# Patent

## Title
Printing control system and method for an inkjet printer

## Abstract

A printing control system and method for an inkjet printer, wherein a carrier equipped with one or more inkjet cartridges is driven while the line feeding is being executed, and the line printing is initiated after the line feeding of the paper is completed. The printing control method may comprise a number of steps to determine whether a line printing by the ink cartridges has been completed, and if so, executing the line feeding. The printing control method may further comprise estimating an expected length of time TE from a time point TC where the carrier initiates a next movement, to a time point TI where the next line printing is initiated, and comparing a length of feeding time TRX remaining until the line feeding is completed with the expected length of time TE, and driving the carrier if the length of remaining feeding time TRX becomes less than or equal to the expected length of time TE.

## Background
PRIORITY
This application claims priority under 35 U.S.C. § 119(a) to an application entitled “Printing controlling method for inkjet printer”, filed in the Korean Intellectual Property Office on Dec. 11, 2003 and assigned Ser. No. 2003-90020, the entire contents of which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an inkjet printer. More particularly, the present invention relates to a printing control system and method for an inkjet printer that is provided to increase printing speed by substantially eliminating delays between feed and print operations.
2. Description of the Related Art
FIG. 1 shows a construction example of a conventional inkjet printer. Referring to FIG. 1, the conventional inkjet printer comprises ink cartridges 11 and 12, a carrier 20, a paper feeding tray 30, and a feeding roller 40.
The respective ink cartridges 11 and 12 contain an ink, and each comprises a print head (not shown) for ejecting the ink contained therein. The carrier 20 carries the ink cartridges 11 and 12 while reciprocating a predetermined distance along a guide bar 55 installed in the printer body 50, so that the ink cartridges 11 and 12 can perform a line printing on a paper P (shown in outline only). The paper feeding tray 30 is loaded with papers (not shown), and the feeding roller 40 moves a paper P loaded in the paper feeding tray 30 to a printing area beneath the ink cartridges 11 and 12.
The conventional inkjet printer constructed as described above receives printing commands and feeding commands from a host, and a controller controls the driving of the carrier 20 and the feeding roller 40 according to respective commands, so that printing is executed on the paper P. Specifically, a paper P fed from the paper feeding tray 30 is delivered by the feeding roller 40 and stops at a printing position. At this time, the carrier 20 drives the ink cartridges 11 and 12 to pass over the paper P, and the ink cartridges 11 and 12 eject ink, so that a line of printing is performed on the paper P. Then, as the carrier 20 goes beyond the paper P and stops at the opposite side of the paper, the feeding roller 40 performs so-called “line feeding”, in which the feeding roller moves the paper P by a predetermined distance according to a feeding command. After the paper P is stopped, the carrier 20 is driven according to a next printing command and the ink is again ejected onto the paper P. As the line feeding of the paper P and the reciprocation of the carrier 20 are repeated in this manner, one printed page is completed on the paper P.
With the conventional inkjet printer example as described above, the carrier 20 starts to move after a line feeding of a paper P is completed, as shown in FIG. 2. In FIG. 2, the travel period and velocity of the carrier 20 is shown, defining a first and second printing, and a travel period and velocity of the feeding roller 40 is shown, defining a paper line feed, wherein the V-axis represents velocity and the T-axis represents time. However, a printing area, such as DI where the ink is substantially ejected onto the paper P, does not coincide with a time point TC where the feeding roller 40 stops and the carrier 20 starts to move. An actual line printing on a paper P therefore, is delayed for a predetermined time length after a line feeding of a paper P is completed.
As a result, a line printing cannot be initiated right after a line feeding of a paper P is completed, thereby causing a time delay. Therefore, a printing speed of an inkjet printer is reduced.
Accordingly, a need exists for a printing control method for an inkjet printer that can substantially increase printing speeds by reducing the time delays experienced by a printer between a time where a line feeding of a paper is completed, and a time where a line printing is initiated.
SUMMARY OF THE INVENTION
It is therefore an object of the present invention to solve at least the above problems and disadvantages, and to provide at least the advantages described below. Accordingly, an object of the present invention is to provide a printing control system and method for an inkjet printer that can increase printing speed by reducing a time delay between a time point where a line feeding of a paper is completed, and a time point where a line printing is initiated.
In order to achieve the above-described aspects of the present invention, a printing control system and method for an inkjet printer is provided wherein a carrier equipped with one or more inkjet cartridges is adapted to be driven while a line feeding is being executed. A line printing by the ink cartridges is then initiated after a line feeding of the paper is completed.
According to an embodiment of the present invention, the printing control method may comprise the steps of determining whether the line printing by the ink cartridges has been completed or not; initiating the line feeding if it is determined that the line printing has been completed; during line feeding, estimating an expected length of time TE from a time point TC where the carrier initiates a next movement, to a time point TI where the next line printing is initiated; comparing a length of line feeding time TRX remaining until the line feeding is completed, with the expected length of time TE; and driving the carrier if it is determined that the remaining feeding time TRX is less than or equal to the expected length of time TE. In doing so, the carrier 20 can be approaching a point at which printing occurs, while the feed roller 40 is completing a line feed.
In the step of comparing the time TRX with the time TE, the time TRX can be reduced to an interval of predetermined time ΔT to then be compared with the time TE.
According to an embodiment of the present invention, the moving velocity of the carrier is varied, and divided into an acceleration section, a constant-velocity section, and a deceleration section. The acceleration section may be further divided into several unit acceleration sections. Here, if the time TI is positioned in the acceleration section, the expected length of time TE can be determined as a length of time from the time TC to a time point where a corresponding unit acceleration section is initiated.
In addition, the several unit acceleration sections are preferably formed by dividing the length of time from the time TI, to a time point TK where the constant-velocity section is initiated, by a predetermined time interval.
Furthermore, the printing control method may further comprise the steps of: determining whether the line feeding of the paper has been completed at a time point where the next line printing is initiated; and displaying an error message if the line printing is initiated in a state where the line feeding of the paper has not been completed.
In a preferred embodiment of the present invention, the line feeding of the paper for the next line printing is initiated concurrently when the line printing is completed.



BRIEF DESCRIPTION OF THE DRAWINGS
The above objects and other features of embodiments of the present invention will become more apparent by describing certain exemplary embodiments thereof with reference to the attached drawings, wherein;
FIG. 1 is a perspective view illustrating a construction example of part of a conventional inkjet printer;
FIG. 2 is a graph showing a relationship between a carrier movement and a paper feeding movement in a conventional inkjet printer;
FIG. 3 is a block diagram illustrating a construction example of a printer including a printing control method according to an embodiment of the present invention;
FIGS. 4A to 4H are graphs showing the relationships between the movement of the carrier and paper feeding movements as controlled by the printing control method according to an embodiment of the present invention;
FIGS. 5A and 5B are views provided to describe the operation of an example inkjet printer including the printing control method according to an embodiment of the present invention;
FIGS. 6 to 8 are graphs illustrating the relationships between the movement of the carrier and paper feeding movements to describe the printing control method according to an embodiment of the present invention; and
FIG. 9 is a control flowchart illustrating an example of the printing control method according to an embodiment of the present invention.



DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS
Hereinbelow, an example printing control system and method for an inkjet printer according to certain embodiments of the present invention will be described in detail with reference to the accompanying drawings. Further, in referring to the elements having the same structure and operation, the elements will be cited by the same reference numerals throughout.
An inkjet printer, to which the printing control system and method is applied according to an embodiment of the present invention, has a construction similar to the conventional printer shown in FIG. 1. The inkjet printer comprises ink cartridges 11 and 12, a carrier 20, a paper feeding tray 30, a feeding roller 40, a controller 60, a carrier driving device 25, a feeding roller driving device 45 and a display device 70, as shown in FIGS. 1 and 3.
The ink cartridges 11 and 12 are provided with print heads (not shown), respectively, and are removably mounted in the carrier 20. In this example, one of the ink cartridges 11 and 12 is a black-and-white ink cartridge for black-and-white printing, and the other one is a color cartridge for color printing. However, the present invention can also be applied to an inkjet printer equipped with only one of the black-and-white ink cartridge or the color ink cartridge, or any additional cartridge combinations as required.
The carrier 20 is installed to reciprocate along a guide bar 55 provided in the printer body 50. As a line feeding is performed over a predetermined distance, such that a paper P fed from the paper feeding tray 30 is moved to a printing position, the carrier 20 moves in the printing direction C along the guide bar 55. At this time, the ink cartridges 11 and 12 eject the ink onto the paper P, thereby executing a line printing. Such movement of the carrier 20 and the line printing are repeated until one page printing of the paper P is completed.
The controller 60 controls the movement of the carrier 20 and the line feeding of the paper P. As shown in FIG. 3, if the inkjet printer receives a printing command CP and a feeding command CF from a host 100, the controller 60 controls the carrier driving device 25 and the feeding roller driving device 45 based on the commands. In this example, each of the carrier driving device 25 and the feeding roller driving device 45 may employ a number of drive motors, such as a DC motor or a step motor.
In addition, a display device 70 is connected to the controller 60, and any errors detected during the printing operation and/or conditions of the inkjet printer may be displayed through the display device 70.
The inkjet printer has various printing modes according to the desired printing qualities of printout products. The printing modes of an inkjet printer may include a high speed printing mode, a normal printing mode, a high quality printing mode, a best quality printing mode, or other printing modes, and the moving velocity of the carrier 20 (FIG. 1), and the line feeding distance of a paper, DF (FIG. 5A), can be varied according to the respective printing modes.
FIGS. 4A to 4H are graphs illustrating relationships between carrier movement and paper line feeding movement according to various printing modes of an inkjet printer in accordance with an embodiment of the present invention. In the graphs, the travel period and velocity of the carrier 20 is shown, defining a first and second printing, and a travel period and velocity of the feeding roller 40 is shown, defining a paper line feed, wherein the V-axis represents velocity and the T-axis represents time. As can be seen from the illustrated graphs, in the moving distance DC over which the carrier 20 (FIG. 1) is reciprocated, the moving velocity of the carrier 20 is varied, first exhibiting an acceleration section VU, then a constant-velocity section VP, and finally a deceleration section VD. The feeding velocity of a paper P also exhibits variations, including a period of acceleration, constant-velocity and deceleration. Typically, in a high speed printing mode (FIGS. 4A, 4C, 4E, 4G), the constant-velocity section VP of the moving velocity of the carrier 20 appears as a maximum velocity VM, and in a non-high speed printing mode (FIGS. 4B, 4D, 4F, 4H), the constant-velocity section VP of the moving velocity of the carrier 20 appears as a normal velocity VN. The distance DC in FIG. 4A indicates a distance that the carrier 20 moves at one time, and distance DI indicates the area where line printing is actually performed in the moving distance DC of the carrier 20.
The line feeding of a paper P can be established having several patterns of line feeding distances DF, and executed in a predetermined pattern according to a desired printing mode. In addition, as shown in FIGS. 4A to 4H, a line feeding of a paper P can be initiated concurrently with the completion of a line printing so that a time delay is not produced in the printing operation. The time point where a line printing is completed can be easily found by detecting a time point where the ink ejection of the cartridges 11 and 12 (FIG. 1) is completed.
FIGS. 4A and 4B show a line feeding pattern of a very small line feeding distance DF, that appears in a printing operation provided for obtaining a high quality printout product from among several line feeding patterns of a paper P. Because the length of time required for a line feeding is shorter than the length of time from a time point where a line feeding is completed while the carrier is moving, to a time point where the carrier 20 is stopped as shown in FIGS. 4A and 4D, the carrier 20 can start to move for the next line printing immediately after the carrier is stopped from the previous line printing.
If the length of time required for a line feeding is longer than the length of time from a time point where a line feeding is completed while the carrier is moving, to a time point where the carrier 20 (FIG. 1) is stopped as shown in FIGS. 4E to 4H, the carrier 20 should be controlled so that the movement of the carrier 20 is initiated while a line feeding of a paper is performed in order to reduce the length of time required for printing. If the carrier 20 waits, and starts to move for the next line printing after a line feeding is completed as in conventional processes, a time delay can occur since the next line printing is initiated after the line feeding is completed and a length of time passes.
It should be noted that if the ink is ejected from the ink cartridges 11 and 12, and thus the line printing is initiated in the course of feeding a paper P without finishing the line feeding of the paper P, an inferior printing can result. Therefore, the line printing should preferably be initiated after the line feeding of a paper P is completed, while an overlap in time can occur between the line feeding of the paper P and the movement of the carrier 20. For that purpose, as shown in FIG. 4A, an estimate is required for an expected length of time TE from a time point TC where the carrier 20 starts to move for the next line printing, to a time point TI where the next line printing is initiated.
Hereinbelow, methods for estimating the expected length of time TE, and controlling the movement of the carrier 20 and the line feeding of a paper P, are described in accordance with an embodiment of the present invention. The method provides a movement of each so that an overlap in time takes place between the movement of the carrier 20 and the line feeding of the paper P on the basis of the estimation, as illustrated in FIGS. 5 to 9.
As shown in FIGS. 5A and 5B, which illustrate paths of operation as directed by the embodiment of the present invention, the ink cartridges 11 and 12 (FIG. 1) reciprocate within a carrier moving distance DC, and the line feeding of a paper P is performed in the direction perpendicular to the moving direction of the carrier 20. When the paper P is positioned in the printing position and the inkjet printer receives a printing command CP (FIG. 3), the carrier 20 is moved in the printing direction C′ toward an image area I on the paper P. Then, ejection of the ink is initiated at a distance DP from the ink ejection point N of the ink cartridges 11 and 12 equipped in the carrier 20 as the carrier reaches an initial point PS of the image area I. Accordingly, a line printing for the line printing distance DI is executed over the path C′.
The control method resulting in the paths of operation of FIGS. 5A and 5B are outlined in the flow chart of FIG. 9. At this time and referring to the flow chart, the controller 60 (FIG. 3) determines whether the line printing has been completed at step (S10) (FIG. 9), and then allows a line feeding of the paper P to be executed at step (S11) if the line printing has been completed. The line feeding of the paper P is executed as the controller 60 receives a feeding command CF and controls the feeding roller driving device 45 (FIG. 3).
As shown in FIG. 5A, the carrier 20 has moved in the printing direction C′ and stopped at the opposite side of the image area I. Before the carrier is moved for the next line printing, the host 100 (FIG. 3) sends a next printing command CP to the controller 60 (FIG. 3). From this next printing command CP, the controller 60 calculates the distance DP′ (FIG. 5B) from an ink ejection point N to the initiating point PI′ (FIG. 5B) of the next line printing, and the time point TI (FIG. 6) where the next line printing is to be initiated at step (S12) (FIG. 9). Next, the controller 60 estimates an expected length of time TE from the time point TC, where the carrier 20 starts to move, to the time point TI, where the next line printing is initiated, as shown in FIG. 6. The method for estimating the expected length of time TE can be varied according to whether the time TI is positioned in the acceleration section VA or in the constant-velocity section VP in the moving velocity section of the carrier 20. Therefore, upon calculating the TI, the controller 60 determines whether the time TI is ahead of or behind the time point TK where the constant-velocity VP is initiated at step (S13) (FIG. 9).
As shown in FIG. 6, the time TI is positioned in the acceleration section VA and the time TE is determined by a value corresponding to a unit acceleration section, where the time TI is positioned among four unit acceleration sections A0 to A3 of the acceleration section VA in step (S14) (FIG. 9). The unit acceleration sections are determined by dividing the length of time from the time point TC where the carrier 20 starts to move, and the time point TK where the carrier constant-velocity section VP is initiated, by a predetermined interval. In this example embodiment of the present invention, the times TE in respective unit acceleration sections are previously established. The times TE corresponding to the respective unit acceleration sections A0 to A3 are intervals from the time point TC where the carrier 20 starts to move, to the respective time points where the unit acceleration sections are initiated, respectively. As shown in FIG. 6, the time TE in the section A0 is 0, the time TE in the section A1 is TA1, the time TE in the section A2 is TA2, and the time TE in the section A3 is TA3. Therefore, if the time TI is positioned in the A3 section, the time TE will be TA3. The embodiments of the present invention are not limited to these unit acceleration sections of four intervals and, as the interval of each unit acceleration section is reduced or the number of unit acceleration sections are increased, time TE can be obtained more precisely.
If the time TE is estimated in this manner, the controller 60 (FIG. 3) then compares the length of the remaining feeding time TRX, the time until the line feeding of the paper is completed, with the time TE at step (S16) (FIG. 9), to locate a time point where the time TRX becomes equal to or less than the time TE. The time TRX being equal to or less than the time TE provides that the line printing is not initiated until a line feeding of a paper is completed, even if the carrier 20 starts to move. Therefore, the controller 60 drives the carrier 20 at a time point where the time TRX becomes equal to or less than the time TE at step (S60), as shown in FIG. 7. Accordingly, the line feeding of the paper P and the movement of the carrier 20 take place with an overlap in time TA3. The length of remaining feeding time TRX is determined by dividing a total feeding time TRT by ΔT into N sections, wherein the total feeding time TRT is about 100 ms to about 200 ms, and the ΔT is about 2 ms. Therefore, the remaining feeding time TRX is compared with the time TE at an interval of 2 ms at step (S16a) (FIG. 9). As the size of ΔT is made smaller, the control precision becomes larger, therefore, the ΔT may have various values, such as anywhere between 1 ms and 4 ms.
FIG. 8 illustrates a time TE calculating and printing control method in accordance with an embodiment of the present invention, when the time point TI′, where a line printing is initiated, is positioned in the constant-velocity section Vp. Based on a printing command CP sent from the host 100 (FIG. 3), the controller 60 (FIG. 3) estimates if the time point TI′, where a line printing is initiated, will be positioned in the constant-velocity section VP. The controller 60 calculates a length of time TE′ required from the time point TC′, where the carrier 20 starts to move, to the time point TI′, where the line printing is initiated. The controller 60 calculates the length of time TE′ by summing a total length of time TA required for the acceleration section VA, with a length of time TP required from the time point TK′, where the constant-velocity section is initiated, to the time point TI′, where the line printing is initiated at step (S15) (FIG. 9). While a line feeding of the paper P is being executed, the controller 60 compares the length of remaining feeding time TRX′ until the line feeding of the paper P is completed, with the time TE′ at an interval of ΔT, thereby finding a time point where the time TRX′ becomes equal to or less than the time TE′ at step (S16) (FIG. 9). At the time point where the time TRX′ becomes equal to or less than the time TE′ at step (S16), the controller 60 drives the carrier 20 for the next line printing by controlling the carrier driving device 25 (FIG. 3) at step (S17) (FIG. 9). Therefore, the carrier 20 starts to move while the line feeding of the paper P is being executed, and the ink is ejected from the ink cartridges 11 and 12. Accordingly, a line printing is initiated substantially concurrently with the completion of the line feeding of the paper P. As a result, the time delay which occurs from the time point where a line feeding of the paper P is completed, to the time point where a line printing is initiated, is reduced.
Depending on the circumstances of the movement of the carrier 20 and the line feeding of a paper P, the time point where a line feeding is completed or the time point where the ink ejection is initiated may be beyond expected values. Since inferior printing may be caused if the line printing is initiated before the line feeding is completed, an error under these conditions should be detected at an early stage.
For that purpose, the embodiments of the present invention can detect such an error with additional steps provided by the method of FIG. 9. When the line printing is initiated, the controller 60 (FIG. 3) receives information on the paper feeding from the feeding roller driving device 45 (FIG. 3) and information on the ink ejection from the ink cartridges 11 and 12 (FIG. 3). Then, the controller 60 determines whether the time point where the practical line printing is initiated is ahead of or behind the time point where the line feeding of the paper P is completed at step (S18) (FIG. 9). At that time, if it is determined that the line printing takes place after the line feeding of the paper P has been completed, the controller 60 allows the printing to be continued at step (S19) (FIG. 9). If it is determined that the line feeding takes place before the line feeding of the paper P is completed, the controller 60 interrupts the printing operation at step (S20) (FIG. 9), and indicates this error through the display device at step (S21) (FIG. 9). As the printing operation is interrupted right after the inferior printing occurs as detected above, waste of ink and electric consumption can be reduced.
If a normal printing operation is executed without causing inferior printing, the line feeding of a paper and the line printing by the movement of the carrier 20 according to the control system and method as described above will be repeated until one page printing of the paper P is completed.
As described above, according to the embodiments of the present invention, it is possible to estimate an expected length of time TE from a time point where the carrier 20 starts to move, to a time point where the next line printing takes place, and to determine a proper time point for moving the carrier 20 on the basis of the expected length of time TE. Therefore, it is possible to realize an inkjet printer that provides a line feeding of the paper P and a movement of the carrier 20 which are overlapped in time. As a result, the printing speed is enhanced.
While the invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

## Claims

1. A printing control method for an inkjet printer, comprising the steps of:
executing a line feeding of a paper;
driving a carrier equipped with a cartridge; and
operating the cartridge so that a line printing is executed on the paper, wherein the carrier is driven according to a comparison of a duration of time from a point of initiating the carrier driving to a point of initiating the line printing, and a length of feeding time TRX remaining until the line feeding is completed, to be continuously driven while the line feeding is being executed when a carrier driving period exceeds or equals a line feeding period and the carrier driving is paused when the line feeding period exceeds the carrier driving period, and the line printing is initiated after the line feeding of the paper is completed.

2. The method according to claim 1, further comprising steps of:
determining whether the line printing by the cartridge has been completed;
executing the line feeding if it is determined that the line printing has been completed;
estimating an expected length of time TE from a time point TC where the carrier's next movement is initiated, to a time point TI where the next line printing is initiated;
comparing the TRX with the expected length of time TE; and
driving the carrier if the length of the remaining feeding time TRX is less than or equal to the expected length of time TE.

3. The method according to claim 2, wherein:
the moving velocity of the carrier is varied, and the moving velocity of the carrier is further divided into an acceleration section, a constant-velocity section, and a deceleration section, and wherein,
the acceleration section is divided into a plurality of unit acceleration sections, and wherein,
the expected length of time TE is determined as a length of time from the time TC to a time point where a corresponding unit acceleration section is initiated if the time point TI is positioned in the acceleration section.

4. The method according to claim 3, wherein the plurality of unit acceleration sections are formed by dividing a length of time from the time point TI to a time point TK where the constant-velocity section is initiated, by a predetermined time interval.

5. The method according to claim 2, wherein in the step of comparing the time TRX with the time TE, the time TRX is reduced and compared with the time TE at an interval of a predetermined time ΔT.

6. The method according to claim 2, further comprising steps of:
determining whether the line feeding of the paper has been completed at a time point where the next line printing is initiated; and
displaying an error message if it is determined that the line printing has been initiated in a state where the line feeding of the paper has not been completed.

7. The method according to claim 1, wherein the line feeding of the paper for the next line printing is initiated substantially concurrent with the completion of the line printing.

8. The method according to claim 1, wherein the cartridge comprises at least one ink cartridge.

9. A printing control system for an inkjet printer, comprising:
at least one cartridge;
a carrier, having a means to secure the cartridge and perform a line printing;
a feeding roller, to execute a line feeding of a paper and transfer the paper into a print area;
a feeding roller, driving device in communication with the feeding roller;
a carrier driving device, having a means to drive the carrier across the paper in the print area; and
a controller, in communication with the feeding roller driving device and the carrier driving device, the controller directing the carrier driving device according to a comparison of a duration of time from a point of initiating the carrier driving to a point of initiating the line printing, and a length of feeding time TRX remaining until the line feeding is completed, to be continuously driven while the line feeding is being executed when a carrier driving period exceeds or equals a line feeding period and the carrier driving is paused when the line feeding period exceeds the carrier driving period, and wherein the line printing is initiated after the line feeding of the paper is completed.

10. The printing control system for an inkjet printer according to claim 9, wherein the cartridge comprises at least one ink cartridge.

11. A printing control method for an inkjet printer, comprising the steps of:
executing a line feeding of a paper;
driving a carrier equipped with a cartridge;
operating the cartridge so that a line printing is executed on the paper, wherein the carrier is driven while the line feeding is being executed, and the line printing is initiated after the line feeding of the paper is completed;
determining whether the line printing by the cartridge has been completed;
executing the line feeding if it is determined that the line printing has been completed;
estimating an expected length of time TE from a time point TC where the carrier's next movement is initiated, to a time point TI where the next line printing is initiated;
comparing a length of feeding time TRX remaining until the line feeding is completed, with the expected length of time TE; and
driving the carrier if the length of the remaining feeding time TRX is less than or equal to the expected length of time TE.

12. The method according to claim 11, wherein:
the moving velocity of the carrier is varied, and the moving velocity of the carrier is further divided into an acceleration section, a constant-velocity section, and a deceleration section, and wherein,
the acceleration section is divided into a plurality of unit acceleration sections, and wherein,
the expected length of time TE is determined as a length of time from the time TC to a time point where a corresponding unit acceleration section is initiated if the time point TI is positioned in the acceleration section.

13. The method according to claim 12, wherein the plurality of unit acceleration sections are formed by dividing a length of time from the time point TI to a time point TK where the constant-velocity section is initiated, by a predetermined time interval.

14. The method according to claim 11, wherein in the step of comparing the time TRX with the time TE, the time TRX is reduced and compared with the time TE at an interval of a predetermined time ΔT.

15. The method according to claim 11, further comprising steps of:
determining whether the line feeding of the paper has been completed at a time point where the next line printing is initiated; and
displaying an error message if it is determined that the line printing has been initiated in a state where the line feeding of the paper has not been completed.

16. The method according to claim 11, wherein the line feeding of the paper for the next line printing is initiated substantially concurrent with the completion of the line printing.

17. The method according to claim 11, wherein the cartridge comprises at least one ink cartridge.