Abstract:
A power transmitting device having a structure to allow a photoconductor to stably form a visible image on a printing medium. The power transmitting device interconnects a rotator and a drive motor, the drive motor generating drive power to drive the rotator. The power transmitting device includes at least one gear to be rotated upon receiving power from the drive motor, a rotating shaft having one end penetrating the gear and a coupler to interconnect the other end of the rotating shaft and the rotator. An outer diameter of the coupler, an outer diameter of the rotator and an outer diameter of the gear satisfy the following relation: 0.7D1&lt;Dc&lt;D2, where, D1: outer diameter of the rotator, D2: outer diameter of the gear and Dc: outer diameter of the coupler.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of Korean Patent Application No. 10-2013-0132499, filed on Nov. 1, 2013 in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
     BACKGROUND 
     1. Field 
     Embodiments of the present disclosure relate to a power transmitting device to transmit power and an image forming apparatus having the same. 
     2. Description of the Related Art 
     Image forming apparatuses are devised to print an image on a printing medium. Examples of image forming apparatuses include printers, copiers, fax machines and devices combining functions thereof. 
     In operation of an electrophotographic image forming apparatus, after light is emitted to a photoconductor charged with a predetermined potential to form an electrostatic latent image on a surface of the photoconductor, toner is fed to the electrostatic latent image to form a visible image. The visible image formed on the photoconductor is directly transferred to a printing medium or indirectly transferred to the printing medium by way of an intermediate transfer body and, then, the visible image transferred to the printing medium is fixed to the printing medium while passing through a fixing device. 
     To allow the toner image on the photoconductor to be transferred to the printing medium, the photoconductor defines a transfer nip in contact with a transfer roller. Torsion of the photoconductor may occur by shock applied when the printing medium approaching the transfer nip comes into contact with the photoconductor or while the printing medium passes through the transfer nip. Torsion of the photoconductor may vary a position where light reaches the photoconductor, causing a defect in a visible image transferred to the printing medium. This results in deterioration of print quality. 
     SUMMARY 
     It is an aspect to provide a power transmitting device having an improved structure to allow a photoconductor to stably form a visible image on a printing medium and an image forming apparatus having the same. 
     Additional aspects of the disclosure will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the disclosure. 
     In accordance with one aspect of the disclosure, a power transmitting device to interconnect a rotator and a drive motor, the drive motor generating drive power to drive the rotator, includes at least one gear to be rotated upon receiving power from the drive motor, a rotating shaft having one end penetrating the gear, and a coupler to interconnect the other end of the rotating shaft and the rotator, wherein an outer diameter of the coupler, an outer diameter of the rotator and an outer diameter of the gear satisfy the following relation: 0.7D1&lt;Dc&lt;D2, where D1: outer diameter of the rotator, D2: outer diameter of the gear and Dc: outer diameter of the coupler. 
     Torsional rigidity of the coupler may be greater than about 632 kNm/rad. 
     Torsional rigidity of the power transmitting device may be greater than about 149 kNm/rad. 
     In accordance with another aspect of the disclosure, an image forming apparatus includes a photoconductor, an electrostatic latent image being formed on the photoconductor, a drive unit to drive the photoconductor, and a power transmitting unit to transmit power from the drive unit to the photoconductor, wherein the power transmitting unit includes at least one gear connected to and rotated by the drive unit, a rotating shaft having one end connected to the gear so as to be rotated by the gear, and a coupler to interconnect the other end of the rotating shaft and the photoconductor, and wherein the coupler has an outer diameter greater than about 21.5 mm and less than about 120 mm. 
     The outer diameter of the coupler may be substantially equal to or greater than an outer diameter of the photoconductor. 
     The photoconductor may include a flange formed at one end thereof so as to be connected to the coupler, and the flange may include a receiving portion for reception of at least a portion of the coupler. 
     The coupler may include a plurality of coupling protrusions extending from one side of the coupler in a given direction for coupling of the coupler and the photoconductor. 
     The receiving portion may be shaped such that a diameter thereof is gradually reduced in an axial direction inward of the photoconductor, the coupler may include a coupling portion to be received and coupled in the receiving portion, and the coupling portion may be shaped such that a diameter thereof is gradually reduced in a given direction for coupling of the coupler and the photoconductor, so as to correspond to the receiving portion. 
     The flange may include a plurality of first coupling protrusions extending radially outward of the photoconductor and a plurality of first coupling recesses formed between the first coupling protrusions, and the coupler may include a plurality of second coupling protrusions to be inserted into the first coupling recesses and a plurality of second coupling recesses for reception of the first coupling protrusions. 
     The second coupling protrusions may be spaced apart from one another in a circumferential direction of the coupler. 
     In accordance with a further aspect of the disclosure, an image forming apparatus includes a first rotator, a second rotator to apply pressure to the first rotator to define a nip, a drive unit to drive the first rotator, and a power transmitting unit to transmit power from the drive unit to the first rotator, wherein torsional rigidity of the power transmitting unit is greater than about 632 kNm/rad such that a torsion angle variation rate of the first rotator, due to shock applied to the first rotator by a printing medium when the printing medium passes through the nip, becomes less than 2°. 
     The drive unit may include a drive motor, a drive shaft and a driving gear connected to the drive shaft, and the power transmitting unit may include a driven gear engaged with and rotated by the driving gear, a rotating shaft having one end connected to the driven gear so as be rotated by the driven gear and a coupler having one side coupled to the other end of the rotating shaft and the other side coupled to one end of the first rotator. 
     The coupler may have an outer diameter substantially equal to an outer diameter of the first rotator. 
     The photoconductor may include a flange formed at one end thereof so as to be connected to the coupler, and the flange may include a receiving portion for reception of at least a portion of the coupler, the receiving portion being shaped such that a diameter thereof is gradually reduced in an axial direction inward of the photoconductor. The coupler may include a coupling portion to be received and coupled in the receiving portion, and the coupling portion may be shaped such that a diameter thereof is gradually reduced in a given direction for coupling of the coupler and the photoconductor, so as to correspond to the receiving portion. 
     The coupler may have an outer diameter greater than an outer diameter of the first rotator and less than an outer diameter of the driven gear. 
     The flange may include a plurality of first coupling protrusions extending radially outward of the photoconductor and a plurality of first coupling recesses formed between the first coupling protrusions, and the coupler may include a plurality of second coupling protrusions to be inserted into the first coupling recesses and a plurality of second coupling recesses for reception of the first coupling protrusions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects of the disclosure will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which: 
         FIG. 1  is a view showing a configuration of an image forming apparatus according to one embodiment of the present disclosure; 
         FIG. 2  is a perspective view showing a coupled state of a drive unit, a power transmitting unit and a photoconductor; 
         FIG. 3  is a plan view of  FIG. 2 ; 
         FIG. 4  is a perspective view showing a coupling relationship between a flange and a coupler; 
         FIG. 5  is a view for explanation of a relationship between a variation rate of torque applied to a photoconductor by a printing medium, torsional rigidity and a torsion angle variation rate; 
         FIG. 6  is a table showing a relationship between torsional rigidity of a driven gear, a rotating shaft, a coupler and a power transmitting unit and a torsion angle variation rate of a photoconductor; 
         FIG. 7  is a graph showing a relationship between an outer diameter and torsional rigidity of a coupler; 
         FIG. 8  is a perspective view showing one alternative embodiment of a flange and a coupler; and 
         FIG. 9  is a perspective view showing another alternative embodiment of a flange and a coupler. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings.  FIG. 1  is a view showing a configuration of an image forming apparatus according to one embodiment of the present disclosure. 
     As exemplarily shown in  FIG. 1 , the image forming apparatus  1  includes a main body  10 , a paper feed device  20  for storage and rapid feeding of a printing medium S, a developing device  30  to form an image on a printing medium S fed by the paper feed device  20 , a toner device  40  to feed toner to the developing device  30 , a light scan device  50  to form an electrostatic latent image on a photoconductor  32  of the developing device  30 , a fixing device  60  to fix a toner image, transferred to the printing medium S, on the printing medium S, and a discharge device  70  to discharge the printing medium S, on which the image has been completely formed, to the outside of the main body  10 . 
     The paper feed device  20  serves to store and to rapidly feed the printing medium S. The paper feed device  20  is located in a lower region of the main body  10  to feed the printing medium S to the developing device  30 . 
     The paper feed device  20  may include a paper feed tray  21  in the form of a cassette that may be drawn from the main body  10  upon storage of the printing medium S and a delivery member  25  to pick up the printing medium S stored in the paper feed tray  21  one by one and to deliver the printing medium S to the developing device  30 . 
     A knock-up plate  23  may be accommodated in the paper feed tray  21  to guide the loaded printing medium S to the delivery member  25 . To this end, one end of the knock-up plate  23  may be rotatably coupled to the paper feed tray  21  and the other end of the knock-up plate  23  may be supported by a pressure spring  22 . 
     The delivery member  25  may include a pickup roller  27  to pick up the printing medium S loaded on the knock-up plate  23  one by one and a feed roller  28  to deliver the printing medium S picked up by the pickup roller  27  to the developing device  30 . 
     The developing device  30  includes a housing  31  forming an external appearance, the photoconductor  32  rotatably mounted in the housing  31  to form an electrostatic latent image, agitator screws  33   a  and  33   b  to agitate toner fed from the toner device  40 , a developing roller  34  to feed the toner agitated by the agitator screws  33   a  and  33   b  to the photoconductor  32  and a charge member  35  to charge the photoconductor  32 . 
     The toner fed from the toner device  40  is introduced into the housing  31  and agitated and moved to one side of the housing  31  by the agitator screws  33   a  and  33   b . Then, the agitated and moved toner is fed to the photoconductor  32  by the developing roller  34  to form a visible image. 
     To allow the toner fed to the photoconductor  32  for formation of a visible image to be transferred to the printing medium S, the photoconductor  32  comes into contact with a transfer roller  14  to define a transfer nip N1. The transfer roller  14  is rotatably located in the main body  10 . The photoconductor  32  may be a rotator that is rotated upon receiving power from a drive unit ( 110 , see  FIG. 2 ) and a power transmitting unit ( 120 , see  FIG. 2 ) that will be described hereinafter. 
     The toner device  40  is coupled to the developing device  30  and serves to receive and store toner used to form an image on the printing medium S. The toner device  40  feeds toner to the developing device  30  when an image forming operation proceeds. 
     The light scan device  50  emits light containing image information to the photoconductor  32  to form an electrostatic latent image on the photoconductor  32 . 
     The fixing device  60  includes a housing  62  and a heating member  64  and a pressure member  66  rotatably arranged in the housing  62 . 
     As the printing medium S, to which the toner image has been transferred, passes between the heating member  64  and the pressure member  66 , the toner image is fixed to the printing medium S by heat and pressure. 
     The heating member  64  is rotated in engagement with the pressure member  66  to define a fixing nip N2 in conjunction with the pressure member  66 . As such, the heating member  64  is heated by a heat source  68  and transmits heat to the printing medium S passing through the fixing nip N2. The heating member  64  may be a heating roller that is rotated upon receiving power from a drive source (not shown). The heat source  68  is located inside the heating member  64  to apply heat to the printing medium S to which the toner image has been transferred. Although a halogen lamp may be used as the heat source  68 , various other devices, such as a hot wire, induction heater or the like, may be used. 
     The pressure member  66  is located in contact with an outer circumferential surface of the heating member  64  to define the fixing nip N2 between the pressure member  66  and the heating member  64 . The heating member  64  may be a pressure roller that is rotated upon receiving power from a drive source (not shown). 
     The discharge device  70  includes a first discharge roller  71  and a second discharge roller  72  arranged in sequence and serves to discharge the printing medium S, having passed through the fixing device  60 , to the outside of the main body  10 . 
     Hereinafter, a power transmission structure for driving of the photoconductor  32  will be described in detail. 
       FIG. 2  is a perspective view showing a coupled state of the drive unit, the power transmitting unit and the photoconductor,  FIG. 3  is a plan view of  FIG. 2  and  FIG. 4  is a perspective view showing a coupling relationship between a flange and a coupler. 
     As exemplarily shown in  FIGS. 2 and 3 , the image forming apparatus  1  includes the drive unit  110  to drive the photoconductor  32  and the power transmitting unit  120  to transmit power from the drive unit  110  to the photoconductor  32 . 
     The drive unit  110  includes a drive motor  112  to generate drive power, a drive shaft  114  connected to the drive motor  112  and a driving gear  116  connected to the drive shaft  114 . The driving gear  116  is designed such that a maximum outer diameter thereof does not exceed 120 mm due to a limited space of the main body  10  in which the drive unit  110  is received. 
     The power transmitting unit  120  includes a driven gear  122  engaged with and rotated by the driving gear  116 , a rotating shaft  124  having one end  124   a  rotatably connected to the driven gear  122  and a coupler  126  having one side coupled to the other end  124   b  of the rotating shaft  124  and the other side coupled to one end of the photoconductor  32  to interconnect the rotating shaft  124  and the photoconductor  32 . 
     As exemplarily shown in  FIG. 4 , the coupler  126  is coupled to a flange  130  provided at one end of the photoconductor  32  to impede rotation thereof relative to the flange  130 . 
     The coupler  126  has a smaller outer diameter Dc than an outer diameter D1 of the photoconductor  32  and includes a plurality of coupling protrusions  126   a  inserted into the flange  130 . The coupling protrusions  126   a  extend from one side of the coupler  126  in a given direction in which the coupler  126  is coupled to the photoconductor  32 . The coupling protrusions  126   a  are spaced apart from one another in a circumferential direction of the coupler  126 . 
     The flange  130  includes a plurality of receiving portions  132  into which the coupling protrusions  126   a  may be inserted. The receiving portions  132  are formed from one side of the flange  130  facing one side of the coupler  126  provided with the coupling protrusions  126   a  in a given direction in which the coupler  126  is coupled to the photoconductor  32 . The receiving portions  132  are spaced apart from one another in a circumferential direction of the flange  130  so as to correspond to the coupling protrusions  126   a  in a one to one ratio. 
     While the printing medium S approaches or passes through the transfer nip N1 between the photoconductor  32  and the transfer roller  14 , torsion of the photoconductor  32  occurs by shock applied to the photoconductor  32 . When a torsion angle variation rate of the photoconductor  32  excessively increases, light emitted from the light scan device  50  reaches a position on the photoconductor  32  greatly deviated from a predetermined position, which may cause a defect in a visible image transferred to the printing medium S. Therefore, it may be necessary to control the torsion angle variation rate of the photoconductor  32  to prevent generation of a defect in the visible image transferred to the printing medium S while the printing medium S passes through the transfer nip N1. The principle of controlling the torsion angle variation rate of the photoconductor  32  will be described below. 
       FIG. 5  is a view for explanation of a relationship between a variation rate of torque applied to the photoconductor by the printing medium, torsional rigidity and a torsion angle variation rate,  FIG. 6  is a table showing a relationship between torsional rigidity of the driven gear, the rotating shaft, the coupler and the power transmitting unit and a torsion angle variation rate of the photoconductor, and  FIG. 7  is a graph showing a relationship between an outer diameter and torsional rigidity of the coupler.  FIG. 5  assumes that the photoconductor has an approximately cylindrical shape. 
     As exemplarily shown in  FIG. 5 , a relationship between torque M caused by force applied to the photoconductor  32  when the printing medium S enters the transfer nip N1, a torsion angle θ of the photoconductor  32  and torsional rigidity K of the photoconductor  32  and the power transmitting unit  120  that rotatably supports the photoconductor  32  is approximately as follows.
 
 M=K·θ   (Equation 1)
 
     Based on Equation 1, a relationship between a variation rate (dM/dt) of torque M caused by force applied to the photoconductor  32  when the printing medium S enters the transfer nip N1 and the torsion angle variation rate (d θ/dt) of the photoconductor  32  is as follows:
 
 dM/dt=K·d θ/dt   (Equation 2)
 
     To prevent a defect in the visible image transferred to the printing medium S, it may be necessary to control the torsion angle variation rate (d θ/dt) of the photoconductor  32  to a given numerical value or less. When the torque variation rate dM/dt upon entrance of the printing medium S is constant, it may be necessary to increase the torsional rigidity K of the photoconductor  32  and the power transmitting unit  120  to a given numerical value or more based on Equation 2. 
     When an outer diameter D1 and a length L1 of the photoconductor  32  are determined, the torsion angle variation rate (d θ/dt) of the photoconductor  32  may be controlled by increasing the torsional rigidity K of the power transmitting unit  120 . As described above, since the power transmitting unit  120  includes the driven gear  122 , the rotating shaft  124  and the coupler  126 , total torsional rigidity Kt of the power transmitting unit  120  is associated with torsional rigidity Kg of the driven gear  122 , torsional rigidity Ks of the rotating shaft  124  and torsional rigidity Kc of the coupler  126 . A relationship between the total torsional rigidity Kt of the power transmitting unit  120 , the torsional rigidity Ks of the rotating shaft  124 , the torsional rigidity Kg of the driven gear  122  and the torsional rigidity Kc of the coupler  126  is as follows:
 
1 /Kt= 1 /Kg+ 1 /Ks+ 1 /Kc   (Equation 3)
 
     A relationship between the torsional rigidities Kg, Ks, Kc and Kt of the driven gear  122 , the rotating shaft  124 , the coupler  126  and the power transmitting unit  120  and the torsion angle variation rate (d θ/dt) of the photoconductor  32  may be acquired via Computer Aided Engineering (CAE) analysis and results of such analysis are shown in the table of  FIG. 6 . 
     As exemplarily shown in the table, it will be appreciated that greater total torsional rigidity Kt of the power transmitting unit  120  causes smaller torsion angle variation rate (d θ/dt) of the photoconductor  32 . 
     As discovered, no defect occurs in the visible image transferred to the printing medium S when the torsion angle variation rate (d θ/dt) of the photoconductor  32  is below 2%. As shown in the table, the torsion angle variation rate (d θ/dt) of the photoconductor  32  is 2% when the total torsional rigidity Kt of the power transmitting unit  120  is 149 kNm/rad. Thus, it will be appreciated that the total torsional rigidity Kt of the power transmitting unit  120  may need to be above 149 kNm/rad in order to prevent a defect in the visible image transferred to the printing medium S. 
     As represented in Equation 3, the total torsional rigidity Kt of the power transmitting unit  120  is associated with torsional rigidities of constituent elements of the power transmitting unit  120 , i.e. the torsional rigidity Kg of the driven gear  122 , the torsional rigidity Ks of the rotating shaft  124  and the torsional rigidity Kc of the coupler  126 . Thus, the total torsional rigidity Kt of the power transmitting unit  120  may be adjusted by adjusting any one of the torsional rigidity Kg of the driven gear  122 , the torsional rigidity Ks of the rotating shaft  124  and the torsional rigidity Kc of the coupler  126 . In the table, when the torsional rigidity Kg of the driven gear  122  and the torsional rigidity Ks of the rotating shaft  124  remain constant and the torsional rigidity Kc of the coupler  126  is increased to 632 kNm/rad, the torsion angle variation rate (d θ/dt) of the photoconductor  32  is reduced to 2.0%. Accordingly, it will be appreciated that the torsional rigidity Kc of the coupler  126  may need to be above 632 kNm/rad in order to prevent a defect in the visible image transferred to the printing medium S. Although not represented in the table, the torsional rigidity Kg of the driven gear  122  or the torsional rigidity Ks of the rotating shaft  124  as well as the torsional rigidity Kc of the coupler  126  may be adjusted to reduce the torsion angle variation rate (d θ/dt) of the photoconductor  32  to be below 2% in order to prevent a defect in the visible image transferred to the printing medium S. 
     The coupler  126  may have an approximately cylindrical shape and the torsional rigidity Kc of the coupler  126  is defined by the following Equation 4:
 
 Kc=G*J/Lc   (Equation 4)
 
(where, G=a torsional rigidity coefficient, J=πDc 4 /32, Lc=length of the coupler, Dc=outer diameter of the coupler).
 
     As represented in Equation 4, it will be appreciated that the torsional rigidity Kc of the coupler  126  is associated with the outer diameter Dc of the coupler and the length Lc of the coupler and increasing the outer diameter Dc of the coupler is more effective than reducing the length Lc of the coupler. A relationship between the outer diameter Dc of the coupler and the torsion angle variation rate (d θ/dt) of the photoconductor  32  may be acquired via CAE analysis and results of such analysis are shown in the graph of  FIG. 7 . 
     As exemplarily shown in the table of  FIG. 6  and the graph of  FIG. 7 , it will be appreciated that the torsional rigidity Kc of the coupler  126  becomes 632 kNm/rad when the outer diameter Dc of the coupler is 21.5 mm. In addition, since the torsion angle variation rate (d θ/dt) of the photoconductor  32  is 2% when the torsional rigidity Kc of the coupler  126  is 632 kNm/rad, it will be appreciated that the outer diameter Dc of the coupler may need to be above 21.5 mm in order to prevent a defect in the visible image transferred to the printing medium S. 
     Increasing an outer diameter D2 of the driven gear  122  to 120 mm or more may be impossible due to the fact that the power transmitting unit  120  occupies a limited interior space of the main body  10  and the outer diameter Dc of the coupler may need to be smaller than the outer diameter of the driven gear  122 . Therefore, the outer diameter Dc of the coupler may need to be below 120 mm. 
     As described above, in order to prevent a defect in the visible image transferred to the printing medium S, the torsion angle variation rate (d θ/dt) of the photoconductor  32  may need to be below 2% and, in turn, to secure the torsion angle variation rate (d θ/dt) of the photoconductor  32  below 2%, the total torsional rigidity Kt of the power transmitting unit  120  may need to be above 149 kNm/rad. In addition, to increase the total torsional rigidity Kt of the power transmitting unit  120  beyond 149 kNm/rad when the torsional rigidity Kg of the driven gear  122  and the torsional rigidity Ks of the rotating shaft  124  remain constant, the torsional rigidity Kc of the coupler  126  may need to be above 632 kNm/rad and, in this case, the outer diameter Dc of the coupler may need to be above 21.5 mm. 
     Hereinafter, alternative embodiments of the flange and the coupler will be described. 
       FIG. 8  is a perspective view showing one alternative embodiment of the flange and the coupler, and  FIG. 9  is a perspective view showing another alternative embodiment of the flange and the coupler. 
     As exemplarily shown in  FIG. 8 , a flange  230  has a receiving portion  232 , a diameter of which is gradually reduced in an axial direction inward of the photoconductor  32 . 
     A coupler  226  has substantially the same diameter as the photoconductor  32  and includes a coupling portion  226   a  received and coupled in the receiving portion  232 . The coupling portion  226   a  extends from one side of the coupler  226  toward the flange  230 . To correspond to the receiving portion  232 , the coupling portion  226   a  is shaped such that a diameter thereof is gradually reduced in a given direction in which the coupler  226  is coupled to the photoconductor  32 . 
     To prevent relative rotation between the flange  230  and the coupler  226  in a state in which the coupling portion  226   a  is received in the receiving portion  232 , fastening gears  228  and  232   a  to be engaged with each other are formed respectively at an inner surface of the receiving portion  232  and an outer surface of the coupling portion  226   a.    
     As exemplarily shown in  FIG. 9 , a flange  330  includes a plurality of first coupling protrusions  332  extending radially outward of the photoconductor  32  and a plurality of first coupling recesses  334  formed between the first coupling protrusions  332 . The first coupling protrusions  332  and the first coupling recesses  334  are respectively spaced apart from one another in a circumferential direction of the flange  330 . 
     The coupler  326  has a larger diameter than that of the photoconductor  32  and includes a plurality of second coupling protrusions  326   a  to be inserted into the first coupling recesses  334  and a plurality of second coupling recesses  326   b  in which the first coupling protrusions  332  are received. 
     The second coupling protrusions  326   a  and the second coupling recesses  326   b  are spaced apart from one another in a circumferential direction of the flange  130  to correspond to the first coupling recesses  334  and the first coupling protrusions  332  respectively. 
     As is apparent from the above description, according to embodiments of the present disclosure, by improving torsional rigidity of a power transmitting device that interconnects a photoconductor and a drive unit to transmit power, a torsion angle variation rate of the photoconductor may be appropriately controlled, which may prevent a defect in a visible image transferred to a printing medium. 
     Although the embodiments of the present disclosure have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the claims and their equivalents.