Patent Publication Number: US-7591639-B2

Title: Peristaltic pump

Description:
CROSS-REFERENCE TO RELATED PATENT APPLICATION 
   The present application is related to co-pending U.S. patent application Ser. No. 10/832,499 titled Peristaltic Pump and filed on the same date as the present application by Blair M. Kent, the full disclosure of which is hereby incorporated by reference. 
   BACKGROUND 
   Peristaltic pumps are used in a wide variety of applications for pumping fluid. Peristaltic pumps typically include a set of rollers which are rotated against a fluid-filled tube to compress the tube against an occlusion to move the fluid within the tube. Peristaltic pumps are very susceptible to the physical difference or gap between the roller and the occlusion. If the gap is too large, the pump does not move fluid within the tube. If the gap is too small, the tube is excessively compressed which requires additional torque to move the pump and which increases wear of the tube. 
   Multiple peristaltic pump systems rotate one or more rotors about a single axis against multiple fluid-filled tubes to compress the tubes against multiple occlusions. In such systems, a peak torque occurs during the time at which the rollers of each rotor simultaneously compress their respective tubes. During a period of prolonged rest, the rollers create a tube compressive set in each of the tubes. A secondary torque spike also occurs when the rollers of each rotor simultaneously encounter the tube compressive set during pumping. There is a continuing need to minimize torque requirements for multiple peristaltic pump systems to reduce power requirements and associated costs. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic illustrating an example of an image-forming device including an example of a peristaltic pump according to an exemplary embodiment of the present invention; 
       FIG. 2  is a top perspective view of the peristaltic pump of  FIG. 1 , according to an exemplary embodiment; 
       FIG. 3  is an exploded perspective view of portions of the pump shown in  FIG. 2  according to an exemplary embodiment; 
       FIG. 4  is a sectional view of the pump of  FIG. 2  according to an exemplary embodiment; 
       FIG. 5  is a sectional view of the pump of  FIG. 4  taken along line  5 - 5 , according to an exemplary embodiment; 
       FIG. 6  is a perspective view of another embodiment of a pumping unit of the peristaltic pump of  FIG. 2 , according to an exemplary embodiment; 
       FIG. 7  is a side elevational view of a housing of the pumping unit of  FIG. 6 , according to an exemplary embodiment; 
       FIG. 8  is a perspective view of a rotor of the pumping unit of  FIG. 2 , according to an exemplary embodiment; 
       FIG. 9  is a side elevational view of the rotor of  FIG. 8  with portions omitted for purposes of illustration, according to an exemplary embodiment; 
       FIG. 10  is a perspective view of a drive shaft of the pump of  FIG. 2  coupled to a torque source, according to an exemplary embodiment; 
       FIG. 10A  is a sectional view of the drive shaft of  FIG. 10  taken along line  10 A- 10 A, according to an exemplary embodiment; 
       FIG. 10B  is a sectional view of the drive shaft of  FIG. 10  taken along line  10 B- 10 B, according to an exemplary embodiment; 
       FIG. 10C  is a sectional view of the drive shaft of  FIG. 10  taken along line  10 C- 10 C, according to an exemplary embodiment; 
       FIG. 11  is a perspective view of the rotors of the pump of  FIG. 2  supported by the drive shaft of  FIG. 10  with a staggered pitch, according to an exemplary embodiment; 
       FIG. 12  is a perspective view of the rotors and the drive shaft of  FIG. 8  with the rotors having an off pitch, according to an exemplary embodiment; 
       FIG. 13  is a perspective view of the pump of  FIG. 2  while the rotors have a staggered pitch and with portions removed for purposes of illustration, according to an exemplary embodiment; 
       FIG. 14  is a side elevational view of the pump of  FIG. 13  further illustrating movement of a rotor through a tube compression phase; and 
       FIG. 15  is a side elevational view of the pump of  FIG. 13  with the rotors having the off pitch, according to an exemplary embodiment. 
   

   DETAILED DESCRIPTION 
     FIG. 1  schematically illustrates image-forming device  20  utilizing one example of a fluid delivery system  22  of the present invention. In addition to fluid delivery system  22 , image-forming device  20  includes media supply  24 , carriage  26 , fluid-dispensing devices  28 , fluid supplies  30  and controller  32 . Media supply  24  comprises a mechanism configured to supply and position media, such as paper, relative to carriage  26  and fluid-dispensing devices  28 . Carriage  26  comprises a conventionally known or future developed mechanism for moving fluid-dispensing devices  28  relative to the medium provided by media supply  24 . In the particular embodiment illustrated, media supply  24  moves the medium relative to carriage  26  and fluid-dispensing devices  28  in the direction indicated by arrow  34  while carriage  26  moves fluid-dispensing devices  28  repeatedly across the medium in the directions indicated by arrow  36 . 
   Fluid-dispensing devices  28  comprise devices configured to dispense fluid upon a medium. In the particular embodiment illustrated, devices  28  comprise print cartridges including printheads with nozzles for dispensing fluid ink upon the medium. Service station  29  is a conventionally known service station configured to service fluid-dispensing devices  28 . Examples of servicing operations include wiping, spitting, and capping. Fluid supplies  30  provide ink reservoirs containing one or more chromatic or achromatic inks to fluid-dispensing devices  28 . Fluid supplies  30  and fluid delivery system  22  function as an ink supply system for image-forming device. 
   Fluid delivery system  22  moves ink from fluid supplies  30  to fluid-dispensing devices  28 . Fluid delivery system  22  includes peristaltic pump  40  and fluid ink conduits  42 ,  44 . As will be described in greater detail hereafter, peristaltic pump  40  includes pumping tubes  46 . Fluid conduits  42  fluidly connect the ink reservoirs provided by fluid supplies  30  to pumping tubes  46 . Fluid conduits  44  fluidly interconnect pumping tubes  46  to fluid-dispensing devices  28 . In one embodiment, fluid conduits  42 , fluid conduits  44  and pumping tubes  46  form a complete circuit between fluid dispensing devices  28  and fluid supplies  30 . As such, each line shown in  FIG. 1  and designated by reference numerals  42 ,  44  and  46  schematically represents a pair of conduits or tubes. In such an embodiment, conduits  42 , conduits  44  and pumping tubes  46  deliver fluid, such as ink, fluid supplies  30  to dispensing devices  28 . In addition, conduits  42 , conduits  44  and pumping tubes  46  deliver or return fluid from dispensing devices  28  to supplies  30 . In other embodiments, conduits  42 , conduits  44  and pumping tubes  46  may only deliver fluid in one direction from supplies  30  to dispensing devices  28 . As such, each line designated in  FIG. 1  with a reference numeral  42 ,  44  or  46  schematically represents a single tube or conduit. 
   The actual length of conduits  42  and  44  may vary depending upon the actual proximity of fluid supplies  30 , pump  40  and maximum/minimum distance between fluid-dispensing devices  28  and pump  40 . In particular applications, conduits  42  and  44  are releasably connected to pumping tubes  46  by fluid couplers. In alternative embodiments, one of conduits  42 ,  44  or both of conduits  42 ,  44  may be integrally formed as part of a single unitary body with pumping tubes  46 . In the embodiment shown, conduits  42  and  44  have a smaller cross sectional flow area as compared to pumping tubes  46  such that pumping tubes  46  may be sized for higher pumping rates. In alternative embodiments, conduits  42 ,  44  and pumping tubes  46  may have similar internal cross sectional flow areas. In another embodiment, each of the plurality of conduits  44 , each of the plurality of conduits  42  and each of the plurality of tubes  46  are substantially identical to one another. In alternative embodiments, pump  40  may be provided with different individual pumping tubes  46 , different individual conduits  42  or different individual conduits  44 . Although pumping tubes  46  include a flexible wall portion enabling pumping tubes  46  to be compressed, conduits  42  and  44  may be provided by flexible tubing or may be provided by inflexible tubing or other structures having molded or internally formed fluid passages. Although image-forming device is illustrated as having six fluid-dispensing devices  28 , six fluid supplies  30 , six sets of pumping tubes  46 , six sets of conduits  42  and six sets of conduits  44 , image-forming device may alternatively have a greater or fewer number of such components depending upon the number of different inks utilized by image-forming device and whether fluid flow is to be unidirectional or circulated. 
   Controller  32  communicates with media supply  24 , carriage  26 , fluid-dispensing devices  28 , fluid supplies  30  and fluid delivery system  22  via communication lines  33  in a conventionally known manner to form an image upon medium  24  utilizing ink supplied from fluid supplies  30 . Controller  32  comprises a conventionally known processor unit. For purposes of this disclosure, the term “processor unit” shall include a conventionally known or future developed processing unit that executes sequences of instructions contained in a memory. Execution of the sequences of instructions causes the processing unit to perform steps such as generating control signals. The instructions may be loaded in a random access memory (RAM) for execution by the processing unit from a read only memory (ROM), a mass storage device, or some other persistent storage. In other embodiments, hard wired circuitry may be used in place of or in combination with software instructions to implement the functions described. Controller  32  is not limited to any specific combination of hardware circuitry and software, nor to any particular source for the instructions executed by the processing unit. 
   Although fluid delivery system  22  is illustrated as being employed in a image-forming device in which both the medium and fluid-dispensing devices  28  are moved relative to one another to form an image upon a medium, fluid delivery system  22  may alternatively be employed in other printers to move fluid ink from one or more ink supplies to one or more ink-dispensing printheads or nozzles. For example, fluid delivery system  22  may alternatively be employed in a printer in which ink-dispensing nozzles are provided across a medium as the medium is moved in the direction indicated by arrow  34 . This printer is commonly referred to as a page-wide-array printer. In still other embodiments, fluid delivery system  22  may be employed in other image-forming devices where fluid ink is deposited upon a medium by means other than pens or printheads or wherein the medium itself is held generally stationary as the ink is deposited upon the medium. Overall, fluid delivery system  22  may be utilized in any image-forming device which utilizes ink or other fluid to be deposited upon a medium. 
     FIGS. 2-5  illustrate peristaltic pump  40  in greater detail. As best shown by  FIG. 2 , pump  40  includes an outer housing or frame  50 , pump units  52 A- 52 F and a drive shaft  54  (shown in  FIG. 3 ). Frame  50  generally comprises an outer structure configured to support and retain each of units  52 A- 52 F relative to one another as a single assembly. In the particular embodiment illustrated, frame  50  is configured to prevent rotation of units  52 A- 52 F while permitting units  52 A- 52 F to move relative to one another in one or more directions perpendicular to a common rotational axis  68  of units  52 A- 52 F. As a result, each is able to center itself relative to neighboring pumps  52 A- 52 F. Because each pump unit  52 A- 52 F utilizes a common drive shaft  54 , the number of parts, the overall size and the manufacturing and assembly costs are reduced. 
   In alternative embodiments, units  52 A- 52 F may be mounted or secured relative to one another by other structures or may be directly secured to one another while omitting an overall outer frame. In still other embodiments, portions of two or more units  52 A- 52 F may be integrally formed as a single unitary body. Although pump  40  is illustrated as including six individual units, pump  40  may alternatively include a greater or fewer number of such units. 
     FIGS. 3 and 4  illustrate pump units  52 A- 52 F and drive shaft  54  in greater detail. In this example, pump units  52 A- 52 F are substantially identical to one another. Pump units  52 A- 52 F include housings  60 A- 60 F, tubes  46 A- 46 F, tubes  46 A′- 46 F′ and rotors  62 A- 62 F, respectively. Housings  60 A- 60 F comprise one or more structures configured to provide at least one occlusion surface against which tubes  46 A- 46 F and tubes  46 A′- 46 F′ may be compressed. In the particular example shown in  FIGS. 3 and 4 , each housing  60 A- 60 F provides two occlusion surfaces, occlusion surface  64  and occlusion surface  66 . Occlusion surfaces  64  and  66  arcuately extend about axis  68  and generally face one another. Occlusion surfaces  64  and  66  cooperate with rotors  62 A- 62 F to compress tubes  46 A- 46 F or tubes  46 A′- 46 F′. 
   In the particular example shown, each housing  60 A- 60 F includes a main wall  70  and rims  71 ,  72 . Main wall  70  generally extends between rims  71  and  72  and includes rotor bearing surface  73  and drive shaft opening  74 . Rotor bearing surface  73  functions as a surface for locating the associated rotor along axis  68 . Surface  73  faces a direction parallel to axis  68 . 
   Drive shaft opening  74  extends through wall  70  and is sized to allow drive shaft  54  to pass through opening  74  and into connection with the associated rotor  62 . In the particular example, drive shaft opening  74  is radially spaced from outermost portions of drive shaft  54  so as to further enable wall  70  and the associated housing  60  to move or otherwise float relative to drive shaft  54  or the associated rotor  62  in a direction non-parallel to and nominally perpendicular to axis  68 . 
   Rims  71  and  72  extend from wall  70  and from surface  73  in a direction along axis  68 . Rims  71  and  72  include occlusion surfaces  64  and  66 , respectively. In addition, rims  71  and  72  include rotor retaining surfaces  75 , tube retaining surfaces  76  and stacking surfaces  77 . Rotor retaining surfaces  75  extending from surface  70  and are configured to retain their associated rotors  62 A- 62 F in a direction perpendicular to axis  68 . As will be described in greater detail hereafter, rotor retaining surfaces  75  are sufficiently spaced from rotor  62 A- 62 F so as to permit movement of rotor  62 A- 62 F in directions non-parallel and nominally perpendicular to axis  68 . 
   Tube retaining surfaces  76  generally extend between rotor retaining surfaces  75  and occlusion surfaces  64 ,  66 . Tube retaining surfaces  76  are configured to retain tubes  46 A- 46 F and tubes  46 A′- 46 F′ against movement in directions parallel to axis  68 . In the particular example shown, tube retaining surfaces  76  extend perpendicular to axis  68 . In other embodiments, tube retaining surfaces  76  may extend at other angles relative to axis  68 . Moreover, in particular embodiments, rotor retaining surfaces  75  may be omitted. 
   Stacking surfaces  77  comprise those surfaces of each housing  60 A- 60 F which are configured to abut a surface of an adjacent housing  60 A- 60 F, enabling housings  60 A- 60 F to be positioned end-to-end so as to form a stack of pump units  52 A- 52 F. In the example shown in  FIG. 4 , stacking surfaces  77  abut and mate with rear surfaces  78  of wall  70  of an adjacent housing  62 A- 62 F. As a result, a portion of wall  78 , not in abutment with stacking surfaces  77 , extends opposite to tube retaining surface  76  and functions as a second tube retaining surface. Tube retaining surfaces  76  and the opposite portion of rear surfaces  78  of the adjacent housings  62 A- 62 F cooperate to retain tubes  46 A- 46 F and tubes  46 A′- 46 F′ in a direction along axis  68  to facilitate compression of tubes  46 A- 46 F and  46 A′- 46 F′ between rotors  62 A- 62 F and the occlusion surfaces  64  and  66  provided by housings  60 A- 60 F. Rear surfaces  78  further extend opposite to and across rotors  62 B- 62 F to assist in retaining rotors  62 B- 62 F in place in directions parallel to axis  68 . The end most housing  60 A and its end most rotor  62 A do not face an adjacent housing. As a result, the stack of pump units  52 A- 52 F additionally includes a retainer plate  80  which abuts stacking surfaces  77  of housing  60 A and extends opposite to tube retaining surfaces  76  and opposite to rotor retaining surface  73  of housing  60 A to capture and retain rotor  62 A and tubes  46 A,  46 A′ in directions along axis  68 . In the particular embodiment, housing  60 A and retainer plate  80  are permitted to move relative to one another in directions perpendicular to axis  68 . In other embodiments, retaining plate  80  may be omitted where an empty housing is positioned to housing  60 A in lieu of plate  80  or where frame  50  (shown in  FIG. 2 ) is configured to replace plate  80 . In still other embodiments, gear  97  may be coupled to drive shaft  54  on an opposite end of drive shaft  54  adjacent to housing  60 A so as to face surface  73  to capture and retain rotor  62 A and tubes  46 A,  46 A′ within housing  60 A in lieu of plate  80 . 
   In the particular example shown in  FIGS. 3 and 4 , each housing  60 A- 60 F has a generally half-clamshell configuration and is integrally formed as a single unitary body out of one or more polymeric materials. In other embodiments, one or more of housings  60 A- 60 F may alternatively be formed from several structures mounted, welded, bonded or fastened together and may be formed from other materials or combinations of materials. Although pump  40  is illustrated as including a stack of six pump units  52 A- 52 F having six adjacent stacked housings  60 A- 60 F, pump  40  may alternatively include a fewer or greater number of such stacked pump units or adjacent housings. 
   Overall, housing  60 A- 60 F enables pump  40  to be produced and assembled in a more economical and simpler fashion. Because rear surface  78  of wall  70  of each housing functions as both a tube retaining surface and as a rotor retaining surface opposite surfaces  73  and  76  when stacked adjacent another housing  60 A- 60 F, the need for a rotor retaining surface or a tube retaining surface on the adjacent housing  60 A- 60 F is eliminated. As a result, the overall axial length of pump  40  along axis  68  is reduced while maintaining a number of pump units  52 A- 52 F. In addition, because the need for a tube retaining surface and a rotor retaining surface opposite surfaces  73  and  76  is eliminated, each housing  60 A- 60 F may be configured to have a half-clamshell overall shape such that all critical surfaces of the housing  60 A- 60 F are located on a single side, simplifying and reducing the cost of molding (no slides are required) and machining (no secondary operations are required). 
   The half-clamshell shape further simplifies assembly by enabling tops down and rotation methods. In particular, rotor  62 F may be placed within housing  60 F and appropriately rotated as portions of the rotor are assembled with tubes  46 F and  46 F′ in place. Upon completion of pump unit  52 F, housing  60 E may be placed or stacked on top of the completed pump unit  52 F and rotor  62 E and the partially assembled rotor  62 E may be placed within housing  60 E. Rotor  62 E may be appropriately rotated as its assembly is completed with tubes  46 E and  46 E′ in place. This overall process is repeated as necessary depending upon the number of pump units provided by pump  40 . 
   Tubes  46 A- 46 F and  46 A′- 46 F′ comprise elongated conduits having wall portions that are resiliently flexible, permitting tubes  46 A- 46 F and  46 A′- 46 F′ to be occluded by rotors  62 A- 62 F to move fluid through tubes  46 A- 46 F and  46 A′- 46 F′. Tubes  46 A- 46 F and  46 A′- 46 F′ extend between rotors  62 A- 62 F and occlusion surfaces  64  and  66 , respectively. Tubes  46 A- 46 F and  46 A′- 46 F′ each generally has an internal cross sectional diameter smaller than the internal cross sectional diameter of conduits  42  and  44  to achieve higher fluid pumping rates. In the embodiment shown, tubes  46 A- 46 F deliver fluid to a dispensing device  28  (shown in  FIG. 1 ) while tubes  46 A′- 46 F′ return fluid from the fluid dispensing device  28 . Tubes  46 A- 46 F have a smaller cross sectional diameter than the cross sectional diameter of tubes  46 A′- 46 F′. In other embodiments, tubes  46 A- 46 F and  46 A′- 46 F′ may have equal cross sectional diameters. Although tubes  46 A- 46 F and  46 A′- 46 F′ are illustrated as having a generally circular cross sectional shape, tubes  46 A- 46 F and  46 A′- 46 F′ may have other alternative cross sectional shapes, wherein at least a portion of the tube is flexible. 
   In the embodiment shown, tubes  46 A- 46 F and  46 A′- 46 F′ are formed from one or more polymeric materials. Tubes  46 A- 46 F and  46 A′- 46 F′ may be formed from a single layer or multiple layers. Tubes  46 A- 46 F,  46 A′- 46 F′ may be homogenous in nature or may be formed from a plurality of mixed materials. One example of a material from which tubes  46 A- 46 F and  46 A′- 46 F′ may be formed is SANTOPRENE thermoplastic elastomer which is currently sold by Advanced Elastomers, Inc. Although tubes  46 A- 46 F and  46 A′- 46 F′ are illustrated as being formed of common materials, tubes  46 A- 46 F and  46 A′- 46 F′ may alternatively be formed from different materials as compared to one another. 
   Rotors  62 A- 62 F comprise one or more structures providing occluding surfaces that are moved against tubes  46 A- 46 F and tubes  46 A′- 46 F′ while at least partially occluding tubes  46 A- 46 F and  46 A′- 46 F′ to move fluid therethrough. In the particular examples shown in  FIGS. 3-5 , each rotor  62 A- 62 F includes a set of six occluding surfaces  82  that compress and at least partially occlude tubes  46 A- 46 F and tubes  46 A′- 46 F′ while rotating about axis  68 . Each rotor  62 A- 62 F is generally located between occlusion surfaces  64  and  66  of housing  60 A- 60 F, respectively, such that fluid is moved or pumped through tubes  46 A- 46 F and tubes  46 A′- 46 F′ simultaneously. 
   Each rotor  62 A- 62 F generally includes hub  84 , post support  86 , posts  88  and rollers  90 . Hub  84  couples each of post support  86 , posts  88  and rollers  90  to one another about axis  68 , enabling rollers  90  to be simultaneously rotated about axis  68 . Hub  84  couples the remainder of its respective rotor  62 A- 62 F to drive shaft  54 . In the particular embodiment shown, hub  84  additionally includes two opposite detents  96  extending along bore  94 . Detents  96  are configured to receive corresponding projections  120  of drive shaft  54 . 
   Post support  86  radially extend from hub  84  and support posts  88 . Posts  88  extend from post support  86  and rotatably support rollers  90  about axes  112 . Because posts  88  extend from a single side of post support  86 , substantially all of the critical surfaces of each rotor  62 A- 62 F are located on a single side, simplifying and reducing the cost of molding and machining. In other embodiments, rotors  62 A- 62 F may have alternative configurations. Although each of rotors  62 A- 62 F are illustrated as including six posts  88  and six rollers  90 , rotors  62 A- 62 F may alternatively include a greater or fewer number of such components. Although post supports  86  are illustrated as generally annular members extending about hubs  84 , supports  86  may alternatively comprise individual arms radially projecting from hub  84 . 
   Rollers  90  are rotatably supported by posts  88  and provide occluding surfaces  82 . Rollers  90  generally comprise annular rings rotatably supported about axes  112  such that rollers  90  roll against tubes  46 A- 46 F and tubes  46 A′- 46 F′ as rotors  62 A- 62 F are rotatably driven about axis  68 . In other embodiments, occluding surfaces  82  may be provided by other structures rotatably or stationarily coupled to the remainder of rotors  62 A- 62 F. According to one embodiment, rollers  90  are injection molded. Because of their relatively short axial length, less than about 6 millimeters each, rollers  90  may be injection molded from a single side, reducing cost while minimizing dimensional variations. In other embodiments, rollers  90  may be formed using other techniques such as extrusion, blow-molding and the like. Although rotors  62 A- 62 F are illustrated as including six equiangularly spaced sets of posts  88  and rollers  90  about hub  84 , rotors  62 A- 62 F may alternatively include a greater or fewer number of such sets of posts  88  and rollers  90 . 
   Drive shaft  54  rotatably drives rotor  62 A- 62 F. Drive shaft  54  is operably coupled to a source of rotational power or torque (schematically shown), such as a motor. In the particular example shown, drive shaft  54  is coupled to a gear  97  which is in meshing engagement with a remaining portion of a drive train rotatably driven by the torque source  318  (shown in  FIG. 2 ). 
   In the particular embodiment shown, drive shaft  54  includes two opposite projections  120  which radially extend from drive shaft  54  and which are configured to be received within detents  96  of rotors  62 A- 62 F. Projections  120  further extend into corresponding detents  98  formed along a central bore  99  of gear  97 . In the particular example shown, drive shaft  54  includes a main pin  122  having a pair of opposite axial grooves  124  which removably receive engagement pins  126  which provide projections  120 . 
   In other embodiments, drive shaft  54  may have a variety of alternative configurations. For example, in lieu of projections  120  being provided by pins  126  removably received within channels  124  of pin  122 , projections  120  may alternatively be integrally formed as a single unitary body with a remainder of drive shaft  54 . Although drive shaft  54  is illustrated as having a pair of opposite projections  120 , drive shaft  54  may alternatively have a greater or lesser number of such projections which are received within a corresponding number of detents formed within hub  84  of rotors  62 A- 62 F. In particular embodiments, drive shaft  54  may include a multitude of splines or may have other non-circular cross sectional shapes such that rotation of drive shaft  54  further results in rotation of rotors  62 A- 62 F. 
   In the particular embodiment illustrated, drive shaft  54  and hub  84  of each of rotors  62 A- 62 F are configured to enable each rotor  62 A- 62 F to move or float relative to drive shaft  54  and relative to axis  68  in directions non-parallel to and nominally perpendicular to axis  68 . At the same time, drive shaft  54  and hub  84  of each of rotors  62 A- 62 F are configured such that rotation of drive shaft  54  rotatably drives rotors  62 A- 62 F about axis  68 . As shown by  FIG. 4 , the exterior periphery of drive shaft  54  about axis  68  is radially spaced from the corresponding interior surfaces of bore  94  and detents  96  of hub  84  by opposite gaps G 1  and G 2  which, when combined, provide a diametral spacing S 1 . The diametral spacing is large enough to allow sufficient movement of each rotor  62 A- 62 F relative to axis  68  and relative to drive shaft  54  to enable each rotor  62 A- 62 F to automatically center itself between tubes  46 A- 46 F and tubes  46 A′- 46 F′, respectively, in response to opposing tube reaction forces resulting from opposing tube compressions. Because each rotor  62 A- 62 F is self-centering, any dimensional variations which may otherwise result in over-occlusion of one of tubes  46 A- 46 F and under-occlusion of the opposite tube  46 A′- 46 F′ are evenly shared between both tubes of each pump unit  52 A- 52 F. Because dimensional errors or tolerances are shared across both tubes  46 A- 46 F and  46 A′- 46 F′ in each of pump units  52 A- 52 F, the torque required to rotatably drive each rotor  62 A- 62 F is reduced. The self-centering nature of rotors  62 A- 62 F further enables different tube sizes with somewhat similar force and flexion points to be accommodated. In the particular embodiment shown, the diametral spacing S 1  is at least about 0.4 millimeters and nominally at least about 0.6 millimeters. 
   As further shown by  FIG. 4 , surfaces  74  of each of housings  60 A- 60 F are spaced from the exterior most peripheral surfaces of drive shaft  54  while being permitted to independently move relative to adjacent housing  60 A- 60 F. In particular, surfaces  74  are radially spaced from the exterior most surfaces of projections  120  (and from main pin  122  by distances D 1  and D 2 ) to form a diametral spacing S 2  between projections  120  and surfaces  74 . In addition, opposite exterior surfaces  79  of each of housings  60 A- 60 F are spaced from opposite surfaces  81  of frame  50  by distances D 3  and D 4  which together form a diametral spacing S 3 . The smaller of S 2  and S 3  may limit movement of each housing  60 A- 60 F. As a result of these clearances, each housing  60 A- 60 F is permitted to move or float relative to axis  68  and relative to drive shaft  54  in directions non-parallel to and nominally perpendicular to axis  68 . Consequently, each of housings  60 A- 60 F automatically repositions itself and its occlusion surfaces  64 ,  66  using the compression reaction forces of tubes  46 A- 46 F and tubes  46 A′- 46 F′ to appropriately center itself, automatically taking into account the differences between tubes  46 A- 46 F and tubes  46 A′- 46 F′ as well as dimensional variations which may otherwise result in over compression of one of tubes  46 A- 46 F and under compression of the other of tubes  46 A′- 46 F′. In the particular example shown, the smallest of diametral spacings S 2  and S 3  is at least 0.20 millimeters and is nominally at least 0.45 millimeters. In one embodiment, the sum of S 1  and the smallest of S 2  and S 3  is at least 0.6 millimeters. 
   According to one embodiment, each housing  60 A- 60 F and its corresponding rotor  62 A- 62 F have a combined total clearance (S 1 +(smallest of S 2  and S 3 ) of at least 2.0% D mean , wherein D mean  is equal to one-half the sum of the inside diameter of the particular housing  60 A- 60 F (the radial distance between opposite occlusion surfaces  66 ) and the outside diameter of the corresponding rotor  62 A- 62 F (the diameter of the smallest circle which is tangent to and encompassing the outer occluding surfaces of the rotor  62 A- 62 F, i.e., the radial spacing between 2 opposite occluding surfaces  82 ). In one particular embodiment, the inside diameter of the housing is 32.5 millimeters, the outside diameter of the rotor is 30.5 millimeters, and the mean diameter (D mean ) is 31.5 millimeters. In such an embodiment, the sum of the clearances S 1  and the smallest of S 2  and S 3  is greater than or equal to 2.0% of 31.5 millimeters or 0.63 millimeters. In other embodiments, the sum of the clearances S 1  and the smallest of S 2  and S 3  may be increased or decreased depending upon the inside diameter of the housing and the outside diameter of the rotor. 
   Overall, pump  40  provides a mechanism for pumping fluid through a multitude of tubes that is less susceptible to tolerance or dimensional variations and that is less costly and complex. One or both of housings  60 A- 60 F or rotors  62 A- 62 F automatically center themselves between opposing tubes  46 A- 46 F and  46 A′- 46 F′ using tube compressive reaction forces. As a result, fluid pumping efficacy and its torque requirements are reduced as the potential for overly compressing or under compressing tubes  46 A- 46 F and tubes  46 A′- 46 F′ is reduced. In addition, because pump units  52 A- 52 F are interchangeable with one another and may be stacked, tube occlusion forces are not transferred between pumping units, pump  40  is more compact, housings  60 A- 60 F are more easily manufactured and rotors  62 A- 62 F are more easily assembled within housings  60 A- 60 F. Because pump units  52 A- 52 F are substantially identical to one another, pump units  52 A- 52 F may be used in a variety of different pumps having differing numbers of pump units without requiring substantial additional engineering or part modification. 
   Although the particular example illustrates the combination of many features which provide the aforementioned benefits in conjunction with one another, such features may alternatively be used independent of one another in other pumps. For example, in other embodiments, one or more rotors  62 A- 62 F may be configured to move or otherwise float relative to axis  68  within a housing providing occlusion surfaces for multiple rotors or within multiple housings which remain substantially stationary relative to axis  68  as rotors  62 A- 62 F are being rotated. The individual housings  60 A- 60 F of pump units  52 A- 52 F, which float relative to axis  68 , may alternatively be utilized with rotors  62 A- 62 F which are configured to remain substantially stationary relative to axis  68  as they are being rotated between tubes  46 A- 46 F and tubes  46 A′- 46 F′. In particular embodiments, each pump unit  52 A- 52 F may be provided with a dedicated retainer plate  80  in lieu of the pump units  52 A- 52 F utilizing the back side of an adjacent pump unit  52 A- 52 F. 
     FIGS. 6-15  illustrate pump  240 , another embodiment of pump  40 . Pump  240  is similar to pump  40  in that pump  240  includes a plurality of pump units  52 A- 52 F positioned with the frame  50  as shown in  FIG. 2 . However, each pump unit  52 A- 52 F includes an alternatively configured housing, an alternatively configured rotor and is driven by an alternatively configured drive shaft. In the particular embodiment shown in  FIGS. 6-15 , pump  240  is similar to pump  40  in that pump  240  accommodates dimensional variations by permitting its housings and rotor to float relative to the drive shaft and is formed as a stack. In addition, as described in detail below, pump  240  reduces torque requirements by utilizing sets of occluding surfaces having a staggered pitch and by configuring its rotors and housings to flex to accommodate dimensional variations to minimize or prevent over compression or under compression of its tubes. 
     FIG. 6  illustrates a single pump unit  52 A of pump  240  in greater detail. The remaining units  52 B- 52 F of pump  240  are substantially identical to unit  52 A. As shown by  FIG. 6 , unit  52 A generally includes housing  260 A, tubes  46 A,  46 A′ and rotor  262 A. Housing  260 A comprises one or more structures configured to provide at least one occlusion surface against which a tube  46 A may be compressed. In the particular example shown in  FIG. 3 , housing  260 A provides two occlusion surfaces, occlusion surface  264  and occlusion surface  266 . As shown by  FIG. 7  which illustrates housing  260 A in greater detail, occlusion surfaces  264  and  266  each arcuately extend about axis  268  and generally face one another. Occlusion surfaces  264  and  266  are configured to resiliently flex away from one another and substantially away from axis  268 . As a result, occlusion surfaces  264  and  266  automatically account for or adapt to manufacturing variation or tolerances associated with the various components of pump  240  including housing  260 A, tubes  46 A,  46 A′ and rotor  262 A. By accommodating component parts&#39; dimensional variations, occlusion surfaces  264  and  266  facilitate the proper amount of compression of tubes  46 A and  46 A′. In particular, tubes  46 A and  46 A′ are not undercompressed which results in fluid not being consistently pumped. At the same time, tubes  46 A and  46 A′ are not overly compressed or occluded which requires increased torque or power to rotate rotor  262 A and which reduces the useful life of tubes  46 A and  46 A′. 
   In the particular example shown in  FIG. 7 , housing  260 A includes a separation slit  270  extending between surfaces  264  and  266 . Slit  270  provides housing  260 A with a continuous opening or passage radially extending from an exterior of housing  260 A to axis  268 . Slit  270  in conjunction with the materials and dimensions of housing  260 A facilitate flexing of occlusion surfaces  264  and  266  away from one another and away from axis  268 . In the particular example shown in  FIG. 7 , occlusion surfaces  264  and  266  are integrally formed as a single unitary body with appropriate dimensions and formed from appropriate materials enabling portions of housing  260 A to resiliently flex as a living hinge. Because occlusion surfaces  264  and  266  of housing  260 A are integrally formed as a single unitary body, housing  260 A increases the overall flexibility and compliance of pump unit  252 A without requiring additional parts or springs. As a result, manufacturing and assembly complexity and costs are reduced. 
   According to one embodiment, the ability of housing  260 A to flex away from slit  270  (i.e. its spring rate or spring constant) is no greater than about eight times the spring constant of a fully compressed tubes  46 A,  46 A′ at the beginning of occlusion and is no greater than four times the spring constant of a fully compressed tube  46 A or  46 A′ at the maximum occlusion or compression of tube  46 A or  46 A′. In one particular embodiment, tube  46 A has a diameter of approximately 3.0 millimeters and a nominal wall thickness of approximately 0.75 millimeters. Tube  46 A′ has a diameter slightly smaller than 3.0 millimeters and a nominal wall thickness of about 0.75 millimeters. Tubes  46 A and  46 A′ are each generally collapsed at a tube compression of about 1.5 millimeters (a height of 2 times the wall thickness). The range of desired tube compression is generally between 1.6 millimeters and 1.9 millimeters. In such an embodiment, the ratio of spring rates between the housing  260 A and both tubes  46 A,  46 A′ (Kh/Kt) varies from no greater than about eight at the beginning of occlusion (1.6 millimeter compression) and decreases to no greater than about four at the high end of desired tube occlusion (1.9 millimeters). 
   In the particular embodiment shown, housing  260 A additionally accommodates dimensional variations by automatically floating or moving relative to rotor  262 A and drive shaft  254  in directions non-parallel to and nominally perpendicular to axis  268 . Similar to housings  60 A- 60 F described above, housing  260 A includes drive shaft opening  74  which is sized to allow drive shaft  254  to pass through opening  74  in connection with the associated rotor  262 A. Drive shaft opening  74  is radially spaced from outer most portions of drive shaft  254  so as to enable housing  260 A to move or otherwise float relative to drive shaft  254  or the associated rotor  262 A in a direction non-parallel to and nominally perpendicular to axis  268 . In other embodiments, housing  260 A may alternatively be configured so as to be held stationary relative to axis  268 . 
   In the particular example shown in  FIG. 7 , housing  260 A is molded out of a polymeric material such as polycarbonate. Housing  260 A has wall thicknesses 1 mm, 2.5 and 2.3 mm at locations  274 ,  276  and  278 , respectively. Slit  270  has a width of about 1 mm. 
   In other embodiments, housing  260 A may have various other configurations, may be made from one or more alternative materials and may have other dimensions while still permitting occlusion surfaces  264  and  266  to flex away from one another and away from axis  268 . In other embodiments, housing  260 A may be formed from two or more structures that are coupled to one another while permitting surfaces  264  and  266  to flex away from one another. For purposes of this disclosure, the term “coupled” shall mean the joining of two members directly or indirectly to one another. Such joining may be stationary in nature or movable in nature. Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate member being attached to one another. Such joining may be permanent in nature or alternatively may be removable or releasable in nature. In still other embodiments, housing  260 A may alternatively include two or more structures coupled to one another by a mechanical spring opposite slit  270  or may include two or more structures coupled to one another by multiple springs, eliminating slit  270  yet enabling surfaces  264  and  266  to flex away from one another. 
   Rotor  262 A generally comprises one or more structures providing occluding surfaces that are moved against tubes  46 A and  46 A′ while at least partially occluding tubes  46 A and  46 A′ to move fluid therethrough. In the particular example shown in  FIG. 6 , rotor  262 A includes a set of four occluding surfaces  282 A that compress and at least partially occlude tubes  46 A and  46 A′ while rotating about axis  268 . Rotor  262 A is located between occlusion surfaces  264  and  266  such that fluid is moved or pumped through tubes  46 A and  46 A′ simultaneously. 
     FIGS. 8 and 9  illustrate rotor  262 A in greater detail. As shown by  FIGS. 8 and 9 , rotor  262 A includes hub  284 , arms  286 , posts  288  and rollers  290 . Hub  284  couples each of arms  286 , posts  288  and rollers  290  to one another about axis  268 , enabling rollers  290  to be simultaneously rotated about axis  268 . Hub  284  couples the remainder of rotor  262 A to drive shaft  254  (shown in  FIG. 10 ). In the particular example shown, hub  284  includes central bore  294  and projections  296 ,  298 . Bore  294  extends through hub  284  and is configured to receive drive shaft  254  (shown in  FIG. 10 ) such that drive shaft  254  may rotate relative to hub  284 . Although bore  294  is illustrated as having a generally circular cross sectional shape, bore  294  may have other cross sectional shapes. 
   Projections  296  and  298  extend inwardly from bore  294  and are configured to engage portions of drive shaft  254 , enabling drive shaft  254  to transmit torque to rotor  262 A. In the example shown, projection  296  includes circumferentially spaced engagement surfaces  302 ,  304 . Projection  298  includes circumferentially spaced engagement surfaces  306 ,  308 . As will be described in greater detail hereafter, engagement surfaces  302 ,  304 ,  306  and  308  are engaged by drive shaft  254 , depending upon the direction in which drive shaft  254  is being rotatably driven, to rotate rotor  262 A between a staggered pitch and an off pitch. Although projections  296  and  298  are illustrated as elongate teeth extending along the entire axial length of hub  284 , projections  296  and  298  may extend only partially along the axial length of hub  284  and may have various other configurations. In other embodiments, hub  284  may include a greater or fewer number of such projections. In still other embodiments, hub  284  may include one or more grooves which receive projections of drive shaft  254 . 
   In the particular embodiment illustrated, projections  296  and  298  as well as the inner surfaces of bore  294  are radially spaced from opposite surfaces of drive shaft  254  so as to enable rotor  262 A to move or float relative to drive shaft  254  and relative to axis  268  in directions non-parallel to nominally perpendicular to axis  268 . The diametral spacing between projections  296 ,  298  and bore  294  and the opposing surfaces of drive shaft  254  is large enough to enable rotor  262 A to automatically center itself between tube  46 A and  46 A′ in response to opposing tube reaction forces resulting from opposing tube compressions. In the particular embodiment shown, the diametral spacing is at least about 0.4 millimeters and nominally at least 0.6 millimeters. In other embodiments, projections  296 ,  298 , bore  294  and drive shaft  254  may alternatively be configured to prevent movement of rotor  262 A relative to axis  268 . 
   Arms  286  radially extend from hub  284  and support posts  288 . Posts  288  extend from arms  286  and rotatably support rollers  290  about axes  312 . Posts  288  nonsymmetrically extend about axes  312  and have a generally non-circular or non-annular cross sectional shape. Posts  288  are further formed from one or more materials which enable posts  288  to deflect or flex towards axis  268 . In the particular embodiment illustrated, each post  288  has a generally semi-cylindrical shape. As shown by  FIG. 9 , to further facilitate inward flexing of posts  288 , posts  288  obliquely extend from arms  286  in an unflexed state away from axis  268 . Because posts  288  are resiliently compliant in a direction towards axis  268 , rollers  290  are also resiliently compliant in a direction towards axis  268 . As a result, posts  288  and rollers  290  accommodate dimensional variations resulting from the manufacture or assembly of pump  240 . As a result, there is less likelihood that tubes  46 A and  46 A′ will be undercompressed or over compressed. 
   In the particular embodiment illustrated, post  288  are configured so as to be resiliently compliant with a spring constant of no greater than six times a spring constant of fully compressed tubes  46 A,  46 A′. According to one embodiment, tube  46 A has a diameter of about 3.0 millimeters and a wall thickness of approximately 0.75 millimeters. Tube  46 ′ has a diameter less than 3.0 millimeters and a wall thickness of about 0.75 millimeters. Tubes  46 A and  46 A′ each have a range of desired tube compression of between 1.6 millimeters and 1.9 millimeters. Tubes  46 A and  46 A′ are generally collapsed at a tube compression of 1.5 millimeters (height of 2 times the wall thickness). In such an embodiment, posts  288  generally have a nonlinear spring constant. Tubes  46 A and  46 A′ also experience a nonlinear spring constant or compliance. The ratio of spring rates between the rotor provided by an arm  286  and its corresponding post  288  to the spring rate of tubes  46 A and  46 A′ varies from approximately six at the beginning of occlusion (1.6 millimeters) and decreases to approximately four at the high end of the desired tube occlusion (1.9 millimeters). Overall, at the low end of desired tube occlusion (1.6 millimeters of compression) 77% of any additional compression is taken up by tube  46 A while 23% is taken up by housing  60 A or by the combination of housing  60 A and rotor  262 A. At the high end of desired tube occlusion (1.9 millimeters), 64% of additional compression is taken up by tube  46 A while 36% is taken up by the combination of housing  260 A and rotor  262 A. In particular embodiments, the spring constant of post  288  may be modified depending upon other factors such as the spring constant of housing  260 A. 
   Because the overall compliance of rotor  262 A is achieved by integrating compliance into the design of the existing rotor  262 A, the improved performance of rotor  262   a  is achieved without requiring additional parts or springs. Consequently, unit  252 A is more compact and has reduced complexity, manufacturing costs and assembly costs. 
   In the examples shown in  FIGS. 8 and 9 , each of posts  288  obliquely extends from its respective arm  286  at an angle θ of about 2.5 degrees. Hub  284 , arms  286  and posts  288  are integrally formed as a single unitary body out of a polymeric material such as 20% glass filled polycarbonate. Each of arms  286  has a radial length from a center of hub  284  of about 13 mm, a circumferential width of about 6 mm and axial thickness of about 1.5 mm. Each of posts  288  has an axial length extending from arms  286  of about 5 mm and a diameter of about 4 mm. 
   In other embodiments, one or more of hub  284 , arms  286  and posts  288  may be separately formed and coupled to one another in other fashions. Hub  284 , arms  286  and posts  288  may be formed from one or more alternative polymeric or other materials. In addition, arms  286  and posts  288  may have different dimensions, different shapes and may extend at different angles relative to one another while enabling posts  288  to resiliently flex towards axis  268 . 
   As shown by  FIG. 8 , rollers  290  are rotatably supported by posts  288  and provide occluding surfaces  282 A. Rollers  290  generally comprise annular rings rotatably supported about axes  312  such that rollers  290  roll against tubes  46 A and  46 A′ as rotor  262 A is rotatably driven about axis  268 . In other embodiments, occluding surfaces  282 A may be provided by other structures rotatably or stationarily coupled to the remainder of rotor  262 A. Although rotor  262 A is illustrated as including four equiangularly spaced sets of arms  286 , posts  288  and rollers  290  about hub  284 , rotor  262 A may alternatively include a greater or fewer number of such sets of arms  286 , posts  288  and rollers  290 . 
   Drive shaft  254  is shown in  FIGS. 10 ,  10 A,  10 B and  10 C. Drive shaft  254  rotatably drives rotors  262 A as well as rotors  262 B- 262 F (shown in  FIGS. 8 and 9 ) of pump units  52 A- 52 F (shown in  FIG. 2 ). Drive shaft  254  is operably coupled to a source of rotational power or torque  318  (schematically shown), such as a motor. Drive shaft  254  includes rotor interfaces  320 A,  320 A′,  320 B,  320 B′,  320 C,  320 C′,  320 D,  320 D′,  320 E,  320 E′,  320 F and  320 F′. Each of interfaces  320 A- 320 F and  320 A′- 320 F′ includes a drive surface  322  and a drive surface  324 . Drive surfaces  322  and  324  of each interface  320 A- 320 F and  320 A′- 320 F′ are circumferentially spaced from one another and generally face in opposite directions. Drive surfaces  322  and  324  of axially aligned interfaces, such as interfaces  320 A and  320 A′, generally face one another and are separated by an opening or channel  328  through which projections  296  and  298  (shown in  FIG. 8 ) extend and move. As shown by  FIGS. 10 ,  10 A and  10 B, drive surfaces  322  of each of interfaces  320 A- 320 F are angularly offset from one another or have a first staggered pitch. As shown by  FIGS. 10A and 10B , drive surfaces  322  of interfaces  320 A′- 320 F′ are angularly offset from one another and have a first staggered pitch. As further shown by  FIGS. 10A ,  10 B and  10 C, drive surfaces  322  of interfaces  320 A- 320 F are circumferentially spaced from drive surfaces  322  of interfaces  320 A′- 320 F′, respectively, by 180 degrees. 
   As shown by  FIGS. 10A and 10B , drive surfaces  324  of interfaces  320 A- 320 F are angularly or circumferentially positioned relative to one another so as to have a second off pitch. For purposes of this disclosure, the term “off pitch” means any pitch or angular relationship between set of drive surfaces  324  of interfaces  320 A- 320 F or  320 A′- 320 F′ that is distinct from the first relative angular positioning or pitch of the set of drive surfaces  322  of interfaces  320 A- 320 F or  320 A′- 320 F′. In those applications in which drive shaft  254  includes only a single set of interfaces, such as interfaces  320 A- 320 F, the term “off pitch” means that the second angular spacing or pitch between drive surfaces  324  is distinct from the first angular spacing or staggered pitch of drive surfaces  322  of the same set of interfaces. 
   In the particular example shown in  FIGS. 10 ,  10 A,  10 B and  10 C, drive surfaces  324  of interfaces  320 A- 320 F have an off pitch wherein drive surfaces  324  of each of interfaces  320 A- 320 F are angularly aligned with one another. Similarly, drive surfaces  324  of each of interfaces  320 A′- 320 F′ have an off pitch wherein each of drive surfaces  324  of interfaces  320 A′- 320 F′ are also angularly aligned with one another. In other embodiments, drive surfaces  324  of interfaces  320 A- 320 F, drive surfaces  324  of interfaces  320 A′- 320 F′ or drive surfaces  324  of both sets of interfaces may have an off pitch, wherein drive surfaces  324  have a second staggered pitch in which drive surfaces  324  are angularly offset from one another but with a distinct pitch or angular spacing as compared to drive surfaces  322 . 
   In the particular example shown, drive surfaces  322  of each set of interfaces  320 A- 320 F and  320 A′- 320 F′ have the first staggered pitch such that when drive shaft  254  is rotatably driven by torque source  318  in the direction indicated by arrow  332 , drive surfaces  322  of interfaces  320 A- 320 F contact and engage engagement surfaces  302  of hubs  284  of each of rotors  262 A- 262 F (shown in  FIG. 11 ). At the same time, drive surfaces  322  of each of interfaces  320 A′- 320 F′ contact and engage engagement surfaces  306  of hubs  284  of each of rotors  262 A- 262 F, respectively. As a result, as drive shaft  254  is driven in the direction indicated by arrow  332  (shown in  FIG. 10 ), rotors  262 A- 262 F are rotatably driven about axis  268  in the direction indicated by arrow  332  while also having the first staggered pitch between occluding surfaces  282 A provided by rollers  290  as shown in  FIG. 11 . In the particular example, drive surfaces  322  of each set of interfaces  320 A- 320 F and  320 A′- 320 F′ are configured to drive rotors  262 A- 262 F such that each roller  290  is not angularly aligned with any other roller  290  of any of rotors  262 A- 262 F while being driven about axis  268  in the direction indicated by arrow  332  (shown in  FIG. 10 ). In the particular example, each roller  290  is angular spaced from an axially consecutive roller  290  by 15 degrees. In other embodiments, the angular spacing between axially consecutive rollers  290  may vary depending on such factors as the number of rollers  290  on each rotor as well as the total number of rotors. For example, in other embodiments in which pump  240  includes a total of N rotors and wherein each rotor includes a total of C equiangularly spaced occluding surfaces  282 A, such as provided by rollers  290 , the first staggered pitch of drive surfaces  322  as well as the corresponding first staggered pitch of rollers  290  is 360/NC degrees. Although drive surfaces  322  of interfaces  320 A- 320 F and interfaces  320 A′- 320 F′ are illustrated as having uniform angular spacings between axially consecutive drive surfaces  322 , in other embodiments, such spacings may be non-uniform or irregular. 
   Because drive surfaces  324  of interfaces  320 A- 320 F are angularly aligned with one another and because drive surfaces  324  of interfaces  320 A′- 320 F′ are angularly aligned with one another, drive surfaces  324  of interfaces  320 A- 320 F simultaneously engage engagement surfaces  304  of hubs  284  of rotors  262 A- 262 F, respectively, when drive shaft  254  is rotatably driven by torque source  318  about axis  268  in the direction indicated by arrow  336 . At the same time, drive surfaces  324  of interfaces  320 A′- 320 F′ simultaneously engage engagement surfaces  308  of hubs  284  of rotor  262 A- 262 F, respectively, when drive shaft  254  is rotatably driven about axis  268  in the direction indicated by arrow  336 . As shown by  FIG. 12 , this results in each of rotors  262 A- 262 F being rotatably driven about axis  268  in the direction indicated by arrow  336  while in angular alignment with one another such that each occluding surface  282  and each roller  290  of each rotor  262 A- 262 F is in angular alignment with an occluding surfaces  282  and a roller  290  of every other rotor  262 A- 262 F when drive shaft  254  and rotors  262 A- 262 F are rotatably driven in the direction indicated by arrow  336 . 
   As further shown by  FIG. 10 , drive shaft  254  additionally includes keys or splines  337 . Splines  337  are configured to be received within corresponding key ways or openings within a drive element such as a gear, pulley or the like. For example, splines  337  may be configured to be received within corresponding openings within a gear such as gear  97 . As a result, drive shaft  254  may be easily mounted to alternative gears or other drive elements. In other embodiments, splines  337  may have other configurations or may be omitted in those embodiments wherein drive shaft  254  is integrally formed with a drive element or is connected to a drive element by other means. 
     FIGS. 13-15  illustrate the operation of pump  240 .  FIGS. 13 and 14  illustrate torque source  318  rotatably driving rod shaft  254  about axis  268  in the direction indicated by arrow  332 . Initially, drive shaft  254  may rotate relative to rotors  262 A,  262 B (shown in  FIGS. 13 and 14 ) as well as rotors  262 C- 262 F (shown in  FIG. 11 ) within channel  328  until drive surfaces  322  of interfaces  320 A- 320 F and  320 A′- 320 F′ are brought into contact and engagement with engagement surfaces  302  and  306  of hubs  284  of rotors  262 A,  262 B (shown in  FIG. 13 ) and of rotors  262 C- 262 F (shown in  FIG. 11 ). Because drive surfaces  322  of interfaces  320 A- 320 F and because drive surfaces  322  of interfaces  320 A′- 320 F′ have a staggered pitch, rotors  262 A and  262 B and their associated occluding surfaces  282 A and  282 B provided by rollers  290  also are driven with a staggered pitch. 
   As shown by  FIG. 14 , as rotor  262 A is rotatably driven about axis  268 , each of its occluding surfaces  282 A provided by each roller  290  alternates between a tube-compressing state in which the occluding surface  282 A compresses one of tubes  46 A and  46 A′ and an uncompressed state in which a particular occluding surface  282 A is not compressing either of tubes  46 A and  46 A′.  FIG. 14  specifically illustrates movement of a roller  290  of rotor  262 A through a tube compression phase (indicated by angle θ) during which the roller  290  moves from a compression initiation location (indicated by roller  290 , shown in phantom extending along radial line  350 ) to a maximum compression location (indicated with the same roller  290  shown in solid lines and extending along radial line  352 ). It has been observed that torque source  318  experiences a torque increase during movement of each roller  290  through the tube compression phase. 
   In the particular example shown in which each rotor  262 A- 262 F includes four occluding surfaces provided by four spaced rollers  290 , torque source  318  will experience four torque increases for each full revolution of each rotor  262 A- 262 F. However, because rotors  262 A- 262 F have a staggered pitch relative to one another and because each roller  290  is angularly offset relative to every other roller  290  of rotors  262 A- 262 F, each roller  290  will move through the tube compression phase at different times as compared to the remaining rollers  290 . Because none of the tube compression phases of rollers  290  coincide with one another, the peak magnitude of torque required of torque source  318  by pump  240  is reduced. In contrast, had each of rotors  262 A- 262 F been angularly aligned with one another such that the tube compression phases of each of rollers  290  of each of rotors  262 A- 262 F are coincident with one another, the peak magnitude of torque required of torque source  318  would be six times larger than the peak torque of a single rotor caused by each of the six rotors  262 A- 262 F simultaneously moving through the tube compression phase. 
   Because rotors  262 A- 262 F are equiangularly spaced from one another while being rotatably driven in the direction indicated by arrow  332 , torque source  318  experiences a relatively constant torque demand from pump  240 . In other embodiments, rotors  262 A- 262 F may not be equiangularly offset from one another while being driven in the direction indicated by arrow  332 . This would result in torque source  318  experiencing an inconsistent torque demand from pump  240 . 
     FIG. 15  illustrates drive shaft  254  being rotatably driven about axis  268  in the direction indicated by arrow  336 . Initially, interfaces  320 A- 320 F and  320 A′- 320 F′ may rotate relative to one or more of rotors  262 A- 262 F, respectively, until drive surfaces  324  are moved into contact and engagement with engagement surfaces  304  and  308  of hubs  284  of rotors  262 A- 262 F. In instances where rotors  262 A- 262 F have a staggered pitch as a result of being rotatably driven in the direction indicated by arrow  332  (shown in  FIG. 14 ), rotation of drive shaft  254  in the direction indicated by arrow  336  will result in drive surfaces  324  of interfaces  320 A- 320 F and of interfaces  320 A′- 320 F′ being sequentially brought into engagement and contact with engagement surfaces  304  and  308 . As shown by  FIG. 15 , once drive surfaces  324  of each of interfaces  320 A- 320 F and interfaces  320 A′- 320 F′ are in engagement with engagement surfaces  304  and  308  of rotor  262 A- 262 F, respectively, each of rotors  262 A- 262 F will be in angular alignment with one another. As a result, each occluding surface  282 A- 282 F and each roller  290  will be in angular alignment with a roller  290  of every other rotor  262 A- 262 F. 
   When pump  240  is not operating, rollers  290  may be stationarily positioned in a tube-compressing state for a prolonged period of time. As a result, a compression set will form in each tube. Upon start up of a pump  240 , the torque source  318  (shown in  FIG. 13 ) will experience a torque increase each time an occluding surface  282 A, such as a roller  290 , moves across the compression set in its respective tube  46 A,  46 A′. 
   During normal operation of pump  240 , torque source  318  rotatably drives drive shaft  254  to rotate rotors  262 A- 262 F about axis  268  in the direction shown by arrow  332  in  FIG. 14 . This results in fluid being pumped in the direction indicated by arrows  356 . As discussed above; because rotors  262 A- 262 F have a staggered pitch, the torque required of torque source  318  by each rotor  262 A- 262 F is also staggered, minimizing any peak torque required of torque source  318  by pump  240  during such pumping. Once pumping of fluid has been completed, torque source  318  rotatably drives drive shaft  254  in the direction indicated by arrow  336  as shown in  FIG. 15 . This results in each of rotors  262 A- 262 F and their respective rollers  290  being moved into angular alignment with one another. As a result, any compression sets that are formed in tubes  46 A- 46 F and  46 A′- 46 F′ (shown in  FIG. 2 ) will also be in angular alignment with one another. 
   Upon start up of pump  240  in which torque source  318  drives drive shaft  254  in the direction indicated by arrow  332  in  FIG. 14 , each of rotors  262 A- 262 F will once again be driven with a staggered pitch. As a result, the time at which each roller  290  of each rotor  262 A- 262 F encounters and moves through a formed compression set in tubes  46 A- 46 F and  46 A′- 46 F′ will also be staggered. The compression sets are in angular alignment with one another while rollers  290  of rotor  262 A- 262 F are driven while having a staggered pitch relative to one another. Consequently, the peak magnitude of torque required of torque source  318  by pump  240  upon start up of pump  240  is reduced. 
   Although the reduction of the peak magnitude of torque required of torque source  318  by pump  240  upon start up is illustrated as being reduced by angularly aligning the rollers  290  of rotors  262 A- 262 F prior to shut down such that the resulting compression sets within tubes  46 A- 46 F and  46 A′- 46 F′ are also angularly aligned with one another, the peak magnitude of torque required of torque source  318  by pump  240  may alternatively be reduced by repositioning rotors  262 A- 262 F prior to shut down with other off pitches. In lieu of having an off pitch wherein rotors  262 A- 262 F are in angular alignment with one another, rotors  262 A- 262 F may have an off pitch wherein rotors  262 A- 262 F are angularly offset from one another but with a pitch distinct from the staggered pitch at which rotors  262 A- 262 F are driven about axis  268  in the direction indicated by arrow  332  in  FIG. 14 . 
   Although each-of rotors  262 A- 262 F has been described as being moved to the off pitch shown in  FIG. 15  just prior to shut down, rotors  262 A- 262 F may also be rotatably driven about axis  268  in the direction indicated by arrow  336  so as to pump fluid through tubes  262 A- 262 F and  262 A′- 262 F′ in directions opposite to arrows  356  shown in  FIG. 14 . 
     FIGS. 1 ,  2  and  6 - 15  illustrate but one example of peristaltic pump  240 . Although pump  240  is illustrated as having six rotors  262 A- 262 F, pump  240  may alternatively have a greater or fewer number of such rotors. Although each rotor is illustrated as having four equiangularly spaced occluding surfaces provided by rollers  290 , one or more of rotors  262 A- 262 F may alternatively have a greater or fewer number of such rollers  290  or other occluding surfaces. Although pump  240  is illustrated as having drive shaft  254  which passes through each of rotors  262 A- 262 F and engages each of rotors  262 A- 262 F through the interaction between interfaces  320 A- 320 F and  320 A′- 320 F′ with projections  296  and  298 , drive shaft  254  may interact with rotors  262 A- 262 F in other fashions. For example, in lieu of drive shaft  354  having drive surfaces  322  with a staggered pitch and having drive surfaces  324  with an off pitch while hubs  284  have axially extending projections  296  and  298 , drive shaft  254  may alternatively have axially extending projections similar to projections  296  and  298  while hubs  284  of rotor  262 A- 262 F have one or more sets of drive surfaces  322  with a staggered pitch and one or more sets of drive surfaces  324  with an off pitch. In still other embodiments, drive shaft  354  may be omitted, wherein axially adjacent rotors  262 A- 262 F are configured to interact with one another so as to transmit torque from one rotor to the next. In such an alternative embodiment, the consecutive rotors are configured such that rotation of the rotors in a first direction results in the occluding surfaces of the rotors having a staggered pitch relative to one another and such that rotation of the rotors in an opposite direction results in the occluding surfaces of the rotors having an off pitch relative to one another. 
   Although the present invention has been described with reference to example embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention. For example, although different example embodiments may have been described as including one or more features providing one or more benefits, it is contemplated that the described features may be interchanged with one another or alternatively be combined with one another in the described example embodiments or in other alternative embodiments. Because the technology of the present invention is relatively complex, not all changes in the technology are foreseeable. The present invention described with reference to the example embodiments and set forth in the following claims is manifestly intended to be as broad as possible. For example, unless specifically otherwise noted, the claims reciting a single particular element also encompass a plurality of such particular elements.