Image forming apparatus wherein the velocity of the toner supporting medium is higher than recording medium transport velocity

Peripheral velocity of a toner support is set up so as to satisfy the following condition: EQU L/T.ltoreq.vs.ltoreq.(d/t).multidot.cos .theta.-(1/t)(L.sup.2 -d.sup.2 sin .sup.2 .theta.).sup.1/2 assuming that d denotes the distance between centers of two adjacent gates, .theta. the angle of slant connected between centers of the same two gates, L the maximum length of toner-free area on peripheral surface of the toner support, vs the peripheral velocity of the toner support, t the time lag between voltage application to one annular electrode and to the other, and T is the time interval between successive voltage applications to an identical gate (the shortest period of time during which the voltage for inhibiting passage of the toner is applied to the gate).

BACKGROUND OF THE INVENTION 
(1) Field of the Invention 
The present invention relates to an image forming apparatus such as a 
digital copier, facsimile machine, laser printer and the like, in 
particular relating to an image forming apparatus which forms images by 
causing developer particles to jump to the recording medium. 
(2) Description of the Prior Art 
Among image forming apparatuses for outputting image data as a visual image 
on recording medium such as recording paper etc., one type is known which 
directly forms a toner image on the recording medium by making toner, the 
developer, jump onto the recording medium, as has been disclosed in 
Japanese Patent Application Laid-Open Hei 6 No.155,798. As shown in FIG. 
1, the image forming apparatus includes an image forming unit 51 having a 
toner supplying section 52 and a printing section 53. In this apparatus, 
toner 71 is made to jump from toner supplying section 52 and adhere to a 
sheet of paper 55, the recording medium. During this, the jumping of toner 
71 is controlled in accordance with the image data. 
Toner supplying section 52 is composed of a toner reservoir 70 for holding 
toner 71 as developer particles which are negatively charged, and a toner 
support 72 which supports toner 71 on its peripheral surface by magnetic 
force whilst rotating in the direction of arrow E. Printing section 53 is 
composed of an opposing electrode 75 of a cylindrical shape and a control 
electrode 76 which is provided between opposing electrode 75 and toner 
support 72. Opposing electrode 75 rotates in the direction of arrow F so 
that paper 55 is conveyed between opposing electrode 75 and control 
electrode 76 in the direction of arrow G. 
As shown in FIG. 2A, control electrode 76 has a plurality of gates 79 
formed therein, each gate 79 having an annular electrode 77 formed around 
the edge thereof. As the voltage from a control power source 81 shown in 
FIG. 1 is selectively applied to these annular electrodes 77 in accordance 
with the image data, toner 71 supported on the peripheral surface of toner 
support 72 is made to jump toward opposing electrode 75 and pass through 
selective gates 79 hence being made to adhere to paper 55 which is placed 
between opposing electrode 75 and control electrode 76. 
The image forming apparatus configured as above is one which directly forms 
the image on the surface of recording medium such as paper etc. Therefore, 
it is no longer necessary to use a developer medium such as a 
photoreceptor etc., which was used in conventional image forming 
apparatuses. Further, the operation for transferring the image from the 
developer medium to the paper can be omitted, thus making it possible to 
eliminate degradation of the image due to the existence of this operation. 
Moreover, the structure of the apparatus can be simplified needing fewer 
parts, thus making it possible to reduce the apparatus in size and cost. 
However, in the above conventional image forming apparatus, since the 
peripheral velocity of toner support 72 and the conveying speed of paper 
55 are equal, if an arbitrary gate 79n has been made to pass toner 71 
therethrough and subsequently the adjoining gate 79n+1 is made to pass 
toner 71 therethrough as shown in FIG. 2B, a toner-free area will be 
produced on the peripheral surface of toner support 72 by the transfer of 
toner 71 through gate 79n. Because toner support 72 rotates during the 
time between the two events, part of this area overlaps the subsequent 
printing area designated at 72n+1 on the peripheral surface of toner 
support 72 that opposes gate 79n+1 as shown in FIG. 2C. As a result, area 
72n+1 on the peripheral surface of toner support 72 might partially lack 
the toner 71, which may be needed for later transfer. Therefore, the 
amount of toner 71 transferred through gate 79n+1 becomes low resulting in 
insufficient dot density and dot diameter in the formed image, lowering 
the image contrast and degrading the reproduction of halftone. In color 
image forming apparatus, it becomes impossible to reproduce the desired 
colors. Moreover, image deficiency such as white strips and color voids 
may occur. 
In order to avoid such degradation of the image, it is considered that the 
density of toner 71 on the peripheral surface of toner support 72 needs to 
be increased. However, there is a limit for the toner density on toner 
support 72, and it is impossible to obtain an adequate toner density under 
the present conditions. Further, in this case, the thickness of the toner 
layer on toner support 72 tends to become unstable and in some cases, it 
may become difficult to obtain the desired layer thickness, making it 
impossible to form an stable image. 
Moreover, when the thickness of the toner layer on toner support 72 is 
enhanced to increase the density of toner 71, the distance between control 
electrode 76 and toner 71 becomes shortened. This means that toner 71 
becomes more likely to adhere to control electrode 76 and becomes further 
unstable in its layer thickness. If toner 71 has adhered to control 
electrode 76, the potential created by the charge carried by toner 71 
changes the potential of control electrode 76 resulting in an ineptness in 
controlling the potential used for image forming. This also causes 
obstruction or clogging in gates 79. 
In order to avoid the above situation, if control electrode 76 is made more 
distant from toner support 72, the potentials to be applied to toner 
support 72, opposing electrode 75 and control electrode 76 need to be 
increased, resulting in increase in cost for the power source. In 
addition, the elevation of the potential applied to opposing electrode 75 
requires a more thorough insulation and also the price for the 
high-voltage driver for switching the potential applied to control 
electrode 76 increases. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide an image 
forming apparatus wherein the peripheral velocity of the toner support is 
set up based on conditions of the arrangement of the gates in the control 
electrode and the shape and feature of the area where no developer adhere 
to, which is produced on the peripheral surface of the toner support, 
whereby when the developer has been made to jump through an arbitrary gate 
and subsequently the developer is made to jump through its adjoining gate, 
it is possible to prevent the amount of the developer at the second 
transfer from being affected by the developer free-area which has been 
produced on the peripheral support of the toner support by the first 
developer transfer and it is possible to secure an adequate amount of 
developer even when the developer is made to jump through a plurality of 
adjoining gates and thus degradation of image forming states such as image 
defects or void etc., due to an insufficient amount of developer can be 
definitely prevented. 
The present invention has been devised to attain the above object, and the 
gist of the invention is as follows: 
In accordance with the first aspect of the invention, an image forming 
apparatus comprises: a supporting medium for supporting the developer; an 
opposing electrode spaced a predetermined distance apart from the 
supporting medium and disposed facing the supporting medium; a control 
electrode disposed between the supporting medium and the opposing 
electrode and having a plurality of gates which form passage for the 
developer particles; and a drive controlling means which moves the surface 
of the supporting medium at a constant velocity relative to the control 
electrode, so that the image forming apparatus forms a visual image on a 
recording medium conveyed between the opposing electrode and the control 
electrode whilst varying the potential applied to the control electrode so 
as to selectively control transfer of the developer particles through the 
gates, and is constructed such that the moving velocity of the supporting 
medium surface controlled by the drive controlling means is set at a 
higher rate than the moving velocity of the recording medium relative to 
control electrode. 
Next, in accordance with the second aspect of the invention, an image 
forming apparatus having the above first feature is constructed such that 
the moving velocity of the supporting medium surface controlled by the 
drive controlling means is set up based on the moving velocity of 
recording medium relative to the control electrode, conditions of the 
arrangement of the gates in the control electrode and the size of the area 
where no developer adhere to, which is produced on supporting medium 
surface by the transfer of the developer through the gate. 
In accordance with the third aspect of the invention, an image forming 
apparatus having the above second feature is constructed such the moving 
velocity vs of the supporting medium surface controlled by the drive 
controlling means is set up so as to satisfy the following condition: 
EQU vs.ltoreq.(d/t).multidot. cos .theta.-(1 /t )(L.sup.2 -d.sup.2 sin.sup.2 
.theta.).sup.1/2 
where t is the shortest time interval between the voltage application to 
one gate and the voltage application to the proximal gate, d is the 
distance between the centers of the two gates for which the times of 
voltage application is closest to each other, L is the maximum length of 
developer-free area on the supporting medium surface, and .theta. is the 
angle of the slant connected between the centers of the two gates for 
which the times of voltage application is closet to each other, with 
respect to the conveying direction of the recording medium. 
Finally, in accordance with the fourth and fifth aspect of the invention, 
an image forming apparatus having the above second or third feature is 
constructed such that the moving velocity vs of the supporting medium 
surface controlled by the drive controlling means is set up so as to 
satisfy the following condition: 
EQU L.ltoreq.vs.multidot.T 
where L is the maximum length of developer-free area on the supporting 
medium surface and T is the shortest period of time during which the 
voltage for inhibiting passage of the developer is applied to an identical 
gate.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 3 is a view showing the configuration of an image forming apparatus of 
a typical embodiment of the invention. This image forming apparatus has an 
image forming unit 1 which is composed of a toner supplying section 2 and 
a printing section 3. Image forming unit 1 creates a visual image in 
accordance with an image signal, onto a sheet of paper as recording medium 
with toner as the developer. In this image forming apparatus, the toner is 
made to jump and adhere onto the paper whilst the jumping of the toner is 
controlled based on the image forming signal, so as to directly form the 
image on the paper. Provided on the paper input side of image forming 
apparatus 1 is a paper feeder 10, which is composed of a paper cassette 4 
for storing sheets of paper 5 as recording medium, a pickup roller 6 for 
delivering paper 5 supplied from paper cassette 4, and a paper guide 7 for 
guiding paper 5 sent out. Pickup roller 6 receives rotational force from 
an unillustrated driver. 
Provided on the output side of image forming apparatus 1 is a fixing unit 
11 for heating and pressurizing the toner image which was formed on paper 
5 at the image forming unit 1, to fix it onto paper 5. Fixing unit 11 is 
composed of a heat roller 12, a heater 13, a pressure roller 14, a 
temperature sensor 15, and an unillustrated temperature controller 
circuit. Heat roller 12 is made up of, for example, an aluminum pipe of 
about 2 mm thick. Heater 13 is a halogen lamp, for example, which is 
incorporated in heat roller 12. Pressure roller 14 is a pipe made up of 
silicone resin, for example. Heat roller 12 and pressure roller 14 are 
pressed against one another with a constant pressure. Temperature sensor 
15 measures the surface temperature of heat roller 12. Temperature 
controlling circuit (unillustrated) controls the operation of heater 13 
based on the measurement result from temperature sensor 15 so that the 
surface temperature of heat roller 12 is maintained at 150.degree. C., for 
example, which allows the melting of the toner. Fixing unit 11 has an 
unillustrated paper discharge sensor for detecting the discharge of paper 
5. Here, fixing unit 11 may be constructed so that the toner image is 
fixed by heating or pressing paper 5. 
Toner supplying section 2 in image forming apparatus 1 is composed of a 
toner reservoir 20 for storing toner 21 as the developer, a cylindrical 
support 22 for magnetically supporting toner 21, a doctor blade 23 which 
imparts charge to toner 21 and regulates the thickness of the toner layer 
carried on the peripheral surface of toner support 22. Doctor blade 23 is 
arranged on the upstream side of toner support 22 with respect to the 
rotational direction of the peripheral surface of toner support 22, spaced 
with a distance of about 60 .mu.m, for example, from the peripheral 
surface of toner support 22. Toner 21 is of a magnetic type having a mean 
particle diameter of, for example, 6 .mu.m, and is electrified with static 
charge of -4 .mu.C/g to -5 .mu.C/g by doctor blade 23. 
Toner support 22 receives rotational force from driver controller 33 so 
that it rotates at a constant peripheral speed in the direction indicated 
by arrow A. Toner support 22 is grounded and has unillustrated fixed 
magnets therein, at the position opposite doctor blade 23 and at the 
position opposite a control electrode 26 (which will be described later). 
This arrangement permits toner support 22 to magnetically carry toner 21 
on its peripheral surface, and toner 21 supported on the peripheral 
surface of toner support 22 is made to stand up in `spikes` at the areas 
corresponding to the positions of the magnets. Toner support 22 can be 
configured so as to support toner 21 by electric force or combination of 
electric and magnetic forces. 
Printing section 3 includes: a dielectric belt 24 tensioned between a pair 
of support rollers 16a and 16b at the position opposite the peripheral 
surface of toner support 22; an opposing electrode 25 which is in contact 
with the inner peripheral surface of the upper side of dielectric belt 24; 
a high-voltage power source 30 for applying a high voltage to opposing 
electrode 25; a control electrode 26 provided between toner support 22 and 
opposing electrode 25; a charge eraser brush 32 which is in contact with 
the outer peripheral surface of dielectric belt 24; a charge eraser power 
source 17 for imparting a charge eraser voltage to charge eraser brush 32; 
a cleaner 19 abutting the outer peripheral surface of dielectric belt 24; 
and a charging brush 8 for electrifying paper 5 whilst it is being 
conveyed along the upper surface of dielectric belt 24. 
Opposing electrode 25 is made up of an aluminum plate of, for example, 
about 1 mm thick, and is arranged about 1 mm apart from the peripheral 
surface of toner support 22. Dielectric belt 24 is made of, for example, 
PVDF as a base material of about 75 .mu.m thick with a volume resistivity 
of about 10.sup.10 .OMEGA..multidot.cm. Support rollers 16a and 16b 
supporting dielectric belt 24 is rotated by an unillustrated driver in the 
direction of arrow B at a constant peripheral velocity. Applied to 
opposing electrode 25 is a high voltage, e.g., 2.3 kV from high voltage 
power source 30. This arrangement generates an electric field between 
opposing electrode 25 and toner support 22, required for causing toner 21 
being supported on the peripheral surface of toner support 22 to jump 
toward opposing electrode 25. 
Charge eraser brush 32 is pressed against dielectric belt 24 on the control 
electrode 26 side, relative to the rotational direction of dielectric belt 
24. Charge eraser brush 32 has an eraser potential of, for example, about 
2.5 kV applied from charge eraser power source 17 so as to eliminate 
unnecessary charges on the surface of dielectric belt 24. Cleaner 19 
removes the toner adhering to the outer peripheral surface of dielectric 
belt 24. For example, if paper jam or some other defects occur, the toner 
adhering to the outer peripheral surface of dielectric belt 24 stains the 
underside of the next conveyed paper 5. The cleaner prevents this. 
It should be noted that this image forming apparatus includes: a main 
controller as a control circuit for controlling the whole image forming 
apparatus; an image processor for converting the image data which was 
obtained from image pickup device into an image data format by which the 
image can be printed; an image memory for storing the converted image 
data; and an image forming control unit for converting the image data 
obtained from the image processor into the image data to be given to 
control electrode 26. 
FIG. 4 is a plan view showing the control electrode provided in the above 
image forming apparatus. Control electrode 26 is supported parallel to 
opposing electrode 25 by means of an unillustrated supporter member so 
that its distance from the peripheral surface of toner support 22 is set 
at, for example, 100 .mu.m. Control electrode 26 is composed of an 
insulative plate-like member made of a polyimide resin or the like of 
about 75 .mu.m thick with a plurality of annular electrodes 27 formed 
independently of each other. Annular electrodes 27 are individually formed 
around the edges of respective plural holes or gates 29. Annular 
electrodes 27 are formed of copper foil, for example, of 30 .mu.m. Each 
gate 29 forms a passage for toner 21 to jump from the peripheral surface 
of toner support 22 toward opposing electrode 25. Each annular electrode 
27 is connected to a control power source 31 via a respective feeder line 
28 and an unillustrated high voltage driver. In control electrode 26, 
gates 29 as well as annular electrodes 27 are formed at 2,560 sites, for 
instance. This number corresponds to a resolution of 300 DPI across the 
width of A4 sized paper, or in the direction perpendicular to the 
conveyance direction of the paper. The surface of annular electrodes 27 as 
well as the surface of feeder lines 28 is coated with an insulative layer 
of 30 .mu.m thick, thus ensuring insulation between annular electrodes 27, 
insulation between feeder lines 28, and insulation between annular 
electrodes 27 and feeder lines 28, not related to each other. 
By controlling the potential to be applied to annular electrodes 27 of 
control electrode 26, the intensity of the electric field created between 
toner support 22 and opposing electrode 25 is changed so that the jumping 
of toner 21 from toner support 22 to opposing electrode 25 is controlled. 
Specifically, selective voltages are applied to annular electrode 27 from 
control power source 31 in accordance with the image data. When toner 21 
supported on toner support 22 needs to be transferred toward opposing 
electrode 25, control power source 31 applies a voltage, e.g., 150 V to 
annular electrodes 27, whereas it applies another voltage, e.g., -200 V 
when the toner is not to be transferred. In this way, whilst the potential 
to be imparted to control electrode 26 is controlled in accordance with 
the image data, paper 5 is fed along opposing electrode 25 on the side 
thereof facing toner support 22. As a result, the toner image is formed on 
the surface of paper 5 in accordance with the image data. Here, control 
power source 31 is controlled by a control-electrode controlling signal 
transmitted, from an unillustrated image forming control unit. 
FIG. 5 is a flowchart showing the procedural flow of the image forming 
operation of the image forming apparatus. When the copy start key is 
operated with an original set on the image pickup section, the image 
reading operation is effected. Illustratively, the image pickup section 
reads the original image, and the image data thus picked up is image 
processed in the image processing section to be stored into the image 
memory (s1-s3). This image data is transferred to the image forming 
control unit at a predetermined timing (s4) so that the image forming 
control unit transforms the input image data into a control-electrode 
controlling signal to be imparted to control electrode 26 (s5). When the 
image forming control unit has created a predetermined amount of the 
control signal, it causes toner support 22 to rotate (s6, s7) while a 
voltage of -200 V is applied to control electrode 26 (s8). At the same 
time, the same voltage as applied to opposing electrode 25 also is applied 
to roller 16a from high voltage power source 30 (s8). Charging brush 8 is 
applied with a charging potential of 1.2 kV from charger power source 18 
while charge eraser brush 32 is applied with an erasing potential from 
charge eraser power source 17 (s9). 
Thereafter, an unillustrated driver is activated to start rotating pickup 
roller 6 (s10). This rotation of pickup roller 6 delivers a sheet of paper 
out from paper cassette 4 toward image forming unit 1. After it has been 
judged whether paper 5 has been fed normally or not (s1), it is conveyed 
between charging brush 8 and dielectric belt 24. Paper 5 is supplied with 
charge due to the potential difference between charging brush 8 and 
dielectric belt 24. Electrostatically attracted to dielectric belt 24, 
paper 5 is conveyed with the rotational movement of dielectric belt 24, to 
a position in printing section 3, where it faces toner support 22. 
Next, the image forming control unit supplies the control-electrode 
controlling signal to control power source 31 so that control power source 
31 applies a high voltage to annular electrodes 27 of control electrode 26 
(s12). This control-electrode controlling signal is supplied at a time 
synchronized with the conveyance of paper 5 by dielectric belt 24. Control 
power source 31 controls the high voltage to be applied to annular 
electrodes 27 based on the control-electrode controlling signal. 
Illustratively, a voltage, 150 V or -200 V is applied to each of 
designated annular electrodes 27 from control power source 31 so as to 
control the electric field near control electrode 26. That is, at each 
gate 29 of control electrode 26, the jumping of toner 21 from toner 
support 22 toward opposing electrode 25 is inhibited or permitted in 
accordance with the image data so that the toner image, in conformity with 
the image signal, is formed on paper 5 which is moving at the rate of 30 
mm/sec toward the paper output side by the rotational movement of 
dielectric belt 24. Paper 5 with the toner image formed thereon is 
separated from dielectric belt 24 by the curvature of roller 16b and is 
conveyed to fixing unit 11, where the toner image is fixed to paper 5. 
Paper 5 with the toner image fixed thereon is discharged by an 
unillustrated discharge roller onto a paper output tray. 
FIGS. 6A and 6B are enlarged views showing essential components of the 
control electrode. In FIG. 6A, when gate 29n and 29n+1 are both activated 
to allow passage of toner 21 forming an image, voltage is first applied to 
annular electrode 27n of gate 29n and then applied to annular electrode 
27n+1 of gate 29n+1. The voltage application to annular electrode 27n 
causes toner 21 to jump from the portion facing gate 29n on the peripheral 
surface of toner support 22 toward opposing electrode 25 thus forming a 
toner-free area 22n where no toner 21 exists as shown in FIG. 6B. In this 
situation, when the voltage application to annular electrode 27n+1 is 
effected, toner-free area 22n+1 will be formed in the portion facing gate 
29n+1 on the peripheral surface of toner support 22. At this moment, the 
rotation of toner support 22 during the time lag between the voltage 
application to annular electrode 27n and to annular electrode 27n+1 causes 
toner-free area 22n to move to a position indicated by the dashed line in 
FIG. 6B. 
In general, a plurality of gates 29 formed on control electrode 26 as a 
whole correspond to one line at right angle to the conveyance direction of 
the image. Therefore, if the movement of toner-free area 22n due to the 
rotation of toner support 22 during the time interval between voltage 
application to annular electrode 27n and to annular electrode 27n+1 is 
equal to the distance between gates 29n and 29n+1, part of area on toner 
support 22 facing gate 29n+1 overlaps toner-free area 22n as shown in FIG. 
6B when voltage application is performed to annular electrode 27n+1. For 
this reason, when voltage application is performed to annular electrode 
27n+1, the amount of toner 21 transferred from the peripheral surface of 
toner support 22 decreases, causing a partial void in the image formed on 
paper 5. 
In order to avoid such a defect or partial void of the image, it is 
considered that the density of toner 21 on the peripheral surface of toner 
support 22 needs to be increased. However, there is a limit for the toner 
density on toner support 22, and it is impossible to obtain an adequate 
toner density under the present conditions. Further, in this case, the 
thickness of the layer of toner 21 tends to become unstable and in some 
cases, it may become difficult to obtain the desired layer thickness, 
making it impossible to form an stable image. 
Moreover, as the thickness of the toner layer is enhanced to increase the 
density of toner 21, the distance between control electrode 26 and the 
layer of toner 21 becomes shortened. This means that toner 21 becomes more 
likely to adhere to control electrode 26 and becomes even further unstable 
in its layer thickness. If toner 21 has adhered to control electrode 26, 
the potential created by the charge carried by toner 21 changes the 
potential of control electrode 26 resulting in an ineptness in controlling 
the potential used for image forming. This also causes obstruction or 
clogging in gates 29. In order to avoid the above situation, if control 
electrode 26 is made more distant from toner support 22, the potentials to 
be applied to toner support 22, opposing electrode 25 and control 
electrode 26 need to be increased, resulting in increase in cost for the 
power source. In addition, the elevation of the potential applied to 
opposing electrode 25 requires a more thorough insulation and also the 
price for the high-voltage driver for switching the potential applied to 
control electrode 26 increases. 
More detailedly, the aforementioned problem arises in the following 
mechanism. That is, when toner 21 has been made to jump through an 
arbitrary gate 29n and subsequently toner 21 is made to jump through its 
adjoining gate 29n+1, toner-free area 22n produced on the peripheral 
surface of toner support 22 by the previous transfer through gate 29n 
overlaps the subsequent printing area designated at 22n+1 on the 
peripheral surface of toner support 22 that opposes gate 29n+1, thus area 
22n+1 on the peripheral surface of toner support 22 partially lacks toner 
21. Therefore, the amount of toner 21 supplied becomes low resulting in 
insufficient dot density and dot diameter in the formed image, lowering 
the image contrast and degrading the reproduction of halftone. In color 
image forming apparatus, it becomes impossible to reproduce the desired 
colors. Moreover, image deficiency such as white strips and color voids 
may occur. 
The above problem can be solved by specifying the peripheral velocity of 
toner support 22 based on the diameter and positional relationship of 
gates 29. More detailedly, the peripheral velocity of toner support 22 is 
regulated so that toner-free area 22n on the peripheral surface of toner 
support 22 which has been produced by the transfer of toner 21 through 
gate 29n, moves to a position where it will not overlap toner-free area 
22n+1 facing gate 29n+1 when annular electrode 27n+1 provided in gate 
29n+1 adjoining gate 29n is voltage applied. 
As shown in FIG. 7A, assuming that d denotes the distance between the 
centers of gate 29n and 29n+1, .theta. the angle of the slant connected 
between the centers of gate 29n and 29n+1, L the maximum length of 
toner-free area 22n on the peripheral surface of toner support 22, vs the 
peripheral velocity of toner support 22, t the time lag between voltage 
application to annular electrode 27n and to annular electrode 27n+1, the 
following condition should be satisfied: 
EQU vs.multidot.t.ltoreq.dcos .theta.-(L.sup.2 -d.sup.2 sin .sup.2 .theta.) 
.sup.1/2. 
Accordingly, the peripheral velocity vs of toner support 22 must satisfy 
the following condition (1): 
EQU vs.ltoreq.(d/t).multidot.cos .theta.-(1/t)(L.sup.2 -d.sup.2 sin .sup.2 
.theta.).sup.1/2 (1) 
In this way, it is possible to set the peripheral velocity vs of toner 
support 22 at a rate higher than the conveyance speed of paper 5. 
Further, when successive voltage applications to the same annular electrode 
27n of gate 29n are effected, the currently forming toner-free area 22n on 
the peripheral surface of toner support 22 needs to be adapted so as not 
to overlap the toner-free area 22n' formed at the time of the previous 
application of voltage to annular electrode gate 29n. To meet this 
requirement, by the time when annular electrode 27n of gate 29n is voltage 
applied again, the previous toner-free area 22n' must at least move up to 
the position shown in FIG. 7B, or the position where it does not overlap 
the toner-free area 22n to be formed at the current event. 
When annular electrode 27n of gate 29n is voltage applied successively at a 
time interval of T, the following condition also needs to be satisfied: 
EQU L.ltoreq.vs.multidot.T (2) 
From the above conditions (1) and (2), the peripheral velocity vs of toner 
support 22 should fall within the following range: 
EQU L/T.ltoreq.vs.ltoreq.(d/t).multidot.cos.theta.-(1/t)(L.sup.2 -d.sup.2 sin 
.sup.2 .theta.).sup.1/2 
Now, suppose L=203 .mu.m, d=370 .mu.m, .theta.=13.degree., t=400 .mu.sec 
and T=2.5 .mu.sec, the peripheral velocity vs of toner support 22 should 
be above about 81 mm/sec and below about 438 mm/sec. 
Thus, when L.ltoreq.d, the peripheral velocity vs of toner support 22 will 
take a realistic value, but when L.gtoreq.d, the peripheral velocity vs of 
toner support 22 will take an extremely large value resulting in an 
unreality. For example, in a control electrode 46 with a plurality of 
gates 49 and annular electrodes 47 arranged as shown in FIG. 8A, in order 
to solve the above problem, toner-free area 43n needs to be moved to the 
position clearing toner-free area 43n+1 as shown in FIG. 8B when the toner 
is made to pass through gate 49n+1. To meet this, the peripheral velocity 
vs of toner support 22 must satisfy the following condition: 
EQU vs.gtoreq.(d/t).multidot. cos .theta.-(1/t)(L.sup.2 -d.sup.2 sin .sup.2 
.theta.).sup.1/2. 
In this case, the peripheral velocity vs will take such a large value as 
vs.gtoreq.1803 mm/sec. Therefore, the peripheral velocity of toner support 
22 should and can be limited within a realistic range by imposing the 
condition, i.e., L.ltoreq.d. 
In the above embodiment, although toner was used as the developer, it is 
also possible to use ink. Further, instead of using control electrode 26 
having annular electrodes 27, it is also possible to control toner 
transfer from the toner support by providing a plurality of strip-like 
electrodes 51 and 52 matrix-wise on both sides of the substrate as shown 
in FIG. 9 and governing the voltage to be applied to the strip-like 
electrodes crossing over each other at right angles or at an angle. 
Further, the present invention can be applied in the same manner to a color 
image forming apparatus, as shown in FIG. 10, which has a plurality of 
image forming units 1a-1d made up of toner supplying sections 2a-2d and 
control electrodes 26a-26d wherein toner supplying sections 2a-2d are 
filled with toners, e.g., yellow, magenta, cyan and black. By applying the 
present invention to the thus configured color image forming apparatus, it 
is possible to secure the desired amount of toner to obtain adequate dot 
size and dot density, making it possible to create color images excellent 
in color reproduction. 
The present invention can be also applied in the same manner to a 
configuration which uses an ion flow process in its toner supplying 
section. 
Although in the above example, the conditions were defined based on the 
relationship between two gates which are positionally located next to each 
other was defined, it is also possible to apply the invention in a similar 
manner to a case where two gates which allow passage of toner in the 
closest timing are not positionally located next to each other. 
According to this invention, when the developer has been made to jump 
through an arbitrary gate of the control electrode and subsequently the 
developer is made to jump through its adjoining gate, it is possible to 
prevent the amount of the developer at the second transfer from being 
affected by the developer free-area which has been produced on the 
peripheral support of the toner support by the first developer transfer, 
and therefore it is possible to secure an adequate amount of developer 
even when the developer is made to jump through a plurality of adjoining 
gates. Accordingly, degradation of image forming states such as image 
defects or void etc., due to an insufficient amount of developer can be 
definitely prevented.