embodiments of the present invention will be described below with reference to the accompanying drawings . referring to fig1 to 4 , the clock spring is mainly constituted by a lower case 1 , an upper case 2 supported on the lower case 1 so as to be rotatable relative to the same , a spacer 3 rotatably interposed between the two cases 1 and 2 , a gear 4 for rotatingly driving the spacer 3 , and flexible cables 5 coiled in the two cases 1 and 2 . the lower case 1 has a bottom plate 7 in which a central opening 6 is formed and inner and outer circumferential walls 8 and 9 perpendicularly extending from the inner and outer circumferential ends of the bottom plate 7 . the lower case 1 has a cylindrical shape generally opened at its top and closed at its bottom . a plurality of threads of projections 10 are formed on the bottom plate 7 concentrically with the central opening 6 so as to extend perpendicularly from the bottom plate 7 . a plurality ( five threads in this embodiment ) of first cable accommodation grooves 11 are formed between the projections 10 . cable outlet holes ( not shown ) are formed in portions of the bottom plate 7 corresponding to the bottoms of the first cable accommodation grooves 11 . a first rack 12 which meshes with the gear 4 described later is formed on the bottom plate 7 at a position between the outermost projection 10 and the outer circumference wall 9 so as to have a ring - like shape as viewed in plan . a window hole 27 is formed in the outer circumferential wall 9 , and a transparent cover 28 is fitted in the window hole 27 . as shown in fig5 the upper case 2 has a ceiling plate 14 having a central opening 13 and is rotatably connected to the lower case 1 by being fitted around internal surfaces of the inner circumferential wall 8 in a snap connection manner . a plurality of threads of projections 15 are formed on the ceiling plate 14 concentrically with the central opening 13 so as to extend perpendicularly from the ceiling plate 14 . a plurality ( five threads in this embodiment ) of second cable accommodation grooves 16 are formed between the projections 15 . the second cable accommodation grooves 16 and the first cable accommodation grooves 11 face each other with the later - described spacer 3 interposed therebetween . cable outlet holes 17 are also formed in portions of the ceiling plate 14 corresponding to the bottoms of the second cable accommodation grooves 16 . a second rack 18 having a ring - like shape as viewed in plan is formed on a circumferential portion of the ceiling plate 14 . the gear 4 also meshes with the second rack 18 . the spacer 3 is formed of a material such as a molded synthetic resin having a good sliding property , and has a generally ring - like shape with a cut opening 19 . the spacer 3 is rotatably interposed between the first cable accommodation grooves 11 of the lower case 1 and the second cable accommodation grooves 16 of the upper case 2 . as shown in fig6 a shaft member 20 having two arm portions is set in the opening 19 , and a first roller 21 and a second roller 22 are respectively supported axially on the arms of the shaft member 20 so as to be freely rotatable . the gear 4 is fixed to one end of the first roller 21 by press fitting . as mentioned above , the gear 4 meshes with the first and second racks 12 and 18 . a mark 29 indicating a reference point for positioning is provided on a surface of the gear 4 . the flexible cables 5 are formed of cables called wire harness , i . e ., conductor wires covered with an insulating material . in this embodiment , five wire harness cables are used . fig4 shows a state in which flexible cables 5 are coiled in the first cable accommodation grooves 11 of the lower case 1 . that is , one end of each flexible cable 5 extending from the upper case 2 into the lower case 1 through the opening 19 while being turned at the second roller 22 through about a half round is accommodated in the corresponding first cable accommodation groove 11 of the lower case 1 , while the other end is coiled in the opposed second cable accommodation groove 16 of the upper case 2 . one end of each flexible cable 5 is led through the unillustrated cable outlet hole to the outside of the lower case 1 , is fixed by being cranked in a holder 23 attached to the lower surface of the bottom plate 7 of the lower case 1 and is connected to a lower connector 24 while being combined with the ends of the other cables 5 . the other end of each flexible cable 5 is led through the cable outlet hole 17 to the outside of the upper case 2 , is fixed by being cranked in a holder 25 attached to the upper surface of the ceiling plate 14 of the upper case 2 and is connected to an upper connector 26 while being combined with the ends of the other cables 5 . next , the operation of the clock spring in accordance with the above - described embodiment will be described below with respect to a case in which the lower case 1 is used as a stationary member while the upper case 2 is used as a movable member . in fig7 ( a ) to 7 ( c ), one of the flexible cables 5 is illustrated schematically while the lower and upper cases 1 and 2 , the spacer 3 and other members are omitted . fig7 ( a ) shows a neutral state in which the amounts of coiling of the flexible cable 5 in the first cable accommodation groove 11 of the lower case 1 and the second accommodation groove 16 of the upper case 2 are equal . in this case , the mark 29 of the gear 4 is located at right - above position as shown in fig8 ( a ), and the gear 4 can be seen from the outside through the cover 28 . when the upper case 2 is rotated counterclockwise ( in the direction of arrow a in fig7 ( a )) to a predetermined extent from the state shown in fig7 ( a ), the gear 4 meshing with the racks 12 and 18 of the lower and upper cases 1 and 2 revolves in the direction of arrow a to an extent corresponding to half the extent of rotation of the upper case 2 while rotating clockwise ( in the direction of arrow b ) on its axis , and the spacer 3 supporting the shaft of the gear 4 is driven by the gear 4 to rotate in the direction of arrow a to the same extent as the revolution of the gear 4 . also , the turned portion 5 &# 39 ; of the flexible cable 5 wrapped round the second roller 22 is also moved in the direction of arrow a to the same extent as the spacer 3 ( i . e ., half the extent of rotation of the upper case 2 ), and a length of flexible cable 5 equal to the extent of this movement is payed out from the first cable accommodation groove 11 of the lower case 1 and is coiled in the second cable accommodation groove 16 of the upper case 2 . thus , when the upper case 2 is rotated in the direction of arrow a to make n revolutions , the spacer 3 , the gear 4 and the second roller 22 make n / 2 revolutions , so that a length of flexible cable 5 corresponding to n / 2 rounds is payed out from the first cable accommodation groove 11 through the opening 19 to be coiled in the second cable accommodation groove 16 . the upper case 2 can be rotated in the direction of arrow a until the whole of the flexible cable 5 coiled in the first accommodation groove 11 of the lower case 1 is coiled in the second cable accommodation groove 16 of the upper case 2 , as shown in fig7 ( b ). that is , the upper case 2 can make revolutions twice as much as the number of windings of flexible cable 5 in the lower case 1 . the counterclockwise rotation of the upper case 2 is terminated at the position corresponding to the state shown in fig7 ( b ). when the upper case 2 is rotated reversely relative to the above rotation , that is , rotated clockwise ( in the direction of arrow c ) from the state shown in fig7 ( a ), the gear 4 revolves in the direction of arrow c to an extent corresponding to half the extent of rotation of the upper case 2 while rotating counterclockwise ( in the direction of arrow b &# 39 ;), so that , as shown in fig7 ( c ), a length of flexible cable 5 equal to the extent of revolution of the gear 4 is payed out from the second cable accommodation groove 16 of the upper case 2 through the opening 19 to be coiled in the first cable accommodation groove 11 of the lower case 1 . if the number of teeth of the gear 4 is z 1 ; the number of teeth of each of the racks 12 and 18 is z 2 ; and the number of revolutions ( rotational frequency ) of the gear 4 during the period of time in which the gear 4 rolls on the racks 12 and 18 one round ( revolves one time ) is n , the relationship therebetween is : for example , z 1 = 18 and z 2 = 96 are set and are substituted in equation ( 1 ). then , is obtained . the gear 4 rotates 51 / 3 times during its one revolution . in this case , therefore , when the upper case 2 is rotated counterclockwise ( in the direction of arrow a ) two times from the neutral position shown in fig8 ( a ), the gear 4 makes one revolution while rotating clockwise ( in the direction of arrow b ) 51 / 3 times , so that the mark 29 of the gear 4 is shifted clockwise by 1 / 3 of one revolution , i . e ., 120 °, as shown in fig8 ( b ). when the upper case 2 is rotated clockwise ( in the direction of arrow c ) two times from the neutral position shown in fig8 ( a ), the gear 4 makes one revolution corresponding to half of the revolutions of the upper case 2 while rotating counterclockwise ( in the direction of arrow b &# 39 ;) 51 / 3 times , so that the mark 29 is shifted counterclockwise by 120 °. thus , if the numbers of teeth z 1 and z 2 are set so that n in equation ( 1 ) is not a natural number , the mark 29 is shifted by a predetermined angle during the period of time in which the gear 4 makes one revolution . it is thereby possible to set the lower and upper cases 1 and 2 in a correct state ( neutral state ) with respect to the relative position therebetween in the direction of rotation . in the above - described embodiment , the setting of the clock spring is correct only when the state of the mark 29 at the tight - above position is seen through the cover 28 . in other cases , i . e ., a case in which the gear 4 is not seen through the cover 28 and a case in which the gear 4 is seen but the mark 29 is not at the right - above position , it is indicated that the setting of the clock spring is incorrect . in such cases , the upper case 2 may be rotated until the mark 29 is set to the right - above position to adjust the relative position of the lower and upper case 1 and 2 . in the above - described embodiment , only a length of flexible cable 5 may be provided such that each flexible cable 5 forms windings corresponding to about half the necessary amount of rotation may be provided . it is thus possible to greatly reduce the length of flexible cable 5 in comparison with the conventional device . moreover , a wire harness can be used as flexible cable 5 to reduce the total cost of the clock spring . since each flexible cable 5 used is short , the diameter of the cable housing can be reduced , which effect is advantageous in reducing the overall size of the clock spring . the first and second cable accommodation grooves 11 and 16 concentrically formed in the opposed surfaces of the lower and upper cases 1 and 2 at equal pitches and the spacer 3 interposed between the cable accommodation grooves 11 and 16 prevent the flexible cables 5 from entangling with each other and also prevent each flexible cable 5 from entangling itself between the first and second cable accommodation grooves 11 and 16 , thereby making it possible to smoothly coil and uncoil the flexible cables 5 . the shaft of the gear 4 is supported on the spacer 3 , and the gear 4 is meshed with the ring - like racks 12 and 18 formed on the lower and upper cases 1 and 2 , so that the spacer 3 can follow the movement of the turned portions 5 &# 39 ; of the flexible cables 5 . there is therefore no possibility of an excessive force being applied to the flexible cables . by this effect as well , the flexible cables 5 can be smoothly coiled and uncoiled . the mark 29 is provided on the gear 4 to function as an indicator , whereby the lower and upper cases 1 and 2 can be positioned relative to each other by observing the gear 4 with the eye from the outside through the cover 28 . moreover , this positioning mechanism can be accommodated in the lower and upper cases 1 and 2 . in this respect as well , the construction of the present invention is advantageous in reducing the size of the clock cable . in the above - described embodiment , first and second cable accommodation grooves 11 and 16 are integrally formed on the lower and upper cases 1 and 2 , respectively . alternatively , projections 10 and 15 may be integrally formed on the upper and lower surfaces of the spacer 3 to provide the cable accommodation grooves 11 and 16 on the spacer 3 , or only the cable accommodation grooves 11 or 16 may be provided on the spacer 3 . in the above - described embodiment , the lower case 1 is used as a stationary member while the upper case 2 is used as a movable member . however , the relationship between these members may be reversed ; the upper case 2 may be used as a stationary member and the lower case 1 as a movable member . in the above - described embodiment , gear 4 and first and second racks 12 and 18 are used as a means for driving the spacer 3 . the arrangement may alternatively be such that , in accordance with another embodiment of the present invention shown in fig9 a roller 30 formed of rubber or the like is axially supported on the spacer 3 and is made to contact and roll on the opposed surfaces of the lower and upper cases 1 and 2 . in this case , if the radius of the roller 30 is r ; the radius of the locus of rolling of the roller 30 is r ; and the number of rotations of the roller 30 during one revolution of the same is n , the relationship therebetween is : for example , if r = 55 mm and r = 10 mm are substituted in equation ( 2 ), n = 5 . 5 is obtained , that is , the roller 30 rotates 5 . 5 times while making one revolution . accordingly , in this example , when the clock spring is in the neutral state , a mark 29 provided on the roller 30 faces in the right - above direction , and , if the upper case 2 is rotated two times in the normal or reverse direction from the neutral state , the roller 30 makes one revolution while rotating 5 . 5 times on its axis and the mark 30 is shifted by 180 ° to the right - below position . in each of the above - described embodiments , a transparent cover 28 for observing the gear 4 ( or roller 30 ) with the eye is fitted in the outer peripheral wall 9 of the lower case 1 . however , it is possible to eliminate the need for the cover 28 by forming the whole case of a transparent resin . in the above - described embodiments , five flexible cables 5 and the same numbers of first and second cable accommodation grooves 11 and 16 are used . needless to say , the selection of this number is not exclusive . also , it is not always necessary to coil all the plurality of flexible cables in the same direction ; the flexible cables can be coiled in opposite directions . in such a case , the spacer can be driven and rotated by the flexible cables , and the gear 4 or the roller 30 can serve as an indicator alone . in accordance with the present invention , as described above , the necessary length of the cables can remarkably be reduced and the rolling member serving as a positioning indicator can be accommodated inside the movable and stationary members . it is thus possible to provide a clock spring which can suitably be reduced in price and size .