, thereby improving a precision of measurement. In addition, a pressure inside the cover  112  is kept higher than that of the pressure of the environment outside the cover  112 , because air ejecting out of the air bearings and the hollow tubes  14  fills the cover  112 . Thus, dust and other particles are prevented from entering the cover  112  through any openings thereof. 
   The second contour measuring probe  20  has a same structure as the first contour measuring probe  10 . The processor  30  is electrically connected to the linear measuring scale  18  of the first contour measuring probe  10  and a linear measuring scale of the second contour measuring probe  20 . 
   Referring to  FIG. 4  and  FIG. 5 , before measuring, the first contour measuring probe  10  is secured on a slidable platform  51  that is mounted on a machine (not shown) and slidable parallel to the XY-plane. The second contour measuring probe  20  is secured on a slidable platform  52  that is mounted on the machine and slidable parallel to the XY-plane. An object  40  has a first surface  401  and a second surface  402  opposite to the first surface  401 . The first tip extension  16  of the first contour measuring probe  10  gently pushes against the first surface  401 , and a second tip extension  26  of the second contour measuring probe  20  gently pushes against the second surface  402 . The first contour measuring probe  10  and the second contour measuring probe  20  are positioned in a manner such that the first tip extension  16  and the second tip extension  26  are aligned pointing toward each other perpendicular a same point on the XY plane. 
   In a measuring process, the slidable platforms  51 ,  52  are moved in a same direction and drives the first tip extension  16  and the second tip extension  26  to move along a same linear axis. When the first and second tip extensions  16 ,  26  move along the X-axis, the first tip extension  16  remains gently pushing against the first surface  401  of the object  40  and the second tip extension  26  remains gently pushing against the second surface  402  of the object  40 . After the first and second tip extensions  16 ,  26  linearly move across the object  40  once, the processor  30  can compute (map) a cross-section S of the object  40  according to the displacement information provided by the first contour measuring probe  10  and the second contour measuring probe  20 . 
   A method for computing the cross-section S is detailed described as follows. 
   (1) The first contour measuring probe  10  is moved to a first predetermined position such that the first tip extension  16  is dragged along and gently pushes against the first surface  401  of the object  40  at a first predetermined point. Then, the processor  30  records a coordinate of the first predetermined point such as (0, Y 0 , Z m0 ). The second contour measuring probe  20  is moved to a second predetermined position such that the second tip extension  26  is dragged along and gently pushes against the second surface  402  of the object  40  at a second predetermined point. At the same time, the processor  30  records the coordinate of the second predetermined point such as (0, Y 0 , Z n0 ). The first predetermined point and the second predetermined point lies on a straight line parallel to the Z-axis.
 
(2) The slidable platforms  51 ,  52  move parallel to the X-axis of a distance X 1  at a same speed, thus the first contour measuring probe  10  is driven to move parallel to the X-axis with the first tip extension  16  pushing against the first surface  401  to the third predetermined point, and the second contour measuring probe  20  is driven to move parallel to the X-axis with the first tip extension  26  pushing against the second surface  402  to the third predetermined point. The third predetermined point and the fourth predetermined point are lies on a straight line parallel to the Z-axis. The linear measuring scale  18  of the first contour measuring probe  10  measures the displacement Z m1  along the Z-axis of the first tip extension  16 , and sends the information to the processor  30 . The processor  30  records a coordinate of the third predetermined point as (X 1 , Y 0 , Z m0 +Z m1 ). The linear measuring scale of the second contour measuring probe  20  measures the displacement Z n1  along the Z-axis of the second tip extension  26 , and sends the information to the processor  30 . The processor  30  records a coordinate of the fourth predetermined point as (X 1 , Y 0 , Z n0 +Z n1 ).
 
(3) The first tip extension  16  of the first contour measuring probe  10  is sequentially moved to a series of predetermined point, thus the processor  30  will obtain a series of point coordinates of (X 2 , Y 0 , Z m0 +Z m2 ), (X 3 , Y 0 , Z m0 +Z m3 ) . . . (X j , Y 0 , Z m0 +Z mj ). The second tip extension  26  of the second contour measuring probe  20  is moved to a series of predetermined point on a straight line across the object, thus the processor  30  will obtain a series of point coordinates of (X 2 , Y 0 , Z n0 +Z n2 ), (X 3 , Y 0 , Z m0 +Z m3 ) . . . (X j , Y 0 , Z m0 +Z mj ).
 
(4) The processor  30  computes curvatures of a curve A of the object  40  in a plane of Y=Y 0 , according to the series of point coordinates of (0, Y 0 , Z m0 ), (X 1 , Y 0 , Z m0 +Z m1 ), (X 2 , Y 0 , Z m0 +Z m2 ) . . . (X j , Y 0 , Z m0 +Z mj ). The processor  30  computes curvatures of a curve B of the object  40  in the plane of Y=Y 0 , according to the series of point coordinates of (0, Y 0 , Z n0 ), (X 1 , Y 0 , Z n0 +Z n1 ), (X 2 , Y 0 , Z n0 +Z n2 ) . . . (X j , Y 0 , Z n0 +Z nj ). Then, the processor  30  computes a distance D between the curve A and the curve B according to the formula of D j =|(Z m0 +Z mj )−(Z n0 +Z nj )|. Therefore, the cross-section S 0  of the object  40  including the curves can be derived by the processor  30  via the curve A, the curve B and the distance D between the curve A and the curve B.
 
   After computing the cross-section S 0  in the plane of Y=Y 0 , the first contour measuring probe  10  and the second contour measuring probe  20  can move into planes of Y=Y 1 , Y=Y 2  . . . Y=Y j  carried by the slidable platforms  51 ,  52  respectively. Afterwards, the measuring device  100  repeats the above described four steps (1), (2), (3), (4) in each plane to get a plurality of cross-sections S 1 , S 2  . . . S j  of the object  40 . Then, the plurality of cross-sections S 0 , S 1 , S 2  . . . S j  is compiled by the processor  30  to obtain an aspect of the object  40 . 
   Because the first and second contour measuring probes  10 ,  20  of the measuring device  100  can measure the displacements of the first and second tip extensions  16 ,  26  by the displacement sensors, and the displacement sensors send the displacement information on the first and second tip extensions  16 ,  26  to the processor  30  immediately, the measuring device  100  have a high measuring precision. Furthermore, the object  40  does not need to be rotated during the measuring process, thus the measuring precision of the measuring device  100  further increases. 
   It should be understood that the slidable platforms  51 ,  52  can also carry the contour measuring probes  10 ,  20  to move along the Y-axis, in order to get a plurality of cross-sections of the object  40  parallel to the YZ plane. The plurality of cross-sections also can be compiled by the processor  30  to obtain an aspect of the object  40 . In addition, the first tip extension  10  and the second tip extension  20  may not lies on a straight line when moving along the X-axis, but should remain in a plane. 
   The measuring method can also use other contour measuring probes, for example, referring to  FIG. 6  and  FIG. 7 , a contour measuring probe  60  in accordance with a second embodiment described as follows. 
   The contour measuring probe  60  is similar to the first contour measuring probe  10  except that the contour measuring probe  60  does not include the pipes  111  (shown in  FIG. 2 ), but includes a plurality of tubes  604 ,  606  disposed obliquely in a tube guide  62  relative to hollow tubes  63 . The contour measuring probe  60  includes the tube guide  62 , two hollow tubes  63 , and a tip extension  66 . The tubes  604  are oblique relative to an axis of the hollow tubes  63 . That is, an angle defined by extension directions of the tubes  604  relative to the axis of the hollow tubes  63  is in a range from larger than 0 degree and smaller than 90 degrees. The tubes  604 ,  606  are respectively parallel to and spaced from each other, and are communicated with tube chutes  621  defined in the tube guide  62 . The tubes  606  are symmetrical to the tubes  604  relative to the axis of the hollow tubes  63 , and the tubes  604 ,  606  are disposed in a same plane. Also, the tubes  606  may be not symmetrical to the tubes  604 , but stagger with the tubes  604  so long as a force performed on the hollow tubes  63  at all directions except a moving direction of the tip extension  66  is balance. Alternatively, the tubes  606  can be omitted. With the condition, the hollow tubes  63  may offset under a force performed thereon in a direction perpendicular to the axis of the hollow tubes  63 . 
   Referring to  FIG. 8 , when air is pumped into the tube chutes  621  and hits a sidewall of the hollow tubes  63  via the tubes  604 ,  606 , air from the tubes  604  applies a force F 1  and air from the tubes  606  applies a force F 2  on the hollow tubes  63 . A value of the force F 1  is the same as that of the force F 2  because the number of the tubes  604  is the same as that of the tubes  606 , and also because the tubes  606  and the tubes  604  are symmetrically disposed. Therefore, a force applied to the hollow tubes  63  in an X-direction shown in  FIG. 8  is F 1X +F 2X , and a force applied to the hollow tubes  63  in a Y-direction is 0. The force F 1X +F 2X  pushes the hollow tubes  63  together with the tip extension  66  to move. In addition, an air bearing is formed when air is filled in a gap between the tube guide  62  and the hollow tubes  63 . Therefore, a frictional forces between the tube guide  62  and the hollow tubes  63  is significantly small. 
   Referring to  FIG. 9 , a contour measuring probe  70  in accordance with a third embodiment described as follows may also be used in the contour measuring method. 
   The contour measuring probe  70  is similar in principle to the first contour measuring probe  10  except that tube guides  72 A,  72 B holding hollow tubes  73 A,  73 B offset each other in the contour measuring probe  70 . That is, the tube guide  72 A is configured at a front portion of the base  71 , and the tube guide  72 B is configured at a back portion of the base  71 . Because the tube guides  72 A,  72 B offset each other, the tube guides  72 A,  72 B of the contour measuring probe  70  collectively hold the hollow tubes  73 A,  73 B along a greater length as measured along a slidable direction of the tip extension (not labeled), than the first contour measuring probe  10 . Therefore, the tip extension of the contour measuring probe  70  can move very steadily forward and backward with little or no lateral displacements. Alternatively, the contour measuring probe  70  can includes one pipe  701  only. Accordingly, air is pumped into one of the hollow tubes  73 A,  73 B. Thereby, the contour measuring probe  70  is further simplified. 
   It is believed that the present embodiments and their advantages will be understood from the foregoing description, and it will be apparent that various changes may be made thereto without departing from the spirit and scope of the invention or sacrificing all of its material advantages, the examples hereinbefore described merely being preferred or exemplary embodiments of the invention.