Abstract:
A coreless electric machine apparatus includes: a permanent magnet arranged on the first member; two-phase coreless electromagnetic coils arranged on the second member; a coil back yoke arranged on the second member, wherein the electromagnetic coils include effective coil areas for generating a force to move the first member relatively to the second member, and coil end areas, the effective coil areas of the two-phase electromagnetic coils have same shape and are arranged in a cylindrical area between the permanent magnet and the coil back yoke, the coil end area of a first phase electromagnetic coil of the two-phase electromagnetic coils is bent in an inside direction or an outside direction of the cylindrical surface, the two-phase electromagnetic coils have same electric resistance value, and the coil back yoke covers outer peripheral areas of the effective coil areas and does not cover outer peripheral areas of the coil end areas.

Description:
BACKGROUND 
       [0001]    1. Technical Field 
         [0002]    The present invention relates to an electric machine apparatus such as a coreless electric motor or a generator. 
         [0003]    2. Related Art 
         [0004]    An electric motor is known in which an inner coil and an outer coil are wound around teeth, and a coil end of the outer coil is bent outward (for example, JP 2010-246342). In this electric motor, the teeth and the coils (electromagnetic coils) form an electromagnet, and the motor rotates by the interaction between the electromagnet and a permanent magnet. 
         [0005]    However, in a coreless electric motor without teeth, an electromagnetic coil does not form an electromagnet, and rotates by the Lorentz force between current flowing through the electromagnetic coil and a permanent magnet and the reaction thereof. In the coreless electric motor as stated above, the electric resistance and inductance of the electromagnetic coil influence the Lorentz force. In the case of the coreless electric motor including two-phase electromagnetic coils, there is a problem that it is difficult to arrange the electromagnetic coils in such a way that the electric resistances and inductances of the electromagnetic coils of the respective phases becomes equal to each other, and it is difficult to improve the efficiency of the coreless electric motor (electric machine apparatus). 
       SUMMARY 
       [0006]    An advantage of some aspects of the invention is to improve the efficiency of a coreless electric machine apparatus by causing electric resistances and inductances of two-phase electromagnetic coils to be substantially equal to each other. 
       Application Example 1 
       [0007]    This application example of the invention is directed to a coreless electric machine apparatus including a first and second cylindrical members movable relative to each other, and includes a permanent magnet arranged on the first member, two-phase coreless electromagnetic coils arranged on the second member, a coil back yoke arranged on the second member. The electromagnetic coils include effective coil areas for generating a force to move the first member relatively to the second member, and coil end areas. The effective coil areas of the two-phase electromagnetic coils have same shape and are arranged in a cylindrical area between the permanent magnet and the coil back yoke. The coil end area of a first phase electromagnetic coil of the two-phase electromagnetic coils is bent in an inside direction or an outside direction of the cylindrical surface. The two-phase electromagnetic coils have same electric resistance value, and the coil back yoke covers outer peripheral areas of the effective coil areas and does not cover outer peripheral areas of the coil end areas. 
         [0008]    In the case of the coreless electric machine apparatus including the coil back yoke, a portion of the electromagnetic coil overlapping the coil back yoke greatly contributes to the value of the inductance of the electromagnetic coil. Accordingly, according to this application example of the invention, since the electric resistances and the inductances of the two-phase electromagnetic coils can be made substantially the same, the efficiency of the coreless electric machine apparatus can be improved. 
       Application Example 2 
       [0009]    This application example of the invention is directed to the coreless electric machine apparatus according to the above application example, wherein a shape of the first phase electromagnetic coil before the coil end area is bent is equal to a shape of a second phase electromagnetic coil, and the coil end area of the first phase electromagnetic coil is bent in the inside direction or the outside direction of the cylindrical surface. 
         [0010]    According to this coreless electric machine apparatus, the two-phase electromagnetic coils have the same shape, that is, the same electric resistance and the same inductance in the flat state where the coil end areas are not bent, and the one-phase electromagnetic coil is formed by bending the portion of the coil end which hardly influences the value of the inductance. Thus, the electric resistances and inductances of the two-phase electromagnetic coils can be made substantially the same. 
       Application Example 3 
       [0011]    This application example of the invention is directed to the coreless electric machine apparatus according to Application Example 1 or 2, wherein the coil end area of the second phase electromagnetic coil of the two-phase electromagnetic coils is bent in a direction opposite to the direction in which the coil end area of the first phase electromagnetic coil is bent. 
         [0012]    According to this coreless electric machine apparatus, since the other electromagnetic coil is also bent, a slight difference between the inductance values of the two-phase electromagnetic coils can be reduced. 
       Application Example 4 
       [0013]    This application example of the invention is directed to the coreless electric machine apparatus according to any of Application Examples 1 to 3, wherein an interval between the two-phase electromagnetic coils forming the effective coil areas is twice a thickness of the electromagnetic coil in the effective coil area of the electromagnetic coil. 
         [0014]    According to this coreless electric machine apparatus, since an occupancy factor of the electromagnetic coil can be raised, the efficiency of the coreless electric machine apparatus can be improved. 
       Application Example 5 
       [0015]    This application example of the invention is directed to a moving body including the coreless electric machine apparatus according to any of Application Examples 1 to 4. 
       Application Example 6 
       [0016]    This application example of the invention is directed to a robot including the coreless electric machine apparatus according to any of Application Examples 1 to 4. 
         [0017]    The invention can be realized in various forms, and can be realized in forms of, for example, a coreless electric machine apparatus such as a motor or a generating apparatus, and further, in forms of a moving body or a robot using the same. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
           [0019]      FIGS. 1A and 1B  are explanatory views showing a first embodiment. 
           [0020]      FIGS. 2A to 2D  are enlarged explanatory views showing the vicinity of a coil end area of an electromagnetic coil. 
           [0021]      FIG. 3  is an enlarged explanatory view showing a difference between the coil shapes of electromagnetic coils  100 A and  100 B. 
           [0022]      FIG. 4A  is an explanatory view showing a state where the electromagnetic coils  100 A and  100 B are formed on a plane. 
           [0023]      FIG. 4B  is an explanatory view showing a state before the electromagnetic coils  100 A and  100 B are overlapped. 
           [0024]      FIG. 4C  is an explanatory view showing a state where the electromagnetic coils  100 A and  100 B are overlapped. 
           [0025]      FIGS. 5A and 5B  are explanatory views showing a second embodiment. 
           [0026]      FIG. 6  is an enlarged explanatory view showing a difference between coil shapes of electromagnetic coils  100 A and  100 B of the second embodiment. 
           [0027]      FIGS. 7A and 7B  are explanatory views showing a third embodiment. 
           [0028]      FIG. 8  is an enlarged explanatory view showing a difference between coil shapes of electromagnetic coils  100 A and  100 B of the third embodiment. 
           [0029]      FIG. 9  is an explanatory view showing an electric bicycle (electric assist bicycle) as an example of a moving body using a motor/generator according to a modified example of the invention. 
           [0030]      FIG. 10  is an explanatory view showing an example of a robot using a motor according to a modified example of the invention. 
           [0031]      FIG. 11  is an explanatory view showing a rail vehicle using a motor according to a modified example of the invention. 
       
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     First Embodiment 
       [0032]      FIGS. 1A and 1B  are explanatory views showing a first embodiment.  FIG. 1A  is a schematic view showing a section of an electric motor  10  cut along a plane parallel to a rotation shaft  230  and viewed from a direction perpendicular to the section.  FIG. 1B  is a schematic view showing a section of the electric motor  10  cut along a cut line  1 B- 1 B perpendicular to the rotation shaft  230  and viewed from a direction perpendicular to the section. The electric motor  10  is an inner rotor motor of a radial gap structure in which a substantially cylindrical stator  15  is arranged on an outside and a substantially cylindrical rotor  20  is arranged on an inside. The stator  15  includes a coil back yoke  115  arranged along an inner periphery of a casing  110 , and plural electromagnetic coils  100 A and  100 B arranged inside the coil back yoke  115 . In this embodiment, if the electromagnetic coils  100 A and  100 B are not distinguished from each other, each of them is simply called an electromagnetic coil  100 . The coil back yoke  115  is formed of a magnetic material and has a substantially cylindrical shape. The electromagnetic coils  100 A and  100 B are molded with a resin  130  and are arranged on the same cylindrical surface. The lengths of the electromagnetic coils  100 A and  100 B in the direction along the rotation shaft  230  are longer than the length of the coil back yoke  115  in the direction along the rotation shaft  230 . That is, in  FIG. 1A , ends of the electromagnetic coils  100 A and  100 B in the right-and-left direction do not overlap the coil back yoke  115 . In this embodiment, an area where the electromagnetic coil overlaps the coil back yoke  115  is called an effective coil area, and an area where the electromagnetic coil does not overlap the coil back yoke  115  is called a coil end area. In this embodiment, although the effective coil area and the coil end area of the electromagnetic coil  100 B, and the effective coil area of the electromagnetic coil  100 A are on the same cylindrical surface, the coil end area of the electromagnetic coil  100 A is bent outward from the cylindrical surface. 
         [0033]    The stator  15  further includes a magnetic sensor  300  as a position sensor to detect the phase of the rotor  20 . As the magnetic sensor  300 , for example, a hall sensor including a hole element can be used. The magnetic sensor  300  generates a substantially sine-wave sensor signal. The sensor signal is used to generate a drive signal to drive the electromagnetic coil  100 . Accordingly, it is preferable to provide two magnetic sensors  300  corresponding to the electromagnetic coils  100 A and  100 B. The magnetic sensor  300  is fixed on a circuit board  310 , and the circuit board  310  is fixed to the casing  110 . 
         [0034]    The rotor  20  includes the rotation shaft  230  at the center, and includes plural permanent magnets  200  at the outer periphery. Each of the permanent magnets  200  is magnetized along a radius direction (radiation direction) from the center of the rotation shaft  230  to the outside. Incidentally, in  FIG. 1B , reference characters N and S given to the permanent magnets  200  represent polarities of the permanent magnets  200  on the electromagnetic coils  100 A and  100 B side. The permanent magnet  200  and the electromagnetic coil  100  are arranged to face the cylindrical facing surfaces of the rotor  20  and the stator  15 . Here, the length of the permanent magnet  200  in the direction along the rotation shaft  230  is the same as the length of the coil back yoke  115  in the direction along the rotation shaft  230 . That is, an area where an area sandwiched between the permanent magnet  200  and the coil back yoke  115  overlaps the electromagnetic coil  100 A or  100 B is the effective coil area. The rotation shaft  230  is supported by a bearing  240  of the casing  110 . In this embodiment, a wave spring washer  260  is provided inside the casing  110 . The wave spring washer  260  performs positioning of the permanent magnet  200 . However, the wave spring washer  260  can be replaced by another component. 
         [0035]      FIGS. 2A and 2D  are enlarged explanatory views showing the vicinity of the coil end area of the electromagnetic coil.  FIG. 2A  is a schematic view showing a section of the electric motor  10  cut along the plane parallel to the rotation shaft  230  and viewed from a direction perpendicular to the section.  FIG. 2B  is a view showing a section of the electric motor  10  cut along a cut line  2 B- 2 B perpendicular to the rotation shaft  230  and viewed from a direction perpendicular to the section.  FIG. 2C  is a view showing a section of the electric motor  10  cut along a cut line  2 C- 2 C perpendicular to the rotation shaft  230  and viewed from a direction perpendicular to the section.  FIG. 2D  is a view showing a section of the electric motor  10  cut along a cut line  2 D- 2 D perpendicular to the rotation shaft  230  and viewed from a direction perpendicular to the section.  FIGS. 2A and 2D  show a coil guide  270 . Here, the cut line  2 B- 2 B and the cut line  2 C- 2 C are cut lines crossing the coil end areas of the electromagnetic coils  100 A and  100 B, and the cut line  2 D- 2 D is a cut line crossing the effective coil areas of the electromagnetic coils  100 A and  100 B. The coil guide  270  is used to facilitate positioning of the electromagnetic coils  100 A and  100 B when the electromagnetic coils  100 A and  100 B are arranged. 
         [0036]    In the section shown in  FIG. 2B , both a conductive wire forming the electromagnetic coil  100 A and a conductive wire forming the electromagnetic coil  100 B are in a direction along the circumference of the cylindrical surface. Besides, in this section, since the electromagnetic coil  100 A is bent in the outside direction of the cylindrical surface, the electromagnetic coil  100 A is on the outside circumference, and the electromagnetic coil  100 B is on the inside circumference. The electromagnetic coil  100 A is bent in the outside direction of the cylindrical surface in order to prevent the occurrence of such a state that the electromagnetic coils  100 A and  100 B collide with each other and can not be installed. In the section shown in  FIG. 2C , although the wiring direction of the conductive wire forming the electromagnetic coil  100 A is the direction along the circumference of the cylindrical surface, the wiring direction of the conductive wire forming the electromagnetic coil  100 B is a front-back direction of the drawing, and is a direction parallel to the rotation shaft  230 . In the section shown in  FIG. 2D , the wiring directions of both the conductive wire forming the electromagnetic coil  100 A and the conductive wire forming the electromagnetic coil  100 B are the front-back direction of the drawing, and are the direction parallel to the rotation shaft  230 . 
         [0037]      FIG. 3  is an enlarged explanatory view showing a difference between the coil shapes of the electromagnetic coils  100 A and  100 B. The electromagnetic coil  100 A is bent outward at P 1  where the electromagnetic coil  100 A does not overlap the coil back yoke  115 . The length from the bent part P 1  to an end P 2  of the electromagnetic coil  100 A is (L 1 +φ1). Here, φ1 denotes the thickness of a set of conductors forming the electromagnetic coil  100 A in the direction along the cylindrical surface. Besides, the length of the electromagnetic coil  100 B from P 1  where the coil  100 A is bent to an end P 3  of the electromagnetic coil  100 B is (L 1 +φ1). That is, the electromagnetic coils  100 A and  100 B before bending have the same length in the rotation shaft direction of the rotor, and the electric resistance of the electromagnetic coil  100 A and the electric resistance of the electromagnetic coil  100 B have the same value. 
         [0038]      FIG. 4A  is an explanatory view showing a state where the electromagnetic coils  100 A and  100 B are formed on a plane. FIG.  4 A(A 1 ) is a plan view of the electromagnetic coil  100 A, and  FIG. 4A  (B 1 ) is a plan view of the electromagnetic coil  100 B. The electromagnetic coil  100 A and the electromagnetic coil  100 B are formed of conductors of the same material and the same diameter. FIG.  4 A(A 2 ) is a side view of the electromagnetic coil  100 A, and FIG.  4 A(B 2 ) is a side view of the electromagnetic coil  100 B. As is understood from the comparison between FIG.  4 A(A 1 ) and FIG.  4 A(B 1 ) and between FIG.  4 A(A 2 ) and FIG.  4 A(B 2 ), in the state where the electromagnetic coils  100 A and  100 B are formed on the plane, the electromagnetic coils  100 A and  100 B have the same shape. Besides, the number of turns of the electromagnetic coil  100 A and the number of turns of the electromagnetic coil  100 B are the same number. Accordingly, the electric resistance of the electromagnetic coil  100 A and the electric resistance of the electromagnetic coil  100 B have the same value. Besides, the inductance of the electromagnetic coil  100 A and the inductance of the electromagnetic coil  100 B have the same value. When the thickness of the bundle of conductors of each of the electromagnetic coils  100 A and  100 B is φ1, and when the interval between the coil bundles in the effective coil area is L 2 , a relation of L 2 ≈2×φ1 is established. 
         [0039]      FIG. 4B  is an explanatory view showing a state before the electromagnetic coils  100 A and  100 B are overlapped. FIG.  4 B(A 1 ) is a view showing the electromagnetic coil  100 A viewed from the radiation direction of the rotation shaft  230 , and FIG.  4 B(B 1 ) is a view showing the electromagnetic coil  100 B viewed from the radiation direction of the rotation shaft  230 . FIG.  4 B(A 2 ) is a view showing the electromagnetic coil  100 A viewed from the direction parallel to the rotation shaft  230 , and FIG.  4 B(B 2 ) is a view showing the electromagnetic coil  100 B viewed from the direction parallel to the rotation shaft  230 . As shown in FIG.  4 B(A 1 ) and  4 B(A 2 ), although the whole of the electromagnetic coil  100 A is bent from the plane shape along the cylindrical surface, and the coil end area of the electromagnetic coil  100 A is bent in the outside direction from the cylindrical surface. On the other hand, as shown in (B 1 ) and (B 2 ) in  FIG. 4B , the whole of the electromagnetic coil  100 B is bent from the plane shape along the cylindrical surface, and the coil end area of the electromagnetic coil  100 B is not bent in the outside direction from the cylindrical surface. Incidentally, even if the shape is changed, the electric resistance is not changed, and therefore, the electric resistance of the electromagnetic coil  100 A and the electric resistance of the electromagnetic coil  100 B have the same value. On the other hand, although the electromagnetic coil  100 A and the electromagnetic coil  100 B have the same shape in the effective coil area, the shapes in the coil end area are different. That is, with respect to the inductance, although the inductances caused by the effective coil area are the same, the inductances caused by the coil end area are different. That is, the inductance of the electromagnetic coil  100 A and the inductance of the electromagnetic coil  100 B are slightly different from each other. In general, when the coil end area is bent, an area s of the electromagnetic coil  100 A in the magnetic flux direction is reduced, and therefore, the inductance is reduced. For example, the inductance L of the coil is expressed by the following expression. 
         [0000]    
       
         
           
             L 
             = 
             
               
                 k 
                 × 
                 μ 
                 × 
                 
                   n 
                   2 
                 
                 × 
                 s 
               
               l 
             
           
         
       
     
         [0040]    Here, k represents Nagaoka coefficient, μ represents magnetic permeability, n represents the number of turns of the electromagnetic coil, s represents the cross section of the electromagnetic coil, and l represents the length of the electromagnetic coil. 
         [0041]      FIG. 4C  is an explanatory view showing a state where the electromagnetic coils  100 A and  100 B are overlapped. Incidentally,  FIG. 4C  shows the coil back yoke  115 . The conductor bundles of the two electromagnetic coils  100 B in the effective coil area are received between the two conductor bundles of the electromagnetic coil  100 A in the effective coil area. Besides, the conductor bundles of the two electromagnetic coils  100 A in the effective coil area are received between the two conductor bundles of the electromagnetic coil  100 B in the effective coil area, and the electromagnetic coils  100 A and  100 B do not overlap each other. Besides, the coil end area of the electromagnetic coil  100 A is bend outward from the cylindrical surface, and is shifted from the coil end area of the electromagnetic coil  100 B in the radius direction. As stated above, the coil end area of the electromagnetic coil  100 A is bent outward, so that the electromagnetic coils  100 A and  100 B can be arranged on the same cylindrical surface without collision. In this embodiment, the thickness φ1 of the conductor bundle of each of the electromagnetic coils  100 A and  100 B and the interval L 2  between the coil bundles in the effective coil area have the relation of L 2 ≈2×φ1. That is, since the cylindrical surface on which the electromagnetic coils  100 A and  100 B are arranged is almost occupied by the conductor bundles of the electromagnetic coils  100 A and  100 B, the occupancy factor of the electromagnetic coils can be increased and the efficiency of the electric motor  10  ( FIGS. 1A and 1B ) can be improved. 
         [0042]    Next, the electric resistances and inductances of the electromagnetic coils  100 A and  100 B will be described. The shapes of the electromagnetic coils  100 A and  100 B shown in  FIG. 4B  are the same as the shapes of the electromagnetic coils  100 A and  100 B shown in  FIG. 4C . Accordingly, as described in  FIG. 4B , the electric resistance of the electromagnetic coil  100 A and the electric resistance of the electromagnetic coil  100 B have the same value. As described in  FIG. 4B , with respect to the inductance when the coil back yoke  115  does not exist, although the inductances caused by the effective coil area are the same, the inductances caused by the coil end area are different, and the inductance of the electromagnetic coil  100 A is slightly different from the inductance of the electromagnetic coil  100 B. However, as in the embodiment, in the state where the coil back yoke  115  and the electromagnetic coil  100 A overlap each other, with respect to the inductance of the electromagnetic coil  100 A, the inductance of the portion where the coil back yoke  115  and the electromagnetic coil  100 A overlap each other, that is, the effective coil area becomes dominant. The same applies to the electromagnetic coil  100 B. Here, since the effective coil area of the electromagnetic coil  100 A and the effective coil area of the electromagnetic coil  100 B have the same shape, the inductance of the electromagnetic coil  100 A and the inductance of the electromagnetic coil  100 B have almost the same value. Accordingly, since the Lorentz force between the electromagnetic coil  100 A and the permanent magnet  200  and the Lorentz force between the electromagnetic coil  100 B and the permanent magnet  200  have the same magnitude, both are balanced, and consequently, the efficiency of the electric motor  10  can be improved. 
         [0043]    The electric motor  10  of this embodiment includes the permanent magnet  200 , the two-phase coreless (air core) electromagnetic coils  100 A and  100 B, and the coil back yoke  115 . Each of the electromagnetic coils  100 A and  100 B of the respective phases includes the effective coil area and the coil end area. The effective coil areas of the electromagnetic coils  100 A and  100 B of the respective phases have the same shape. The effective coil areas of the electromagnetic coils  100 A and  100 B of the respective phases are arranged on the cylindrical surface between the permanent magnet  200  and the coil back yoke  115 . The coil end area of the electromagnetic coil  100 A is bent in the outside direction of the cylindrical surface. Further, the electromagnetic coils  100 A and  100 B of the respective phases have the same electric resistance value. Besides, the coil back yoke  115  covers the effective coil areas of the electromagnetic coils  100 A and  100 B of the respective phases, and does not cover the coil end area. Thus, the inductances of the electromagnetic coils  100 A and  100 B of the respective phases have substantially the same value. Accordingly, since the Lorentz force between the electromagnetic coil  100 A and the permanent magnet  200  and the Lorentz force between the electromagnetic coil  100 B and the permanent magnet  200  have the same magnitude, both can be balanced, and consequently, the efficiency of the electric motor  10  can be improved. 
         [0044]    Further, as described in  FIG. 4A  to  FIG. 4C , the electromagnetic coils  100 A and  100 B of the respective phases are formed such that the electromagnetic coils  100 A and  100 B having the same shape on the plane are bent along the cylindrical surface, and the coil end area of the electromagnetic coil  100 A of an A-phase is bent in the outside direction of the cylindrical surface. Thus, the electromagnetic coils  100 A and  100 B of the respective phases can be easily made to have the same electric resistance value. 
         [0045]    Besides, the interval L 2  between the bundles of the conductors forming the coils in the two effective coil areas of the electromagnetic coils  100 A and  100 B of the respective phases is twice the thickness φ1 of the bundle of the conductor coil in the effective coil areas of the electromagnetic coils  100 A and  100 B. Thus, the occupancy factor of the electromagnetic coil can be increased by mutually arranging the two-phase coils effectively, and the efficiency of the electric motor  10  can be improved. 
       Second Embodiment 
       [0046]      FIGS. 5A and 5B  are explanatory views showing a second embodiment.  FIG. 5A  is a schematic view showing a section of an electric motor  10  cut along a plane parallel to a rotation shaft  230  and viewed from a direction perpendicular to the section.  FIG. 5B  is a schematic view showing a section of the electric motor  10  cut along a cut line  5 B- 5 B perpendicular to the rotation shaft  230  and viewed from a direction perpendicular to the section. In the first embodiment, the coil end area of the electromagnetic coil  100 A is bent in the outside direction of the cylindrical surface on which the effective coil areas of the electromagnetic coils  100 A and  100 B are arranged. On the other hand, in the second embodiment, the coil end area of the electromagnetic coil  100 A is bent in the inside direction of the cylindrical surface on which the effective coil areas of the electromagnetic coils  100 A and  100 B are arranged. Besides, in the second embodiment, the magnetic sensor  300  is not provided, and instead, an encode  320  is provided. The reason why the magnetic sensor  300  is not provided is as follows. That is, in the second embodiment, since the coil end area of the electromagnetic coil  100 A is bent in the inside direction of the cylindrical surface, if the magnetic sensor  300  is arranged similarly to the first embodiment, the coil end area of the electromagnetic coil  100 A is positioned between the magnetic sensor  300  and the permanent magnet  200 . That is, the magnetic sensor  300  is positioned near the coil end area of the electromagnetic coil  100 A. As a result, there is a fear that the magnetic flux density received by the magnetic sensor  300  is influenced by the magnetic flux generated by the current flowing through the electromagnetic coil  100 A. Incidentally, in this embodiment, the encoder  320  for detecting a mechanical angle of the permanent magnet  200  is provided instead of providing the magnetic sensor  300 . 
         [0047]      FIG. 6  is an enlarged explanatory view showing a difference between the coil shapes of the electromagnetic coils  100 A and  100 B of the second embodiment. The electromagnetic coil  100 A is bent in the inside direction of the cylindrical surface at a point P 4  and extends to a point P 5 . The electromagnetic coil  100 B is not bent at the point P 4  and extends to a point P 6  along the cylindrical surface. The length L 3  of the electromagnetic coil  100 A from the point P 4  to the point P 5  is equal to the length L 3  of the electromagnetic coil  100 B from the point P 4  to the point P 6 . The shapes of the electromagnetic coils  100 A and  100 B from the point P 4  to the point P 5  and the point P 6  are the same. Accordingly, the values of the electric resistances of the electromagnetic coils  100 A and  100 B are the same. Besides, the point P 4  does not overlap the coil back yoke  115 . That is, a portion of the electromagnetic coil  100 A which is not bent is the effective coil area, and the effective coil area of the electromagnetic coil  100 A and the effective coil area of the electromagnetic coil  100 B have the same shape. The effective coil areas of the electromagnetic coils  100 A and  100 B overlap the coil back yoke  15 , and the inductance in the effective coil area is dominant in both the inductance of the electromagnetic coil  100 A and the inductance of the electromagnetic coil  100 B. Accordingly, the inductances of the electromagnetic coils  100 A and  100 B have substantially the same value. 
         [0048]    Accordingly, also in the second embodiment, the electric resistance of the electromagnetic coil  100 A and the electric resistance of the electromagnetic coil  100 B can be made to have the same value, and the inductance of the electromagnetic coil  100 A and the inductance of the electromagnetic coil  100 B can be made to have substantially the same value. As a result, the Lorentz force between the electromagnetic coil  100 A and the permanent magnet  200  and the Lorentz force between the electromagnetic coil  100 B and the permanent magnet  200  can be made to have the same magnitude. Thus, both is balanced, and consequently, the efficiency of the electric motor  10  can be improved. 
       Third Embodiment 
       [0049]      FIGS. 7A and 7B  are explanatory views showing a third embodiment.  FIG. 7A  is a schematic view showing a section of an electric motor  10  cut along a plane parallel to a rotation shaft  230  and viewed from a direction perpendicular to the section.  FIG. 7B  is a schematic view showing a section of the electric motor  10  cut along a cut-line  7 B- 7 B perpendicular to the rotation shaft  230  and viewed from a direction perpendicular to the section. In the first and the second embodiments, the coil end area of the electromagnetic coil  100 A is bent in the outside direction or the inside direction of the cylindrical surface, and the coil end area of the electromagnetic coil  100 B is not bent in the outside direction or the inside direction of the cylindrical surface. On the other hand, in the third embodiment, differently from the first and the second embodiments, the coil end area of the electromagnetic coil  100 A is bent in the outside direction of the cylindrical surface, and the coil end area of the electromagnetic coil  100 B is bent in the inside direction of the cylindrical surface. 
         [0050]      FIG. 8  is an enlarged explanatory view showing a difference between the coil shapes of the electromagnetic coils  100 A and  100 B of the third embodiment. The electromagnetic coil  100 A is bent in the outside direction of the cylindrical surface at a point P 7  and extends to a point P 8 . The electromagnetic coil  100 B is bent in the inside direction of the cylindrical surface at the point P 7  and extends to a point P 9 . A length L 4  of the electromagnetic coil  100 A from the point P 7  to the point P 8  is the same as a length L 4  of the electromagnetic coil  100 B from the point P 7  to the point P 9 . The electromagnetic coils  100 A and  100 B in the left direction from the point P 7  in the drawing have the same shape. Accordingly, the electric resistances of the electromagnetic coils  100 A and  100 B have the same value. 
         [0051]    When the length of each of the electromagnetic coils  100 A and  100 B is L 5 , the coil end area of the electromagnetic coil  100 A is bent in the outside direction by L 5 /2, and the coil end area of the electromagnetic coil  100 B is bent in the inside direction by L 5 /2. Incidentally, in the first embodiment, the coil end area of the electromagnetic coil  100 A is bent in the outside direction by L 5 . That is, the deformation amount of the electromagnetic coil  100 A in the third embodiment is half of the deformation amount of the electromagnetic coil  100 A in the first embodiment. Accordingly, the inductance value of the electromagnetic coil  100 A of the third embodiment is closer to the inductance value of the electromagnetic coil  100 B deformed cylindrically as shown in  FIG. 4B  than the inductance value of the electromagnetic coil  100 A of the first embodiment. Besides, also with respect to the electromagnetic coil  100 B, since the coil end area of the electromagnetic coil  100 B is bent in the inside direction by L 5 /2, the inductance value of the electromagnetic coil  100 B of the third embodiment is closer to the inductance value of the electromagnetic coil  100 A of the first embodiment than the inductance value of the electromagnetic coil  100 B deformed cylindrically as shown in  FIG. 4B . Accordingly, the difference between the inductance of the electromagnetic coil  100 A and the inductance of the electromagnetic coil  100 B of the third embodiment is small as compared with the first embodiment. 
         [0052]    Accordingly, also in the third embodiment, the electric resistance of the electromagnetic coil  100 A and the electric resistance of the electromagnetic coil  100 B can be made to have the same value, and the inductance of the electromagnetic coil  100 A and the inductance of the electromagnetic coil  100 B can be made to have substantially the same value. As a result, since the Lorentz force between the electromagnetic coil  100 A and the permanent magnet  200  and the Lorentz force between the electromagnetic coil  100 B and the permanent magnet  200  can be made to have the same magnitude, both are balanced, and consequently, the efficiency of the electric motor  10  can be improved. 
         [0053]    Incidentally, in the third embodiment, although the magnetic sensor  300  is provided, since the electromagnetic coil  100 B is bent in the inside direction of the cylindrical surface, similarly to the second embodiment, the encoder  320  may be provided without providing the magnetic sensor  300 . 
         [0054]      FIG. 9  is an explanatory view showing an electric bicycle (electric assist bicycle) as an example of a moving body using a motor/generator according to a modified example of the invention. In a bicycle  3300 , a motor  3310  is provided on a front wheel, and a control circuit  3320  and a rechargeable battery  3330  are provided on a frame below a saddle. The motor  3310  uses power from the rechargeable battery  3330  and drives the front wheel to assist the traveling. Besides, at the time of braking, the power regenerated by the motor  3310  is charged into the rechargeable battery  3330 . The control circuit  3320  is a circuit to control driving and regeneration of the motor. As the motor  3310 , the foregoing various electric motors  10  can be used. 
         [0055]      FIG. 10  is an explanatory view showing an example of a robot using a motor according to a modified example of the invention. A robot  3400  includes a first arm  3410 , a second arm  3420  and a motor  3430 . The motor  3430  is used when the second arm  3420  as a driven member is horizontally rotated. As the motor  3430 , the foregoing various electric motors  10  can be used. 
         [0056]      FIG. 11  is an explanatory view showing a railway vehicle using a motor according to a modified example of the invention. A railway vehicle  3500  includes an electric motor  3510  and a wheel  3520 . The electric motor  3510  drives the wheel  3520 . Further, the electric motor  3510  is used as a generator at the time of braking of the railway vehicle  3500 , and the power is regenerated. As the electric motor  3510 , the foregoing various electric motors  10  can be used. 
         [0057]    Although the embodiments of the invention have been described based on some examples, these embodiments of the invention are intended to facilitate the understanding of the invention and are not limit the invention. The invention can be modified and improved without departing from the gist thereof and the scope recited in the claims, and the invention naturally includes the equivalent thereof. 
         [0058]    The present application claims priority based on Japanese Patent Application No. 2011-108958 filed on May 16, 2011, the disclosure of which is hereby incorporated by reference in its entirety.