Patent Publication Number: US-10322902-B2

Title: Sheet processing apparatus and image forming apparatus having the same

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to a sheet processing apparatus for processing sheets, and to an image forming apparatus, more particularly to a technique of improving the alignment of sheets temporarily placed on a sheet tray. 
     2. Description of the Related Art 
     Some of the image forming apparatuses for use in copiers, laser-beam printers, facsimiles and composite apparatuses, each comprising these, have a sheet processing apparatus that performs a sheet processing such as binding sheets each having an image formed on it. 
     In such an image forming apparatus, the sheet processing apparatus will make an untidy sheet bundle if the sheets are not aligned on the sheet tray. The untidy sheet bundle must be unbundled and bundled again. Therefore, it is important to align the sheets well in the sheet processing apparatus. 
     It is recently demanded that the sheet processing apparatus should hold many sheets and process them at high speed. An apparatus that may meet this demand is disclosed in Japanese Patent No. 4,298,360 (corresponding to U.S. Pat. No. 7,192,020 B2 and to Chinese Patent 100335388 C, hereinafter referred to as “patent documents”). This apparatus, shown in  FIG. 22  attached thereto, is a sheet processing apparatus BO to be incorporated into image forming apparatuses. In the sheet processing apparatus BO, a relatively large number of sheets are placed on the sheet tray T, bound together in the binding unit TSP and delivered, in the form of a bundle, by the delivery rollers R onto the accumulating tray AT. The sheet processing apparatus comprises a saddle-binding tray NT and a saddle-binding unit NSP. The saddle-binding tray NT branches from the conveyance path at the inlet port of the apparatus. The saddle-binding unit NSP binds sheets at the middle part of the saddle-binding tray NT. 
     In this apparatus, while the binding unit TSP is binding the sheets placed on the sheet tray T, the following sheets are kept waiting at a standby tray BT so that they may be processed in a large number and at high speed. The standby tray BT (generally called “buffer tray”) is designed to keep one to three sheets waiting. While the sheets are so kept waiting, the sheets on the sheet tray T are bound together, forming a bundle. 
     As shown in  FIG. 23A , the sheet bundle BP and the bundle of the following sheets are conveyed from the sheet tray T and the standby tray BT, respectively, with a prescribed offset, are nipped at delivery rollers R (i.e., upper delivery roller R 1  and lower delivery roller R 2 ), and are delivered onto the accumulating tray AT. The sheet bundle BP is thereby fed from the delivery rollers R and mounted on the accumulating tray AT. 
     Meanwhile, the following sheets (WP 1  to WP 3 ) are nipped by the delivery rollers R. At this time, the delivery rollers R are stopped for some time and then rotated in the reverse direction. The following sheets are thereby switched back above the sheet tray T and then placed on the sheet tray T. This method of delivering the sheets is generally called “simultaneous bundle delivering”, and enhances the speed of delivering the following sheets from the standby tray BT. Ultimately, the apparatus can operate at high speed. 
     In the apparatus disclosed in the above-identified patent document, the last following sheet WP 3  is set nearer to the front end of the sheet bundle BP than the other following sheets WP 1  and WP 2  by distance wp 11 . This is because the following sheets may be conveyed in wrong order as the delivery rollers R rotate, and such wrong-order conveyance must be prevented. (See FIG. 47 of the above-identified patent document.) 
     SUMMARY OF THE INVENTION 
     In the apparatus disclosed in the above-identified patent document, only the third following sheet is set off toward the front end of the sheet bundle. Therefore, when 50 to 70 sheets are mounted, forming a bundle BP as shown in  FIG. 23B , the delivery rollers R pull out the sheet bundle BP, and the upper delivery roller R 1  moves up around the fulcrum RP of the roller arm RA, toward the sheet tray T (located upstream). As the upper delivery roller R 1  moves so, the following sheet WP 3 , which contacts the upper delivery roller R 1 , greatly moves in the direction of arrow PM. 
     Thus, the uppermost following sheet WP 3  contacting the upper delivery roller R 1  moves to the right as shown in  FIG. 23B . As the uppermost following sheet WP 3  moves so, the second following sheet WP 2  may deviate rightward from the following sheet WP 1  and may not be corrected in position by gathering roller KR which arranged at the front end of the sheet tray T. In other words, the last following sheet may fail to lie leftmost and may lie rightmost instead. If this happens, the uppermost following sheet wp 3  fed by the gathering roller KR will abut on the front-end stopper KJ. In this case, the following sheets WP 2  and WP 1  lying below the following sheet WP 3  fail to reach the front-end stopper KJ and may not be aligned with the following sheet WP 3  on the sheet tray T. 
     If there are two following sheets, they may be set off by a longer distance wp 11 . In this case, however, they will move too much, and it will take a long time to align them or they will not be aligned at all. 
     In view of the above, the object of this invention is to provide a sheet processing apparatus and an image forming apparatus, in which the offset distance of the following sheets is changed in accordance with the thickness of the sheet bundle (i.e., number of sheets forming the bundle) mounted on the sheet tray, thereby reducing the erroneous alignment of sheets, regardless of the thickness of the sheet bundle. 
     To achieve the above-mentioned object, there is provided a sheet processing apparatus which comprises: conveyance rollers configured to convey sheets in a prescribed conveyance direction; a sheet tray configured to collect the sheets conveyed from the conveyance rollers, thereby forming a sheet bundle, and to hold the sheet bundle at a prescribed position; a wait path provided upstream in the conveyance direction of the conveyance rollers, and configured to keep waiting the following sheets conveyed by the conveyance rollers; second conveyance rollers configured to cooperate with the conveyance rollers to make following sheets wait in the wait path and to convey the following sheet from the wait path; an outlet port configured to deliver the sheet bundle from the sheet tray in a prescribed direction; an accumulating tray configured to receive the sheet bundle delivered from the outlet port; delivery rollers configured to nip the sheet bundle mounted on the sheet tray and a plurality of following sheets including the following sheet conveyed from the wait path, while setting off the following sheets by a prescribed offset distance, to deliver the sheet bundle through the outlet port onto the accumulating tray, and to switch back the plurality of following sheets onto the sheet tray; and a conveyance member configured to convey the following sheets from the sheet tray toward the prescribed position. The offset distance between the following sheets nipped together with the sheet bundle is changed in accordance with the thickness of the sheet bundle delivered by the delivery rollers. 
     The configuration described above can provide a sheet processing apparatus and an image forming apparatus in which the offset distance between the following sheets is changed in accordance with the thickness of the sheet bundle (number of sheets forming a sheet bundle) mounted on the sheet tray, thereby reducing the erroneous alignment of sheets, regardless of the thickness of the sheet bundle. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram showing the overall configuration of a combination of an image forming apparatus and a sheet processing apparatus, both according to the present invention; 
         FIG. 2  is a diagram showing the overall configuration of the sheet processing apparatus according to the present invention; 
         FIG. 3  is an enlarged side view of the sheet tray (i.e., first processing tray) incorporated in the sheet processing apparatus; 
         FIG. 4  is a diagram explaining how the conveyance rollers, branching rollers and delivery rollers are driven in the sheet processing apparatus; 
         FIGS. 5A and 5B  are diagrams explaining how a relatively thin sheet bundle (i.e., bundle consisting of three sheets) is mounted on the sheet tray and how the following sheets (i.e., three sheets) remain in the standby tray,  FIG. 5A  showing how the conveyance rollers convey a sheet from the conveyance path, and  FIG. 5B  showing how the sheet delivered is switched back onto the sheet tray; 
         FIGS. 6A and 6B  are diagrams explaining the process following the process of  FIGS. 5A and 5B ,  FIG. 6A  showing the first three sheets mounted on the sheet tray, and  FIG. 6B  showing the first following sheet wp 1  conveyed to the sheet tray; 
         FIGS. 7A and 7B  are diagrams explaining the process following the process of  FIGS. 6A and 6B ,  FIG. 7A  showing how the first following sheet wp 1  is switched back by the conveyance rollers and then waits in the branch path (i.e., wait path), and  FIG. 7B  showing how the first following sheet wp 1  waits in the branch path and how the second following sheet wp 2  is conveyed; 
         FIGS. 8A and 8B  are diagrams explaining the process following the process of  FIGS. 7A and 7B ,  FIG. 8A  showing how the two following sheets wp 1  and wp 2  wait in the branch path and how the third following sheet wp 3  is conveyed, and  FIG. 8B  showing how the sheet bundle BP 1  is delivered from the sheet tray, how the three following sheets wp 1  to wp 3  are nipped together with the sheet bundle BP 1  and how the bundle BP 1  and the following sheets wp 1  to wp 3  are delivered at the same time; 
         FIGS. 9A and 9B  are diagrams explaining the process following the process of  FIGS. 8A and 8B ,  FIG. 9A  showing how the first sheet bundle BP 1  is delivered from the sheet tray, while the following sheets wp 1  to wp 3  left on the sheet tray are switched back, and  FIG. 9B  showing how the first sheet bundle BP 1  is placed in the accumulating tray, how the second sheet bundle BP 2  is placed in the sheet tray, and how the seventh following wp 1  is conveyed in; 
         FIGS. 10A and 10B  are diagrams explaining the process following the process of  FIGS. 5A and 5B , i.e., mounting a relatively thick sheet bundle (i.e., 65 sheets) on the sheet tray and keeping the following sheets (i.e., three sheets) in wait,  FIG. 10A  showing how the first following sheet wp 1  of the second bundle is conveyed in, and  FIG. 10B  showing how the rear end of the first following sheet wp 1  of the second bundle is detected and how the first following sheet wp 1  is then switched back; 
         FIGS. 11A and 11B  are diagrams explaining the process following the process of  FIGS. 10A and 10B ;  FIG. 11A  showing how the first sheet wp 1  of the second bundle is guided, as waiting sheet, into the branch path, and  FIG. 11B  showing how the second following sheet wp 2  of the second bundle is guided into the branch path; 
         FIGS. 12A and 12B  are diagrams explaining the process following the process of  FIGS. 11A and 11B ,  FIG. 12A  showing how two following sheets wp 1  and wp 2  wait in the branch path and how the third following sheet wp 3  is guided into the branch path, and  FIG. 12B  showing how the delivery rollers deliver the sheet bundle BP 1  from the sheet tray and how the sheet bundle BP 1  is nipped and delivered together with the three following sheets wp 1  to wp 3 ; 
         FIGS. 13A and 13B  are diagrams explaining the process following the process of  FIGS. 12A and 12B ,  FIG. 13A  showing how the sheet bundle BP 1  is delivered from the sheet tray and how three following sheets wp 1  to wp 3  left on the sheet tray start are switched back, and  FIG. 13B  showing the first sheet bundle BP 1  mounted on the accumulating tray, the following sheets wp 1  to wp 3  mounted on the sheet tray, and the fourth following sheet being conveyed onto the sheet tray; 
         FIGS. 14A to 14C  are diagrams explaining the relation between the thick sheet bundle and the following sheets, all shown in  FIG. 13A ,  FIG. 14A  showing the relation observed immediately after the sheet bundle has been delivered from the sheet tray,  FIG. 14B  showing how the offset distance between the following sheets increases in proportion to the thickness of the sheet bundle, and  FIG. 14C  showing how the offset distance between the following sheets is increased stepwise with respect to the thickness of the sheet bundle; 
         FIG. 15  is a diagram explaining the relation between a sheet following the thick sheet bundle shown in  FIGS. 13A and 14A  and the sheet following this sheet; 
         FIG. 16  is a flowchart showing how the offset distance between the following sheets is set and how the sheet switch back position of the following sheet is set at the sheet tray; 
         FIG. 17  is a block diagram of the control system used in the apparatus shown in  FIG. 1 ; 
         FIG. 18  is a diagram showing the configuration of a sheet processing apparatus according to the second embodiment of this invention; 
         FIGS. 19A and 19B  are diagrams explaining how a sheet bundle and following sheets are fed in the sheet processing apparatus shown in  FIG. 18 ,  FIG. 19A  showing the case where the sheet bundle is relatively thin, and  FIG. 19B  showing the case where the sheet bundle is relatively thick; 
         FIG. 20  is a diagram showing the configuration of a sheet processing apparatus according to the third embodiment of this invention; 
         FIGS. 21A and 21B  are diagrams explaining the states a sheet bundle and sheets following the bundle may take in the sheet processing apparatus shown in  FIG. 20 ,  FIG. 21A  showing the state the sheet bundle and the following sheets assume if the sheet bundle is relatively thin, and  FIG. 21B  showing the case where the sheet bundle is relatively thick; 
         FIG. 22  is a diagram explaining a conventional sheet processing apparatus; and 
         FIGS. 23A and 23B  are diagrams explaining the structural features of the conventional sheet processing apparatus, which should be improved,  FIG. 23A  showing the state the apparatus assumes if the sheet bundle is relatively thin, and  FIG. 13B  showing the state the apparatus assumes if the sheet bundle is relatively thick. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Embodiments of the present invention will be described, with reference to the accompanying drawings.  FIG. 1  shows an image forming system comprising an image forming apparatus A and a sheet processing apparatus B, both according to this invention.  FIG. 2  is a diagram showing, in detail, the configuration of the sheet processing apparatus B. 
     In the drawings attached hereto, the components of an embodiment, which are similar to those of any other embodiment, shall be designated by the same reference numerals. 
     [Image Forming System] 
     The image forming system shown in  FIG. 1  comprises an image forming apparatus A and a sheet processing apparatus B. The sheet inlet port  30  of the sheet processing apparatus B is connected to the outlet port  3  of the housing of the image forming apparatus A. The sheets, each having an image formed on it in the image forming apparatus A, can be staple-bound in the sheet processing apparatus B and can be stored in the first accumulating tray  24  or in the second accumulating tray  26 . Above the first accumulating tray  24 , an escape tray  22  is arranged to hold sheets not bounded. 
     [Image Forming Apparatus A] 
     The image forming apparatus A will be described with reference to  FIG. 1 . In the image forming apparatus A, a sheet is supplied from the sheet supplying unit  1  to the image forming unit  2 . In the image forming unit  2 , an image is formed on the sheet, and the sheet is delivered through the sheet delivering port  3  made in the housing. The sheet supplying unit  1  has sheet cassettes  1   a  and  1   b . The sheet cassette  1   a  hold sheets of one size, and the sheet cassette  1   b  holds sheets of another size. The sheets of the size designated are supplied, one by one, to the image forming unit  2 . 
     The image forming unit  2  incorporates, for example, an electrostatic drum  4 , a printing head (i.e., laser-beam emitter)  5 , a developing device  6 , a transfer charger  7 , and a fixing device  8 . In the image forming unit  2 , the laser-beam emitter  5  forms a latent electrostatic image on the electrostatic drum  4 , and the developing device  6  applies toner to the electrostatic drum  4 , forming a toner image. The transfer charger  7  transfers the toner image to a sheet. The fixing device  8  applies heat to the sheet, fixing the image on the sheet. The sheets, each having an image so fixed, are sequentially delivered through the fixing device  8 . Numeral  9  indicates a circulating path, in which a sheet having an image printed on the obverse side is turned upside down while passing through a switch back path  10  and is delivered again to the image forming unit  2  to be printed on the reverse side. The sheet printed on both sides is turned upside down again in the switch back path  10  and is delivered through the sheet delivering port  3  of the image forming apparatus A. 
     Numeral  11  indicates an image reading device, in which a scanning unit  13  scans the original sheet set on a platen  12 , and a photoelectric transducer (e.g., CCD)  14  electrically reads the image from the original sheet. The image data read from the original sheet is digital-processed in, for example, an image processing unit. The digital data generated in an image processing unit is transferred to a data storing unit  17  and then to the laser-beam emitter  5 . Numeral  15  indicates an original feeder, which feeds original sheets from an original stacker  16  to the platen  12 . 
     As shown in  FIG. 17 , the image forming apparatus A has an image-forming control unit  200 . The image-forming control unit  200  receives various image-forming conditions through a control panel  18  via an input unit  203 . The image-forming conditions include, for example, sheet-size, and the printing conditions include, for example, color/monochrome print, number of prints, single-side/double side printing, and enlarged/reduced printing. In the image forming apparatus A, the data storing unit  17  stores the image data read by the scanning unit  13  or the image data transferred from any external network. The image data is transferred from the data storing unit  17  (see  FIG. 1 ) to a buffer memory  19 . Data signals are sequentially supplied from the buffer memory  19  to the laser-beam emitter  5 . 
     At the control panel  18 , sheet-processing modes are designated, along with the image-forming modes such as single-side/double side printing, enlarged/reduced printing, color/monochrome printing. The sheet-processing modes are, for example, “print-out mode”, “side-binding mode”, “jog-delivering mode” and “saddle-binding mode”. The sheet-processing modes will be described later. 
     [Sheet Processing Apparatus B] 
     As shown in  FIG. 1  and  FIG. 2 , the sheet processing apparatus B incorporates a sheet inlet port  30  made in one frame  20  and the escape tray  22  provided on the side opposing the sheet inlet port  30 . The escape tray  22  holds one sheet or a relatively thick sheet. Below the escape tray  22 , the first accumulating tray  24  is positioned, which can move up and down and can hold side-bound sheets or a relatively large number of sheets. Below the first accumulating tray  24 , the second accumulating tray  26  is provided to accumulate side-bound sheets or folded sheets. In this invention, the word “side” means the surfaces around any sheet end, namely the obverse and reverse sides at sheet edges. Hence, the side-binding processing indicates the binding of an end of a sheet bundle. 
     [Sheet Conveyance Path] 
     The sheet processing apparatus B has a feed-in path  32  and a conveyance path  42 . The conveyance path  42  extends from the above-mentioned sheet inlet port  30 , namely from the feed-in path  32 , to the outlet port (sheet-delivering port)  50  of the sheet tray. In the feed-in path  32 , a punching unit  31  is provided to punch the sides of a sheet and, if necessary, that part of a sheet, which is middle in the conveyance direction. Below that part of the punching unit  31 , which lies below the above-mentioned feed-in path  32 , a punch-chip box  31   b  is provided, detachably secured to the frame  20  of the apparatus B, to receive punch chips made in the punching process. 
     Downstream the punching unit  31 , feed-in rollers  34  are arranged to feed sheets at a relatively high speed. In the conveyance path  42  located below the feed-in rollers  34 , a sheet tray  54  and conveyance rollers  44  are provided. The sheet tray  54  is the first processing tray, and the conveyance rollers  44  can rotate in forward direction and reverse direction to guide sheets to the first accumulating tray  24  located downstream of the sheet tray  54 . At the back of the conveyance rollers  44 , a sheet-conveyance outlet port  46  is provided. 
     Downstream of the sheet-conveyance outlet port  46 , delivery rollers  48  are provided. The delivery rollers  48  switch back a sheet and then deliver the sheet onto the sheet tray  54 , deliver the sheet directly onto the first accumulating tray  24 , or deliver a sheet bundle formed by side-binding the sheets on the sheet tray  54 , from the sheet tray  54  to the first accumulating tray  24 . Further, the delivery rollers  48  can perform jog-delivering to shift a sheet bundle without binding the sheets at the sheet tray  54  and to sort sheet bundles at the first accumulating tray  24 . 
     [Escape Path and Branch path] 
     The conveyance path  42  is branched at a branch position  36  into an escape path  38  and a branch path  70 . The escape path  38  guides sheets to the escape tray  22 . The branch path  70  guides relatively long sheets to a stacker  84 . The stacker  84  is the second processing tray (i.e., second sheet tray) at which relatively long sheet may be saddle-bound or folded. At the branch position  36 , a switching gate  37  is provided to convey a sheet directly to the conveyance path  42  or to the escape path  38 , or to switch back a sheet in the conveyance path  42  and then guide the sheet to the branch path  70 . 
     As shown in  FIG. 2  and  FIG. 3 , the branch path  70  is a path curved downward, surrounding the sheet tray  54  at one side thereof. The branch path  70  is used as a wait path in which any following sheet switched back is kept waiting as will be described later in detail. In the escape path  38 , escape rollers  39  and escape delivery rollers  40  are provided. The escape rollers  39  convey a sheet, and the delivery rollers  40  deliver a sheet to the escape tray  22 . 
     [Side-Binding Unit] 
     Below the sheet-conveyance outlet port  46  of the conveyance path  42 , the sheet tray  54  (i.e., first processing tray) is arranged. Below the sheet tray  54 , a side-binding unit  60  is provided to bind the sides of any sheet temporarily mounted on the sheet tray  54 . The side-binding unit  60  will be described later, with reference to  FIG. 3  and  FIG. 5 . 
     [Saddle-Binding Unit] 
     Relatively long sheets are first conveyed in the conveyance path  42  toward the sheet tray  54 , then conveyed to the downstream side of the switching gate  37 , next switched back to the branch path  70 , then conveyed from a branch outlet port  76 , and collected in the stacker  84 , i.e., second sheet tray. Near the stacker  84 , a saddle-binding unit  80  is arranged. The saddle-binding unit  80  is configured to bind the sheets collected in the stacker  84 , at part middle in the conveyance direction. As shown in  FIG. 2 , a flapper  78  is provided at the branch outlet port  76 . Every time a sheet is supplied from branch delivery rollers to the stacker  84 , the flapper  78  biases the sheet to the left, preventing the rear end of the sheet from abutting on the front end of the following sheet. 
     [Stacker (i.e., Second Sheet Tray)] 
     To the stacker  84 , a stopper  85  is secured to hold a sheet at the position where the sheet should be fed in. The stopper  85  is moved in the direction of the arrow if a stopper-moving motor  85 M drives a belt  88  wrapped around upper and lower pulleys  86 ,  87  at one side of the stacker  84 . The stopper  85  can be held at the position where the flapper  78  may change the position of the rear end of the sheet delivered into the stacker  84 , at the position where the saddle binder  82  performs saddle binding on sheets, binding the sheets together, at the part middle in the conveyance direction, and at the position where a folding blade  94  that makes reciprocating motion is pushed into the nip between a pair of holding rollers  92 , thereby to hold a sheet bundle double. Two alignment plates  81  are provided above one folding roller  92  and below the other folding roller  92 , respectively, to align each sheet conveyed into the stacker  84  with those already held in the stacker  84 . 
     [Saddle-Binding Unit] 
     The saddle-binding unit  80  has an anvil  83  that opposes a driver provided in the saddle binder  82 . The anvil  83  is configured to bend the leg parts of a stable driven by the driver. The saddle binder  82  is a well-known type, and will not be described here. The saddle-binding unit may not be limited to one that drives a stable through a sheet bundle, thereby binding the sheets together. Rather, it may be a mechanism that applies adhesive to each sheet at part middle in the conveyance direction and then bonds the sheets together. 
     [Second Sheet Tray] 
     The sheet bundle, saddle-bound at the saddle binder  82 , is folded double by the folding roller  92  and the folding blade  94  pushing the sheet bundle. While being so folded, the sheet bundle is delivered onto the second accumulating tray  26  by the folding roller  92  and the bundle-delivery rollers  96  located downstream the folding roller  92 . To the front end of the second accumulating tray  26 , onto which the sheet bundle folded double and being delivered first at the front end may be dropped, free-rotatable rollers, a rotatable holding roller  102  and a holding lever  104  are secured. The lever  104  touches the upper side of a sheet bundle, preventing the sheets from moving sideways. The rotatable holding roller  102  and a holding lever  104  loosen the sheet bundle, lowering the sheet-bundling efficiency. 
     [Branch Position and Side-Binding Unit] 
     The branch position  36  and the side-binding unit  60  will be further described with reference to  FIG. 3 . As described above,  FIG. 3  shows the feed-in path  32 , conveyance path  42 , escape path  38  and branch path  70 . In the feed-in path  32 , the feed-in rollers  34  have been inserted though the sheet inlet port  30 . The conveyance path  42  extends straight from the feed-in path  32  toward the sheet tray  54 . The escape path  38  extends upward from the conveyance path  42  as shown in  FIG. 3 . The branch path (i.e., wait path) curves downward and guides a sheet to the stacker  84 . At the branch position  36 , the switching gate  37  is provided to guide the sheet switched back from the escape path  38  or conveyance path  42 , to the branch path  70 . 
     In this embodiment, the switching gate  37  may assume the position indicated by solid lines in  FIG. 3  to close the escape path  38 , thereby to guide the sheet into the conveyance path  42  from the feed-in path  32 . The switching gate  37  may assume the position indicated by broken lines in  FIG. 3 , thereby to guide the sheet transported from the feed-in path  32 , to the escape path  38 , and to guide the sheet to switch back, to the branch path  70 . 
     In the conveyance path  42 , the conveyance rollers  44  are arranged immediately before the sheet-conveyance outlet port  46 , which is the final end and can rotate in forward direction and reverse direction and can contact and leave each other. Therefore, the conveyance rollers  44  can convey a sheet toward the sheet tray  54  if they contact and rotate in one direction, and can switch back a sheet toward the branch path (wait path)  70  located in the opposite direction if they contact and rotate in the other direction. 
     [Switch-Back Conveyance] 
     The switch-back conveyance is performed by rotating the conveyance rollers  44  in the reverse direction after the sheet sensor  42 S arranged at the back of the switching gate  37  provided in the conveyance path  42  detects the passing of the rear end of a sheet. If the conveyance rollers  44  are rotated in the reverse direction, the switching gate  37  is positioned, closing the feed-in path  32  (see the broken lines in  FIG. 3 ). The sheet is therefore transported to the branch path  70  and further transported by branch rollers  72  (i.e., second conveyance rollers). When the rear end of the sheet reaches a prescribed position, the branch rollers  72  are stopped, making the sheet wait in the branch path  70  as a following sheet. 
     The branch rollers  72  thus cooperate with the conveyance rollers  44 , making one sheet to a few sheets wait in the branch path  70 . 
     The delivery rollers  48  are arranged in the outlet port  50  (i.e., sheet-delivering port of the sheet tray  54 ) located downstream the conveyance rollers  44 . The delivery rollers  48  rotate forward and backward and come into contact with and separated from each other. The delivery rollers  48  are an upper delivery roller  48   a  and a lower delivery roller  48   b . These rollers  48   a  and  48   b  may contact each other and rotate in one direction to cooperate with the conveyance rollers  44 , thereby to deliver a sheet onto the first accumulating tray  24 . The delivery rollers  48  are used to deliver the sheet bundle from the sheet tray  54  onto the first accumulating tray  24  after the sheet bundle has been pushed out onto the first accumulating tray  24  by a pushing member that has a reference surface  57 . 
     [Delivery onto the Sheet Tray  54 ] 
     How to deliver a sheet onto the sheet tray  54  will be explained. To deliver a sheet onto the sheet tray  54 , the delivery rollers  48  located downstream are rotated in reverse direction, conveying a sheet from the conveyance rollers  44  to the right on the inclined surface of the sheet tray  54  as shown in  FIG. 3 . The sheet is further conveyed as a rotating gathering roller  56  is rotated in the counterclockwise direction. The sheet abuts on the reference surface  57  and is stopped. At this point, the gathering roller  56  slips on the sheet, preventing the sheet, as much as possible, from bending at the front part. The delivery rollers  48  have the function of switching back the sheet delivered from the conveyance rollers  44  and transporting the sheet to the reference surface  57  of the sheet tray  54 . 
     [Moving of the Side-Binding Unit, and Binding Process] 
     Every time a sheet is delivered from the conveyance rollers  44 , the delivery rollers  48  and the gathering roller  56  rotate, conveying the sheet to the reference surface  57  to lay the sheet onto the uppermost sheet laid in the sheet tray  54 . Further, as the sheet is laid so, alignment plates  58  are made to abut on both sides of the sheet, aligning the sheet with the other sheets that part of the sheet tray  54 , which is middle in the widthwise direction of the sheet tray  54 . This sheet aligning is repeated until sheets are piled in the sheet tray  54  to a prescribed number. When sheets are piled to the prescribed number, a side-binding unit  62  is moved on a table  63  in the widthwise direction of the sheets to the desired binding position. The side-binding unit  62  is so moved, as the motion pin  62   b  of the side-binding unit  62  slides in a groove cut in the table  63  and extending in the widthwise direction of the sheets. 
     The side-binding process, i.e., the process the side-binding unit  62  adapted for the first process of the present invention performs, is known in the art, and is not explained herein. When the side-binding unit  62  stops at the designated position, a side-binding motor  62 M is driven, moving a driver (not shown) and driving a stable into the sheet bundle. The anvil bends the staple thus driven, performing side binding on the sheet bundle. The side binding is performed also at several parts of the sides and ends of the sheet bundle. 
     [Delivering of the Side-Bound Sheets] 
     A reference-surface moving belt  64  is wrapped around a right pulley  65  and a left pulley  66  arranged below the sheet tray  54 . As the reference-surface moving belt  64  is driven counterclockwise, the reference surface  57 , as a moving member, of the sheet tray  54  coupled to the belt  64  moves to the left, pushing the sheet bundle with its bound end facing the first accumulating tray  24 . As the sheet bundle is so pushed, the sheet bundle bound at the delivery rollers  48  (i.e., upper and lower delivery rollers  48   b  and  48   b ) located at the delivering port of the sheet tray  54  is pressed at both the obverse and reverse sides. As the delivery rollers  48  are rotated clockwise, the sheet bundle is delivered from the first accumulating tray  24 . 
     [Up-Down Motion of the First Accumulating Tray] 
     The first accumulating tray  24  configured to receive a sheet bundle will be explained. As shown in  FIG. 3 , the first accumulating tray  24  is inclined at almost the same angle as the sheet tray  54 . The first accumulating tray  24  receives the sheet bundle delivered from the sheet tray  54  and also the sheets delivered, one by one, from the conveyance path  42  by the conveyance rollers  44  and delivery rollers  48 . 
     On the bottom of the first accumulating tray  24 , a lift motor  24 M is located to move the first accumulating tray  24  up and down. The drive force of the motor  24 M is transmitted to a pinion  109 . The pinion  109  meshes with two lift lacks  107  that are secured to the two lateral parts of the vertical wall  28  of the frame  20 . The first accumulating tray  24  can move up and down on the rails (not shown) that are laid on the vertical wall  28  of the first accumulating tray  24 . 
     The position of the first accumulating tray  24  or the position of the sheet laid in the first accumulating tray  24  are detected by a sheet-surface sensor  24 S that is provided on the vertical wall  28 . If the sheet-surface sensor  24 S detects the surface of the sheet, the lift motor  24 M is driven, rotating the pinion  109  and lowering the first accumulating tray  24 .  FIG. 3  shows a state in which the sheet-surface sensor  24 S detects the top sheet on the the first accumulating tray  24 . At the lower position, the first accumulating tray  24  receives a sheet bundle. Thus, the delivering port of the sheet tray  54  lies above the upper surface of the first accumulating tray  24 . 
     How the conveyance rollers  44  and the delivery rollers  48  are rotated, and how the conveyance rollers  44  and the delivery rollers  48  respectively are moved toward and away from each other will be described with reference to  FIG. 4 . 
     [Driving of the Upper Conveyance roller] 
     The upper conveyance roller  44   a  and the lower conveyance roller  44   b  are driven by a conveyance roller motor  44 M. The conveyance roller motor  44 M is a hybrid-type stepping motor. A speed detection sensor  44 S is provided to detect the rotation speed of the shaft of the motor  44 M. The rotation of the motor shaft is transmitted via transmission gears  120   122  and a transmission belt  124  to an arm gear  126 . The rotation of the arm gear  126  is transmitted by a transmission belt  128  to the upper roller shaft  44   ui  of an upper conveyance roller  44   a  supported by a conveyance roller supporting arm  136 . 
     [Motion of the Upper Conveyance roller] 
     The upper conveyance roller  44   a  can rotate around the shaft of the arm gear  126 , and can contact and leave the lower conveyance roller  44   b  fixed in place. The upper conveyance roller  44   a  can contact and leave the roller  44   b , thanks to a conveyance roller moving arm  130 . The arm  130  has a fan-shaped gear flaring backwards and fixed to the shaft of the arm gear  126  and a spring  134  biasing the upper conveyance roller  44   a  and attached to the moving arm tip at the end. That is, if an arm motor  130 M for moving the conveyance rollers in mesh with the fan-shaped gear is driven in one direction, the arm  130  will move in the direction of arrow O, releasing the lower conveyance roller  44   b . If the arm motor  130 M is driven in the other direction, the arm  130  will move in the direction of arrow C to push the upper conveyance roller  44   a  onto the lower conveyance roller  44   b . The arm motor  130 M is a stepping motor, too. The position of the conveyance roller moving arm  130  is detected by a conveyance roller moving arm sensor  130 S. 
     [Rotation of the Lower Conveyance Roller] 
     The lower conveyance roller  44   b  is rotated by transmitting the drive force of the conveyance roller motor  44 M via the transmission gears  120  and a transmission belt  138  to a gear  142  mounted on a lower conveyance shaft  44   sj.    
     As the gear  142  is driven, a gear  144  that has a one-way clutch gear and a belt  146  that has a projection and functions as transmission belt rotate the gathering roller  56 . The gathering roller  56 , which is driven via the gear  144 , rotates in only one direction indicated by the solid-line arrow shown in  FIG. 4  even if the gear  142  rotates in the forward direction or the reverse direction, as described above. That is, the gathering roller  56  rotates to convey the sheet only toward the reference surface  57  of the sheet tray  54 . 
     At the front end of the belt  146  having a projection, the gathering roller  56  rotates. The gathering roller  56  may be dispensed with, and a circular gathering belt may be rotated instead. 
     The drive force of the conveyance roller motor  44 M is transmitted via the transmission gear  120  and a transmission belt  148 , also to a lower branch roller shaft  72   sj  of the lower branch roller  72   b  of the branch roller  72  that conveys sheets in the branch path  70 . 
     In the apparatus B configured as described above, as the conveyance roller motor  44 M is driven in the forward direction and the reverse direction, the conveyance rollers  44  and the branch rollers  72  rotate in one direction indicated by the solid-line arrow and the other direction (i.e., switch back direction) indicated by the broken-line arrow, and the gathering roller rotates toward the reference surface  57  as indicated by the solid-line arrow. The conveyance roller motor  44 M can be set to convey sheets at a prescribed speed toward the sheet tray  54  or to switch back sheets toward the branch path  70 . 
     [Rotation of the Upper Delivery Roller] 
     The delivery rollers  48 , i.e., upper delivery roller  48   a  and lower delivery roller  48   b , are driven by a delivery roller motor  48 M. The delivery roller motor  48 M is a hybrid-type stepping motor, too. A speed detection sensor  48 S is provided to detect the rotation speed of the shaft of the motor  48 M. The rotation of the motor shaft is transmitted via transmission gears  150  and  152  and a transmission belt  154  to an arm gear  156 . The rotation of the arm gear  156  is transmitted by a transmission belt  158  to the upper roller shaft  48   uj  of the upper delivery roller  48   a  supported by a delivery roller supporting arm  166 . 
     [Motion of the Upper Delivery Roller] 
     The upper delivery roller  48   a  can rotate around the shaft of the arm gear  156 , and can contact and leave the lower delivery roller  48   b  fixed in place. The upper delivery roller  48   a  can contact and leave the lower delivery roller  48   b , by virtue of a delivery roller moving arm  160 . The arm  160  has a fan-shaped gear flaring backwards and fixed to the shaft of the arm gear  156  and a spring  164  biasing the upper delivery roller  48   a  and attached to the moving arm tip at the end. If an arm motor  160 M in mesh with the fan-shaped gear is driven in one direction, the arm  160  will move in the direction of arrow O, releasing the lower conveyance roller  44   b . If the arm motor  160 M is driven in the other direction, the arm  160  will move in the direction of arrow C to push the upper delivery roller  48   a  onto the lower delivery roller  48   b.    
     The arm motor  160 M for moving the delivery roller is a stepping motor, too. The position of the delivery roller moving arm  160  is detected by a conveyance roller moving arm sensor  160 S. The lower delivery roller  48   b  is rotated by transmitting the drive force of the delivery roller motor  48 M via the transmission gear  150  and a transmission belt  168  to a gear  169  amounted on a lower delivery roller shaft  48   sj.    
     [Setting of the Speed of the Delivery Roller Motor] 
     In the configuration described above, as the delivery roller motor  48 M rotates in the forward and reverse directions, the delivery rollers  48  rotate in one direction indicated by the solid-line arrow or in the other direction indicated by the broken-line arrow (thereby switching back the following sheet on the sheet tray  54  toward the reference surface  57  after the following sheet has been released from the conveyance rollers  44 ). The delivery roller motor  48 M can be driven at a preset speed to drive the conveyance rollers  44  at a prescribed speed. 
     [Wait Conveyance and Second Tray Conveyance] 
     Referring back to  FIG. 3 , it will be described how sheets are switched back and kept waiting in the branch path  70  to achieve the above-described side binding. To perform the side binding in the side-binding unit  62  located near the sheet tray  54 , sheets must be prevented from being conveyed to the side-binding unit  62  if the preceding sheets have not been side-bound because they, each having an image formed in the image forming apparatus A, are conveyed at high speed and spaced apart by a short distance. Therefore, the first to third following sheets conveyed to the conveyance path  42  via the feed-in path  32  are switched back in the conveyance path  42  and then kept waiting in the branch path  70 . The first following sheet is then overlapped on the second or third following sheet. The overlapping sheets are conveyed from the branch path  70 , thereby spacing the sheet bundles sufficiently. (This technique is disclosed in, for example, FIG. 10 of Japanese Patent No. 5,248,785.) 
     Hereinafter, the process of switching back a sheet from the conveyance path  42  to the branch path  70 , keeping one or more sheets waiting in the branch path  70  and convey the sheet or sheets from the branch path  70  together with the next sheet shall be referred to as “wait conveyance”. Most sheets undergoing the wait conveyance to be side-bound are relatively short, such as A4-size, B5-size and letter-size sheets. Hence, these sheets can be switched back without extending greatly into the downstream area of the sheet tray  54 . Nor will they be bent while they are conveyed. Even if they are bent a little, they can be straightened up as they are aligned by the aligning plates  58  since the distance to the sheet tray  54  is comparatively short. 
     When the completion of the side binding means not only the completion of sheet delivery from the sheet tray  54  to the first accumulating tray  24 , but also the initial setting of the aligning plates  58  provided on the sheet tray  54  and the returning of the reference-surface moving belt  64  to its initial position or the setting of each mechanism at the initial position to receive the next sheet. 
     It will be explained how the sheets saddle-bound in the saddle binder  82  are conveyed to the stacker  84  in order to fold them double by the folding roller  92  and folding blade  94  into a folded sheet bundle. The sheets conveyed to the conveyance path  42  via the feed-in path  32  are first switched back in the conveyance path  42  and then conveyed from the branch path  70  to the stacker  84 . The step of conveying the switched-back sheets from the branch path  70  to the stacker  84  shall be called “second tray conveyance” hereinafter. 
     [Switch-Back Conveyance] 
     In this embodiment, the “wait conveyance” of a sheet is achieved by first detecting the rear end of the sheet by the sheet sensor  42 S provided at the branch position between the conveyance path  42  and the branch path  70 . Then, the sheet is switched back to the branch path  70  and nipped by the branch rollers  72  positioned at the branch path  70 , and the branch rollers  72  are stopped rotating. To perform the “second tray conveyance” for collecting the sheets in the stacker  84  positioned downstream the branch path  70 , the sheets switched back by the conveyance rollers  44  are conveyed to the branch rollers  72  provided at the branch path  70  and then continuously conveyed to the stacker  84 . 
     The delivery rollers  48  can rotate in both the forward direction and the reverse direction. When the rear end of a following sheet (i.e., sheet waiting in the branch path  70 , sheet conveyed from the feed-in path or a sheet overlapping another) comes out of the conveyance rollers  44 , it is nipped by the delivery rollers  48 . When the delivery rollers  48  are rotated in the reverse direction, the following sheet is switched back and stored into the sheet tray  54 . 
     Here, it will be described how the position the front end of any following sheet switched back at the sheet tray  54  takes with respect to the reference surface  57 . In the sheet bundle of following sheets switched back on the sheet tray  54 , the front end of the first following sheet should be nearest to the reference surface  57 , and the front ends of the second and third following sheets should be far from the reference surface  57 . This is because when the sheets are being conveyed by the gathering roller  56 , if the uppermost following sheet reaches the reference surface  57  earlier, any lower following sheet will slip with the other lower following sheet and will no longer be conveyed. Consequently, the sheets will be bound with their front ends not aligned, forming an untidy sheet bundle. Thus, the above-mentioned order in which the sheets are conveyed is important to prevent a sheet-alignment failure. 
     [Delivery of the Sheet Bundle] 
     As explained above, the upper delivery roller  48   a  can be moved up and down. When it moves down to the position (indicated by the broken line in  FIG. 4 ), it pushes the lower delivery roller  48   b . When it moves up, it assumes the position (indicated by solid line in  FIG. 4 ). After the sheets have been bundled at the sheet tray  54 , the reference-surface moving belt  64  moves the reference surface  57  up toward the outlet port  50 . Then, the upper delivery roller  48   a  is lowered and cooperates with the lower delivery roller  48   b , nipping the sheet bundle and conveying the sheet bundle to the outlet port  50 . The sheet bundle is then delivered onto the first accumulating tray  24 . 
     [Sheet Processing Unit] 
     The sheet bundle delivered by the delivery rollers  48  is processed in the sheet processing unit provided at the sheet tray. The sheet processing includes two processes. The first process is a side binding performed in the side-binding unit  62 . The second process is a so-called jog process of first arranging the sheets at different positions on the sheet tray  54  by using the aligning plates  58 , then delivering the sheets to the first accumulating tray  24 , and finally sorting the sheets without binding them. The sheet processing further includes a sheet bonding process of bonding the sheets with glue and punching process of punching the sheets. 
     [Acquisition of Sheet-Bundle Thickness Data BPt] 
     The sheet tray  54  has, on the upper frame thereof, a bundle thickness sensor  230  configured to acquire data representing the thickness of the sheet bundle (sheet-bundle thickness data BPt) that is laid on the sheet tray  54 . The sensor  230  is a reflection-type sensor. The reflection-type sensor may be replaced by a sensor having a lever that may enter the space between the two sensor elements. 
     The sensor  42 S may be used to count the sheets delivered onto the sheet tray  54 , and the count data acquired may be used as thickness data (i.e., sheet-bundle thickness data Bpt). The thickness data may be acquired from the image forming apparatus A. The thickness data (i.e., sheet-bundle thickness data Bpt) is used, setting the space between the sheets switched back and waiting, or the space between the sheets waiting in the branch path  70 . Therefore, the thickness data (i.e., sheet-bundle thickness data Bpt) is acquired before the sheets are bundled at the sheet tray  54 , more precisely before the following sheets are switched back and kept waiting in the branch path  70 . 
     [Simultaneous Bundle Delivering] 
     With reference to  FIG. 5A  to  FIG. 16  it will be explained how the sheet bundle on the sheet tray  54  and the sheets and some following sheets waiting in the branch path  70  are simultaneously delivered by the delivery rollers  48  and are switched back to the first accumulating tray  24  and the sheet tray  54 , respectively. Referring to  FIG. 5A  to  FIG. 9B , it will be described how a relatively thin sheet bundle (i.e., bundle composed of relatively small number of sheets) and the following sheets are delivered at the same time. Referring to  FIG. 10  to  FIG. 13B  and  FIG. 16 , it will be described how a relatively thick sheet bundle (i.e., bundle composed of relatively large number of sheets) and the following sheets are delivered at the same time. Referring to  FIG. 14  and  FIG. 15 , it will be described how the sheets are positioned, where the following sheets are positioned, how much they are spaced apart, and where the following sheets are switched back on the sheet tray  54 . 
     [Simultaneous Delivery of a Thin Bundle (Small Number of Sheets) and Following Sheets] 
       FIG. 5A  to  FIG. 9B  are diagrams explaining how a relatively thin bundle (composed of three sheets) is held on the sheet tray and the following sheets (three sheets) are kept waiting. As seen from FIG.  FIG. 5A , the conveyance rollers  44  may convey the first sheet P 1  from the conveyance path  42  onto the sheet tray  54 . If the sheet sensor  42 S detects the rear end of the sheet P 1  and the counter (not shown) counts the first sheet P 1 , the sheet P 1  is conveyed from the conveyance rollers  44  to the sheet tray  54 . At the same time the sheet P 1  is so conveyed, the upper delivery roller  48   a  is moved from the position (indicated by broken lines) to the position (indicated by solid lines). Thereafter, the upper delivery roller  48   a  is rotated counterclockwise, switching back the first sheet P 1  on the sheet tray  54 , and conveying the first sheet P 1  toward the reference surface  57 . 
     Next, as shown in  FIG. 5B , the delivery rollers  48  are rotated counterclockwise, switching back the first sheet P 1 . The first sheet P 1  switched back is conveyed toward the reference surface  57  by the gathering roller  56  and the belt  146  having a projection and is mounted on the sheet tray  54 . Then, the aligning plates  58  are moved, aligning the sheet at the center of the aligning plates  58 . When the second sheet is conveyed onto the sheet tray  54  and its front end is detected by the sheet sensor  42 S, the delivery rollers  48   a  are moved from the position indicated by broken lines to the position indicated by solid lines. Then, the second sheet is conveyed in the same way as shown in  FIG. 5A , forming a sheet bundle BP 1  composed of three sheets (P 1 , P 2  and P 3 ). The process goes to the step shown in  FIGS. 6A and 6B . The step of “Start setting the offset distance for the following sheets, and start setting the switch back position on the following-sheet tray” (S 10 ), shown in  FIG. 16 , is performed before the operation of  FIGS. 5A and 5B . 
       FIGS. 6A and 6B  are diagrams explaining the process following the process of  FIGS. 5A and 5B .  FIG. 6A  shows how the sheet bundle BP 1  (composed of first three sheets P 1 , P 2  and P 3 ) is mounted on the sheet tray  54 .  FIG. 16  describes this state as “Mount the sheet bundle on the sheet tray  54 ” (S 20 ). 
     In the step of  FIGS. 6A and 6B , the side-binding unit  62  performs the side binding. Prior to this process, the bundle thickness sensor  230  described with reference to  FIG. 4  detects the thickness of the sheet bundle, acquiring the bundle-thickness data BPt showing the bundle is relatively thin (S 30 ). The conveyance of the first following sheet (wp 1 ), i.e., fourth sheet, starts as shown in  FIG. 6A . The sheets forming the bundle BP 1  on the sheet tray  54  are completely aligned, and the side-binding unit  62  is moved to perform the side binding. 
     Upon receiving the bundle-thickness data BPt, a unit (i.e., sheet conveyance control unit  210  to be described later) sets an offset distance wp 11  for any two following sheets. In  FIG. 16 , this step is described as “Set the offset distance wp 11  between the following sheets (the thicker the sheet bundle, the longer the distance)” (S 40 ). Further, the step of setting the position on the sheet tray  54 , where the sheets are switched back, is described as “Set a switch back position (SB 1 ) on the sheet tray  54  (the thicker the sheet bundle, the farther from the sheet sensor  42 S” (S 50 ). 
     As shown in  FIG. 6B , the fourth sheet P 4  (i.e., first waiting sheet wp 1 ) is conveyed by the conveyance rollers  44  beyond the delivery rollers  48 . When the sheet sensor  42 S detects the rear end of the sheet wp 1 , the sheet wp 1  is switched back. At this point, the switching gate  37  located between the conveyance path  42  and the branch path  70  assumes the position indicated by solid lines, and guides the sheet wp 1  to the branch path  70 . 
       FIGS. 7A and 7B  are diagrams explaining the process following the process of  FIGS. 6A and 6B . As shown in  FIG. 7A , the side-binding unit  62  starts side-binding the sheet bundle BP 1  mounted on the sheet tray  54 . During the side-binding process, the fourth sheet wp 1  cannot be conveyed onto the sheet tray  54 . Therefore, the conveyance rollers  44  continues the switch-back conveyance, and the branch rollers  72  located at the branch path  70  and rotating in synchronism with the conveyance rollers  44  convey the sheet bundle BP 1  downstream the branch path  70 . When the branch rollers  72  nip the following sheet P 3 , the switching gate  37  is moved up, opening the conveyance path  42 . 
     While the branch rollers  72  are conveying the sheet P 3 , the sheet sensor  42 S may detect the rear end of the fourth sheet wp 1  (as viewed in the conveyance direction). If the rear end of the fourth sheet wp 1  is detected, a counter (not shown) detects the distance the rear end of the fourth sheet has moved. When the distance is found wp 11  from the sheet sensor  42 S, the branch rollers  72  are stopped rotating, and the branch rollers  72  wait for the fifth sheet wp 2 . 
     As shown in  FIG. 7B , a binding process is performed on the sheet bundle BP 1  on the sheet tray. Meanwhile, the fifth sheet wp 2  is conveyed by the feed-in rollers  34  toward the conveyance rollers  44 . If the sheet sensor  42 S detects the rear end of the fifth sheet wp 2 , the sheet wp 1  (i.e., fourth sheet P 4  following) and the fifth sheet wp 2  are conveyed toward the conveyance rollers  44 , with offset distance wp 11  between them. 
     The setting of the offset distance is described in  FIG. 16  as “Set the sheets off by distance wp 1 , and make them wait (that is, making them wait in the branch path  70  (wait path) as waiting sheets)” (S 60 ). If the sheet bundle BP 1  is thin, the offset distance is set to wp 11 . If two or more sheets follow, the offset distance has the value of wp 11 , too. It should be noted that the waiting sheets are conveyed at the speed of 650 mm/sec. In this step of the process, the sheets are completely bound together, forming a bundle BP 1 . 
     While the following fourth sheet wp 1  (P 4 ) waiting at the branch path  70  and the fifth sheet wp 2  (P 5 ) conveyed from the feed-in rollers are spaced by distance wp 11 . This distance wp 11  is an important factor that enhances the alignment of the sheets switched back onto the sheet tray  54  and bent in the form of inverted V. 
       FIGS. 8A and 8B  explain the process following the process of  FIGS. 7A and 7B . As shown in  FIG. 8A , two following sheets wp 1  and wp 2  (P 4  and P 5 ) wait in the branch path, and a following third sheet wp 3  (P 6 ) is conveyed. As shown in  FIG. 7B , the following fourth and fifth sheets wp 1  and wp 2  (P 4 , P 5 ) waiting in the branch path  70  are conveyed to the conveyance rollers  44 , with the front end of the following sheet wp 2  at the head. The conveyance rollers  44  nip the fifth sheet P 4  and the fifth sheet P 5  at the same time and convey them to the conveyance rollers  44 . If the sheet sensor  42 S detects the rear end of the fifth sheet P 4 , the conveyance rollers  44  are rotated counterclockwise again. 
     At this point, the switching gate  37  assuming the branch position  36  closes the feed-in path  32 , guiding the two following sheets wp 1  and wp 2  (P 4  and P 5 ), respectively, to the branch path  70 . Eventually, the rear end of the following fifth sheet wp 3  (P 5 ) is detected by the sheet sensor  42 S, and the sheet wp 2  set off by distance wp 11  is conveyed to the branch path  70 . Then, the branch rollers  72  are stopped, and the following sixth sheet wp 3  (P 6 ) is fed to have its front end detected by the sheet sensor  42 S.  FIG. 8A  illustrates this state. At this point, the following sheets wp 1  to wp 3  are set off by distance wp 11 . 
       FIG. 8B  shows how the delivery rollers  48  nip and deliver the sheets wp 1  to wp 3  together with the sheet bundle BP 1  while making the sheets wp 1  to wp 3  set off from one another by distance wp 11  and the sheet wp 1  set off from the front end of the sheet bundle BP 1  by distance Bp 11 . That is, the sheet bundle BP 1  is pushed on the reference surface  57  toward the outlet port of the sheet tray  54 , and the upper delivery roller  48   a  is lowered, nipping the sheets wp 1  to wp 3 . The sheets wp 1  to wp 3  are so nipped in order to set off the front end of the uppermost following sheet wp 3  from the front end of the sheet bundle BP 1  by distance Bp 11 . The sheet bundle BP 1  set off by this distance Bp 11  is delivered by the delivery rollers to the first accumulating tray  24 . 
     Since the three following sheets wp 1  to wp 3  have the same length, the uppermost following sheet wp 3 , the intermediate following sheet wp 2  and the lowermost following sheet wp 1  are set off toward the accumulating tray  24  by distance wp 11 . In other words, the uppermost sheet wp 3  is farthest from the reference surface  57 , the lowermost sheet wp 1  is nearest to the reference surface  57 , and the sheet wp 2  is at an intermediate distance from the reference surface  57  while they are being switched back on the sheet tray  54 . This state is described In  FIG. 16  as “Deliver the sheet bundle and the following sheets at the same time from the sheet tray  54  (after the sheets have been aligned, side-bound and punched)” (S 70 ). 
       FIGS. 9A and 9B  following the process of  FIGS. 8A and 8B  illustrate how the sheet bundle BP 1  is delivered onto the first accumulating tray  24  and how the following sheets wp 1  to wp 3  are switched back on the sheet tray  54 . As shown in  FIG. 9A , the sheet bundle BP 1  mounted on the sheet tray  54  and the following sheets wp 1  to wp 3  conveyed by the conveyance rollers  44  are nipped and delivered at the same time by the delivery rollers  48 , the sheet bundle BP 1  is held on the first accumulating tray  24 , and the following sheets wp 1  to wp 3 , overlapping one another and set off from one another by distance Bp 11 , are held on the sheet tray  54 . 
     In this process, the rear ends of the following sheets wp 1  to wp 3  are set off by distance wp 11  and are bent in the form of inverted V, as described above (see the enlarged part of  FIG. 9A , encircled by an ellipse). Even if the delivery roller  48   a  rotates in this state around a support arm shaft  167  located upstream the delivery roller  48   a , the delivery roller  48   a  rotates only a little because the sheet bundle BP 1  delivered is composed of three sheets and relatively thin. Hence, the distance wp 11  by which the following sheets wp 1  to wp 3  are set off changes only a little. Therefore, the following sheets wp 1  to wp 3  are left on the sheet tray  54  and are switched back toward the reference surface  57  as the delivery rollers  48  rotate in the direction reverse to the sheet-delivering direction. 
     The switch back position is set so that the sheet bundle BP 1  may be delivered before the rear end of the following sheet wp 1  (i.e., sheet nearest to the reference surface  57 ) reaches a position away from the sheet sensor  42 S by distance SB 11 , and the following sheets wp 1  to wp 3  may then be switched back. The distance SB 11  is not influenced so much by the delivering of the sheet bundle BP 1 , and the following sheets remains on the sheet tray  54 . In  FIG. 16 , this state is described as “Switch back the following sheets at the switch back position (SB 1 ) (convey the following sheets switched back by the gathering roller  56  to the reference surface)” (S 80 ). As shown in  FIG. 9B , the gathering roller  56  and the belt  146  having a projection make the front ends of the following sheets wp 1  to wp 3  sequentially abut and aligned on the reference surface  57 . 
       FIG. 9B  shows the following sheets wp 1  to wp 3  abutting on the reference surface  57 . The second sheet bundle BP 2  (composed of sheets P 4  to P 6 ) is mounted on the sheet tray  54 . Before this bundle is so mounted, the upper delivery roller  48   a  is moved from the lower delivery roller  48   b  to the position indicated by solid lines, allowing the seventh sheet wp 1  of the third bundle to move above the first accumulating tray  24 . The state shown in  FIG. 9B  is substantially identical to the state shown in  FIG. 6B . The operation is repeated until a prescribed number of sheet bundles are formed. Only the last sheet bundle is delivered onto the first accumulating tray  24 , completing the operation. This state is described in  FIG. 16  as “Set the offset distance for the following sheets, completing the conveyance and the switch back on the sheet tray  54 ” (S 80 ). 
     [Delivering of a Bundle, along with a Relatively Thick Bundle (Large Number of Sheets)] 
     It will be explained how a sheet bundle is delivered together with a relatively thick sheet bundle (i.e., bundle composed of many sheets), with reference to  FIG. 10A  to FIG.  13 B and  FIG. 16 .  FIGS. 10A and 10B  are diagrams explaining the process following the process of  FIGS. 5A and 5B , i.e., mounting a relatively thick sheet bundle on the sheet tray and keeping the following sheets (i.e., three sheets) waiting. As has been explained with reference to  FIGS. 5A and 5B , the sheet conveyed by the feed-in rollers  34  is further conveyed onto the sheet tray  54  by the conveyance rollers  44 . The sheet is then switched back by the delivery rollers  48 . Further, the sheet is conveyed by the gathering roller  56  and the belt  146  having a projection, abutting on the reference surface  57 . Then, the sheets are mounted, in designated number, on the sheet tray  54 . Prior to these operations, as in the case where a relatively thin sheet bundle is mounted, the step S 10  of “setting the offset of the following sheets” and “setting the switch back position on the following-sheet tray” is started as shown in  FIG. 16 . 
       FIG. 10A  shows 65 sheets P 1  to P 65  mounted on the sheet tray  54 . That is, as specified in  FIG. 16 , “the sheet bundle has been mounted on the sheet tray  54 ” (S 20 ). The side-binding unit  62  starts side-binding the sheet bundle. As explained with reference to  FIG. 4 , the bundle thickness sensor  230  described with reference to  FIG. 4  detects the thickness of the sheet bundle, acquiring the bundle-thickness data BPt showing the bundle is relatively thin (S 30 ).  FIG. 10A  also shows the conveyance of the following sheet wp 1  (i.e., 66 th  sheet) is started. The sheets of the bundle BP 1  are completely aligned on the sheet tray  54 , and the side-binding unit  62  moves to the binding position to side-bind the sheet bundle. 
       FIG. 10B  shows how the sheet sensor  42 S detects the rear end of the first following sheet wp 1  of the second bundle BP 2  and how the first following sheet wp 1  is then switched back. At this point, the switching gate  37  configured to guide the sheet wp 1  into the conveyance path  42  or the branch path  70  has been moved to the position indicated by solid lines and can guide the sheet wp 1  into the branch path  70 . 
       FIGS. 11A and 11B  are diagrams explaining the process following the process of  FIGS. 10A and 10B . As shown in  FIG. 11A , the side-binding unit  62  starts side binding on the sheet bundle BP 1  composed of 65 sheets mounted on the sheet tray  54 . Since the 66 th  sheet wp 1  cannot be conveyed into the sheet tray  54 , the conveyance rollers  44  keeps switching back the sheet bundle. Then, the branch rollers  72  located in the branch path  70  convey the sheet bundle downstream the branch path  70 . When the branch rollers  72  nip the following sheet P 3 , the switching gate  37  is moved up, opening the conveyance path  42 . 
     While the following 66 th  sheet wp 1  is being conveyed in the branch path  70 , its rear end is detected by the sheet sensor  42 S. Then, a counter (not shown) detects the distance the rear end of the sheet wp 1  has moved. When it is found that the sheet wp 1  has moved by distance wp 12 , the branch rollers  72  are stopped rotating and wait for the 67 th  sheet wp 2  coming. 
     If the sheet bundle on the sheet tray  54  as shown in  FIG. 7B  is thin, the branch rollers  72  are stopped when the sheet bundle is positioned at distance wp 11  from the sheet sensor  42 S. If the sheet bundle is thick, the branch rollers  72  are stopped when the sheet bundle is positioned at a longer distance wp 12  from the sheet sensor  42 S. In practice, the distance wp 11  is about 1 to 2 mm, and the distance wp 12  is longer than the distance wp 11  by about 4 to 6 mm. Why the distance wp 12  is longer will be explained later with reference to  FIG. 14 . Note that the distance wp 11  is set in accordance with the distance the upper delivery roller  48   a  moves after the delivery rollers  48  deliver the sheet bundle from the sheet tray  54 . 
     As shown in  FIG. 11B , the sheet bundle BP  1  is bound on the sheet tray. Meanwhile, the 67 th  sheet wp 2  is conveyed by the feed-in rollers  34  toward the conveyance rollers  44 . If the 67 th  sheet, i.e., following sheet wp 2 , is detected by the sheet sensor  42 S, it is conveyed toward the conveyance rollers  44 , set off from the following sheet wp 1  (i.e., 66 th  sheet P 66  waiting in the branch path  70 ) by the above-mentioned distance wp 12 . 
     In  FIG. 16 , the setting of this offset distance is described as “Set the sheets off by distance wp 1 , and make them wait (that is, making them wait in the branch path  70  (wait path))” (S 60 ). If the sheet bundle is thick, distance wp 12  longer than the distance wp 11  is set. Also in the case where two or more following sheets exist, they are set off by the distance wp 12 . The conveyance speed of the waiting sheets is set to 650 mm/sec. At this point, the sheet bundle BP 1  (composed of sheets P 1  to P 65 ) is completely side-bound on the sheet tray  54 . 
     As seen from  FIG. 11B , the distance wp 12  between the following 66 th  sheet wp 1  (P 66 ) waiting in the branch path  70  and the following 67 th  sheet wp 2  (P 67 ) conveyed from the feed-in rollers has such a value that when a sheet is switched back to the sheet tray  54 , the following sheet is bent in the form of inverted V. This is important for enhancing the alignment, as in the case shown in  FIGS. 7A and 7B . 
       FIGS. 12A and 12B  are diagrams explaining the process following the process of  FIGS. 11A and 11B .  FIG. 12A  shows how two following sheets wp 1  and wp 2  (P 66  and P 67 ), respectively, wait in the branch path and how the following sheet wp 3  (P 68 ) is fed in. As shown in  FIG. 11B , the following 67 th  sheet wp 2  (P 67 ) and the following 66 th  sheet wp 1  (P 66 ) waiting in the branch path  70  are conveyed to the conveyance rollers  44 , with the front end of the following sheet wp 2  first forwarded. The conveyance rollers  44  nip these two sheets (i.e., sheets P 66  and P 67 ) at the same time and covey them forward. When the sheet sensor  42 S detects the rear end of the sheet P 67 , the conveyance rollers  44  are rotated counterclockwise again. 
     At this point, the switching gate  37  at the branch position  36  closes the feed-in path  32 , guiding the two following sheets wp 1  and wp 2  (P 66  and P 67 ), to the branch path  70 . Eventually, the sheet sensor  42 S detects the rear end of the following 67 th  sheet wp 2  (P 67 ). When the sheet wp 2  is conveyed to the branch path  70 , set off by distance wp 12 , the branch rollers  72  are stopped, the sheet following 68 th  sheet wp 3  (P 68 ) is conveyed in, and the front end of the sheet wp 3  will be detected by the sheet sensor  42 S.  FIG. 12A  illustrates this state. In this state, the following sheets wp 1  to wp 3  are set off, one from the next, by offset distance wp 12 . The offset distance wp 12  is longer than the offset distance wp 11  set in the case where a relatively thin sheet bundle is mounted. 
       FIG. 12B  shows how the delivery rollers  48  nip and deliver the sheets wp 1  to wp 3  together with the sheet bundle BP 1  while making the sheets wp 1  to wp 3  set off from one another by distance wp 12  and the sheet wp 1  set off by distance Bp 1  from the front end of the sheet bundle BP 1  mounted on the sheet tray  54 . That is, the sheet bundle BP  1  is pushed on the reference surface  57  toward the outlet port of the sheet tray  54 , and the delivery rollers  48  are then lowered, nipping the sheets wp 1  to wp 3 . The sheets wp 1  to wp 3  are so nipped in order to set off the front end of the uppermost following sheet wp 3  from the front end of the sheet bundle BP 1  by distance Bp 1 . The sheet bundle BP  1  set off by this distance Bp 1  is delivered by the delivery rollers  48  to the first accumulating tray  24 . 
     Since the three following sheets wp 1  to wp 3  have the same length, the uppermost sheet wp 3 , intermediate sheet wp 2  and lowermost sheet wp 1  extend toward the first accumulating tray  24 , one from another by distance wp 12 , in the order they are mentioned. In other words, when they are switched back on the sheet tray  54 , the uppermost sheet wp 3  and the intermediate sheet wp 2  are remotest and second remotest from the reference surface  57 , respectively, and the lowermost sheet wp 1  is nearest to the reference surface  57 . This state is described in  FIG. 16  as “Deliver the sheet bundle and the following sheets at the same time from the sheet tray  54  (after the alignment, side binding, and punching) (S 70 )”. 
       FIG. 13A  and  FIG. 13B  following the process of  FIGS. 12A and 12B  show how the sheet bundle BP 1  (P 1  to P 65 ) is delivered from the sheet tray and how three following sheets wp 1  to wp 3  left on the sheet tray  54  are switched back. As shown in  FIG. 13B , the sheet bundle BP 1  mounted on the sheet tray  54  and the following sheets wp 1  to wp 3  conveyed by the conveyance rollers  44  are simultaneously nipped and delivered by the delivery rollers  48 . The sheet bundle BP 1  remains on the first accumulating tray  24 . The following sheets wp 1  to wp 3  overlapping and set off from one another by distance Bp 1  remain on the sheet tray  54 . 
     The following sheets wp 1  to wp 3  are set off one from another by distance Bp 1  and are bent in the form of inverted V (see the enlarged part of  FIG. 13A , encircled by an ellipse). In this state, the support arm shaft  167  located upstream the delivery roller  48   a  is rotated. Then, the delivery roller  48   a  rotates by a large angle after the sheet bundle BP 1  is delivered, because the sheet bundle BP 1  composed of  65  sheets is relatively thick. As a result, the following sheets wp 1  to wp 3  are set off by distance wp 12  at rear end, greatly toward the reference surface  57 , and remain on the sheet tray  54 . The delivery rollers  48  are then rotated in the direction reverse to the sheet-delivering direction. The following sheets wp 1  to wp 3  are therefore switched back toward the reference surface  57 . 
     The switch back position is so set that the sheet bundle BP 1  may be delivered before the rear end of the following sheet wp 1  (nearest to the reference surface  57 ) moves from the sheet sensor  42 S by distance SB 12  and the following sheets wp 1  to wp 3  may be switched back. The following sheets wp 1  to wp 3  move toward the reference surface  57  as the sheet bundle BP 1  is delivered. From the distance the following sheets wp 1  to wp 3  so move, too, the switch back position (SB 1 ) of the following sheets wp 1  to wp 3  is determined. That is, if the sheet bundle BP 1  is thin as described in  FIG. 9 , the switch back position (SB 1 ) is the position to which the sheet bundle BP 1  moves from the sheet sensor  42 S by distance SB 11 . If the sheet bundle BP 1  is thick as in the case of  FIG. 13 , the switch back position (SB 1 ) is the position to which the sheet bundle BP 1  moves from the sheet sensor  42 S by distance SB 12  longer than distance SB 11 . 
     This state is described in  FIG. 16  as “Switch back the following sheets at the switch back position (SB 1 ) (and convey the following sheets, so switched back, by the gathering roller  56  to the reference surface)”. As shown in  FIG. 9B , the front ends of the following sheets wp 1  to wp 3  sequentially abut on, and are aligned, on the reference surface  57 . 
       FIG. 13B  shows the following sheets wp 1  to wp 3  abutting on the reference surface  57 . The second sheet bundle BP 2  (sheets P 66  to P 68 ) is mounted on the sheet tray  54 . In this case, the upper delivery roller  48   a  moves to the position (indicated by solid lines) from the lower delivery roller  48   b , allowing the 69 th  to 130 th  sheets to move onto the sheet tray  54 .  FIG. 13B  also shows how the sheets assume the state shown in  FIGS. 10A and 10B . The operation is repeated until the sheets are convey onto the sheet tray  54  in a designated number (in this case,  130 , and 65 sheets on the sheet tray  54 ). Thereafter, the operation shown in  FIG. 10A  to  FIG. 13B  is performed. Finally, the last sheet bundle is delivered onto the first accumulating tray  24 . This state is described in  FIG. 16  as “Set the offset distance for the following sheets and finish conveying the sheets, and then switch back the following sheets onto the sheet tray  54 ”. 
     In the process of  FIG. 8A  to  FIG. 9B , the offset distance is wp 11  for the following sheets wp 1  to wp 3  and the switch back position is at distance SB 11  from the sheet sensor  42 S if the sheet bundle is relatively thin. If the sheet bundle is relatively thick, the offset distance is wp 12  for the following sheets wp 1  to wp 3 , and the switch back position is at distance SB 12  from the sheet sensor  42 S. Here, offset distance wp 11 &lt;offset distance wp 12 , and distance SB 11 &lt;distance SB 12 . Namely, the offset distance and the switch back position at the sheet tray  54  are changed in accordance with the thickness of the sheet bundle mounted on the sheet tray  54  that is nipped together with the following sheets. This point will be confirmed with reference to  FIGS. 114A, 14B and 14C . 
       FIG. 14A  shows a relatively thick sheet bundle BP (i.e., thick sheet bundle Bpt) nipped together with the following sheets wp 1  to wp 3  by the upper delivery roller  48   a  and lower delivery roller  48   b  immediately before it is delivered from the sheet tray  54 . To deliver the sheet bundle BP from the sheet tray  54 , the upper delivery roller  48   a  is rotated around by the support arm shaft  167  located above it (namely, upstream the outlet port of the sheet tray  54 ), and cooperates with the lower delivery roller  48   b , nipping the sheet bundle BP for switch back. 
     As may be seen from  FIG. 14A , the upper delivery roller  48   a  moves down from the upper position Hp spaced above the lower position Lp by the sum of the thickness Bpt of the sheet bundle BP and the total thickness of the following sheets wp 1  to wp 3 , to the lower position Lp where the upper delivery roller  48   a  and lower delivery roller  48   b  nip only the following sheets wp 1  to wp 3 . Since the upper delivery roller  48   a  moves down in an arc locus, it contacts the following sheet wp 1  at a point in the reference surface  57  of the sheet tray  54 . Consequently, unless the offset distance wp 1  for the following sheets wp 1  to wp 3  is long enough, the following sheets wp 1  to wp 3  may abut on the reference surface  57  in a wrong order, and may not be aligned as desired on the reference surface  57 . In view of this, the offset distance wp 1  for the following sheets wp 1  to wp 3  is changed in accordance with the thickness of the sheet bundle BP 1  mounted on the sheet tray  54 . 
       FIG. 14B  and  FIG. 14C  show the relation between the thickness Bpt of the sheet bundle BP and the offset distance wp 1  of the following sheets wp 1  to wp 3 . More precisely,  FIG. 14B  shows that the offset distance wp 1  of the following sheets wp 1  to wp 3  is gradually increased in proportion to the thickness Bpt of the sheet bundle BP, and  FIG. 14C  shows that the offset distance wp 1  is increased stepwise in proportion to the thickness Bpt of the sheet bundle BP. If the offset distance wp 1  is increased in proportion to the thickness Bpt, the following sheets wp 1  to wp 3  can be easily and neatly aligned on the sheet tray  54 . 
       FIG. 15  shows the following sheets wp 1  to wp 3  and the switch back position, all moved from the sheet sensor  42 S for the distance SB 12  while the sheet tray  54  is holding a relatively thick sheet bundle. In practice, however, any following sheet never waits as shown in  FIG. 15  when the sheet bundle BP is delivered. If a relatively thick sheet bundle is held on the sheet tray  54 , the following sheets wp 1  and wp 2  having front ends set off by the distance wp 12  wait in the branch path  70  as a wait path, and the following sheet wp 3  is conveyed to the branch path  70  from the feed-in path  32  and is set off from the following sheet wp 2  by offset distance wp 12  at the position detected by the sheet sensor  42 S. 
     The position where any sheet is switched back onto the sheet tray  54  is set at the distance SB 12  from the sheet sensor  42 S toward the delivery rollers  48 . The following sheets wp 1  to wp 3  contacting the upper delivery roller  48   a  to be delivered together with the sheet bundle BP are set off by the offset distance wp 12 . The offset distance wp 12  is longer than the offset distance wp 11  by which the following sheets wp 1  to wp 3  to be nipped together with a relatively thin sheet bundle BP are set off. Further, the switch back position is remote from the sheet sensor  42 S. At the switch back position, the following sheets may be switched back more slowly than the case where the sheet bundle is thin. 
     [Control System] 
     The image forming apparatus A incorporates a control system. The control system will be described with reference to  FIG. 17  that is a block diagram. The image forming apparatus shown in  FIG. 1  comprises an image-forming control section  200  and a sheet-processing control section  204  (i.e., control CPU) for controlling the sheet processing apparatus B. The image-forming control section  200  has a sheet-supplying control unit  202  and an input unit  203 . The image-forming control section  200  has a control panel  18 . The control panel  18  of the input unit  203  may be operated to set a “print mode” and a “sheet processing mode”. 
     The sheet-processing control section  204  is a control CPU designed to make the sheet processing apparatus B process sheets in the sheet processing mode designated. The sheet-processing control section  204  comprises a ROM  206  storing an operation program and a RAM  207  storing control data. The sheet-processing control section  204  receives signals from a sensor-input unit  208 . The sensor-input unit  208  receives signals from various sensors such as a feed-in sensor  30 S configured to detect any sheet existing in the feed-in path  32 , a sheet sensor  42 S configured to detect any sheet existing the conveyance path  42 , a branch sensor  70 S configured to detect any sheet in the branch path  70 , a sheet-surface sensor  24 S configured to detect the surface of any sheet on the first accumulating tray  24 , a sheet vacancy sensor  25  and a bundle thickness sensor  230  configured to detect the thickness of the sheet bundle mounted on the sheet tray  54 . 
     The sheet-processing control section  204  comprises a sheet conveyance control unit  210 . The sheet conveyance control unit  210  controls a feed-in roller motor  34 M provided in the feed-in path  32 , the conveyance roller motor  44 M arranged at the conveyance path  42 , the delivery roller motor  48 M arranged at the outlet port of the sheet tray  54 , and the arm motor  160 M used to move up and down the upper delivery roller  48   a . The sheet-processing control section  204  further comprises a punch drive control unit  211  and a sheet tray (process tray) control unit  212 . The punch drive control unit  211  controls a punch motor  31 M in the punching unit  31  to make holes in a sheet. The sheet tray control unit  212  controls the aligning plates  58  to align the sheets on the sheet tray  54 . The sheet-processing control section  204  comprises a side-binding control unit  213  and a first accumulating-tray lift control unit  214 , too. The side-binding control unit  213  controls the side-binding motor  62 M of the side-binding unit  62  that binds the sides of a sheet bundle on the sheet tray  54 . The first accumulating-tray lift control unit  214  controls motor  24 M that can move up and down the first accumulating tray  24  in accordance with the number of sheets mounted on the first accumulating tray  24 . 
     The sheet-processing control section  204  has a stacker control unit  216  and a saddle-binding control unit  217 . The stacker control unit  216  controls the alignment plates  81  and the stopper  85  to align the sheets and stop the front end of each sheet, respectively, on the stacker  84  (i.e., second tray). The saddle-binding control unit  217  controls the saddle binder  82  that binds the sheets at the part middle in the conveyance direction. 
     The sheet-processing control section  204  further has a folding unit and a saddle-folding/delivering control unit  218 . The folding unit folds the saddle-bound sheet bundle double and then delvers the sheet bundle to the second accumulating tray  26 . The saddle-folding/delivering control unit  218  controls the folding roller, folding blade and a delivery motor  92 M that drive the bundle delivering rollers  98 . How these control units are connected to the various sheet sensors and various drive motors and how the sheets are conveyed and delivered have been explained above in conjunction with the function of each control unit. 
     [Sheet Processing Modes] 
     The sheet-processing control section  204  so configured as described above controls the sheet processing apparatus B, causing the same to operate in, for example, “printout mode,” “side binding mode (first process),” “sorting mode (jog mode)” and “saddle binding mode.” The setting of any of these processing modes is carried out by a mode setting means  201  by way of the input unit  203  of the control panel  18 . The sheet processing modes will be described blow. 
     (1) Printout Mode 
     In this mode, the sheet processing apparatus B receives a sheet having an image formed on it, and the conveyance rollers  44  and delivery rollers  48  deliver the sheet onto the first accumulating tray  24 . 
     (2) Side Binding Mode 
     In this mode, sheets conveyed from the outlet port  3 , each having an image formed on it, are received on the sheet tray  54 , aligned and bundled. The resultant bundle is side-bound at the side-binding unit  62  and mounted on the first accumulating tray  24 . During the side binding, “wait conveyance” is performed, switching back the following sheets and making the following sheets wait for some time in the branch path  70 , so that the delivery of the following sheets coming out of the outlet port  3  are not stopped. Further, the offset distance wp 1  is set for the following sheets, and the switch back position SB 1  is shifted from the sheet sensor  42 S. 
     (3) Sorting Mode (Jog Mode) 
     In this mode, the sheet tray  54  receives the sheets, each having an image formed on it, from the outlet port  3  of the image forming apparatus. The sheets are held on the first accumulating tray  24  and aligned at the front or rear end by the aligning plates  58 , but are not bound together. 
     (4) Side Binding Mode 
     The stacker  84  receives the sheets each having an image formed on it, from the outlet port  3  of the image forming apparatus. In the stacker  84 , the sheets are aligned to form a bundle. The saddle binder  82  binds the sheets at the part substantially middle in the conveyance direction and then folds the sheets, forming a booklet. The sheets so bound are placed on the second accumulating tray  26 . In the saddle binding, the sheets delivered from the outlet port  3  of the image forming apparatus are temporarily held on the first accumulating tray  24 , then switched back into the branch path  70  and conveyed to the stacker  84 , performing “second-tray conveyance”. 
     As described above, the embodiment can provide an apparatus in which the offset of the following sheets can be changed in accordance with the thickness of the sheet bundle held on the sheet tray  54 , to prevent sheet-alignment failure on the sheet tray  54 . 
     Other embodiments of the invention will be described hereinafter. The second embodiment will be described with reference to  FIG. 18  and  FIGS. 19A and 19B . The third embodiment will be described with reference to  FIG. 20  and  FIGS. 21A and 21B . The components of the second and third embodiments, which are similar to those of the embodiment described above, are designated by the same reference numbers. 
     [Second Embodiment] 
       FIG. 18  shows a sheet processing apparatus B according to the second embodiment. This apparatus B has a sheet conveyance path of the type shown in  FIG. 22 . The apparatus B differs from the sheet processing apparatus B of the first embodiment shown in  FIGS. 1 to 17  in one respect. Namely, in the apparatus B of the first embodiment, the wait path for holding the following sheets has the branch path  70  and branch rollers  72  for guiding sheets to the stacker  84  holding sheets subject to saddle-binding, whereas in the apparatus B of the second embodiment, the conveyance path  42  extending from the feed-in rollers  34  to the sheet tray  54  is comparatively long and used as wait path. In the middle part of the conveyance path  42 , a wait roller  170  is provided to keep waiting the sheet switched back by the conveyance rollers  44 . 
     The wait roller  170  is supported by a wait roller arm  172 . The wait roller arm  172  is pivotally secured to the shaft  174  of the wait roller  170 . Immediately after the feed-in rollers  34 , a sheet holder  176  is provided to hold the end of a following sheet, preventing the following sheet from being moved by the next following sheet switched back and waiting. The feed-in rollers  34  can rotate at a solenoid SoL around a lower feed-in roller shaft  180 . Right below the feed-in rollers  34 , a sheet stopper  178  is positioned, functioning as a control member on which the first following sheet switched back may abut at the end. 
     To make two following sheets wait in the conveyance path  42 , the first following sheet wp 1  is held at the end near the feed-in rollers  34  and the second following sheet wp 2  is positioned below the wait roller  170 . Since the sheet holder  176  holds the following sheet at position (wpn), the offset distance wp 1  can be set. The sheet tray  54  can be positioned and the switch back position above the sheet tray  54  can be changed in accordance with distance SB (SBarea) from the sheet sensor  42 S as in the first embodiment. 
     [Setting of the Offset Distance between the Following Sheets in the Second Embodiment] 
     How the thickness of the sheet bundle BP on the sheet tray  54  and the distance between the following sheets are changed in the sheet processing apparatus B according to the second embodiment will be explained with reference to  FIG. 19A  and  FIG. 19B .  FIG. 19A  shows how a sheet bundle relatively thin and mounted on the sheet tray  54  and following sheets wp 1  and wp 2  are delivered at the same time by the delivery rollers  48 . In this case, the sheet bundle BP is relatively thin, and the upper delivery roller  48   a  moves down for a short distance after delivering the sheet bundle BP, scarcely influencing the distance the following sheets wp 1  and wp 2  are set off from each other. Therefore, the following sheets wp 1  and wp 2  are set off from each other by distance wp 11 , and the switch back position is spaced from the sheet sensor  42 S by distance SB 11 . 
       FIG. 19B  shows how a sheet bundle relatively thick and mounted on the sheet tray  54  and following sheets wp 1  and wp 2  are delivered at the same time by the delivery rollers  48 . In this case, the sheet bundle BP is relatively thick, and the upper delivery roller  48   a  moves down for a long distance after delivering the sheet bundle BP, inevitably influencing the distance the following sheets wp 1  and wp 2  are set off from each other. Therefore, if the following sheets wp 1  and wp 2  are set off by distance wp 11  and the switch back position is moved by distance SB 11  from the sheet sensor  42 S, the following sheets move upstream the delivery rollers  48  as the upper delivery roller  48   a  is rotated counterclockwise. As a result, the following sheets are no longer set off on the sheet tray  54  or the following sheet wp 2  protrudes above the reference surface  57 , and the following sheets wp 1  and wp 2  therefore cannot be aligned at all or can be aligned but insufficiently. 
     In view of this, an offset distance wp 12  longer than the distance wp 11  is set for the following sheets wp 1  and wp 2  and the conveyance distance determining the switch back position is SB 12  that is longer than the distance SB 11 . In other words, when the sheet bundle on the sheet tray  54  is thick, the switch back position between the conveyance rollers  44  and the delivery rollers  48  is set closer to the delivery rollers  48  than in the case where the sheet bundle is thin. The displacement of the following sheets wp 1  and wp 2  and the influence of the sheet conveyance at the switch back position are thus predicted. Therefore, the sheet processing apparatus B can align sheets well even if the upper delivery roller  48   a  is rotated greatly after the roller  48   a  has delivered the sheet bundle BP. 
     [Third Embodiment] 
       FIG. 20  shows the configuration of a sheet processing apparatus B according to the third embodiment of this invention. This apparatus B differs from the first embodiment shown in  FIG. 1  to  FIG. 17  and the second embodiment shown in  FIG. 18  and  FIGS. 19A and 19B . In the first and second embodiments, the support arm shaft  167  is located upstream the upper delivery roller  48   a , which nips and delivers, jointly with the lower delivery roller  48   b , the sheet bundle on the sheet tray  54  together with the following sheet and delivers the sheet bundle onto the first accumulating tray  24  and the following sheet to the sheet tray  54 . In the third embodiment, the support shaft  194  of the upper delivery roller  48   a  is located downstream the delivery rollers  48 . In other words, the fulcrum of the upper delivery roller  48   a  is positioned below the first accumulating tray  24  in the third embodiment, whereas the fulcrum is positioned above the sheet tray  54  in the first and second embodiments. 
     As shown in  FIG. 20 , a fulcrum  196  is provided above the support shaft  194  of the upper delivery roller  48   a . Around the fulcrum  196 , an upper cover  190  can be rotated upward in the direction of the arrow to open the apparatus B. Once the upper cover  190  is so opened, the conveyance path  42  and the feed-in path  32  can be accessed. Hence, jammed sheets can be removed and the devices provided in the apparatus B can be maintained and inspected. 
     Also In the sheet processing apparatus B, i.e. the third embodiment, following sheets cannot be conveyed onto the sheet tray  54  while the sheet bundle BP is being bound on the sheet tray  54 . Therefore, the following sheets wait in the branch path  70  as a wait path and are then nipped and delivered by the delivery rollers  48 , together with the sheet bundle after completion of, e.g., binding process. Therefore, the following sheets wp 1  to wp 3  are set off by the offset distance wp 1  from one another and by the distance BP 1  from the sheet bundle BP mounted on the sheet tray  54  as in the first and second embodiments. Since the upper delivery roller  48   a  is rotated in the direction opposite to the direction it is rotated in the first and second embodiments, the delivery rollers  48  switch back and convey the following sheets wp 1  to wp 3  to the sheet tray  54  in the direction opposite to the direction they are switched back and conveyed in the first and second embodiments. This will be explained with reference to  FIGS. 21A and 21B . 
     [Setting the Offset Distance Between the Following Sheets in the Third Embodiment] 
     It will be explained how the distance between the following sheets is changed in accordance with the thickness of the sheet bundle BP mounted on the sheet tray  54  in the sheet processing apparatus B according to the third embodiment, in which the fulcrum of the upper delivery roller  48   a  is located downstream the delivery rollers  48 . As shown in  FIG. 21A , the delivery rollers  48  start delivering a relatively thin sheet bundle from the sheet tray  54 , together with the following sheets wp 1  and wp 2 . Since the sheet bundle on the sheet tray  54  is relatively thin and the upper delivery roller  48   a  lowers by a short distance after the sheet bundle BP is delivered from the upper delivery roller  48   a . Hence, the upper delivery roller  48   a  does not influence the distance the following sheets wp 1  and wp 2  are moved. Therefore, the offset distance wp 12  is set for the following sheets wp 1  and wp 2  as indicated in an enlarged part of  FIG. 21A , encircled by an ellipse, and the switch back position is set at distance SBL 2  from the sheet sensor  42 S. 
     As shown in  FIG. 21B , a relatively thick sheet bundle may be mounted on the sheet tray  54 , and the delivery rollers  48  may start delivering the relatively thick sheet bundle from the sheet tray  54 , together with the following sheets wp 1  and wp 2 . Since the sheet bundle is relatively thick, the distance the upper delivery roller  48   a  lowers after delivering the sheet bundle BP is long, influencing the distance the following sheets wp 1  and wp 2  move. Hence, if offset distance wp 12  is set for the following sheets sw 1  and sw 2  as shown in  FIG. 21A  and the switch back position is moved by distance SBL 2  from the sheet sensor  42 S, the following sheets will move downstream the delivery rollers  48  due to the rotation of the upper delivery roller  48   a  in the clockwise direction. Consequently, the following sheets wp 1  and wp 2  will no longer be set off from one another on the sheet tray  54 , or the following sheet wp 2  will not be aligned or not aligned enough. 
     In view of the above, the following sheets wp 1  and wp 2  are set off from each other by distance wp 11  shorter than distance wp 12 . (Note, wp 11 &lt;wp 12 , and the distance SB 11  the switch back position is moved from the sheet sensor  42 S is shorter than distance SB 12 .) In other words, the following sheets are positioned between the conveyance rollers  44  and the delivery rollers  48 , closer to the conveyance rollers  44 , if the sheet bundle BP on the sheet tray  54  is thick. The displacement of the following sheets wp 1  and wp 2  and the influence of the sheet conveyance at the switch back position are thus predicted. Therefore, the sheet processing apparatus B can align sheets well even if the upper delivery roller  48   a  is rotated greatly after the roller  48   a  has delivered the sheet bundle BP. 
     As has been described, in the first and third embodiments, the following sheets wp 1  to wp 3  can be aligned well when they are switched back to the sheet tray  54 , because the delivery rollers  48  changes the distances among the sheets wp 1  to wp 3  in accordance the thickness of the sheet bundle laid on the sheet tray  54 . When the following sheets wp 1  to wp 3  are switched back onto the sheet tray  54 , they are aligned well, never insufficiently aligned or laid in disorder on the sheet tray  54 . 
     The present invention is not limited to the embodiments described above. Accordingly, various modifications may be made without departing from the spirit or scope of this invention. The technical points contained in the idea described in the following claims pertain to the present invention. The embodiments described above are preferred examples. Based on the technical disclosure of the specification, any person with ordinary skill in the art may make various alternatives, modifications, changes or improvements, which are in the technical scope of the claims attached hereto. 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2016-206436 filed Oct. 21, 2016, Japanese Patent Application No. 2016-206437 filed on the same day, and Japanese Patent Application No. 2016-206438 filed on the same day, the entire contents of which are incorporated herein by reference.