Patent Publication Number: US-6338543-B1

Title: Methods and apparatus for thermally-insensitive mounting of multiple actuators

Description:
BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     The invention relates to making a multiple actuator device insensitive to thermally-induced expansions and contractions. 
     2. Description of Related Art 
     In existing thermal ink jet printing devices, the printhead cartridge comprises one or more ink-filled printheads. In a common design for an ink jet printer, the cartridge is mounted upon a movable carriage. The printheads of the object printer are arranged opposite a sheet of recording medium on which an image is to be printed. During printing, the cartridge is moved with the carriage across the sheet in repeatable swaths to form an image, much like a typewriter. During non-printing, the cartridge is at rest awaiting instructions from, for instance, an electronic controller. In another common ink jet printer design, the cartridge is stationary and the paper is moved across an array of printhead nozzles that span the full-width of the cartridge. In yet another multi-head device, for example, a charged coupled device (CCD) array having a plurality of sensor heads, the sensor heads receive varying color and image information for subsequent reproduction on a recording medium. 
     SUMMARY OF THE INVENTION 
     Mounting the sensor or print-heads on the carriage of a multi-head device requires the multi-heads to be initially spaced apart a designated, or nominal, distance relative to the other respective heads. Thus, when the temperature of the carriage on which all of the printheads, or sensor heads, are mounted changes, the carriage undergoes thermal expansion or contraction. Whenever the temperature of the carriage changes from a nominal temperature, at which the heads are at the nominal spacing, the thermal expansion or contraction of the carriage will cause the actual spacing between the printheads, or sensor heads, to differ from the nominal spacing. As a result, ink droplets are deposited on the recording medium at improper locations in the case of a multi-head printer. Similarly, image data is received at improper locations in the case of, for example, a CCD sensor array. Thus, the thermally-induced movement of the printheads or sensor heads tends to cause a mis-registration of colors or print images, or of sensed color separation layers, of due to improper, or at least inconsistent, positioning of the printheads or sensor heads relative to one another. 
     Precision placement of ink droplets, or the precision reception of image data, is essential to lessen contaminating color shifts, or blurring or shifting of colors that otherwise occur due to thermal expansion of the carriage the plurality of printheads, or sensor heads, are mounted upon. The correct droplet, or pixel, alignment becomes increasingly important in high-end printing, such as photographic printing or acoustic inkjet printing, in which very small droplets of ink are used. 
     This invention provides apparatus that are insensitive to thermally-induced spacing variations between multiple actuators, such as printheads or sensor heads, in a multi-actuator device. This invention separately provides methods and apparatus that increase the efficiency of image generating multi-actuator devices. This invention also separately provides methods and apparatus resulting in precision placement of image producing materials for accurate image reproductions and increased color clarity. 
     The methods and apparatus of the invention are derived, in part, from an 18 th  century application for controlling pendular motions in clocks. In the pendular motion controlling technique, materials having different thermal expansion properties carefully controlled the effective swing length of a clock&#39;s pendular arm. By using materials of known thermal expansion properties, the time period of the pendular swing was consistently controlled relative to gears within the clock casing housing the pendular arm and the clock&#39;s gears. The technique permitted the precision necessary for proper and consistently reliable time-keeping notwithstanding the changing thermal conditions the clock was subjected to. In the systems and methods according to this invention, that concept is applied to control spacing in multi-actuator devices. 
     Further, while previous printers required manual correction of the multiple printheads of an image producing device to achieve proper alignment of the multiple printheads relative to one another, the methods and apparatus according to this invention reduces the need for manual correction, decreasing the occurrence of human error and increasing the precision placement of ink droplets, or the precision reception of image data. As a result, multiple actuator imaging devices are easier to operate and become more effective. 
     In various exemplary embodiments of the invention, the spacing between multiple actuators, such as printheads or sensor heads, is controlled or rendered insensitive to thermally-induced expansion or contraction by fixing a first actuator to an underlying common carriage or frame. All of the other actuators are linked to the first actuator by links of two dissimilar materials having different coefficients of thermal expansion. In particular, the other actuators are not fixed to the carriage or frame. Instead, the other actuators are “cantilevered” off, i.e., fixed to, the first actuator by the link and are merely supported by the carriage or frame. In other words, the other actuators “float” relative to the carriage or frame. As a result, when the underlying carriage or frame undergoes thermal expansion or contraction, the distance between the linked actuators remains constant. This tends to reduce, if not eliminate, thermally-induced spacing shifts between the actuators. In a printer having printheads as the actuators, this also tends to improve the placement of the ink droplets ejected from each printhead onto the recording medium. In a scanner having multiple CCD array sensor heads as the actuators, the reception of image data by a sensor head for subsequent reproduction onto a recording medium is improved. In CCD array sensor heads, for example, the reduction of thermally-induced spacing shifts tends to reduce mis-registration between the various color separations. 
     Thus, the apparatus and methods according to this invention reduce the need for an operator to manually correct the spacing between actuators due to thermally-induced spacing shifts. Further, the apparatus and methods according to this invention enable the proper ink droplet placement onto a recording medium in a multiple printhead ink jet printer to be maintained. The apparatus and methods according to this invention make a multiple actuator image forming or printing process easier and more precise than previous multiple actuator image forming or printing devices. 
     These and other features and advantages of this invention are described in, or are apparent from, the following detailed description of various exemplary embodiments of the systems and methods according to this invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Various exemplary embodiments of this invention will be described in detail, with reference to the following figures, wherein: 
     FIG. 1 is a perspective view of an ink jet printer including a movable printhead cartridge; 
     FIG. 2 is a schematic view of a movable printhead cartridge and related structures of an ink jet printer; 
     FIG. 3 is a schematic view of a first exemplary embodiment of four linked multiple printheads, or sensor heads, according to this invention; 
     FIG. 4 is a schematic view of the first exemplary embodiment of showing two linked multiple printheads, or sensor heads, according to this invention; 
     FIG. 5 is a schematic view of a second exemplary embodiment showing two linked multiple printheads, or sensor heads, according to this invention; 
     FIG. 6 is a schematic view of a third exemplary embodiment showing two linked multiple printheads, or sensor heads, according to this invention; 
     FIG. 7 is a schematic view of a fourth exemplary embodiment showing two linked multiple printheads, or sensor heads, according to this invention; and 
     FIG. 8 is a schematic view of a fifth exemplary embodiment showing two linked multiple printheads, or sensor heads, according to this invention. 
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S) 
     FIG. 1 shows a perspective view of one exemplary embodiment of an exemplary carriage-type ink jet printing device  1 . FIG. 2 shows a schematic view of one exemplary embodiment of the carriage and related structures of the ink jet printer  1  shown in FIG. 1. A linear array of ink-droplet producing channels are housed within each of a plurality of printhead cartridges  2  mounted upon a reciprocal carriage  3 . The array of ink-droplet producing channels extends along a first direction, indicated by the arrow A, i.e., the printing direction. Ink droplets  4  are propelled onto a recording medium  5 , such as a sheet of paper, that is stepped a preselected distance (often equal to the size of the array), often by a motor  6 , in the printing direction A each time the carriage  3  and the printhead cartridges  2  traverse across the recording medium  5  along the swath axis B. The recording medium  5  can be stored on a supply roll  7  and stepped onto takeup roll  8  by the motor  6 , or can be stored in and/or advanced using other structures, apparatuses or devices well known to those of skill in the art. 
     The printhead cartridges  2  are mounted, for instance on a support base  9 , and move reciprocally in the swath axis B direction using any well-known structure, apparatus or device, such as two parallel guide rails  10 . The printhead cartridges  2  generally move across the recording medium  5  perpendicularly to the direction in which the recording medium  5  moves. Of course, other structures for reciprocating the carriage  3  are possible. 
     The ink jet printing device  1  is operated under the control of a print controller  20 . The print controller  20  transmits commands to the motor  6  and to the printhead cartridges  2  to produce an image on recording medium  5 . 
     FIG. 3 shows a number of heads  11 ,  12 ,  13  and  14  of the printhead cartridge  2  provided on the carriage  3 . It should be appreciated that FIG. 3 is schematic only and is not intended to show scale. All of the printheads  12 ,  13  and  14  are positioned linearly relative to the printhead  11 . As shown in FIG. 3, the printhead  11  is fixed to the carriage  3 , while the printheads  12 - 14  are not directly connected to the carriage  3 . That is, the printheads  12 - 14  may be supported by the carriage  3 , but are not fixed or attached directly to the carriage  3 . The printhead  13  is linked to the first printhead  11  a distance x on one side of the printhead  11 . The distance x is a design, or nominal, distance. A first link  16 , having an appropriate physical structure and made of a first material, connects the first printhead  11  to a linking structure  17 . The first link  16  has a length L 1  extending from the first printhead  11  on one end to the linking structure  17  on the opposite end furthest from the printhead  11 . The first link  16  has a property of thermal expansion, μ1, known as its thermal expansion co-efficient. 
     At the end of the first link  16  furthest from the printhead  11 , the linking structure  17  connects the first link  16  to a second link  18 . The linking structure  17  provided between the first and second links  16  and  18  may be any known or later developed structure or device or mechanism usable to attach together the links  16  and  18 , such as a pin, a weld or the like. Of course, it should be appreciated that the linking structure  17  can be the end portions of each of the links  16  and  18  that have been suitably formed and arranged relative to each other so that the links  16  and  18  can be connected directly to each other by welding, brazing, gluing, or fastening. In this case, the linking structure  17  need not be an independent element that is physically distinct from the links  16  and  18 . 
     The second link  18  has an appropriate physical structure and is made of a second material. The second link  18  extends a length L 2  extending from the linking structure  17  back towards the first printhead  11  before connecting to the printhead  13 . The second link  18  has a thermal expansion co-efficient μ 2  different than the thermal expansion co-efficient μ 1  of the first link  16 . The lengths, L 1  and L 2 , and the coefficients of thermal expansion, μ 1  and μ 2 , of the first and second links  16  and  18 , respectively, are selected such that: 
     
       
         L 1 −L 2 =x; and  (1) 
       
     
     
       
         μ 1 L 1 =μ 2 L 2   (2) 
       
     
     where: 
     L 1  is the length of the first link  16 , i.e., the distance between the first printhead  11  and the linking structure  17 ; 
     L 2  is the length of the second link  18 , i.e., the distance between the printhead  13  and the linking structure  17 ; 
     μ 1  is the thermal expansion co-efficient for material of the first link  16 ; 
     μ 2  is the thermal expansion co-efficient for material of the second link  18 ; and 
     x is the design, or nominal, distance between the first printhead  11  and the printhead  13 . 
     As a result of the relationship between L 1 , L 2 , μ 1  and μ 2 , the design, or nominal, distance x is maintained between the fixed first printhead  11  and the printhead  13  during a printing or sensing process, notwithstanding the varying thermal conditions. That is, while the printhead  11  remains in its originating position relative to the carriage  3  since it is fixed to the carriage  3 , the position of the printhead  13  relative to the fixed first printhead  11  does not change, even though the position of the printhead  13  relative to the carriage  3  changes according to the instantaneous temperature of the carriage  3  and the first and second links  16  and  18 . If the ambient temperature in or around the printer carriage  3  causes the first link  16  to expand in accordance with the thermal expansion properties μ 1  of the first link  16 , shifting the printhead  13  away from the first fixed printhead  11 , then the thermal expansion properties μ 2  of the second link  18  will expand a similar amount in the opposite direction in order to maintain the design, or nominal, distance x between the printheads  11  and  13 . Similarly, if the carriage temperature causes a thermally-induced contraction of the first link  16 , thus drawing the printhead  13  toward printhead  11 , then the thermal expansion properties μ 2  of the second link  18  causes the second link  18  also to contract, thus drawing the printhead  13  away from the printhead  11  in an equal amount, again maintaining the design, or nominal, distance x spacing originally established between the printheads  11  and  13 . 
     FIG. 3 also shows the relationship of the printhead  12  relative to the fixed printhead  11  as well. The printhead  12 , in this instance, is positioned on the opposite side of the printhead  11  relative to the printhead  13 . Similar to the originating design, or nominal, distance x position of printhead  13  relative to fixed printhead  11 , the printhead  12  has an originally established design, or nominal, distance y relative to the printhead  11 . Similarly to the printhead  13 , the printhead  12  is connected to the printhead  11  by a third link  19 , a linking structure  17  and a fourth link  20 . The third and fourth links  19  and  20  will be formed of materials having coefficients of thermal expansion μ 3  and μ 4 , respectively, and will have lengths L 3  and L 4 , respectively, such that: 
     
       
         L 3 −L 4 =y; and  (3) 
       
     
     
       
         μ 3 L 3 =μ 4 L 4;   (4) 
       
     
     where: 
     L 3  is the length of the third link  19 , i.e., the distance between the first printhead  11  and the linking structure  17 ; 
     L 4  is the length of the fourth link  20 , i.e., the distance between the printhead  12  and the linking structure  17 ; 
     μ 3  is the thermal expansion co-efficient for material of the third link  19 ; 
     μ 4  is the thermal expansion co-efficient for material of the fourth link  20 ; and 
     y is the design, or nominal, distance between the first printhead  11  and the printhead  12 . 
     In particular, it should be appreciated that the third and fourth links  19  and  20  can be formed of the same materials as the first and second links  16  and  18 , respectively, or could be formed of any other combination of materials having the appropriate coefficients of thermal expansion. Of course, if the links  16  and  19 , and the links  18  and  20 , are respectively formed of the same materials, the lengths L 3  and L 4  will be related to the lengths L 1  and L 2 , respectively, by the ratio of y to x. Thus, if y is twice x (y=2x), the lengths L 3  and L 4  will be twice the lengths L 1  and L 2 , respectively (L 3 =2L 1 ; L 4 =2L 2 ). 
     Thus, like the printhead  13 , the position of the printhead  12  relative to the printhead  11  will remain essentially constant. At the same time, any spacing change occurring to the printhead  12  relative to the carriage  3  would therefore occur at the same y:x ratio of thermal expansion or contraction provided to the printhead  13  whenever a temperature-induced expansion or contraction of the first-fourth links  16  and  18 - 20  occurs, as all of the links  16  and  18 - 20  would be subject to the same thermal conditions within the carriage  3 . Thus, the design, or nominal, distance y of the printhead  12  from the printhead  11  is controlled by the inversely-oriented expansion or contraction in equal amounts of the third and fourth links  19  and  20  for the printhead  12 . Again, the relationship between the lengths, L 3  and L 4 , and the coefficients of thermal expansion μ 3  and μ 4  of the third and fourth links  19  and  20 , compensate for any thermally-induced spacing changes experienced by the printhead  12  relative to the carriage  3 . 
     FIG. 3 also shows a third printhead  14  that is independently linked to the printhead  11  at approximately a design, or nominal, distance z from the printhead  11 . Similarly to either of the printheads  12  or  13 , the printhead  14  is connected to the printhead  11  by a fifth link  21 , a linking structure  17  and a sixth link  22 . The fifth and sixth links  21  and  22  will be formed of materials having coefficients of thermal expansion μ 5  and μ 6 , respectively, and will have lengths L 5  and L 6 , respectively, such that: 
     
       
         L 5 −L 6 =z; and  (5) 
       
     
     
       
         μ 5 L 5 =μ 6 L 6   (6) 
       
     
     where: 
     L 5  is the length of the fifth link  21 , i.e., the distance between the first printhead  11  and the linking structure  17 ; 
     L 6  is the length of the second link  22 , i.e., the distance between the printhead  14  and the linking structure  17 ; 
     μ 5  is the thermal expansion co-efficient for material of the fifth link  21 ; 
     μ 6  is the thermal expansion co-efficient for material of the sixth link  22 ; and 
     z is the design, or nominal, distance between the first printhead  11  and the printhead  14 . 
     In particular, it should be appreciated that the fifth and sixth links  21  and  22  can be formed of any of the same materials as any of the first through fourth links  16  and  18 - 20 , respectively, or could be formed of any other combination of materials having the appropriate coefficients of thermal expansion. Of course, if the links  16  and  21 , and the links  18  and  22 , are respectively formed of the same materials, the lengths L 5  and L 6  will be related to the lengths L 1  and L 2 , respectively, by the ratio of z to x. Thus, if z is three-times x (y=3x), the lengths L 5  and L 6  will be three-times the lengths L 1  and L 2 , respectively (L 5 =3L 1 ; L 6 =3L 2 ). 
     Thus, like either of the printheads  12  or  13 , the position of the printhead  14  relative to the printhead  11  will remain essentially constant. At the same time, any spacing change occurring to the printhead  14  relative to carriage  3  would therefore occur at the same z:x ratio of thermal expansion or contraction provided to printhead  13  whenever a temperature-induced expansion or contraction of the first-sixth links  16  and  18 - 22  occurs, as all would be subject to the same thermal conditions within the carriage  3 . Thus, again the design, or nominal, distance z of the printhead  14  from printhead  11  is controlled by the inversely-oriented expansion or contraction in equal amounts of the fifth and sixth links  21  and  22  for the printhead  14 . Again, the relationship between the lengths, L 5  and L 6 , and the coefficients of thermal expansion μ 5  and μ 6  of the fifth and sixth links  21  and  22 , compensate for any thermally-induced spacing changes experienced by the printhead  12  relative to the carriage  3 . 
     As should be appreciated from the various descriptions of FIG. 3 above, any combination of materials may be used to form the pairs of links  16  and  18 ,  19  and  20 , and  21  and  22 , provided their respective thermal expansion coefficients μ combine to offset the expansion or contraction of one link of the pair, for example the first link  16 , by the expansion or contraction of the other link, for example the second link  18 , in an equal amount in an opposite direction. The inversely-oriented expansions or contractions of the first and second links of the pair of links maintain the design, or nominal, distances x, y, or z, originally established for the respective printheads,  12 ,  13 , or  14  relative to the first fixed printhead  11  regardless of the thermal conditions present. 
     In other words, when the underlying carriage  3  supporting the printheads  11 ,  12 ,  13  and  14  undergoes a thermal expansion or contraction, only the first printhead  11  moves, because only the first printhead  11  is fixed to the carriage  3 . The other printheads  12 ,  13  and  14  remain in their original positions relative to printhead  11 . Only when a temperature sufficient to induce expansion or contraction of the materials of the pairs of links exists are the positions of the other printheads  12 ,  13  and  14  changed relative to the carriage  3 . However, even when the positions of the printheads  12 ,  13  and  14  relative to the carriage  3  change, the relationships of lengths of the first and second links of each pair of links and the respective coefficients of thermal expansion of the first and second links of each pair of links are such that the first and second links of each pair of links expand or contract equal amounts in opposite directions to maintain the desired original spacing between the printhead  11  and the printheads  12 ,  13  and  14 . 
     Of course, it should be appreciated that while FIG. 3 shows a series of four printheads  11 ,  12 ,  13  and  14 , any number of printheads could be used with similar link configurations to maintain desired spacing between the fixed printhead and those printheads. 
     It should also be appreciated that the configuration shown in FIG. 3 depicting the printheads,  11 ,  12 ,  13  and  14  equally depicts embodiments where sensor heads are used in place of the printheads. Further, the configuration of the plurality of printheads  11 ,  12 ,  13  and  14  shown in FIG. 3 equally depicts configurations where the printheads  11 - 14  are stationary full-width print bars, or sensor bars. In this case, one of the full width print bars, or sensor bars, is fixed to a stationary frame member or the like of the apparatus. The other full-width print bars or sensor bars are then connected to the fixed print bar or sensor bars in the same manner that the printhead  11  is connected to the carriage  3  and the other printheads  12 - 14  are connected to the printhead  11  as shown in FIG.  3 . 
     Of course, in any of the embodiments set forth, the printheads, or sensor heads, are merely specific examples of any type of actuator that input or output information data, where the actuators, forming a set of actuators, are desirably maintained at predetermined distances from each other. 
     FIGS. 5-8 shows four additional exemplary configurations for connecting the printhead  11  and one or more of the printheads  12 - 14  differently than that shown in FIG.  3 . The relationship shown in FIG. 3 between the printhead  13  and fixed printhead  11  is illustrated in FIG. 4 as a reference to explain the differences of the additional exemplary configurations. In particular, the 1-fold configuration shown in FIG. 4 illustrates the configuration of the printheads  11  and  13  shown in FIG.  3 . In FIG. 4, the printhead  13  is linked to the fixed first printhead  11  using a pair of links  16  and  18 . The first link  16  extends the length L 1  from the first printhead  11  to the linking structure  17 , while the second link  18  extends the length L 2  from the linking structure  17  back towards the printhead  11  to the printhead  13 . The lengths L 1  and L 2  of the first and second links  16  and  18  maintain the original design, or nominal, distance x between the printhead  11  and the printheads  13  because of the coefficients of thermal expansion μ 1 , μ 2  associated with the link  16  and  18 , respectively. 
     The additional exemplary configurations shown in FIGS. 5-8 illustrate that the same printhead spacing thermal insensitivity achieved by the matched thermal expansions of the pair of first and second links  16  and  18  may be achieved incrementally by dividing one or both of the first and second links  16  and  18  into, for example, one or more sublinks that each have a length that is less than the corresponding length L 1  and/or L 2  of the links  16  and  18  in the 1-fold configuration shown in FIG.  4 . In FIGS. 5-8, a first layer  24  thus comprises the pair of a first sublink  16   a  and either the link  18  or a first sublink  18   a , while a second layer  26  includes at least a second sublink  16   b . As shown in FIGS. 6-8, the second layer  26  comprises the pair of second sublinks  16   b  and  18   b , while a third layer  28  includes at least a third sublink  16   c . As shown in FIGS. 7 and 8, the links  16  and  18  are divided into the layers  24 ,  26  and  28  in the 2.5-fold configuration shown in FIG. 7, and the layers  24 ,  26 ,  28  and  30  in the 4-fold configuration shown in FIG.  8 . The layers  24 ,  26 ,  28  and/or  30  are connected using additional linking structures  17 , which are similar to the linking structure  17 . 
     The 1.5-fold configuration shown in FIG.  5  and the 2-fold configuration shown in FIG. 6 each illustrates that the same design, or nominal, distance x spacing between the printhead  13  and the fixed printhead  11  may be maintained using the first and second layers  24  and  26  of the sublinks  16   a  and  16   b  and  18   a  and  18   b . It should also be appreciated that, while FIG. 6 shows the 2-fold configuration as equally dividing the links  16  and  18  into the sublinks  16   a  and  16   b , and  18   a  and  18   b , respectively, any of the links  16  and  18  can be divided in any manner to form the sublinks  16   a  and  16   b , and  18   a  and  18   b , as shown in the 1.5-fold configuration shown in FIG.  5 . Thus, it should further be appreciated that the links  16  and  18  do not have to be divided into equal portions, or even in the same proportions, so long as the sum of the length of the sublinks  16   a  and  16   b , and  18   a  and  18   b , equal the lengths L 1  and L 2 , respectively. 
     Moreover, it should further be appreciated that the sublinks  16   a  and  16   b , and/or the sublinks  18   a  and  18   b , need not be formed of the same materials, so long as the total length change per unit of temperature change over the total lengths of the sublinks  16   a  and  16   b  substantially equals the total length change per unit of temperature change over the total lengths of the sublinks  18   a  and  18   b . Thus, in this case, in the 1.5-fold and 2-fold configuration shown in FIGS. 5 and 6, the total lengths L 1a  and L 1b  of the sublinks  16   a  and  16   b  may not necessarily equal the length L 1  that would be used for a single link  16  in the 1-fold configuration shown in FIGS. 3 and 4. Likewise, in the 2-fold configuration shown in FIG. 6, the total lengths L 2a  and L 2b  of the sublinks  18   a  and  18   b  may not necessarily equal the length L 2  that would be used for a single link  18  in the 1-fold configuration shown in FIGS. 3 and 4. 
     It should further be appreciated that the preceding descriptions of the 1.5-fold and 2-fold configurations shown in FIGS. 5 and 6 equally apply to the 2.5-fold and 4-fold configuration shown in FIGS. 7 and 8, as well as for any other number of layers of links. 
     Thus, provided the materials forming the pairs of first and second sublinks,  16   a  and  18   a , and  16   b  and  18   b , of the first and second layers  24  and  26  have the appropriate lengths and thermal expansion properties, total movement of the links oriented in one direction is inversely offset by an equal total movement of the links oriented in the other direction, so that there is no overall change in the position of the printhead  13  relative to the first printhead  11 . Thus, the pairs of first and second links,  16   a  and  18   a , and  16   b  and  18   b , of the first and second layers  24  and  26  may comprise a combination of many materials having differing thermal expansion properties to achieve the same space maintaining or compensating quality between the actuators. For example, the first link  16   a  in the first layer  24  may be the same material as that of the first link  16   b  in the second layer  26 . Similarly, the material of the second links  18   a  and  18   b  in the first and second layers  24  and  26 , respectively, may also be the same. Of course, like materials would exhibit like thermal expansion properties. Thus, the design, or nominal, distance x spacing between printheads  11  and  13  would be maintained in one-half increments using the 2-fold configuration shown in FIG.  6 . 
     It is possible, however, that the first link  16   a  of the first layer  24  would be formed of one material, while the first link  16   b  of the second layer  26  would be formed of another material. Thus, the coefficients of thermal expansion μ of the links  16   a  and  16   b , in this instance, would likely be different. Likewise, the second links  18   a  or  18   b  could be made of materials different from each other that have different coefficients of thermal expansion μ as well. The combination of materials and lengths of the respective sublinks  16   a ,  16   b ,  18   a  and  18   b  will be selected to ensure the design, or nominal, distance x of the printhead  13  from the printhead  11  remains substantially the same. Thus, as long as combinations of links of appropriate thermal expansion properties are provided to compensate for the thermally-induced expansions or contractions of the links, so that the proper spacing of the printheads relative to one another is maintained, then any combination of link materials may be used. 
     The first and second layers  24  and  26  of the first and second sublinks  16   a  and  16   b , and  18   a  and  18   b , necessarily require an additional linking structure  17  to connect these layers to one another. As a result, the design, or nominal distance x, between the printhead  11  and the printhead  13  is substantially maintained using the one-half lengths of the 2-fold configuration shown in FIG. 6, just as the same distance x is substantially achieved using the full lengths L 1  and L 2  of the links  16  and  18  in the 1-fold configuration shown in FIGS. 3 and 4. The 2-fold configuration of FIG. 6 thus allows the first and second links  16  and  18  to occupy a smaller longitudinal space, which can minimize the size of the carriage  3 . 
     Similarly, the 4-fold configuration shown in FIG. 8 illustrate the first and second links  16  and  18  divided into quarters, so that each of the sub-links  16   a - 16   d  and  18   a - 18   d  have lengths L 1 /4 and L 2 /4, respectively. The 4-fold configuration, similarly to the 1.5-fold, 2-fold and 2.5-fold configurations, achieves the same space compensating methods for the printheads  11  and  13  relative to the carriage  3  in even smaller increments using even less longitudinal space than the 1.5-fold, 2-fold and 2.5-fold configurations described above. Again, the materials used for the series of first-fourth sub-links  16   a - 16   d  and  18   a - 18   d  may be any combination of the same or different materials provided the materials have appropriate coefficients of thermal expansion μ for the lengths of the sub-links  16   a - 16   d  and  18   a - 18   d  to ensure that the overall thermally-induced expansions or contractions of the sub-links  16   a - 16   d  and  18   a - 18   d  are compensated for to maintain the design, or nominal distance x between the printheads  11  and  13 . Necessarily, the 4-fold configuration requires additional linking structures  17  between the various layers  24 ,  26 ,  28  and  30  of the sub-links  16   a - 16   d  and  18   a - 18   d  to achieve the same design, or nominal, distance x between the printheads  11  and  13 . 
     While this invention has been described in conjunction with the exemplary embodiments outlined above, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, the exemplary embodiments of the invention, as set forth above, are intended to be illustrative, not limiting. Various changes may be made without departing from the spirit and scope of the invention.