Patent Publication Number: US-2019168893-A1

Title: Reaction wheel apparatus

Description:
TECHNICAL FIELD 
     The present invention relates to a reaction wheel apparatus. 
     BACKGROUND ART 
     Compact attitude control modules incorporating reaction wheels have been studied as attitude control modules for compact satellites and as compact modular robots. These modules are equipped with motors, inertia wheels, control circuits, and the like to generate the rotational torque necessary for the attitude control of satellites, robots, and the like. 
     These compact attitude control modules are required to further downsize, and therefore the present inventors have proposed a triaxial reaction wheel apparatus whose size is not larger than 10 cm 3  (refer to Patent Literature 1). 
     PRIOR ART LITERATURE 
     Patent Literature 
     Patent Literature 1: Japanese Patent Application No. 2015-130133 
     SUMMARY OF INVENTION 
     Problem to be Solved by Invention 
     Although the present inventors have realized the triaxial reaction wheel apparatus whose size is not larger than 10 cm 3  as mentioned above, further miniaturization of the compact attitude control modules is required. 
     In view of the above, the present invention intends to provide a further compact reaction wheel apparatus. 
     Means for Solving Problem 
     One aspect of the present invention provides a reaction wheel apparatus that is a reaction wheel apparatus including a reaction wheel provided in a polyhedral housing, in which respective faces constituting a polyhedron are constituted by frame parts corresponding to the respective faces constituting the polyhedron, and at least two of the frame parts are constituted by at least two rigid circuit board parts of a rigid flexible substrate. 
     The rigid flexible substrate may include a first rigid circuit board part. The first rigid circuit board part of the rigid flexible substrate may have a first through opening penetrating in the thickness direction of the first rigid circuit board part. The first through opening may have a nut accommodation part extending substantially parallel to a side edge of the first rigid circuit board part and a screw accommodation part that opens to the side edge of the first rigid circuit board part and extends orthogonally to the nut accommodation part. A nut may be accommodated in the nut accommodation part. At least one first frame part neighboring the first rigid circuit board part may have a through hole at a position aligned with the screw accommodation part of the first through opening of the first rigid circuit board part and the nut accommodated in the nut accommodation part. And, the at least one first rigid circuit board part and the first frame part may be connected by driving the screw inserted from the outside of the at least one first frame part into the nut through the through hole and the screw accommodation part. 
     A cutout part opening outward may be formed at a side edge of at least one rigid circuit board part of the rigid flexible substrate. A frame part connected to the side edge formed with the cutout part may be disposed so as to cover an opening edge of the cutout part, in such a way as to form an opening between the frame part connected to the side edge formed with the cutout part and the cutout part. And, a wiring from a component provided inside the housing may be connected to a terminal provided on an outer surface of the at least one rigid circuit board part, through the opening. 
     A stepped cutout part opening outward may be formed at least one side edge of the rigid flexible substrate where a flexible cable is connected, of at least one rigid circuit board part of the rigid flexible substrate, and the flexible cable may extend from a deeper part of the stepped cutout part. 
     A connection assist member to which an external device can be connected may be attached to at least one vertex part or side region of the polyhedron. 
     The reaction wheel may be provided so as to face the frame part. 
     The reaction wheel may be provided so as to face the frame part other than the frame part constituted by the rigid flexible substrate. 
     The reaction wheel may include a rotary body disposed so as to face the frame part, an electromagnet disposed between the frame part and the rotary body, and an urging member attached to the frame part and urging the electromagnet toward the frame part. At least a partial portion of the rotary body facing the electromagnet may be formed of a ferromagnetic material. The electromagnet may be urged by the urging member in such a manner that the electromagnet and the rotary body are separated from each other when the electromagnet is not energized, and the electromagnet may come into contact with the rotary body against an urging force of the urging member when the electromagnet is energized, thereby braking the rotary body. 
     A motor for rotating the rotary body may be disposed between the rotary body and the frame part, and a wiring from the motor may be drawn out between the urging member and the frame part. 
     The polyhedron may be a hexahedron. 
     The component provided inside the housing may be an electromagnet of the reaction wheel. 
     Advantageous Effect of Invention 
     According to the present invention having the above-mentioned configurations, a further compact reaction wheel apparatus can be provided. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a perspective view illustrating a reaction wheel apparatus according to a first embodiment of the present invention. 
         FIG. 2  is a plan view illustrating a rigid flexible substrate that can be used in the reaction wheel apparatus according to the first embodiment of the present invention. 
         FIG. 3  is an exploded perspective view illustrating the reaction wheel apparatus according to the first embodiment of the present invention. 
         FIG. 4  is a perspective view illustrating a reaction wheel according to the first embodiment of the present invention. 
         FIG. 5  is an exploded perspective view illustrating the reaction wheel according to the first embodiment of the present invention. 
         FIG. 6  is a cross-sectional view taken along a line VI-VI in  FIG. 4 . 
         FIG. 7  is a perspective view illustrating a reaction wheel system apparatus according to a second embodiment of the present invention. 
         FIG. 8  is a diagram illustrating the principle of a first embodiment of a motor rotation speed detection device. 
         FIG. 9  is a diagram illustrating the entire configuration of the first embodiment of the motor rotation speed detection device. 
         FIG. 10  is a diagram illustrating an exemplary circuit configuration of a section determination unit and a clock signal output unit of the first embodiment of the motor rotation speed detection device. 
         FIG. 11  is a diagram illustrating an exemplary relationship between slots and divided sections. 
         FIG. 12  is a diagram illustrating the entire configuration of a second embodiment of the motor rotation speed detection device. 
         FIG. 13  is a diagram illustrating an exemplary circuit configuration of a section determination unit and a clock pulse output unit according to the second embodiment of the motor rotation speed detection device. 
         FIG. 14  is a diagram illustrating values of output signals of Hall sensors HS 1 , HS 2 , and HS 3  and the output of the section determination unit with respect to the rotor rotation phase angle. 
         FIG. 15  is a diagram illustrating an exemplary circuit configuration of a section determination unit and a clock pulse output unit according to the second embodiment of the motor rotation speed detection device. 
         FIG. 16  is a diagram illustrating values of output signals of Hall sensors HS 1 , HS 2 , and HS 3  and the output of the section determination unit with respect to the rotor rotation phase angle. 
         FIG. 17  is a diagram illustrating an exemplary circuit configuration of a section determination unit and a clock pulse output unit according to the second embodiment of the motor rotation speed detection device. 
         FIG. 18  is a diagram illustrating values of the output signals of Hall sensors HS 1 , HS 2 , HS 3 , and HS 4  and the output of the section determination unit with respect to the rotor rotation phase angle. 
         FIG. 19  is a diagram illustrating an exemplary circuit configuration of a section determination unit and a clock pulse output unit according to the second embodiment of the motor rotation speed detection device. 
         FIG. 20  is a diagram illustrating the operation principle of a conventional three-phase brushless motor. 
         FIG. 21  is a diagram illustrating the state of output signals Hu, Hv, and Hw of Hall sensor HS 1 , HS 2 , and HS 3  with respect to the rotation phase angle of the rotor. 
         FIG. 22  is a diagram illustrating values of the output signals Hu, Hv, and Hw of the Hall sensor HS 1 , HS 2 , and HS 3  with respect to the rotation phase angle of the rotor. 
         FIG. 23  is a diagram illustrating values of the output signals Hu and Hv of the Hall sensors with respect to the rotor rotation phase angle. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments of a reaction wheel apparatus according to the present invention will be described with reference to drawings. 
     &lt;Reaction Wheel Apparatus&gt; 
     First Embodiment 
       FIG. 1  is a perspective view illustrating a reaction wheel apparatus according to the first embodiment of the present invention.  FIG. 2  is a plan view illustrating a rigid flexible substrate that can be used in the reaction wheel apparatus according to the first embodiment of the present invention.  FIG. 3  is an exploded perspective view illustrating the reaction wheel apparatus according to the first embodiment of the present invention. 
     A reaction wheel apparatus  5  has a cubic (regular hexahedral) shape. A cube has respective faces that are constituted by frame parts corresponding to the respective faces. The frame parts are mutually connected to constitute a housing of the reaction wheel apparatus  5 . The shape of the reaction wheel apparatus may be any appropriate polyhedron shape. 
     The reaction wheel apparatus  5  includes three reaction wheels  1 ,  2 , and  3 . The reaction wheels  1 ,  2 , and  3  are disposed in such a manner that directions of rotational axes of flywheels  13 ,  23 , and  33  (described below) of the reaction wheels  1 ,  2 , and  3  are mutually orthogonal. As a result, the angular momentum can be generated with respect to three orthogonal axes. Frames  10 ,  20 , and  30  of respective reaction wheels, each having the same substantially square shape, constitute three of six frame parts of the reaction wheel apparatus  5 . 
     Rigid circuit board parts  40 ,  41 , and  42  of a rigid flexible substrate  4  described below constitute the remaining three of the frame parts of the reaction wheel apparatus  5 . 
     The frames  10 ,  20 , and  30  and the rigid circuit board parts  40 ,  41 , and  42  are mutually connected in such a manner that the reaction wheel apparatus  5  has a cubic shape as a whole, as described in detail below. 
     As illustrated in  FIG. 2 , the rigid flexible substrate  4  includes the rigid circuit board parts  40 ,  41 , and  42 , a flexible cable  45  connecting the rigid circuit board part  40  and the rigid circuit board part  41 , and a flexible cable  46  connecting the rigid circuit board part  40  and the rigid circuit board part  42 . 
     The rigid flexible substrate  4  is provided with circuit elements such as circuit elements constituting a control unit, and other circuit elements including MEMS sensor inertial measurement units (IMUs)  52 . 
     The control unit controls the rotational state of respective flywheels  13 ,  23 , and  33  by controlling respective motors  14 ,  24 , and  34  of the reaction wheels  1 ,  2 , and  3  and the excitation current supplied to each of electromagnets  12 ,  22 , and  32 , as described below. Further, the control unit  51  acquires detection information, which includes angular speed and acceleration in each of three axes, from the MEMS sensor IMUs  52 , and performs various calculations based on the acquired information and controls the motors  14 ,  24 , and  34 , the electromagnets  12 ,  22 , and  32 , and the like based on the acquired information and the calculation result. 
     A plurality of MEMS sensor IMUs  52  is disposed on the rigid circuit board parts, at positions adjacent to respective corners of vertices of the cube. Information from each IMU  52  is transmitted to the control unit. The control unit may determine the gravitational acceleration direction and the like based on this information and control the rotational state of respective flywheels  13 ,  23 , and  33 . 
     The rigid circuit board parts  40 ,  41 , and  42  have the same substantially square shape. When the flexible cables  45  and  46  are bent so that the rigid circuit board parts  40 ,  41 , and  42  are mutually orthogonal, the rigid flexible substrate  4  constitutes three of the faces constituting the cube of the reaction wheel apparatus  5 . 
     In addition, first cutout parts  401 ,  411 , and  421  each being rectangular and opening outward are formed at side edges of the rigid circuit board parts  40 ,  41 , and  42 , and second cutout parts  402 ,  412 , and  422  each being rectangular and opening outward are formed so as to be separated from the first cutout parts  401 ,  411 , and  421  by predetermined distances. First residual parts  403 ,  413 , and  423  each being rectangular are formed between the first cutout parts  401 ,  411 , and  421  and the second cutout parts  402 ,  412 , and  422 . Second residual parts  404 ,  414 , and  424  each being rectangular are formed on sides of the second cutout parts  402 ,  412 , and  422  opposing the first residual parts  403 ,  413 , and  423 . 
     In addition, at respective corners of the rigid circuit board parts  40 ,  41 , and  42 , first through opening  405 ,  415 , and  425  and first through holes  406 ,  416 , and  426  each penetrating in the thickness direction thereof are formed. More specifically, the first residual parts  403 ,  413 , and  423  are formed with the first through holes  406 ,  416 , and  426  on the corner sides of the rigid circuit board parts  40 ,  41 , and  42 . The first through openings  405 ,  415 , and  425  are formed on the second residual parts  404 ,  414 , and  424  sides of the second cutout parts  402 ,  412 , and  422 . The first through openings  405 ,  415 , and  425  have nut accommodation parts  405   a ,  415   a , and  425   a  extending substantially parallel to the side edges of the rigid circuit board parts  40 ,  41 , and  42 , more specifically, bottom lines of the second cutout parts  402 ,  412 , and  422 , and screw accommodation parts  405   b ,  415   b , and  425   b  opening to the second cutout parts  402 ,  412 , and  422  being the side edges of the rigid circuit board parts  40 ,  41 , and  42  and extending orthogonally to the nut accommodation parts  405   a ,  415   a , and  425   a . The sectional shape of respective first through openings  405 ,  415 , and  425  transversal with respect to the thickness direction of the rigid circuit board parts  40 ,  41 , and  42  is cruciform in the present embodiment, although it may be T shape. A nut  801  is fitted into each of the nut accommodation parts  405   a ,  415   a , and  425   a . The nut  801  may be configured so as to leave a gap in each of the nut accommodation parts  405   a ,  415   a , and  425   a  when accommodated, instead of being fitted into the nut accommodation parts  405   a ,  415   a , and  425   a.    
     The frames  10 ,  20 , and  30  of the reaction wheels  1 ,  2 , and  3  are substantially square in shape, as mentioned above. Third cutout parts  101 ,  201 , and  301 , each being rectangular and opening outward, are formed at side edges of the frames  10 ,  20 , and  30 . Fourth cutout parts  102 ,  202 , and  302 , each being rectangular and opening outward, are formed so as to be separated from the third cutout parts  101 ,  201 , and  301  by predetermined distances. Third residual parts  103 ,  203 , and  303  each being rectangular are formed between the third cutout parts  101 ,  201 , and  301  and the fourth cutout parts  102 ,  202 , and  302 . Fourth residual parts  104 ,  204 , and  304  each being rectangular are formed on sides of the fourth cutout parts  102 ,  202 , and  302  opposing the third residual parts  103 ,  203 , and  303 . 
     In addition, at respective corners of the frame  10 , second through holes  106 ,  206 , and  306  each penetrating in the thickness direction thereof are formed. More specifically, the third residual parts  103 ,  203 , and  303  are formed with the second through holes  106 ,  206 , and  306  on the corner sides of the frames  10 ,  20 , and  30 . Further, the fourth cutout parts  102 ,  202 , and  302  have bottom surfaces provided with female screw parts  105 ,  205 , and  305 , on the fourth residual parts  104 ,  204 , and  304  sides. 
     The cutout parts and the residual parts formed on respective rigid circuit board parts  40 ,  41 , and  42  and the cutout parts and the residual parts formed on the frames  10 ,  20 , and  30  of the reaction wheel are fitted with each other. 
     Side edges of the rigid circuit board parts  40 ,  41 , and  42  and the side edges of the frames  10 ,  20 , and  30  may have any appropriate shape such as a linear shape. 
     The frame  10 , which is a frame part neighboring the rigid circuit board part  40 , has the second through hole  106  at a position aligned with the screw accommodation part  405   b  of the first through opening  405  of the rigid circuit board part  40 , the nut  801  accommodated in the nut accommodation parts  405   a , and a screw hole  911  of a connection assist member  91 . Accordingly, by driving a screw  811  inserted from the outside of the frame  10  into the nut  801  through the screw hole  911  of the connection assist member  91 , the second through hole  106 , and the screw accommodation part  405   b , the rigid circuit board part  40  and the frame  10  can be connected with each other. 
     Similarly, the rigid circuit board part  40 , which is a frame part neighboring the rigid circuit board part  41 , has a first through hole  406  at a position aligned with the screw accommodation part  415   b  of the first through opening  415  of the rigid circuit board part  41 , a nut  802  fitted into the nut accommodation part  415   a , and a screw hole  912  of the connection assist member  91 . Accordingly, by driving a screw  812  inserted from the outside of the rigid circuit board part  40  into the nut  802  through the screw hole  912  of the connection assist member  91 , the first through hole  406 , and the screw accommodation part  415   b , the rigid circuit board part  40  and the rigid circuit board part  41  are connected with each other. 
     The frame  10 , which is a frame part neighboring the frame  20 , has the second through hole  106  at a position aligned with the female screw part  205  of the frame  20  and a screw hole  921  of a connection assist member  92 . Accordingly, by driving a screw  813  inserted from the outside of the frame  10  into the female screw part  205  through the screw hole  921  of the connection assist member  92  and the second through hole  106 , the frame  20  and the frame  10  are connected with each other. 
     Further, by driving a screw  814  inserted from the outside of the rigid circuit board part  41  into the female screw part  105  of the frame  10  through a screw hole  913  of the connection assist member  91  and the first through hole  416  of the rigid circuit board part  41 , the frame  10  and the rigid circuit board part  41  are connected with each other. 
     Similar structures are employed for connection between other rigid substrate and the rigid circuit board part, between the rigid circuit board part and a neighboring frame, and between two frames. 
     According to such a connection structure, the rigid circuit board part itself can be used as a frame part. More specifically, since the rigid circuit board part is very small in thickness and is therefore fragile in a direction perpendicular to a side edge surface thereof, it is difficult to form a screw hole opening on the side edge surface and therefore the side edge surface could not be used as a connection surface to be connected to a neighboring frame part. However, with the above-mentioned connection structure, the side edge surface can be used as a surface for connection to a neighboring frame part. Therefore, the rigid circuit board part itself can be used as a frame part. 
     The above-mentioned connection structure, more specifically the connection structure in which a plate-like first member has a first through opening penetrating in the thickness direction of the first member, the first through opening has a nut accommodation part extending substantially parallel to a side edge of the first member and a screw accommodation part opening to the side edge of the first member and extending orthogonally to the nut accommodation part, a nut is accommodated in the nut accommodation part, the second member has a through hole at a position aligned with the screw accommodation part of the first through opening of the first member and the nut accommodated in the nut accommodation part, and the first member and the second member are connected with each other by driving a screw inserted from the outside of the first member into the nut through the through hole and the screw accommodation part, is not limited to connection structure between a rigid circuit board part and other frame part, but may be generally employed for connecting a plate-like member to other member by using a side edge surface of the plate-like member as a connection surface. 
     According to the present embodiment, since the rigid circuit board part itself can be used as a frame part, the entire volume of the circuit elements occupying the inside of the housing of the reaction wheel apparatus can be remarkably reduced and accordingly the apparatus can be further downsized. 
     Further, the second cutout parts  402 ,  412 , and  422  of the rigid circuit board parts  40 ,  41 , and  42  include fifth cutout parts  407 ,  417 , and  427  each being rectangular and opening outward are formed on the first residual parts  403 ,  413 , and  423  sides, so as to form stepped cutout parts as a whole. The third residual parts  103 ,  303 , and  203  of the frames  10 ,  30 , and  20 , which are frame parts connected to the second cutout parts  402 ,  412 , and  422  respectively serving as side edges along which the fifth cutout parts  407 ,  417 , and  427  are formed, are disposed so as to cover the opening edges of the fifth cutout parts  407 ,  417 , and  427 , thereby forming openings  408 ,  418 , and  428 . A wiring  122  from an electromagnet  12  of a reaction wheel  1 , which is a component provided inside the housing of the reaction wheel apparatus  5 , is connected to a terminal  409  provided on an outer surface of the rigid circuit board part  40  through the opening  408 . Similarly, wirings from electromagnets  22  and  33  of reaction wheels  2  and  3  are connected to terminals  429  and  419  provided on outer surfaces of the rigid circuit board parts  42  and  41  through the openings  428  and  418 . 
     According to the above-mentioned configuration, since the wirings from the components provided inside the housing can be connected to the terminals provided on the outer surfaces of the rigid circuit board parts through the openings, it is possible to mount the circuit elements on the outer substrate surfaces of the rigid circuit board parts. As a result, the entire volume of the circuit elements occupying the inside of the housing of the reaction wheel apparatus can be further reduced. The maintenance of the circuits becomes easy. In addition, assembling and disassembling of the reaction wheel apparatus become realistically feasible. 
     In general, a large force acts on a flexible cable when the bending radius is small. However, adopting the above-mentioned configuration in which the flexible cable extends from the fifth cutout part, which is a deeper part of the stepped cutout part, can lengthen not only the flexible cable itself but also the distance between the parts to which the flexible cables attached, thereby relieving the force applied to the flexible cable. 
     Subsequently, the configuration of the reaction wheels  1 ,  2 , and  3  will be described with reference to  FIGS. 4 to 6 .  FIG. 4  is a perspective view illustrating the reaction wheel according to the present embodiment.  FIG. 5  is an exploded perspective view illustrating the reaction wheel according to the present embodiment.  FIG. 6  is a cross-sectional view taken along a line VI-VI in  FIG. 4 . 
     As illustrated in  FIGS. 4 to 6 , the reaction wheel  1  according to the present embodiment includes the frame  10 , a leaf spring  11  serving as an urging member, the electromagnet  12 , the flywheel  13  serving as a rotary body, and the motor  14 . 
     The frame  10  has a substantially square shape, as mentioned above, and cutout parts and residual parts are respectively formed at side edges thereof. The frame  10  is formed with four openings  109  each penetrating in the thickness direction. By adopting the frame configured to include openings as mentioned above, it is possible to reduce the weight of the frame. Alternatively, the frame may be configured as a plate-like member having no opening. The number of openings and the shape of each opening may be appropriately determined. A circular recessed part  107  is formed at the center of the frame  10 . The opening  108  penetrating in the thickness direction is provided at the center of the recessed part  107 . 
     The motor  14  includes a motor body  141  and a shaft  143 , and rotates the flywheel  13  (described below) attached to the motor body  141  via a connection member  18 . The motor body  141  includes a substantially cylindrical stator part  141   a  having a flange and a disk-shaped rotor part  141   b  having a cylindrical protrusion protruding toward the center in the axial direction. When the stator part  141   a  is fitted into and bonded to the recessed part  107  and the opening  108  of the frame  10 , the motor  14  can be fixed to the frame  10 . 
     The flywheel  13  has a substantially truncated conical shape, and a peripheral portion thereof has an annular surface parallel to the axis of rotation. The flywheel  13  is formed of a ferromagnetic material. A recessed part  131  that can accommodate the electromagnet  12  is formed on a side of the flywheel  13  facing the electromagnet  12 , and a surface of the recessed part  131  facing the electromagnet is a plane. A hole  133  for passing the shaft  143  of the motor  14  is provided at the center of the flywheel  13 . By driving screws  136  through screw holes  135  formed at the top of the flywheel  13 , the cylindrical connection member  18  is fixed to the surface of the recessed part  131  facing the electromagnet. A surface of the connection member  18  positioned on the side of the frame  10  and the rotor part  141   b  of the motor  14  are fixed by means of an adhesive. 
     Although the flywheel  13  and the connection member  18  can be integrally formed, adopting the configuration forming them as separate members is useful in that a shim thin material can be inserted between the flywheel  13  and the connection member  18 . As a result, the size of the gap between the electromagnet  12  and the flywheel  13  can be adjusted so as to prevent the electromagnet  12  and the flywheel  13  from being positioned too closely or too far when the electromagnet  12  is not energized. 
     When the motor is disposed on the upper side, a cantilever structure or a two-support beam structure for supporting the motor is required and the shape of the flywheel cannot be formed into a substantially truncated cone. As mentioned above, when the motor is disposed on the frame side and the shape of the flywheel is a substantially truncated conical shape, neighboring reaction wheels can be positioned closely and the apparatus can be further downsized. 
     The leaf spring  11  has a disc-like shape having a circular opening at the center thereof. The leaf spring  11  has four arc-shaped first slits  111  each being convex in a radially outer direction, which are provided on an inner circumferential side of the leaf spring  11  at an angular interval of 90° in the circumferential direction. Each first slit  111  extends so as to penetrate the leaf spring  11  in the thickness direction. In addition, the leaf spring  11  has four arc-shaped second slits  113 , which are provided an outer circumferential side of the leaf spring  11  at an angular interval of 90° in the circumferential direction. Each second slit  113  extends so as to penetrate the leaf spring  11  in the thickness direction. The first slits  111  and the second slits  113  are alternately disposed. The leaf spring  11  has four ear parts  116  each extending in a radially outer direction and having a screw hole, which are provided along a circumferential edge thereof at an angular interval of 90° in the circumferential direction. The leaf spring  11  is fixed to the frame  10  by means of screws. As described below, the wiring  122  from the electromagnet and a wiring  144  from the motor  14  extend substantially parallel to the frame. Therefore, in order to prevent interference between the wiring  122  from the electromagnet and the wiring  144  from the motor  14 , the ear parts  116  are disposed in such a way as to be offset in the circumferential direction with respect to the wiring  122  from the electromagnet and the wiring  144  from the motor  14 . The shape, arrangement, number, and the like of the slits can be determined arbitrarily and appropriately. The shape of the leaf spring can be determined arbitrarily and appropriately, too. 
     The electromagnet  12  has a ring shape, and its cross section in the radial direction is rectangular. The electromagnet  12  can be partly ring-shaped, that is arc-shaped, and one or more arc-shaped electromagnets  12  may be arranged. The shape of the electromagnet and the cross sectional shape thereof in the radial direction can be determined arbitrarily and appropriately. A surface of the electromagnet  12  facing the frame  10  is fixed to the leaf spring  11  by means of screws, and the leaf spring  11  urges the electromagnet  12  toward the frame  10 . More specifically, even when the frame  10  is not disposed vertically below the electromagnet  12 , the electromagnet  12  is urged by the leaf spring  11  in such a manner that the electromagnet  12  and the flywheel  13  separate from each other when the electromagnet  12  is not energized, thereby letting the electromagnet  12  be movable in the axial direction. The gap between the electromagnet  12  and the flywheel  13  can be maintained at a predetermined interval. The structure (its shape, shape and number of an elasticity imparting portion, etc.) and the rigidity (material, thickness, etc.) of the leaf spring  11  may be determined by optimizing the relationship between leaf spring deflection due to gravity and attracting magnetic force. 
     The wiring  122  from the electromagnet  12  is drawn out between the leaf spring  11  and the frame  10  through a hole  115  penetrating in the thickness direction of the leaf spring  11  and is connected to the terminal  409  provided on the outer surface of the rigid circuit board part  40  through the opening  408  as mentioned above. 
     The wiring  144  from the motor  14  is a flat cable drawn out along a side surface of the stator part of the motor  14 . The wiring  144  from the motor  14  is also drawn out between the leaf spring  11  and the frame  10 , bend in the vicinity of an outer edge of the leaf spring  11 , and connected to a terminal provided on an inner surface of the rigid circuit board part  41 . As mentioned above, in the present embodiment, by adopting the configuration in which the leaf spring is interposed between the wiring from the motor and the flywheel, interference between the wiring  144  from the motor  14  and the flywheel  13  can be prevented. In this case, if the outer edge of the leaf spring  11  is located outside the outer edge of the flywheel  13 , such an effect can be more surely achieved. 
     In place of such a configuration, by drawing out the wiring  144  from the motor  14  through the openings  408 ,  418 , and  428  formed by disposing the third residual parts  103 ,  303 , and  203  of the frames  10 ,  30 , and  20 , which are the frame parts connected to the second cutout parts  402 ,  412 , and  422 , which are side edges at which the above-mentioned fifth cutout parts  407 ,  417 , and  427 , so as to cover the opening edges of the fifth cutout parts  407 ,  417 , and  427 , interference between the wiring  144  from the motor  14  and the flywheel  13  can be prevented. 
     In the above-mentioned embodiment, although the wiring  122  from the electromagnet and the wiring  144  from the motor  14  are disposed so as to be orthogonal to each other by 90°, they may be disposed in the same direction or in opposite direction. 
     In such a configuration, when the electromagnet  12  is energized while the flywheel  13  is rotating, the electromagnetic force by the generated magnetic flux causes the electromagnet  12  to be attracted to and come into contact with the flywheel  13  formed of the ferromagnetic material against the urging force of the leaf spring  11 , thereby braking the flywheel  13 . Changing the magnitude of the magnetic flux generated by the electromagnet  12  or the change rate of the magnetic flux can control the braking state. Making the magnetic flux of the electromagnet  12  change stepwise and generating a large magnetic force can rapidly stop the rotating flywheel  13 . As a result, the reaction wheel  1  can instantaneously set the generating angular momentum to zero. 
     Rapidly stopping the flywheel  13  with higher responsiveness can be realized by increasing the braking force. One approach is to increase the contact area between the flywheel  13  and the electromagnet  12 . 
     More specifically, a first braking surface  121  that is a surface coming into contact with the flywheel  13  of the electromagnet  12  when the electromagnet  12  is energized and a second braking surface  134  that is a surface coming into contact with the electromagnet  12  of the flywheel  13  may be complementary in shape. In the present embodiment, the first braking surface  121  of the electromagnet  12  and the second braking surface  134  of the flywheel  13  are mutually parallel planes and complementary in shape. As a complementary shape, adopting a shape having a larger contact area between the electromagnet  12  and the flywheel  13 , for example, a shape having a circular cross section, can increase the braking force. 
     Further, when the electromagnet  12  is configured to come into contact with an outer peripheral side of the flywheel  13  at the time of energization of the electromagnet  12 , the braking surface can be larger compared to a case where the electromagnet  12  is configured to come into contact with a central side of the flywheel  13 . In the present embodiment, by adopting the configuration for causing the electromagnet  12  to come into contact with the outer peripheral portion of the flywheel  13  at the time of energization of the electromagnet  12 , the contact area is increased and the braking force is increased. 
     In the above-mentioned embodiment, the flywheel  13  is entirely formed of the ferromagnetic material. However, when at least a partial portion of the flywheel  13  facing the electromagnet  12  is formed of a ferromagnetic material, the braking can be performed. In addition, if the remaining portion is formed of a material (for example, tungsten) having a density higher than that of the ferromagnetic material, the mass of the flywheel  13  can be increased without increasing the volume of the flywheel  13 , and the accumulated angular momentum per same rotation speed of the reaction wheel  1  can be increased. 
     With such a configuration, the reaction wheel apparatus can be further downsized. While the above-mentioned conventional reaction wheel apparatus  5  has the size of 10 cm 3 , a very small reaction wheel apparatus whose size is not larger than 30 mm 3  can be realized. 
     In the above-mentioned embodiment, the number of the reaction wheels is three, and the flywheels of the reaction wheels are mutually orthogonal in the direction of the axis of rotation. However, the number of the reaction wheels can be an arbitrary number not smaller than two as long as the flywheels are mutually different in the direction of the axis of rotation. 
     Second Embodiment 
       FIG. 7  is a perspective view illustrating a reaction wheel apparatus according to a second embodiment of the present invention. The configuration and the operation principle of the second embodiment of the present invention will be described with reference to  FIG. 7 . In  FIG. 7 , portions corresponding to those in  FIGS. 1 to 6  are denoted by the same reference numerals and explanations similar to those in the first embodiment will be omitted. 
     In the present embodiment, an external device such as an expansion substrate can be connected to the reaction wheel apparatus according to the first embodiment. 
     The connection assist members  91  to  98  according to the first embodiment have three branches extending in three directions orthogonal to each other along each side of the housing of the reaction wheel apparatus  5 . On the other hand, connection assist members  93 ′,  94 ′,  95 ′, and  98 ′ and connection assist members  91 ″,  92 ″,  96 ″, and  97 ″ according to the present embodiment have branches  93 ′ d ,  94 ′ d ,  95 ′ d , and  98 ′ d  extending in one direction outside the reaction wheel apparatus  5  and branches  91 ″d,  92 ″d,  96 ″d,  97 ″d,  91 ″e,  92 ″e,  96 ″e, and  97 ″e extending in two directions outside the reaction wheel apparatus  5 . These branches are formed with female screw parts  93 ′ f ,  94 ′ f ,  95 ′ f ,  98 ′ f ,  91 ″f,  92 ″f,  96 ″f, and  97 ″f. An expansion substrate  7  is screwed to the branches  91 ″e,  92 ″e,  96 ″e, and  97 ″e. 
     Further, if a connection assist member having a male screw part is prepared instead of the configuration in which the branch is formed with the female screw part, a connection assist member formed with a female screw part and a connection assist member formed with a male screw part can be screwed beforehand, and then two reaction wheel apparatuses  5  can be connected to this so that two or more reaction wheel apparatuses  5  can be mutually connected. 
     As mentioned above, when the connection assist member to be used when connecting frame parts with each other is configured to be connectable to an external device, an external device such as an expansion substrate or an additional reaction wheel apparatus can be attached to a reaction wheel apparatus. 
     When the external device to be attached is an expansion substrate, it becomes possible to control an external device. For example, if a propulsion mechanism such as a thruster or a fan is connected as the external device, one module is usable for both of attitude control and translation control. 
     In addition, when the external device to be attached is a reaction wheel apparatus, by interconnecting a plurality of reaction wheel apparatuses for clustering them, an increased amount of torque can be generated and a necessary amount of torque according to the purpose can be generated. Also, even if a single axis in a multi-axis configuration fails, triaxial control is still feasible using other axes, so that the robustness of the system can be improved. 
     In the above-mentioned embodiment, the connection assist member to which an external device can be connected is attached to a vertex part of the housing of the reaction wheel apparatus. However, it may be attached to a side region of the housing of the reaction wheel apparatus. 
     Although the present invention has been described with reference to some exemplary embodiments, the present invention is not limited to them and it will be apparent to those skilled in the art that the form and details can be modified and changed in various ways without departing from the scope and spirit of the present invention. 
     &lt;Motor Rotation Speed Detection Device&gt; 
     The above-mentioned reaction wheel apparatus includes the motor. Hereinafter, a motor rotation speed detection device will be described. 
     As a method for detecting the rotational speed of a brushless motor, a method for using a Hall sensor or an encoder is generally used. In particular, among various rotational speed detection methods using Hall sensors, a method using three Hall sensors is generally and widely known. 
       FIG. 20  is a view illustrating the operation principle of a conventional three-phase brushless motor. Operations of a conventional motor rotation speed detection device will be described with reference to  FIG. 20 . 
     A rotor of the brushless motor includes a magnetic pole pair constituted by an N-pole and an S-pole. Three Hall sensors, i.e., Hall sensor HS 1 , Hall sensor HS 2 , and Hall sensor HS 3 , are disposed around the rotor as position sensors at equal intervals of electrical angle 120°. 
     The rotor is configured to rotate in the brushless motor. When the magnetic pole switches from the S-pole to the N-pole or from the N-pole to the S-pole while the rotor is rotating around its rotation axis, each Hall sensor detects this switching and changes the state (Hi-level or Low-level) of its output signal as illustrated in  FIG. 21 .  FIG. 21  illustrates the state of output signals Hu, Hv, and Hw of the Hall sensors HS 1 , HS 2 , and HS 3  with respect to the rotation phase angle of the rotor.  FIG. 22  illustrates the same state with values (Hi-level=1, and Low-level=0) of the output signals. By combining the values of the output signals Hu, Hv, and Hw, the rotor rotation phase angle can be divided into sections B 1  to B 6  (i.e., six states) at equal intervals of 60 degrees. 
     Accordingly, the rotational speed of the rotor can be detected by using the output signals of respective Hall sensors. More specifically, by counting the number of clock pulses in each of the sections B 1  to B 6  with a counter, the rotational speed of the motor (average rotational speed in respective sections B 1  to B 6 ) can be detected. Assuming that the frequency of the clock pulse is fc [Hz], since the counter counts the number n of clock pulses with respect to ⅙ rotation in each of the sections B 1  to B 6  with a phase interval of 60°, the rotational speed ω can be calculated as follows. 
       Ω=60 fc/ 6 n= 10 fc/n [rpm]  (1)
 
     Problem to be Solved 
     Here, for example, in order to reduce the cost of the motor rotation speed detection device or reduce the device size for installation into a small-sized device, it will be discussed to detect the rotational speed by using a smaller number of Hall sensors than the number of phases of the motor, for example, by using two signals Hu, Hv of the output signals Hu, Hv, and Hw of the Hall sensors.  FIG. 23  illustrates the values of the output signals Hu and Hv of the Hall sensors with respect to the rotor rotation phase angle. In this case, the rotor rotation phase angle can be divided into sections B 1 ′ to B 4 ′ (four states). 
     In this case, although the phase interval of the sections B 1 ′ and B 3 ′ is 120°, the phase interval of the sections B 2 ′ and B 4 ′ is 60° and is different from the phase interval of the sections B 1 ′ and B 3 ′. Accordingly, since the time for counting the clock pulses is different between the sections B 2 ′ and B 4 ′ and the sections B 1 ′ and B 3 ′, it is impossible to precisely detect the rotational speed by directly applying the conventional method. 
     In view of the above, one object of the present motor rotation speed detection device is to provide a motor rotation speed detection device that can precisely detect the rotational speed with a smaller number of Hall sensors than the number of phases of the motor. 
     Means for Solving Problem 
     One aspect of the present motor rotation speed detection device is to provide a motor rotation speed detection device, which is a rotation speed detection device for an M-phase motor whose number of magnetic pole pairs is P, including first to Nth (N is an integer larger than 1 and smaller than M) Hall sensors disposed at intervals of an integral multiple of electrical angle 180/M°, a section determination unit configured to generate and output first to Nth signals in which only the i-th signal is a signal representing a first state and all the remaining signals are signals representing a second state that is different from the first state from the output signals of the first to Nth Hall sensors, in each of sections Bij (j is an integer not smaller than 1 and not larger than 2P) having a phase interval of (180/MP).Li° (i is an integer not smaller than 1 and not larger than N, and Li is any integer not smaller than 1 and not larger than (M−N+1)), obtained by dividing each section obtained by dividing the phase section of one rotation of the M-phase motor into 2P pieces into N pieces, a clock pulse output unit configured to output clock pulses of frequency fc/Li in respective sections Bij when the i-th signal of the first to Nth signals is the signal representing the first state, a counter for counting the clock pulses output from the output unit for each section Bij, and a rotational speed calculation unit configured to calculate the rotational speed of the motor based on the counting value of the counter. 
     The clock pulse output unit includes first to K-th clock generators capable of generating clock pulses of first to K-th frequencies with respect to first to K-th frequencies mutually different among the frequency fc/Li, first to Nth operation units, and an OR operation unit. The i-th operation unit can be configured to output the output from the clock generator that generates clock pulses of frequency fc/Li, when the i-th signal is the signal representing the first state. The OR operation unit can be configured to calculate a logical sum of the output signals from the first to Nth operation units and output clock pulses of frequency fc/Li in section B 1 . 
     The first state is a first logic, and the second state is a second logic different from the first logic. The first to Nth operation units are AND operation units. The i-th operation unit can be configured to calculate a logical product of the output from the clock generator that generates clock pulses of frequency fc/Li and a logic represented by the i-th signal. 
     The clock pulse output unit can be configured to include a clock generator for generating clock pulses of frequency fc and a clock frequency converter for multiplying the output of the clock generator by 1/Li when the i-th signal is the signal representing the first state so as to generate clock pulses of frequency fc/Li in respective sections Bij. 
     Another aspect of the present motor rotation speed detection device is to provide a motor rotation speed detection device that is a rotation speed detection device for an M-phase motor whose number of magnetic pole pairs is P, including first to Nth (N is an integer larger than 1 and smaller than M) Hall sensors disposed at intervals of an integral multiple of electrical angle 180/M°, a section determination unit configured to generate and output first to Nth signals in which only the i-th signal is a signal representing a first state and all the remaining signals are signals representing a second state that is different from the first state from the output signals of the first to Nth Hall sensors, in each of sections Bij (j is an integer not smaller than 1 and not larger than 2P) having a phase interval of (180/MP).Li° (i is an integer not smaller than 1 and not larger than N, and Li is any integer not smaller than 1 and not larger than (M-N+1)), obtained by dividing each section obtained by dividing the phase section of one rotation of the M-phase motor into 2P pieces into N pieces, a clock pulse output unit configured to output clock pulses of frequency fc, a counter for counting the clock pulses output from the output unit for each section Bij, and a rotational speed calculation unit configured to calculate the rotational speed of the motor based on a value obtained by multiplying the counting value of the counter by 1/Li, for each section Bij, when the i-th signal of the first to Nth signals is the signal representing the first state. 
     P=1, M=3, N=2, and the section determination unit can be configured to calculate an exclusive OR of the output signals of the first and second Hall sensors and a negation of the exclusive OR and then output the calculation results as a first signal and a second signal, respectively. 
     Advantageous Effect of Invention 
     According to the present motor rotation speed detection device having the above-mentioned configuration, the motor rotation speed detection device capable of precisely detecting the rotational speed with a smaller number of Hall sensors than the number of phases of the motor can be provided. 
     Hereinafter, an embodiment of the motor rotation speed detection device will be described with reference to the drawings. 
     First Embodiment of Motor Rotation Speed Detection Device 
       FIG. 8  is a diagram illustrating the principle of the first embodiment of the motor rotation speed detection device. 
     As mentioned above, when the number of usable Hall sensors is three, clock pulses are counted by the counter for each of respective sections B 1  to B 6 , and the rotational speed of the motor can be calculated based on the counting values. 
     In the conventional method, the problem when the number of usable Hall sensors is reduced to two is caused by counting clock pulses of the same frequency in sections with different phase intervals. The present inventors have found that switching the frequencies of the clock pulses to be counted between the sections B 1 ′ and B 3 ′ and the sections B 2 ′ and B 4 ′ can solve the problem. 
     To this end, it is necessary to discriminate between the sections B 1 ′ and B 3 ′ having the phase interval of 120° and the sections B 2 ′ and B 4 ′ having the phase interval of 60°. For example, respective sections can be distinguished by an XOR operation of the output signals Hu and Hv of the Hall sensors and a NOT operation thereof.  FIG. 8  illustrates calculation results. 
     Accordingly, the same counter can be used to detect the rotational speed by counting clock pulses of fc/2 [Hz] in the sections B 1 ′ and B 3 ′ having the phase interval of 120° and counting clock pulses of fc [Hz] in the sections B 2 ′ and B 4 ′ having phase interval of 60° (i.e., ½ of 120°). 
     More specifically, in the sections B 1 ′ and B 3 ′ having the phase interval of 120°, since the number N of clock pulses of fc/2 [Hz] is counted with respect to ⅓ rotation, the rotational speed Q can be calculated as follows. 
       Ω=60 fc/ ⅔ N= 10 fc/N [rpm]  (2).
 
     On the other hand, in the sections B 2 ′ and B 4 ′ having the phase interval of 60°, since the number N of clock pulses of fc [Hz] is counted with respect to ⅙ rotation, the rotational speed can be calculated as follows. 
       Ω=60 fc/ 6 N= 10 fc/N [rpm]  (3)
 
     Accordingly, the same counter can be used to detect the rotational speed even when the number of usable Hall sensors is two, i.e., the number smaller than the number of phases of the motor. 
       FIG. 9  is a diagram illustrating the entire configuration of the first embodiment of the motor rotation speed detection device.  FIG. 10  is a diagram illustrating an exemplary circuit configuration of the section determination unit and the clock pulse output unit of the first embodiment of the motor rotation speed detection device. 
     The motor rotation speed detection device  1001  includes first Hall sensor HS 1 , second Hall sensor HS 2 , section determination unit  1011 , clock pulse output unit  1013 , counter  1015  that counts clock pulses output from the clock pulse output unit  1013  for each of the sections B 1 ′ to B 4 ′, and rotational speed calculation unit  1017  that calculates the rotational speed of the motor based on the counting value of the counter  1015 . 
     The first Hall sensor HS 1  and the second Hall sensor HS 2  are disposed at an interval of electrical angle 120° in the clockwise direction. 
     The section determination unit  1011  includes XOR element  1111  and NOT element  1113 . The clock pulse output unit  1013  includes first clock pulse generator  1131   1  that generates clock pulses of frequency fc/2, second clock pulse generator  1131   2  that generates clock pulses of frequency fc, first AND element  1133   1 , second AND element  1133   2 , and OR element  1135 . 
     The first Hall sensor HS 1  and the second Hall sensor HS 2  have output lines connected to input lines of the XOR element  1111 . The XOR element  1111  has an output line and the first clock pulse generator  1131   1  has an output line, which are connected to input lines of the first AND element  1133   1 . Further, the output line of the XOR element  1111  is connected to an input line of the second AND element  1133   2  via the NOT element  1113 . The second clock pulse generator  1131   2  has an output line connected to an input line of the second AND element  1133   2 . The first AND element  1133   1  has an output line and the second AND element  1133   2  has an output line, which are connected to input lines of the OR element  1135 . The OR element  1135  generates an output, which is output as an output of the clock pulse output unit  1013 . 
     The counter  1015  counts the clock pulses output from the clock pulse output unit  1013  and resets its counting value based on the output from the XOR element  1111 , when any one of the sections B 1 ′ to B 4 ′ changes to another section. As a result, the counter  1015  can count the clock pulses output from the clock pulse output unit  1013  for each of the sections B 1 ′ to B 4 ′. 
     The rotational speed calculation unit  1017  calculates the rotational speed of the motor based on the counting value of the counter  1015 . 
     Operations of the first embodiment of the motor rotation speed detection device will be described on the premise of the above-mentioned apparatus configuration. 
     Referring to  FIG. 8 , in the sections B 1 ′ and B 3 ′, the output from the XOR element  1111  is 1. Therefore, the section determination unit  1011  generates and outputs the first signal indicating the first state by the value of 1 and the second signal indicating the second state by the value of 0. The first signal having the value of 1 from the section determination unit  1011  and the clock pulses of frequency fc/2 from the first clock pulse generator  1131   1  are input to the first AND element  1133   1 . On the other hand, the second signal having the value of 0 from the section determination unit  1011  is input to the second AND element  1133   2 . Accordingly, the clock pulses of frequency fc/2, i.e., the output from the first clock pulse generator  1131   k , are directly output from the OR element  1135 , more specifically from the clock pulse output unit  1013 . In this case, since the phase interval of the sections B 1 ′ and B 3 ′ is 120°, the counter  1015  counts the number n of the clock pulses of fc/2 [Hz] with respect to ⅓ rotation. Therefore, based on this, the rotational speed calculation unit  1017  calculates the rotational speed Q according to the above-mentioned formula (2). 
     On the other hand, in the sections B 2 ′ and B 4 ′, the output from the XOR element  1111  is 0. Therefore, the section determination unit  1011  generates and outputs the first signal indicating the second state by the value of 0 and the second signal indicating the first state by the value of 1. The second signal having the value of 0 from the section determination unit  1011  is input to the first AND element  1133   1 . On the other hand, the second signal having the value of 1 from the section determination unit  1011  and the clock pulses of frequency fc from the second clock pulse generator  1131   2  are input to the second AND element  1133   2 . Accordingly, the clock pulses of frequency fc, i.e., the output from the second clock pulse generator  1131   2 , are directly output from the OR element  1135 , more specifically, from the clock pulse output unit  1013 . In this case, since the phase interval of the sections B 2 ′ and B 4 ′ is 60°, the counter  1015  counts the number n of clock pulses of fc [Hz] with respect to ⅙ rotation. Therefore, based on this, the rotational speed calculation unit  1017  calculates the rotational speed Q according to the above-mentioned formula (3). 
     In this case, as understood from  FIG. 8 , since the output signal of the first AND element  1133   1  is contrary to the output signal of the second AND element  1133   2  (when one is 1, the other is 0), the output signal of the first AND element  1133   1  and the output signal of the second AND element  1133   2  are never input simultaneously to the counter  1015 . 
     In the above-mentioned embodiment, although the value “0” is used to indicate the first state and the value “1” is used to indicate the second state, the circuit configurations of the section determination unit and the clock pulse output unit may be modified to use “1” to indicate the first state and use “0” to indicate the second state, or any appropriate discriminable different states may be used. 
     If it is difficult to prepare two types of clock pulse generators of fc [Hz] and fc/2 [Hz], only the clock pulse generator of fc [Hz] may be used and configured in such a manner that the clock pulse output unit  1013  discriminates each section based on the output from the XOR element  1111 , divides the clock pulses from the clock pulse output unit  1013  by 2 when the section is B 1 ′ or B 3 ′, and directly outputs the clock pulses when the section is B 2 ′ or B 4 ′. 
     Alternatively, when using only the clock pulse generator of fc [Hz], the counter  1015  may be configured to discriminate each section based on the output from the XOR element  1111 , divide the counting value of each clock pulse from the clock pulse output unit  1013  by 2 and output it the rotational speed calculation unit  1017  when the section is B 1 ′ or B 3 ′, and directly output the counting value of each clock pulse from the clock pulse output unit  1013  to the rotational speed calculation unit  1017  when the section is B 2 ′ or B 4 ′. 
     With such a configuration, the rotational speed of the motor can be detected by using a smaller number of Hall sensors than the number of phases of the motor. 
     Second Embodiment of Motor Rotation Speed Detection Device 
     In the first embodiment of the motor rotation speed detection device, two Hall sensors are used to detect the rotational speed of a three-phase motor whose number of magnetic pole pairs is 1. In the present embodiment, as a generalized expression, N Hall sensors disposed at intervals of an integral multiple of electrical angle 360/N° (N is an integer larger than 1 and smaller than M) in the clockwise direction are used to detect the rotational speed of an M-phase motor whose number of magnetic pole pairs is P. 
     First, the case where the number of magnetic pole pairs is 1 is considered. In the case of using N Hall sensors, since the phase can be divided into two per Hall sensor, the phase can be divided into 2N sections. On the other hand, the minimum value of the phase interval of the divided section is 180/M°. Therefore, when the section of the minimum value 180/M° of the phase interval is referred to as “slot”, the number of slots per complete rotation of the rotor is 360/(180/M)=2M. 
     When the number N of Hall sensors to be used is determined in this manner, the division number of the rotor phase is uniquely determined. However, the phase interval of the divided section (hereinafter, the minimum value 180/M° is assumed to be the basic unit  1 ) is variable depending on which Hall sensor output signal is used among the N Hall sensors. 
     In this case, cases whose number can be expressed by the number obtained by dividing a phase interval M into N pieces, namely  M C N , occur. When the phase interval of (N−1) pieces of sections is 1, the maximum phase interval of the section is M−N+1 that is the phase interval of the remaining one section.  FIG. 11  illustrates an exemplary relationship between slots and divided sections. 
     It is possible to configure a logical operation circuit that generates first to Nth signals in which only the i-th signal is a signal representing the first state (for example, Hi-level=1) and all the remaining signals are signals representing the second state (for example, Low-level=0) different from the first state, in each section Bi having a phase interval of (180/M).Li (i is an integer not smaller than 1 and not larger than N, and Li is any integer not smaller than 1 and not larger than (M−N+1)), obtained by dividing the phase section corresponding to one complete rotation of an M-phase motor into N pieces, from the output signals of the first to Nth Hall sensors. More specifically, since the section Bi has a one-to-one correspondence relationship with a combination of the output signals of the first to Nth Hall sensors, it is possible to consider a logical function in which the output signals of the first to Nth Hall sensors are regarded as logical values and the signals are output in such a manner that only the i-th signal is the signal representing the first state (for example, Hi-level=1) and all the remaining signals are the signals representing the second state (for example, Low-level=0) different from the first state. There are many logical formulae expressing the same logical function, it is possible to constitute the logical operation circuit that can create a logical formula to be generated from the output signals of the first to Nth Hall sensors. 
     Accordingly, when a clock pulse generator of frequency fc/Li [Hz] corresponding to the phase interval Li of each section is prepared, and when the i-th signal of the first to Nth signals is the signal representing the first state, by configuring in such a way as to output clock pulses of the frequency fc/Li in the section Bi and by counting the clock pulses with a counter, the rotational speed can be detected by the same counter. 
     More specifically, since the number n of the clock pulses of fc/Li [Hz] is counted with respect to Li/2M rotation, the rotational speed Q can be calculated as follows. 
       Ω=60×( Li/ 2 M )×( fc /( nLi ))=30 fc/Mn [rpm]  (4)
 
     Therefore, regardless of the section phase interval Li, it is feasible to detect the rotational speed by the same counter with a smaller number of N Hall sensors than the number of phases of the motor. 
     Although the above discussion was made assuming that the number of magnetic pole pairs  1 , it is easy to expand it by generalizing the number of magnetic pole pairs with P. When the number of magnetic pole pairs is P, the phase division number is P times. The output signal of the Hall sensor in the division state of P times is merely the repetition of the same cycle. Each section Bij (j is an integer not smaller than 1 and not larger than 2P) having a phase interval of (180/MP).Li (i is an integer not smaller than 1 and not larger than N, and Li is any integer not smaller than 1 and not larger than (M−N+1)), obtained by dividing the phase section corresponding to one complete rotation of the M-phase motor into 2P pieces and further dividing each section into N pieces, has the following properties. 
     (1) The logic in respective sections Bij in which the numerical values of j are odd numbers or the numerical values of j are even numbers is consistent. More specifically, 
         Bi 1= Bi 3= . . . = Bi ,(2 m −1)
 
         Bi 2= Bi 4= . . . = Bi, 2 m.    
     (2) The logic in respective sections Bij in which the numerical values of j differ by 1 has an inverted relationship. More specifically, 
         Bi 1=   Bi 2   
         Bi 3=   Bi 4   
         B i ,(2 m− 1)=   Bi, 2 m     
     Here, m is an integer not larger than P. 
     Further, it is possible to configure a logical operation circuit that generates first to Nth signals in which only the i-th signal is a signal representing the first state and all the remaining signals are signals representing the second state that is different from the first state, in respective sections Bij, from the output signals of the first to Nth Hall sensors. More specifically, since the section Bij has a one-to-one correspondence relationship with a combination of the output signals of the first to Nth Hall sensors, it is possible to consider a logical function in which the output signals of the first to Nth Hall sensors are regarded as logical values and the signals are output in such a manner that only the i-th signal is the signal representing the first state (for example, Hi-level=1) and all the remaining signals are the signals representing second state (for example, Low-level=0) different from the first state. There are many logical formulae expressing the same logical function, it is possible to constitute the logical operation circuit that can create a logical formula to be generated from the output signals of the first to Nth Hall sensors. 
     Accordingly, when a clock pulse generator of frequency fc/Li [Hz] corresponding to the phase interval Li of each section is prepared, and when the i-th signal of the first to Nth signals is the signal representing the first state, by configuring in such a way as to output clock pulses of the frequency fc/Li in the section Bij and by counting the clock pulses with a counter, the rotational speed can be detected by the same counter. 
     More specifically, since the number n of the clock pulses of fc/Li [Hz] is counted with respect to Li/2MP rotation, the rotational speed Q can be calculated as follows. 
       Ω=60×( Li /(2 MP ))×( fc /( nLi ))=60 fc/ 2 MPn [rpm]  (5)
 
     Therefore, regardless of the section phase interval Li, it is feasible to detect the rotational speed by the same counter with a smaller number of N Hall sensors than the number of phases of the motor. 
       FIG. 12  is a diagram illustrating the entire configuration of the second embodiment of the motor rotation speed detection device.  FIG. 13  is a diagram illustrating an exemplary circuit configuration of a section determination unit and a clock pulse output unit according to the second embodiment of the motor rotation speed detection device. In  FIGS. 12 and 13 , portions similar to those in  FIGS. 9 and 10  are denoted by the same reference numerals and explanations similar to those in the first embodiment will be omitted. 
     A motor rotation speed detection device  1  includes first to Nth Hall sensors HS 1  to HS N , section determination unit  1011 , clock pulse output unit  1013 , counter  1015  for counting clock pulses output from the clock pulse output unit  1013  for each section Bij, and rotational speed calculation unit  1017  configured to calculate the rotational speed of the motor based on the counting value of the counter  1015 . 
     The first to Nth Hall sensors HS 1  to HS N  are disposed at intervals of an integral multiple of electrical angle 180/M° in the clockwise direction. 
     The section determination unit  1011  generates and outputs first to Nth signals in which only the i-th signal is a signal representing the first state and all the remaining signals are signals representing the second state that is different from the first state, in respective sections Bij (j is an integer not smaller than 1 and not larger than 2P) having a phase interval of (180/MP)·Li° (i is an integer not smaller than 1 and not larger than N, and Li is any integer not smaller than 1 and not larger than (M−N+1)), obtained by dividing the phase section corresponding to one complete rotation of the M-phase motor into 2P pieces and further dividing each section into N pieces, from the output signals of the first to Nth Hall sensors HS 1  to HS N . 
     The clock pulse output unit  1013  includes first to K-th clock pulse generators  1131   1  to  1131   K  capable of generating clock pulses of first to K-th frequencies with respect to first to K-th frequencies mutually different among the frequency fc/Li, first to Nth AND element  1133   1  to  1133   N  serving as first to Nth operation units, and OR element  1135  serving as an OR operation unit. The i-th signal output from the section determination unit  1011  and clock pulses of the clock pulse generator  1131   j  (i.e., one of the first to K-th clock pulse generators  1131   1  to  1131   K ) that generates clock pulses of frequency fc/Li are input to the i-th AND element  1133   j . Outputs from the first to Nth AND elements  1133   1  to  1133   N  are input to the OR element  1135 . The output from the OR element  1135  is output as an output of the clock pulse output unit  1013 . 
     The counter  1015  counts the clock pulses output from the clock pulse output unit  1013  and resets its counting value based on the output from the section determination unit  1011 , when any one of the sections Bij changes to another section. As a result, the counter  1015  can count the clock pulses output from the clock pulse output unit  1013  for each of the sections Bij. 
     The rotational speed calculation unit  1017  calculates the rotational speed ω of the motor based on the counting value of the counter  1015 , according to the above-mentioned formula (4). 
     If it is difficult to prepare K types of clock pulse generators of fc/Li [Hz] (i=1, 2, . . . , K), only the clock pulse generator of fc [Hz] may be used and configured in such a way as to discriminate each section based on the output from the section determination unit  1011 , divide the clock pulses from the clock pulse output unit  1013  by 1/Li according to the section phase interval, and output the divided clock pulses. 
     Alternatively, when using only the clock pulse generator of fc [Hz], it may be configured to discriminate each section based on the output from the section determination unit  1011 , multiply the counting value of the counter by 1/L according to the section phase interval, and output the multiplied counting value to the rotational speed calculation unit  1017 . 
     Hereinafter, some specific examples will be described. 
     &lt;1 Magnetic Pole Pair, 5 Phases, and 3 Hall Sensors&gt; 
     In the case of P=1 with respect to the number of magnetic pole pairs, M=5 with respect to the number of phases, and N=3 with respect to the number of Hall sensors, the division number of the rotor phase is 2N=6 and six states are detectable. When using the output signals of the Hall sensors HS 1 , HS 2 , and HS 3  disposed at intervals of electrical angle 180/5=36° in the clockwise direction,  FIG. 14  illustrates values of the output signals of the Hall sensors HS 1 , HS 2 , and HS 3  with respect to the rotor rotation phase angle. 
     From  FIG. 14 , since phase intervals L 1  and L 2  of respective sections B 11 , B 21 , B 12 , and B 22  are 2 when the angle 36° is the basic unit and phase interval L 3  of respective sections B 31  and B 32  is 1 when the angle 36° is the basic unit, it is sufficient to prepare a first clock pulse generator for generating clock pulses of the frequency fc/2 [Hz] and a second clock pulse generator for generating clock pulses of the frequency fc [Hz].  FIG. 15  illustrates an exemplary circuit configuration adoptable in this case.  FIG. 14  illustrates the output of the section determination unit  1011  in this case. 
     Next, when using the output signals of the first and second Hall sensors HS 1  and HS 2  disposed at an interval of electrical angle 180/5=36° in the clockwise direction and the fourth Hall sensor HS 4  disposed at an interval of electrical angle 72° with respect to the second Hall sensor HS 2  in the clockwise direction,  FIG. 16  illustrates values of the output signals of the first, second, and fourth Hall sensors HS 1 , HS 2 , and HS 4  with respect to the rotor rotation phase angle. 
     From  FIG. 17 , since phase intervals L 1  and L 2  of respective sections B 11 , B 21 , B 12 , and B 22  are 1 when the angle 36° is the basic unit and phase interval L 3  of respective sections B 31  and B 32  is 3 when the angle 36° is the basic unit, it is sufficient to prepare a first clock pulse generator for generating clock pulses of the frequency fc [Hz] and a second clock pulse generator for generating clock pulses of the frequency fc/3 [Hz].  FIG. 17  illustrates an exemplary circuit configuration adoptable in this case.  FIG. 16  illustrates the output of the section determination unit  11  in this case. 
     &lt;1 Magnetic Pole Pair, 5 Phases, and 4 Hall Sensors&gt; 
     In the case of P=1 with respect to the number of magnetic pole pairs, M=5 with respect to the number of phases, and N=4 with respect to the number of Hall sensors, the division number of the rotor phase is 2N=8 and eight states are detectable. When using the output signals of the first to fourth Hall sensors HS 1 , HS 2 , HS 3 , and HS 4  disposed at intervals of electrical angle 180/5=36° in the clockwise direction,  FIG. 18  illustrates values of the output signals of the Hall sensors HS 1 , HS 2 , HS 3 , and HS 4  with respect to the rotor rotation phase angle. 
     From  FIG. 18 , since phase intervals L 1 , L 2 , and L 4  of respective sections B 11 , B 21 , B 41 , B 12 , B 22 , and B 42  are 1 when the angle 36° is the basic unit and phase interval L 3  of respective sections B 31  and B 32  is 2 when the angle 36° is the basic unit, it is sufficient to prepare a first clock pulse generator for generating clock pulses of the frequency fc [Hz] and a second clock pulse generator for generating clock pulses of the frequency fc/2 [Hz].  FIG. 19  illustrates an exemplary circuit configuration adoptable in this case.  FIG. 18  illustrates the output of the section determination unit  1011  in this case. 
     With such configurations, the rotational speed of the motor can be detected by a smaller number of Hall sensors than the number of phases of the motor. 
     The above-mentioned embodiments are not limited to the brushless motor, although they have been described with reference to the brushless motor. It is needless to say that they are applicable to any motor (e.g., a synchronous motor) that is similar to the brushless motor in configuration. 
     The motor rotation speed detection device may have any of the following constituent features 1 to 6. 
     1. A motor rotation speed detection device for an M-phase motor whose number of magnetic pole pairs is P, including first to Nth (N is an integer larger than 1 and smaller than M) Hall sensors disposed at intervals of an integral multiple of electrical angle 180/M°, a section determination unit configured to generate and output first to Nth signals in which only the i-th signal is a signal representing a first state and all the remaining signals are signals representing a second state that is different from the first state from the output signals of the first to Nth Hall sensors, in each of sections Bij (j is an integer not smaller than 1 and not larger than 2P) having a phase interval of (180/MP)·Li° (i is an integer not smaller than 1 and not larger than N, and Li is any integer not smaller than 1 and not larger than (M−N+1)), obtained by dividing each section obtained by dividing the phase section of one rotation of the M-phase motor into 2P pieces into N pieces, a clock pulse output unit configured to output clock pulses of frequency fc/Li in respective sections Bij when the i-th signal of the first to Nth signals is the signal representing the first state, a counter for counting the clock pulses output from the output unit for each section Bij, and a rotational speed calculation unit configured to calculate the rotational speed of the motor based on the counting value of the counter.
 
2. The motor rotation speed detection device according to the above-mentioned 1, wherein the clock pulse output unit includes first to K-th clock generators for generating clock pulses of first to K-th frequencies with respect to first to K-th frequencies mutually different among the frequency fc/Li, first to Nth operation units, and an OR operation unit, wherein the i-th operation unit outputs the output from the clock generator that generates clock pulses of the frequency fc/Li when the i-th signal is the signal representing the first state, and the OR operation unit calculates a logical sum of output signals of the first to Nth operation units and outputs clock pulses of the frequency fc/Li in each section Bi.
 
3. The motor rotation speed detection device according to the above-mentioned 2, wherein the first state is a first logic, the second state is a second logic different from the first logic, the first to Nth operation units are AND operation units, and the i-th operation unit calculates a logical product of the output from the clock generator that generates clock pulses of the frequency fc/Li and a logic represented by the i-th signal.
 
4. The motor rotation speed detection device according to the above-mentioned 1, wherein the clock pulse output unit includes a clock generator for generating clock pulses of frequency fc, and a clock frequency converter for multiplying the output of the clock generator by 1/Li when the i-th signal is the signal representing the first state and generating clock pulses of frequency fc/Li in each section Bij.
 
5. A motor rotation speed detection device for an M-phase motor whose number of magnetic pole pairs is P, including first to Nth (N is an integer larger than 1 and smaller than M) Hall sensors disposed at intervals of an integral multiple of electrical angle 180/M°, a section determination unit configured to generate and output first to Nth signals in which only the i-th signal is a signal representing a first state and all the remaining signals are signals representing a second state that is different from the first state from the output signals of the first to Nth Hall sensors, in each of sections Bij (j is an integer not smaller than 1 and not larger than 2P) having a phase interval of (180/MP)·Li° (i is an integer not smaller than 1 and not larger than N, and Li is any integer not smaller than 1 and not larger than (M−N+1)), obtained by dividing each section obtained by dividing the phase section of one rotation of the M-phase motor into 2P pieces into N pieces, a clock pulse output unit configured to output clock pulse of frequency fc, a counter for counting the clock pulses output from the output unit for each section Bij, and a rotational speed calculation unit configured to calculate the rotational speed of the motor based on a value obtained by multiplying the counting value of the counter by 1/Li, for each section Bij, when the i-th signal of the first to Nth signals is the signal representing the first state.
 
6. The motor rotation speed detection device according to any one of the above-mentioned 3 to 5, wherein P=1, M=3, N=2, and the section determination unit calculates an exclusive OR of the output signals of the first and second Hall sensors and a negation of the exclusive OR and then outputs the calculation results as first and second signals.
 
     REFERENCE SIGNS LIST 
     
         
           1 ,  2 ,  3  reaction wheels 
           10 ,  20 ,  30  frames 
           101  third cutout part 
           102  fourth cutout part 
           103  third residual part 
           104  fourth residual part 
           105  female screw part 
           106  second through hole 
           107  recessed part 
           108  hole 
           109  opening 
           11  leaf spring 
           111  first slit 
           113  second slit 
           115  hole 
           116  ear part 
           12  electromagnet 
           121  first braking surface 
           122  wiring 
           13  flywheel (first flywheel) 
           131  recessed part 
           133  hole 
           134  second braking surface 
           135  screw hole 
           136  screw 
           14  motor 
           141  motor body 
           141   a  stator part 
           141   b  rotor part 
           143  shaft 
           144  wiring 
           18  connection member 
           4  rigid flexible substrate 
           40 ,  41 , and  42  rigid circuit board parts 
           401 ,  411 , and  421  first cutout parts 
           402 ,  412 , and  422  second cutout parts 
           403 ,  413 , and  423  first residual parts 
           404 ,  414 , and  424  second residual parts 
           405 ,  415 , and  425  first through openings 
           405   a ,  415   a , and  425   a  nut accommodation parts 
           405   b ,  415   b , and  425   b  screw accommodation parts 
           406 ,  416 , and  526  first through holes 
           407 ,  417 , and  427  fifth cutout parts 
           408 ,  418 , and  428  openings 
           409 ,  419 , and  429  terminals 
           45  and  46  flexible cables 
           5  reaction wheel apparatus 
           51  control unit 
           52  MEMS sensor IMU 
           7  expansion substrate 
           801 ,  802  nuts 
           811 ,  812 ,  813 , and  814  screws 
           91 ,  92 ,  93 ′,  94 ′,  95 ′,  98 ′,  91 ″,  92 ′,  96 ′,  97 ″ connection assist member (motor rotation speed detection device) 
         HS 1 , HS 2 , HS 3 , HS 4 , HS N  first to fourth and Nth Hall sensors 
           1001  motor rotation speed detection device 
           1011  section determination unit 
           1111  XOR element 
           1113  NOT element 
           1013  clock pulse output unit 
           1131   1 ,  1131   2 ,  1131   j ,  1131   K  first, second, j-th, and K-th clock pulse generator 
           1133   1 ,  1133   2 ,  1133   3 ,  1133   i ,  1133   N  first, second, third, i-th, and Nth AND element 
           1135  OR element 
           1015  counter 
           1017  rotational speed calculation unit