Patent Publication Number: US-2023134202-A1

Title: Door opening and closing device

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is based on and claims priority under 35 U.S.C. § 119 to Japanese Patent Application No. 2021-176528, filed on Oct. 28, 2021, the entire content of which is incorporated herein by reference. 
     TECHNICAL FIELD 
     This disclosure generally relates to a door opening and closing device. 
     BACKGROUND DISCUSSION 
     Conventionally, there is known a vehicle that includes a vehicle body including a door opening at a rear portion and that includes a back door opening and closing the door opening. In such a vehicle, the vehicle body includes a hinge that couples, to each other, a portion on an upper side of the door opening and an upper end portion of the back door. The back door rotates around an axis of the hinge, and thereby moves between a fully closing position of fully closing the door opening and a fully opening position of fully opening the door opening. 
     EP1764248A (Reference 1) discloses a vehicle in which a hinge rotatably supporting a back door is movable in a front-rear direction along a roof of a vehicle body. In this vehicle, accompanying an opening movement of the back door, the hinge is moved to a front side while the back door is rotated. In this manner, in the vehicle, a rearward overhang at a time of opening and closing movements of the back door is reduced. 
     In a back door as described above, there has been room for improvement in terms of further reducing an overhang at a time of opening and closing movements. 
     A need thus exists for a door opening and closing device which is not susceptible to the drawback mentioned above. 
     SUMMARY 
     A door opening and closing device that solves the above-described problem is applied to a vehicle that includes a vehicle body and a door. The vehicle body includes a door opening. The door opens and closes the door opening. A part in the door corresponding to an upper end portion of the door opening when the door is at a fully closing position of fully closing the door opening is defined as a proximal end portion of the door. The door opening and closing device includes a slider and a main link mechanism. The slider moves along a roof of the vehicle body in a direction intersecting with a width direction of the door, in a state of supporting the proximal end portion of the door in such a way as to be rotatable around an axis extending in the width direction. The main link mechanism includes one end rotatably coupled to the vehicle body and an opposite end rotatably coupled to the door. The main link mechanism adjusts a posture of the door, depending on a door opening degree by changing a distance between coupling points that is a distance between the coupling point to the vehicle body and the coupling point to the door. The main link mechanism decreases the distance between the coupling points as the door opening degree becomes larger. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and additional features and characteristics of this disclosure will become more apparent from the following detailed description considered with the reference to the accompanying drawings, wherein: 
         FIG.  1    is a perspective view of a vehicle rear portion; 
         FIG.  2    is an elevational view of the vehicle rear portion; 
         FIG.  3    is a perspective view of a drive mechanism of a door opening and closing device; 
         FIG.  4    is an exploded perspective view of a positioning mechanism of the door opening and closing device; 
         FIG.  5    is an exploded perspective view of a sub-link mechanism of the positioning mechanism; 
         FIG.  6    is a sectional view of the sub-link mechanism; 
         FIG.  7    is a sectional view of the sub-link mechanism; 
         FIG.  8    is a side view of the vehicle rear portion when a back door is at a fully closing position; 
         FIG.  9    is an enlarged view of the positioning mechanism illustrated in  FIG.  8   ; 
         FIG.  10    is a side view of the vehicle rear portion when the back door is at an intermediate position; 
         FIG.  11    is an enlarged view of the positioning mechanism illustrated in  FIG.  10   ; 
         FIG.  12    is a side view of the vehicle rear portion when the back door is at a fully opening position; 
         FIG.  13    is an enlarged view of the positioning mechanism illustrated in  FIG.  12   ; 
         FIG.  14    is a sectional view of the sub-link mechanism when the back door is at the fully closing position; 
         FIG.  15    is a sectional view of the sub-link mechanism when the back door is positioned at the intermediate position; 
         FIG.  16    is a sectional view of the sub-link mechanism when the back door is at the fully opening position; and 
         FIG.  17    is a side view of a vehicle rear portion in a modified example. 
     
    
    
     DETAILED DESCRIPTION 
     The following describes one embodiment of a vehicle that includes a door opening and closing device. 
     &lt;Vehicle  10 &gt; 
     As illustrated in  FIG.  1    and  FIG.  2   , a vehicle  10  includes a vehicle body  20 , a back door  40 , and a door opening and closing device  60 . As illustrated in  FIG.  1   , the vehicle  10  is what is called an SUV type vehicle. In another embodiment, as long as the vehicle  10  includes the back door  40 , the vehicle  10  may be a minivan type vehicle, a sedan type vehicle, or any other type of vehicle. 
     &lt;Vehicle Body  20 &gt; 
     As illustrated in  FIG.  1    and  FIG.  2   , the vehicle body  20  includes a roof  21  that forms a ceiling portion of the vehicle body  20 , two rear pillars  22  that extend from the roof  21 , and a door opening  23  that is open rearward. Although illustrations of configurations on one side are omitted in  FIG.  1    and  FIG.  2   , the vehicle body  20  includes two brackets  30  fixed to the two respective rear pillars  22 . 
     The roof  21  includes two accommodation recess portions  24  whose depth directions are each downward, and two cover panels  25  that cover the two accommodation recess portions  24 . The accommodation recess portions  24  are located at a rear end portion of the roof  21  and at both width-direction end portions of the roof  21 . When viewed from an upper side, the accommodation recess portion  24  has a rectangular shape whose longitudinal direction is a front-rear direction and whose lateral direction is the width direction. 
     The rear pillars  22  are parts of a frame constituting the vehicle body  20 . The two rear pillars  22  extend in an up-down direction while being spaced apart from each other in the width direction. The two rear pillars  22  are connected to both width-direction end portions of the roof  21 , at positions near a rear end of the roof  21 . The rear pillars  22  may be formed integrally with quarter panels. 
     When the vehicle body  20  is viewed from a rear side, the door opening  23  has a shape close to a rectangle whose longitudinal direction is the width direction and whose lateral direction is the up-down direction. Specifically, in the door opening  23 , a width-direction length of a lower edge is longer than a width-direction length of an upper edge. In other words, the door opening  23  has a trapezoidal shape when the vehicle body  20  is viewed from a rear side. The door opening  23  is located between the two rear pillars  22  in the width direction. 
     The bracket  30  is a part coupled to the door opening and closing device  60 . The bracket  30  is described later together with the door opening and closing device  60 . 
     &lt;Back Door  40 &gt; 
     As illustrated in  FIG.  1    and  FIG.  2   , the back door  40  is moved between a fully closing position of fully closing the door opening  23  and a fully opening position of fully opening the door opening  23 . A door opening degree becomes minimum when the back door  40  is at the fully closing position, and becomes maximum when the back door  40  is at the fully opening position. In the following description, a part of the back door  40  corresponding to an upper end portion of the door opening  23  when the back door  40  is at the fully closing position is referred to as a proximal end portion of the back door  40 , and a part of the back door  40  corresponding to a lower end portion of the door opening  23  when the back door  40  is at the fully closing position is referred to as a distal end portion of the back door  40 . When the back door  40  is at the fully closing position, the proximal end portion of the back door  40  is an upper end portion, and the distal end portion of the back door  40  is a lower end portion. 
     The back door  40  includes a door body  41  covering the door opening  23 . Although illustrations of configurations on one side are omitted in  FIG.  1    and  FIG.  2   , the back door  40  includes two coupling arms  42  that extend from the door body  41 , and two stays  50  that are fixed to the door body  41 . The door body  41  has a shape corresponding to the door opening  23 . The two coupling arms  42  extend from the proximal end portion of the door body  41 , in a state of being spaced apart from each other in the width direction. The stay  50  is a part coupled to the door opening and closing device  60 . The stay  50  is described later together with the door opening and closing device  60 . In this embodiment, the width direction of the vehicle  10  is also a width direction of the back door  40 . 
     &lt;Door Opening and Closing Device  60 &gt; 
     Although illustrations of configurations on one side are omitted in  FIG.  1    and  FIG.  2   , the door opening and closing device  60  includes two drive mechanisms  100  that drive the back door  40 , and two positioning mechanisms  200  that position the back door  40 , depending on a door opening degree. The two drive mechanisms  100  are accommodated in the accommodation recess portions  24  of the roof  21 , in a state of being spaced apart from each other in the width direction. The two positioning mechanisms  200  are each arranged between the rear pillar  22  and the back door  40 , in a state where the positioning mechanisms  200  are spaced apart from each other in the width direction. The two drive mechanisms  100  are configured in such a way as to be symmetrical to each other in the width direction, and the two positioning mechanisms  200  configured in such a way as to be symmetrical to each other in the width direction. For this reason, the following describes the drive mechanism  100  and the positioning mechanism  200  on a left side in the vehicle  10 . 
     &lt;Drive Mechanism  100 &gt; 
     As illustrated in  FIG.  3   , the drive mechanism  100  includes an actuator  110 , a linear motion mechanism  120 , a slider  130 , and a guide rail  140 . 
     As illustrated in  FIG.  3   , the actuator  110  includes an electric motor  111 , a reduction mechanism  112  that reduces a rotational speed of an output shaft of the electric motor  111 , and a support portion  113  that supports the electric motor  111 . The actuator  110  is installed in the accommodation recess portion  24  of the roof  21 . The linear motion mechanism  120  is what is called a feed screw mechanism. The linear motion mechanism  120  includes a screw shaft  121  that rotates based on power transmitted from the actuator  110 , a nut  122  that is screwed onto the screw shaft  121 , and two support portions  123  that rotatably support the screw shaft  121 . The screw shaft  121  extends in the front-rear direction. The two support portions  123  support respective both longitudinal-direction end portions of the screw shaft  121 . The nut  122  is coupled to the slider  130 , and thereby, a degree of rotational freedom of the nut  122  around an axis of the screw shaft  121  is restricted. Accordingly, the nut  122  moves in an axial direction of the screw shaft  121 , accompanying rotation of the screw shaft  121 . A direction in which the nut  122  moves varies depending on a rotational direction of the screw shaft  121 . The actuator  110  corresponds to one example of “a slider actuator”. 
     The slider  130  includes a support plate  131  that rotatably supports the back door  40 , and two main rollers  132  and a sub-roller  133  that are rotatably supported by the support plate  131 . The support plate  131  is joined to the coupling arm  42  of the back door  40  by a pin whose axial direction is the width direction. In this regard, it can be said that the back door  40  is supported by the slider  130  in such a way as to be rotatable around an axis extending in the width direction. Each axial direction of the two main rollers  132  is the width direction, and an axial direction of the sub-roller  133  is the up-down direction. The sub-roller  133  is located between the two main rollers  132  in the front-rear direction. The support plate  131  is coupled to the nut  122  in the width direction. Accordingly, when the nut  122  moves in the axial direction of the screw shaft  121 , the slider  130  moves together with the nut  122 . 
     The guide rail  140  has a long-rod shape. The guide rail  140  is fixed to the accommodation recess portion  24  of the roof  21  in such a way as to be along the screw shaft  121 . In this regard, the guide rail  140  extends along roof  21 . Herein, the matter that the guide rail  140  extends along the roof  21  does not mean only that the guide rail  140  extends parallel to the roof  21 . The guide rail  140  may linearly extend in the front-rear direction, or may extend in the front-rear direction while curving along the roof  21 . The guide rail  140  includes a bottom wall  141 , an upper wall  142  that faces the bottom wall  141  in the up-down direction, and a side wall  143  that connects the bottom wall  141  and the upper wall  142  to each other in the up-down direction. The guide rail  140  accommodates the two main rollers  132  and the sub-roller  133  of the slider  130 . When the slider  130  moves in the axial direction of the screw shaft  121  together with the nut  122 , the two main rollers  132  rotate in a state of contacting with the bottom wall  141  or the upper wall  142  of the guide rail  140 . Meanwhile, the sub-roller  133  rotates in a state of contacting with the side wall  143  of the guide rail  140 . 
     In this manner, in the drive mechanism  100 , the slider  130  can move in the longitudinal direction of the guide rail  140 , in a state of rotatably supporting the proximal end portion of the back door  40 . In other words, the slider  130  can move along the roof  21  in a direction intersecting with the width direction. The matter that the slider  130  moves along the roof  21  does not mean only a movement parallel to the roof  21 , as mentioned above in the description of the guide rail  140 . 
     &lt;Positioning Mechanism  200 &gt; 
     As illustrated in  FIG.  4    and  FIG.  5   , the positioning mechanism  200  includes a main link mechanism  210  that adjusts a posture of the back door  40 , depending on a door opening degree, and a sub-link mechanism  250  that transmits a door opening degree to the main link mechanism  210 . 
     &lt;Main Link Mechanism  210 &gt; 
     As illustrated in  FIG.  4    and  FIG.  5   , the main link mechanism  210  includes a first link  220  that is crank-shaped, and a second link  230  that is rod-shaped. In the following description, in a longitudinal direction of the main link mechanism  210 , an end portion coupled to the vehicle body  20  is also referred to as a proximal end portion, and an end portion coupled to the back door  40  is also referred to as a distal end portion. 
     The first link  220  includes a link body  221  that has a plate shape, a driven shaft  222  that extends in a plate thickness direction from the link body  221 , and a driven gear  223  that rotates integrally with the driven shaft  222 . The driven shaft  222  extends from one end portion of the link body  221 . The second link  230  includes, at one end portion thereof, a first socket  231  that is a ball socket. The second link  230  is longer than first link  220 . An end portion that is included in the second link  230  and at which the first socket  231  is not provided and an end portion that is included in the first link  220  and at which the driven shaft  222  is not provided are coupled to each other in such a way as to be rotatable relative to each other. 
     &lt;Sub-link Mechanism  250 &gt; 
     As illustrated in  FIG.  4    and  FIG.  5   , the sub-link mechanism  250  includes a fixed link  260 , a movable link  270  that moves relative to the fixed link  260 , and a coil spring  280  that biases the movable link  270 . In the following description, in the sub-link mechanism  250 , a longitudinal-direction end portion coupled to the vehicle body  20  is referred to also as a proximal end portion, and a longitudinal-direction end portion coupled to the back door  40  is referred to also as a distal end portion. 
     As illustrated in  FIG.  5   , the fixed link  260  includes an outer tube  261  that has a tubular shape, a bottom wall  262  that closes an opening on a proximal end side in the outer tube  261 , and a shaft body  263  that extends from the bottom wall  262  along the outer tube  261 . The fixed link  260  includes a fixed plate  264  that is fixed to a distal end of the shaft body  263 , a fixing screw  265  that fixes the fixed plate  264  to the distal end of the shaft body  263 , and a transmission portion  266  that is a part engaging with the main link mechanism  210 . 
     The outer tube  261  includes, at a distal end portion thereof, two guide grooves  261 S extending in an axial direction of the outer tube  261 . The two guide grooves  261 S face each other in a radial direction of the outer tube  261 . An outer diameter of the shaft body  263  is smaller than an inner diameter of the outer tube  261 , and a length of the shaft body  263  is shorter than a length of the outer tube  261 . The shaft body  263  is accommodated inside the outer tube  261 , in a state where a gap is provided between the shaft body  263  and the outer tube  261 . The fixed plate  264  has a rectangular-plate shape. The fixed plate  264  is fixed to the distal end of the shaft body  263  in such a way that a plate thickness direction thereof is an axial direction of the shaft body  263 . The transmission portion  266  is integrated with the bottom wall  262 . The transmission portion  266  includes a cylindrical drive shaft  267  and a drive gear  268  that rotates integrally with the drive shaft  267 . In this embodiment, a rotational axis of the drive gear  268  and an axis of the outer tube  261  are in a relation of a skew position. 
     As illustrated in  FIG.  5   , the movable link  270  includes an inner tube  271  that has a tubular shape, two guide pins  275  that are fixed to the inner tube  271 , and an extension part  276  that is fixed to one end portion of the inner tube  271 . 
     The inner tube  271  includes a perimeter wall  272  whose cross section perpendicular to an axial direction thereof is elliptical, and two partition walls  273  and  274  that cover both end portions of the perimeter wall  272 . The partition walls  273  and  274  each include a penetration hole that is rectangular when viewed in an axial direction of the inner tube  271 . As illustrated in  FIG.  4    and  FIG.  5   , the inner tube  271  is accommodated in the fixed link  260 , and the inner tube  271  accommodates the fixed plate  264 . Accordingly, as illustrated in  FIG.  6   , when the inner tube  271  moves in a direction of projecting out from the fixed link  260 , the partition wall  273  of the inner tube  271  is caught by the fixed plate  264 . In this manner, the movable link  270  is prevented from falling off from the fixed link  260 . 
     As illustrated in  FIG.  5    and  FIG.  6   , the two guide pins  275  are provided at positions facing each other in a radial direction of the inner tube  271 . As illustrated in  FIG.  4    and  FIG.  6   , in a state where the inner tube  271  is accommodated in the fixed link  260 , the two guide pins  275  are accommodated in the two respective guide grooves  261 S of the outer tube  261 . The two guide pins  275  engage with the two respective guide grooves  261 S, and thereby, the movable link  270  is allowed to move in the axial direction relative to the fixed link  260 , and is restricted from rotating around the axis relative to the fixed link  260 . 
     In a sectional view illustrated in  FIG.  6   , there is substantially no gap between the shaft body  263  of the fixed link  260  and the partition wall  273  of the movable link  270 . There is substantially no gap also between the fixed plate  264  of the fixed link  260  and the inner tube  271  of the movable link  270 . Further, there is substantially no gap also between the outer tube  261  of the fixed link  260  and the inner tube  271  of the movable link  270 . Accordingly, the movable link  270  cannot swing relative to the fixed link  260 , around an axis perpendicular to the paper surface of  FIG.  6   .  FIG.  6    is the sectional view perpendicular to a rotational axis of the drive shaft  267  of the fixed link  260 . 
     Meanwhile, in a sectional view illustrated in  FIG.  7   , the partition wall  273  does not exist between the shaft body  263  of the fixed link  260  and the inner tube  271  of the movable link  270 . In other words, a gap exists between the shaft body  263  of the fixed link  260  and a proximal end portion end of the inner tube  271  of the movable link  270 . A gap exists also between the fixed plate  264  of the fixed link  260  and the inner tube  271  of the movable link  270 . Further, a gap exists also between the outer tube  261  of the fixed link  260  and the inner tube  271  of the movable link  270 . Accordingly, as indicated by the white arrows, the movable link  270  can swing relative to the fixed link  260  around an axis perpendicular to the paper surface of  FIG.  7   , specifically around the axis of the guide pin  275 . However, a range in which the movable link  270  can swing is limited.  FIG.  7    is the sectional view perpendicular to the axis of the guide pin  275 . 
     As illustrated in  FIG.  4    and  FIG.  5   , the extension portion  276  includes a fixed flange  277  that is fixed to the partition wall  274  of the inner tube  271 , and a coupling shaft  278  that extends from the fixed flange  277 . The fixed flange  277  extends, in a flange shape, from a proximal end portion of the coupling shaft  278 . The fixed flange  277  includes a second socket  279  at a distal end portion thereof. Similarly to the first socket  231 , the second socket  279  is a ball socket constituting a ball joint. 
     As illustrated in  FIG.  6    and  FIG.  7   , the coil spring  280  is arranged between the outer tube  261  and the shaft body  263  of the fixed link  260 , in a state of being compressed between the bottom wall  262  of the fixed link  260  and the partition wall  273  of the movable link  270 . The coil spring  280  always biases the movable link  270 , regardless of a position of the movable link  270 . 
     As described above, in the sub-link mechanism  250 , the fixed link  260  supports the movable link  270  in such a way as to be able to expand and contract in an axial direction of the fixed link  260 . The fixed link  260  supports the movable link  270  in such a way as to be able to swing around the axis extending in a direction perpendicular to the axial direction of fixed link  260 . In this regard, it can be said that the sub-link mechanism  250  can expand and contract, and also bend. 
     &lt;Bracket  30 &gt; 
     As illustrated in  FIG.  4   , the bracket  30  includes a first bracket  31  that is fixed to the vehicle body  20 , and a second bracket  32  that is fixed to the first bracket  31 . The first bracket  31  and the second bracket  32  sandwich, between themselves, the driven gear  223  of the main link mechanism  210  and the drive gear  268  of the sub-link mechanism  250 , and thereby, rotatably support the proximal end portion of the main link mechanism  210  and the proximal end portion of the sub-link mechanism  250 . In other words, the bracket  30  rotatably supports the driven shaft  222  of the main link mechanism  210  and the drive shaft  267  of the sub-link mechanism  250 . In this case, the rotational axes of the driven shaft  222  and the drive shaft  267  are directed in the same direction, and the driven gear  223  of the main link mechanism  210  and the drive gear  268  of the sub-link mechanism  250  mesh with each other. Accordingly, when the drive gear  268  rotates, the driven gear  223  rotates. In this embodiment, a change gear ratio between the drive gear  268  and the driven gear  223  is “2”. For example, the driven gear  223  rotates by “20 degrees” while the drive gear  268  rotates by “10 degrees”. 
     As illustrated in  FIG.  1    and  FIG.  2   , a fixed position of the bracket  30  is closer to an upper end of the door opening  23  than to a lower end of the door opening  23  in the un-down direction. The bracket  30  is fixed to the rear pillar  22  in such a way that the rotational axes of the driven shaft  222  and the drive shaft  267  are directed in the width direction. Accordingly, the axes around which the main link mechanism  210  and the sub-link mechanism  250  rotate relative to the vehicle body  20  extend in the width direction. 
     &lt;Stay  50 &gt; 
     As illustrated in  FIG.  4   , the stay  50  includes a base plate  51  that has a flat-plate shape, and a first protrusion portion  52  and a second protrusion portion  53  that protrude from the base plate  51 . The first protrusion portion  52  includes a first ball  54  at a distal end thereof, and the second protrusion portion  53  includes a second ball  55  at a distal end thereof. The first ball  54  and the second ball  55  are each spherical. The first ball  54  is accommodated in the first socket  231  of the second link  230 , and the second ball  55  is accommodated in the second socket  279  of the movable link  270 . In this manner, the first socket  231  and the first ball  54  constitute a ball joint, and the second socket  279  and the second ball  55  constitute a ball joint. Thus, the stay  50  supports the distal end portion of the main link mechanism  210  and the distal end portion of the sub-link mechanism  250  in such a way as to be rotatable in any direction. 
     As illustrated in  FIG.  1    and  FIG.  2   , the stay  50  is fixed to a side portion of the back door  40 , at a position between the proximal end portion and the distal end portion of the back door  40 . In this case, the first ball  54  is located closer to the distal end portion of the back door  40  than the second ball  55  is. 
     As illustrated in  FIG.  4   , in the following description, a distance between a coupling point at which the main link mechanism  210  and the vehicle body  20  are coupled to each other and a coupling point at which the main link mechanism  210  and the back door  40  are coupled to each other is referred to as “a distance Lm between the coupling points of the main link mechanism  210 ”. Specifically, a distance Lm between the coupling points of the main link mechanism  210  is a distance between the coupling point at which the first link  220  of the main link mechanism  210  and the bracket  30  of the vehicle body  20  are coupled to each other and a coupling point at which the second link  230  of the main link mechanism  210  and the stay  50  of the back door  40  are coupled to each other. Herein, the coupling point between the first link  220  and the bracket  30  corresponds to an axis of the driven shaft  222  of the first link  22 , and the coupling point between the second link  230  and the stay  50  corresponds to a center of the first socket  231  of the second link  230 . 
     A distance between a coupling point at which the sub-link mechanism  250  and the vehicle body  20  are coupled to each other and a coupling point at which the sub-link mechanism  250  and the back door  40  are coupled to each other is referred to as “a distance Ls between the coupling points of the sub-link mechanism  250 ”. Specifically, a distance Ls between the coupling points of the sub-link mechanism  250  is a distance between the coupling point at which the fixed link  260  of the sub-link mechanism  250  and the bracket  30  of the vehicle body  20  are coupled to each other and the coupling point at which the movable link  270  of the sub-link mechanism  250  and the stay  50  of the back door  40  are coupled to each other. Herein, the coupling point between the fixed link  260  and the bracket  30  corresponds to the axis of the drive shaft  267  of the fixed link  260 , and the coupling point between the movable link  270  and the stay  50  corresponds to a center of the second socket  279  of the movable link  270 . 
     As illustrated in  FIG.  2   , the coupling point between the main link mechanism  210  and the vehicle body  20  and the coupling point between the main link mechanism  210  and the back door  40  are offset from each other in the width direction. Specifically, the coupling point between the main link mechanism  210  and the vehicle body  20  is located closer to a center of the vehicle  10  than the coupling point between the main link mechanism  210  and the back door  40  is. Similarly, the coupling point between the sub-link mechanism  250  and the vehicle body  20  and the coupling point between the sub-link mechanism  250  and the back door  40  are offset from each other in the width direction. Specifically, the coupling point between the sub-link mechanism  250  and the vehicle body  20  is located closer to the center of the vehicle  10  than the coupling point between the sub-link mechanism  250  and the back door  40  is. In this regard, in this embodiment, the longitudinal direction of the main link mechanism  210  and a longitudinal direction of the sub-link mechanism  250  are inclined from the up-down direction, and are non-perpendicular to the width direction. 
     &lt;Effect of This Embodiment&gt; 
     With reference to  FIG.  8    to  FIG.  14   , the following describes a manner when the back door  40  is opened from the fully closing position to the fully opening position. 
       FIG.  8    is a diagram illustrating a rear portion of the vehicle  10  when the back door  40  is at the fully closing position, and  FIG.  9    is a diagram of the positioning mechanism  200  extracted from  FIG.  8   . As illustrated in  FIG.  8   , the slider  130  of the drive mechanism  100  is at a position that corresponds to the full closing and that is near a rear end of the guide rail  140 . Accordingly, the back door  40  is at the fully closing position. 
     As illustrated in  FIG.  9   , when the back door  40  is at the fully closing position, the sub-link mechanism  250  has rotated most in a first rotational direction Rs 1 . Accordingly, the drive gear  268  of the sub-link mechanism  250  has rotated most in the first rotational direction Rs 1 , and the driven gear  223  of the main link mechanism  210  has rotated most in a second rotational direction Rm 2 . At this time, the main link mechanism  210  extends substantially linearly. In other words, in the main link mechanism  210 , a longitudinal direction of the first link  220  and a longitudinal direction of the second link  230  are directed in substantially the same direction. At this time, in the main link mechanism  210 , a coupling point between the first link  220  and the second link  230  is at a position between the coupling point at which the first link  220  and the vehicle body  20  are coupled to each other and the coupling point at which the second link  230  and the back door  40  are coupled to each other. As a result, a distance Lm between the coupling points of the main link mechanism  210  has become the longest. 
     As illustrated in  FIG.  10   , when the slider  130  moves to a front side along the guide rail  140  from the position corresponding to the full closing, the proximal end portion of the back door  40  is pulled to a front side. At this time, the back door  40  rotates around a rotational axis passing through the proximal end portion thereof in the width direction, while moving to a front side. In this manner, the movement of the slider  130  to a front side causes the back door  40  to be opened. 
     As illustrated in  FIG.  11   , when the back door  40  is opened from the fully closing position, the sub-link mechanism  250  rotates around the drive shaft  267  in the second rotational direction Rs 2 , accompanying the opening movement of the back door  40 . In other words, the drive gear  268  of the sub-link mechanism  250  rotates in the second rotational direction Rs 2 . In this case, the driven gear  223  included in the main link mechanism  210  and meshing with the drive gear  268  rotates in a first rotational directional Rm 1 , and thus, the first link  220  rotates around the axis of the driven shaft  222  in the first rotational direction Rm 1 . 
     When the first link  220  rotates in the first rotational direction Rm 1 , the coupling point between the first link  220  and the second link  230  moves to a front side of the driven shaft  222  while drawing an arc. As a result, the stay  50  of the back door  40  moves not only to an upper side but also to a front side, as indicated by the solid arrow in  FIG.  11   . Thus, when the back door  40  is opened from the fully closing position, a rearward overhang of the back door  40  becomes less. 
     In the following description, a position of the slider  130  illustrated in  FIG.  10    is referred to as a position corresponding to an intermediacy, and a position of the back door  40  illustrated in  FIG.  10    is referred to as an intermediate position. The intermediate position is a position between the fully closing position and the fully opening position. As illustrated in  FIG.  10    and  FIG.  11   , when the back door  40  is at the intermediate position, the main link mechanism  210  extends linearly. In other words, in the main link mechanism  210 , the longitudinal direction of the first link  220  and the longitudinal direction of the second link  230  are directed in the same direction. At this time, differently from the case illustrated in  FIG.  9   , the coupling point between the first link  220  and the vehicle body  20  is at a position between the coupling point where the first link  220  and the second link  230  are coupled to each other and the coupling point between the second link  230  and the back door  40  are coupled to each other. As a result, a distance Lm between the coupling points of the main link mechanism  210  becomes the shortest. Thus, when the back door  40  moves between the fully closing position and the intermediate position, a distance Lm between the coupling points of the main link mechanism  210  becomes shorter as a door opening degree becomes larger. As a door opening degree becomes larger, a distance Lm between the coupling points of the main link mechanism  210  becomes shorter, and thereby, the stay  50  moves to a front side more than the case where a distance Lm between the coupling points does not become shorter. 
     A door opening degree corresponding to the intermediate position can be set arbitrarily. For example, in the case where a door opening degree when the back door  40  is at the fully closing position is “0%”, and a door opening degree when the back door  40  is at the fully opening position is “100%”, a door opening degree when the back door  40  is at the intermediate position may be “50%”. Alternatively, a door opening degree when the back door  40  is at the intermediate position may be larger than “50%” or smaller than “50%”. 
     As illustrated in  FIG.  12   , when the slider  130  moves along the guide rail  140  to a front side from the position corresponding to the intermediacy, the proximal end portion of the back door  40  is further pulled to a front side. At this time, the back door  40  rotates around the rotational axis passing through the proximal end portion thereof in the width direction, while moving to a front side. In this manner, the movement of the slider  130  to a front side causes the back door  40  to be opened. 
     As illustrated in  FIG.  13   , when the back door  40  is opened from the intermediate position, the sub-link mechanism  250  rotates around the drive shaft  267  in the second rotational direction Rs 2 , accompanying the opening movement of the back door  40 . In other words, the drive gear  268  of the sub-link mechanism  250  rotates in the second rotational direction Rs 2 . In this case, the driven gear  223  included in the main link mechanism  210  and meshing with the drive gear  268  rotates in the first rotational direction Rm 1 , and thus, the first link  220  rotates around the axis of the driven shaft  222  in the first rotational direction Rm 1 . 
     When the first link  220  rotates in the first rotational direction Rm 1 , the coupling point between the first link  220  and the second link  230  moves to an upper side of the driven shaft  222  while drawing an arc. As a result, the stay  50  of the back door  40  moves not only to a front side but also to an upper side, as indicated by the solid arrow in  FIG.  13   . Thus, when the back door  40  is opened from the fully closing position, the back door  40  easily moves upward. 
     In the following description, a position of the slider  130  illustrated in  FIG.  12    is referred to as a position corresponding to the full opening. As illustrated in  FIG.  12    and  FIG.  13   , when the back door  40  is at the fully opening position, an angle made between the longitudinal direction of the first link  220  and the longitudinal direction of the second link  230  in the main link mechanism  210  is approximately 90 degrees. As a result, a distance Lm between the coupling points of the main link mechanism  210  is shorter than that when the back door  40  is at the fully closing position, and is longer than that when the back door  40  is at the intermediate position. In this manner, when the back door  40  moves between the intermediate position and the fully opening position, a distance Lm between the coupling points of the main link mechanism  210  becomes longer as a door opening degree becomes larger. A distance Lm between the coupling points of the main link mechanism  210  becomes longer as a door opening degree becomes larger, and thereby, the stay  50  moves upward more than the case where a distance Lm between the coupling points does not become longer. 
     As illustrated in  FIG.  2   , the coupling point between the sub-link mechanism  250  and the vehicle body  20  and the coupling point between the sub-link mechanism  250  and the back door  40  are offset from each other in the width direction. The coupling point between the sub-link mechanism  250  and the vehicle body  20  and the coupling point between the sub-link mechanism  250  and the back door  40  are each immovable in the width direction. Accordingly, when the back door  40  is opened and closed, a distance Ls between the coupling points of the link mechanism  250  changes without a change in width-direction interval between the coupling point at which the sub-link mechanism  250  and the vehicle body  20  are coupled to each other and the coupling point at which the sub-link mechanism  250  and the back door  40  are coupled to each other. 
     Herein, when the sub-link mechanism  250  can be tilted relative to the up-down direction at the time of the opening and closing movements of the back door  40 , mere expansion and contraction of the sub-link mechanism  250  can deal with a change in a distance Ls between the coupling points of the sub-link mechanism  250 . However, the proximal end portion of the sub-link mechanism  250  is allowed to only rotate around the axis extending in the width direction, and thus, the sub-link mechanism  250  cannot be tilted relative to the up-down direction. In view of it, at the time of the opening and closing movements of the back door  40 , the sub-link mechanism  250  allows the movable link  270  to expand and contract and swing relative to the fixed link  260 , and thereby deals with a change in a distance Ls between the coupling points of the sub-link mechanism  250 . The following describes the details. 
     As illustrated in  FIG.  8    and  FIG.  9   , when the back door  40  is at the fully closing position, a distance Ls between the coupling points of the sub-link mechanism  250  is longer. At this time, as illustrated in  FIG.  14   , in the sub-link mechanism  250 , the movable link  270  is not tilted from the fixed link  260 . In other words, the axis of the fixed link  260  and the axis of the movable link  270  are on the same straight line. 
     As illustrated in  FIG.  10    and  FIG.  11   , when the back door  40  is opened from the fully closing position to the intermediate position, a distance Ls between the coupling points of the sub-link mechanism  250  gradually decreases. In other words, as illustrated in  FIG.  14    and  FIG.  15   , the fixed link  260  moves in the direction of compressing the coil spring  280 . Further, when the back door  40  is opened from the fully closing position to the intermediate position, the movable link  270  is tilted from the fixed link  260 . Specifically, the axis of the movable link  270  is tilted from the axis of the fixed link  260 . In this manner, the sub-link mechanism  250  can contract while maintaining the width direction interval between the coupling point thereof to the vehicle body  20  and the coupling point thereof to the back door  40 . 
     As illustrated in  FIG.  12    and  FIG.  13   , when the back door  40  is opened from the intermediate position to the fully opening position, a distance Ls between the coupling points of the sub-link mechanism  250  gradually increases. In other words, as illustrated in  FIG.  15    and  FIG.  16   , the movable link  270  moves in the direction of projecting out from the fixed link  260 . Further, when the back door  40  is opened from the intermediate position to the fully opening position, a tilt of the movable link  270  from the fixed link  260  gradually decreases to zero. In this manner, the sub-link mechanism  250  can expand while maintaining the width-direction interval between the coupling point thereof to the vehicle body  20  and the coupling point thereof to the back door  40 . 
     As illustrated in  FIG.  9    and  FIG.  13   , when the back door  40  is at the fully opening position, a distance Ls between the coupling points of the sub-link mechanism  250  is longer, similarly to the case where the back door  40  is at the fully closing position. Accordingly, as illustrated in  FIG.  14    and  FIG.  16   , when the back door  40  is at the fully opening position, no tilt of the movable link  270  from the fixed link  260  occurs similarly to the case where the back door  40  is at the fully closing position. 
     The movements of a plurality of the constituent components of the door opening and closing device  60  are described in turn in the above description of the effects of this embodiment in order to facilitate understanding of the description, but to be precise, a plurality of the constituent components of the door opening and closing device  60  simultaneously move while cooperating with one another. In other words, in this embodiment, the vehicle body  20 , the back door  40 , the slider  130  of the drive mechanism  100 , the first link  220  and second link  230  of the main link mechanism  210 , and the fixed link  260  and movable link  270  of the sub-link mechanism  250  constitute a mechanism whose degree of freedom is “1”. 
     &lt;Effects of this Embodiment&gt; 
     (1) The slider  130  is movable in the front-rear direction, in a state of supporting the proximal end portion of the back door  40  in such a way as to be rotatable around the axis extending in the width direction. Thus, when a contact point between the back door  40  and the vehicle body  20  is only the slider  130 , a posture of the back door  40  becomes unstable depending on a door opening degree. In this regard, the door opening and closing device  60  includes the main link mechanism  210  coupling the vehicle body  20  and the back door  40  to each other, and thus, a posture of the back door  40  is determined depending on a door opening degree. Further, when the back door  40  is opened from the fully closing position, a distance Lm between the coupling points of the main link mechanism  210  gradually decreases as a door opening degree becomes larger. Accordingly, by the main link mechanism  210 , a rearward movement of the back door  40  becomes less. As a result, the back door  40  less overhangs in a direction of being separated from the door opening  23 . Thus, the door opening and closing device  60  can suppress an overhang of the back door  40 . 
     (2) When a distance Lm between the coupling points of the main link mechanism  210  decreases as a door opening degree becomes larger, an opened amount of the door opening  23  in the up-down direction tends to be smaller when the back door  40  reaches the fully opening position. In this regard, when the back door  40  moves between the fully closing position and the intermediate position, the door opening and closing device  60  decreases a distance Lm between the coupling points of the main link mechanism  210  as a door opening degree becomes larger. Thus, it is possible to suppress a rearward overhang of the back door  40  when the back door  40  is opened and closed near the fully closing position. Further, when the back door  40  moves between the intermediate position and the fully opening position, the door opening and closing device  60  increases a distance Lm between the coupling points of the main link mechanism  210  as a door opening degree becomes larger. Thus, it is possible to increase an opened amount of the door opening  23  in the up-down direction when the back door  40  is at the fully opening position. As illustrated in  FIG.  10    and  FIG.  12   , an overhang of the back door  40  becomes a problem mainly when the back door  40  moves between the fully closing position and the vicinity of the intermediate position. 
     (3) The door opening and closing device  60  causes the first link  220  to rotate depending on a door opening degree, and thereby, can change a distance Lm between the coupling points of the main link mechanism  210 . In other words, the door opening and closing device  60  can adjust an overhang of the back door  40  by the rotation of the first link  220 . 
     (4) An amount of rotation of the sub-link mechanism  250  around the coupling point thereof to the vehicle body  20  changes depending on a door opening degree. The sub-link mechanism  250  rotates the first link  220 , based on the rotation around the coupling point thereof to the vehicle body  20 . In this manner, the door opening and closing device  60  can rotate the first link  220 , depending on a door opening degree. For example, the door opening and closing device  60  does not need to include an actuator that rotates the first link  220 , depending on a door opening degree, and in this regard, complication of the device can be suppressed. 
     (5) The main link mechanism  210  includes the driven gear  223  rotating around the rotational axis relative to the vehicle body  20 , and the sub-link mechanism  250  includes the drive gear  268  rotating around the rotational axis relative to the vehicle body  20 , in a state of meshing with the driven gear  223 . Thus, the door opening and closing device  60  can implement, by the two gears, power transmission between the main link mechanism  210  and the sub-link mechanism  250 . 
     (6) When the back door  40  is at the fully opening position, the coil spring  280  of the sub-link mechanism  250  biases the movable link  270  in the direction in which a distance Ls between the coupling points of the sub-link mechanism  250  expands. In other words, restoring force of the coil spring  280  acts in the direction of opening the back door  40 . Thus, the door opening and closing device  60  can hold the back door  40  at the fully opening position even when power of the actuator  110  is turned off. 
     (7) In the sub-link mechanism  250 , the movable link  270  can swing relative to the fixed link  260 . Thus, even when the coupling point between the sub-link mechanism  250  and the vehicle body  20  and the coupling point between the sub-link mechanism  250  and the back door  40  are offset from each other in the width direction, the door opening and closing device  60  can expand and contract the sub-link mechanism  250  without a load being applied to the sub-link mechanism  250 . 
     (8) In the door opening and closing device  60 , the actuator  110  is installed in the roof  21 . Thus, a space for installing the actuator  110  is more easily secured. 
     &lt;Modified Examples&gt; 
     This embodiment can be modified and implemented as in the following. This embodiment and the following modified examples can be implemented in combination with each other within a range where technical contradiction does not occur. 
     The drive mechanism  100  does not need to include the actuator  110  driving the back door  40 . In this case, the back door  40  is a door that is manually opened and closed by a user. 
     The actuator  110  of the door opening and closing device  60  may be an actuator that drives the movable component other than the slider  130 . For example, as illustrated in  FIG.  17   , the door opening and closing  60  may be a door opening and closing device  60 A that includes an actuator  301  or an actuator  302  instead of the actuator  110 . 
     The actuator  301  corresponds to “a main actuator”, and rotates the first link  220  of the main link mechanism  210  around the coupling point thereof to the vehicle body  20 . The actuator  301  preferably includes a motor and a transmission mechanism that transmits rotation of an output shaft of the motor to the driven gear  223  of the first link  220 . The actuator  302  corresponds to “a sub-actuator”, and rotates the fixed link  260  of the sub-link mechanism  250  around the coupling point thereof to vehicle body  20 . The actuator  302  preferably includes a motor and a transmission mechanism that transmits rotation of an output shaft of the motor to the drive gear  268  of fixed link  260 . 
     According to this modified example, the first link  220  or the fixed link  260  is driven by the actuator  301  or  302 , and thereby, the back door  40  can be opened and closed. According to this modified example, the actuator  301  or  302  can be installed near the driven gear  223  or the drive gear  268 , and in this regard, a space occupied by the actuator  110  is reduced in the roof  21 . This modified example can improve a degree of freedom in design by avoiding interference with other devices such as a sunroof device. The actuator  301  may directly drive the driven shaft  222 , and the actuator  302  may directly drive the drive shaft  267 . According to this, the above-described transmission mechanisms are unnecessary, and in this regard, the number of components of the door opening and closing device  60 A can be reduced. 
     In the door opening and closing device  60 , in the case of omitting the actuator  110 , the sub-link mechanism  250  may be an electric cylinder that can expand and contract. In this case, expanding and contracting the electric cylinder can cause the back door  40  to be opened and closed. In this modified example, the electric cylinder is a drive source for the back door  40 , and in this regard, a space occupied by the actuator  110  is reduced in the roof  21 . This modified example can improve a degree of freedom in design by avoiding interference with other devices such as a sunroof device. One example of such an electric cylinder is disclosed in JP2015-161157A. 
     The door opening and closing device  60  may include a plurality of actuators driving a plurality of the respective movable components of the door opening and closing device  60 . For example, the door opening and closing device  60  may include two or more actuators among the actuator  110  in the above-described embodiment and the actuators  301  and  302  and the electric cylinder in the modified examples. In this case, the door opening and closing device  60  preferably uses a plurality of the actuators. In this modified example, the back door  40  can be opened and closed by simultaneously driving a plurality of the actuators. Accordingly, in this modified example, output required for each of the actuators is reduced, and in this regard, it is possible to suppress an increase in size of each of the actuators and an increase in space occupied by each of the actuators. This modified example can improve a degree of freedom in design by avoiding interference with other devices such as a sunroof device. 
     In the drive mechanism  100 , the actuator  110  may further include a clutch that switches a state of power transmission between the output shaft of the electric motor  111  and the linear motion mechanism  120 . The actuator  110  preferably disengages the clutch when a user manually opens and closes the back door  40 . According to this, a user can open and close the back door  40 , with small operating force. 
     Instead of including the first link  220  and the second link  230 , the main link mechanism  210  may include a cam that is rotatably supported by the vehicle body  20 , and a driven link whose one end slides on a cam surface of the cam and whose opposite end is rotatably supported by the back door  40 . In this case, a distance Lm between the coupling points of the main link mechanism  210  can be changed by rotating the cam, depending on rotation of the sub-link mechanism  250 . 
     The positioning mechanism  200  does not need to include the sub-link mechanism  250 . In this case, instead of including the first link  220  and the second link  230 , the main link mechanism  210  preferably includes an electric cylinder that can expand and contract, a control device that controls the electric cylinder, depending on a door opening degree, and an opening degree sensor that detects a door opening degree. When the back door  40  moves between the fully closing position and the intermediate position, the control device causes the electric cylinder to be contracted as a door opening degree becomes larger. Meanwhile, when the back door  40  moves between the intermediate position and the fully opening position, the control device causes the electric cylinder to be expanded as a door opening degree becomes larger. 
     In the positioning mechanism  200 , the sub-link mechanism  250  does not need to include the coil spring  280 . In this case, the positioning mechanism  200  preferably includes a biasing member that biases the slider  130  to a front side, a biasing member that biases the driven gear  223  of the main link mechanism  210  in the second rotational direction Rm 2 , and the like. 
     The sub-link mechanism  250  may be an alternative mechanism that rotates the driven gear  223  of the main link mechanism  210 , depending on a door opening degree. 
     The alternative mechanism for the sub-link mechanism  250  may include a drum that is rotatably supported by the vehicle body  20 , a cable whose one end is wound on the drum and whose opposite end is connected to the back door  40 , and a spiral spring that biases the drum in a direction of winding the cable thereon. The drum preferably rotates the driven gear  223  of the main link mechanism  210 , depending on a rotational amount thereof, similarly to the above-described drive gear  268 . 
     The alternative mechanism for the sub-link mechanism  250  may be a mechanism that converts linear motion of the slider  130  in the front-rear direction into rotational motion of the driven gear  223  of the main link mechanism  210 . 
     The coupling point of the sub-link mechanism  250  to the vehicle body  20  and the coupling point of the sub-link mechanism  250  to the back door  40  do not need to be offset from each other in the width direction. In this case, the sub-link mechanism  250  does not need to be configured in such a way that the movable link  270  is swingable relative to the fixed link  260 . 
     The door opening  23  may be open in a side portion of the vehicle body  20 , or may be open in a front portion of the vehicle body  20 . The door opening and closing device  60  may be applied to a door that opens and closes such a door opening  23 . 
     The door opening  23  does not need to be an opening for loading and unloading luggage. The door opening  23  may be an opening for a user to get on and off the vehicle  10 . 
     When the vehicle body  20  includes a roof opening in the roof  21 , the vehicle  10  may include a sunroof device that opens and closes the roof opening. For example, the sunroof device includes rails that extend in the front-rear direction on both sides of the roof opening, a movable panel that opens and closes the roof opening, and a functional component that moves along the rails and thereby opens and closes the movable panel. In this case, the rails of the sunroof device are preferably integrated with the guide rails  140  of the door opening and closing device  60 . This modified example can reduce the number of components constituting the vehicle  10 , as compared to the case where the rails of the sunroof device are separated from the guide rails  140  of the door opening and closing device  60 . 
     The following describes a technical idea that can be understood from the above-described embodiment and modified examples. 
     The sub-link mechanism includes the fixed link that is rotatably coupled to the vehicle body, and the movable link that is rotatably coupled to the door and that is supported by the fixed link in such a way as to be able to expand and contract relative to the fixed link, and the fixed link swingably supports the movable link. 
     In the sub-link mechanism, the movable link can swing relative to the fixed link. Accordingly, even when the coupling point between the sub-link mechanism and the vehicle body and the coupling point between the sub-link mechanism and the back door are offset from each other in the width direction, the door opening and closing device can expand and contract the sub-link mechanism without a load being applied to the sub-link mechanism. 
     A door opening and closing device that solves the above-described problem is applied to a vehicle that includes a vehicle body and a door. The vehicle body includes a door opening. The door opens and closes the door opening. A part in the door corresponding to an upper end portion of the door opening when the door is at a fully closing position of fully closing the door opening is defined as a proximal end portion of the door. The door opening and closing device includes a slider and a main link mechanism. The slider moves along a roof of the vehicle body in a direction intersecting with a width direction of the door, in a state of supporting the proximal end portion of the door in such a way as to be rotatable around an axis extending in the width direction. The main link mechanism includes one end rotatably coupled to the vehicle body and an opposite end rotatably coupled to the door. The main link mechanism adjusts a posture of the door, depending on a door opening degree by changing a distance between coupling points that is a distance between the coupling point to the vehicle body and the coupling point to the door. The main link mechanism decreases the distance between the coupling points as the door opening degree becomes larger. 
     The slider is movable in the direction intersecting with the width direction, in a state of supporting the proximal end portion of the door in such a way as to be rotatable around the axis extending in the width direction. Thus, when a contact point between the door and the vehicle body is only the slider, a posture of the door becomes unstable depending on the door opening degree. In this regard, the door opening and closing device includes the main link mechanism that couples the vehicle body and the door to each other, and thus, a posture of the door is determined depending on the door opening degree. Further, when the door is opened from the fully closing position, the distance between the coupling points of the main link mechanism gradually decreases as the door opening degree becomes larger. Accordingly, by the main link mechanism, the door less overhangs in a direction of being separated from the door opening. Thus, the door opening and closing device can suppress an overhang amount of the door. 
     In the door opening and closing device, a position between the fully closing position and a fully opening position of fully opening the door opening may be defined as an intermediate position. When the door moves between the fully closing position and the intermediate position, the main link mechanism may decrease the distance between the coupling points as the door opening degree becomes larger. 
     In a case that the distance between the coupling points decreases as the door opening degree becomes larger, an opened amount of the door opening in an up-down direction tends to be smaller when the door reaches the fully opening position. In this regard, when the door moves between the fully closing position and the intermediate position, the door opening and closing device decreases the distance between the coupling points of the main link mechanism as the door opening degree becomes larger, and thereby, can suppress an overhang amount of the door. 
     In the door opening and closing device, when the door moves between the intermediate position and the fully opening position, the main link mechanism may increase the distance between the coupling points as the door opening degree becomes larger. 
     When the door moves between the intermediate position and the fully opening position, the door opening and closing device increases the distance between the coupling points of the main link mechanism as the door opening degree becomes larger, and thereby, can increase an opened amount of the door opening in the up-down direction. 
     In the door opening and closing device, the main link mechanism may include a first link that is rotatably coupled to the vehicle body, and a second link that is rotatably coupled to the door and is rotatably coupled to the first link. The first link may rotate around the coupling point to the vehicle body, thereby changing the distance between the coupling points of the main link mechanism. 
     The door opening and closing device causes the first link to rotate depending on the door opening degree, and thereby, can change the distance between the coupling points of the main link mechanism. In other words, the door opening and closing device can adjust an overhang amount of the door by rotation of the first link. 
     The door opening and closing device may include a sub-link mechanism that includes one end rotatably coupled to the vehicle body and an opposite end rotatably coupled to the door, and expands and contracts depending on the door opening degree. The sub-link mechanism may cause the first link to rotate around the coupling point to the vehicle body, depending on an amount of rotation around the coupling point to the vehicle body. 
     An amount of rotation of the sub-link mechanism around the coupling point to the vehicle body changes depending on the door opening degree. The sub-link mechanism causes the first link to rotate, based on rotation around the coupling point to the vehicle body. In this manner, the door opening and closing device can cause the first link to rotate, depending on the door opening degree. For example, the door opening and closing device does not need to include an actuator that causes the first link to rotate, depending on the door opening degree, and in this regard, complication of the device can be suppressed. 
     In the door opening and closing device, the main link mechanism may include a driven gear rotating around a rotational axis relative to the vehicle body. The sub-link mechanism may include a drive gear meshing with the driven gear and rotating around a rotational axis relative to the vehicle body. 
     The door opening and closing device can achieve, by the two gears, power transmission between the main link mechanism and the sub-link mechanism. 
     The door opening and closing device may include a sub-actuator that drives the sub-link mechanism. In the door opening and closing device, the sub-actuator may drive the sub-link mechanism to rotate around the coupling point between the sub-link mechanism and the vehicle body. 
     The door opening and closing device can open and close the door by driving the sub-link mechanism. The actuator can be easily installed near the sub-link mechanism, and in this regard, a space occupied by the actuator is reduced in the roof, as compared to a case where the actuator is installed in the roof. 
     The door opening and closing device may include a main actuator that drives the first link. In the door opening and closing device, the main actuator may drive the first link to rotate around the coupling point between the first link and the vehicle body. 
     The door opening and closing device can open and close the door by driving the first link. The actuator can be easily installed near the first link, and in this regard, a space occupied by the actuator can be reduced in the roof, as compared to a case where the actuator is installed in the roof. 
     The door opening and closing device may include a slider actuator that drives the slider in a direction intersecting with the width direction. The slider actuator may be installed in the roof. 
     The door opening and closing device can open and close the door by driving the slider. The slider actuator is installed in the roof, and in this regard, the door opening and closing device makes it easier to secure a space for installing the slider actuator. 
     In the door opening and closing device, the door opening may be open in a rear portion of the vehicle body. The door may be a back door. 
     The door opening and closing device can reduce a rearward overhang amount of the door when the back door is opened and closed. 
     The principles, preferred embodiment and mode of operation of the present invention have been described in the foregoing specification. However, the invention which is intended to be protected is not to be construed as limited to the particular embodiments disclosed. Further, the embodiments described herein are to be regarded as illustrative rather than restrictive. Variations and changes may be made by others, and equivalents employed, without departing from the spirit of the present invention. Accordingly, it is expressly intended that all such variations, changes and equivalents which fall within the spirit and scope of the present invention as defined in the claims, be embraced thereby.