Stepping motor design

Apparatus for improving the angular resolution of a stepping motor in which the effective step angle of the motor is reduced by a factor of two with no change in the nominal pitch angle. In one embodiment, a group of two stator laminations, angularly offset from one another, are used. In a second embodiment, two rotors, angularly offset from one another, are used, together with two non-offset stator stacks. In an alternative mode of the second embodiment, two stator stacks, angularly offset from one another, are used, together with two non-offset rotors. In a first mode of a third embodiment, a rotor having first and second rotor caps is laterally surrounded by first and second stators, and the two rotor caps, but not the two stators, are angularly offset from one another by the step angle. In a second mode of the third embodiment, the two stators, but not the two rotor caps, are angularly offset from one another by the step angle. In a fourth embodiment, the stator pitch angle is twice the rotor pitch angle so that the stator teeth are not aligned with more than half the rotor teeth at any time.

BACKGROUND OF THE INVENTION 
Stator design for a stepping motor is constrained by equations relating the 
pitch angle, number of poles used, number of phases used, number of rotor 
teeth used, and other parameters. Stator design is also constrained by 
practical manufacturing considerations. Adjacent stator teeth with pitch 
angles less than about 4.degree. are difficult or impossible to construct 
for stepping motors of a size normally used for semiconductor fabrication. 
Use of a smaller pitch angle allows greater resolution, if all other 
factors remain about the same, so that decreasing the stator pitch angle 
is desirable. With present thin metal stamping technology, the lower limit 
on the step angle for a four-phase motor of reasonable size is about 
0.9.degree.. In principle, a 0.45.degree. step angle would require a rotor 
diameter of at least 4.4 cm, which is too large for many applications. 
Another problem of stepping motor design is to increase the number of 
stator poles for a fixed number of phases, such as four or eight, for a 
motor of fixed size. This would allow an improvement in step response. 
However, conventional approaches again confront manufacturing limitations, 
and only a modest number of poles can be included in a motor of rotor 
diameter 4 cm or less. 
Kuo et al, in U.S. Pat. No. 3,809,990, disclose use of three coaxial, 
magnetically independent stator sections or laminations with alternating 
polarity, the stator teeth of one section being angularly offset from the 
teeth of each of the other stator sections. The apparatus operates in a 
stepping mode or in a continuous mode. 
In U.S. Pat. No. 3,866,104, Heine discloses a five-phase stepping motor in 
which a first winding, then a second winding, then a third winding, then a 
fourth winding, then a fifth winding is short-circuited, one winding at a 
time, so that the non-energized winding moves from one pole group to 
another in succession. 
Use of two coaxial rotors, angularly offset from one another and separated 
by a non-magnetic spacer, and eight uniformly spaced stator poles with 
identical stator and rotor pitch angles, is disclosed by Field in U.S. 
Pat. No. 4,025,810. Stator teeth at two opposing positions 180.degree. 
apart are aligned with the adjacent rotor teeth, and stator poles located 
at the 90.degree. and 270.degree. positions are completely misaligned with 
the adjacent rotor teeth. The stator teeth at the 45.degree., 135.degree., 
225.degree. and 315.degree. positions are intermediate between these 
orientations with respect to the adjacent rotor teeth. The stator pole 
windings are alternatingly energized and non-energized. Field, in U.S. 
Pat. No. 4,255,696, discloses another invention using two coaxial rotor 
sections with rotor teeth angularly displaced relative to one another. 
Manson discloses a stepping motor that uses two coaxial stator sections, 
positioned back-to-back with a magnetic spacer therebetween and subjected 
to magnetically independent energization in U.S. Pat. No. 4,355,248. 
However, the angular rotation, if any, of one stator section relative to 
the other stator section is unclear. 
Use of two identical, coaxial stator sections, positioned back-to-back, is 
disclosed in U.S. Pat. No. 4,623,809, issued to Westley. Again, it is 
unclear from the discussion whether the two stator sections are angularly 
offset relative to one another. 
What is needed are stator and rotor designs that allow reduction in step 
angles to angles much less than 1.degree. and/or allow an increase in the 
number of stator poles, consistent with currently available manufacturing 
techniques. 
SUMMARY OF THE INVENTION 
These needs are met by an inventive design that, in one embodiment, 
includes M coaxial stator laminations, numbered m=1, 2, . . . , M 
(M.gtoreq.2), each stator pole having K teeth (K.gtoreq.2) and stator 
laminations number 2, 4, 6, . . . being angularly offset by an angle 
.DELTA..theta..sub.0 =.phi..sub.p /2 relative to stator laminations number 
1, 3, 5, . . . , where .phi..sub.p is the stator pitch angle. This 
embodiment also includes a rotor, coaxial with the M stator laminations, 
having a plurality of uniformly spaced rotor teeth, and having an 
axially-oriented magnetic field. The embodiment also includes 
current-carrying stator windings and activatable current sources to 
sequentially induce magnetic fields in the stator poles. 
In a first mode of the second embodiment, the invention includes two 
coaxial, aligned stator stacks, numbered m=1, 2 and not angularly offset 
from one another. This embodiment also includes two sets of rotors, 
numbered m=1, 2, coaxial with the two stator stacks, with rotor number 2 
being angularly offset by a step angle .DELTA..theta..sub.o =.phi..sub.s 
relative to rotor number 1, each rotor having two rotor components with a 
plurality of uniformly spaced rotor teeth and having an axially-oriented 
magnetic field. In a second mode of this embodiment, the two stator stacks 
may be angularly offset relative to one another by the step angle 
.DELTA..theta..sub.o =.phi..sub.s and the two rotors may be aligned with 
one another. The second embodiment also includes current-carrying stator 
windings and activatable current sources to sequentially induce magnetic 
fields in the stator poles. 
In a third embodiment, two stators and a coaxial rotor with two rotor caps 
are used, and the two stators, or the two rotor caps, but not both in the 
same motor, are angularly displaced from each other by the step angle. In 
a fourth embodiment, the stator pitch angle is twice the rotor pitch angle 
so that at most one half of a group of rotor teeth can be aligned with the 
adjacent stator teeth in a stator pole group.

DESCRIPTION OF BEST MODE OF THE INVENTION 
FIG. 1 illustrates one embodiment 11 of the invention. A first stator 
lamination 21 has a sequence of uniformly spaced teeth 23a, 23b, 23c, 23d, 
. . . . A second stator lamination 31 is coaxial with the first stator 
lamination 21, but is angularly offset therefrom by rotation by an angle 
.DELTA..theta..sub.o, with 
EQU .DELTA..theta..sub.o =.phi..sub.p /2, (1) 
where .phi..sub.p is the nominal pitch angle of the stator. The second 
stator lamination 31 has stator teeth 33a, 33b, 33c, 33d, . . . that are 
angularly offset from the corresponding teeth of the first stator 
lamination 21 by the constant angle .DELTA..theta..sub.o, which is the 
effective pitch angle of the stator. In many stepping motors in the prior 
art, the pitch angle .phi..sub.p, step angle .phi..sub.s and number of 
phases N of the motor are constrained by the relation 
EQU .phi..sub.p =N.phi..sub.s. (2) 
The embodiment 11 in FIG. 1 increases the resolution (or, equivalently, 
decreases the effective step angle .phi..sub.s) for the stator by a factor 
of two, while maintaining the same nominal pitch angle .phi..sub.p for the 
stator teeth. 
In the embodiment 11 shown in FIG. 1, the rotor 35 has uniformly spaced 
rotor teeth with pitch angle .DELTA..theta..sub.o. This embodiment may be 
used, for example, with a hybrid stepping motor, which is discussed 
generally in Stepping Motors: A Guide to Modern Theory and Practice by P. 
P. Acarnley, Peter Peregrinus Ltd. Press, 1982, pp. 1-58, and incorporated 
herein by reference. 
In a hybrid stepping motor, the rotor has a permanent magnet mounted 
thereon, and two separate windings, denoted W1 and W2 herein, which are 
used for the stator poles for a twelve-pole motor, as shown in FIG. 2. 
Winding W1 would be wound positively around poles 1, 5 and 9, (43a, 43e 
and 43i, respectively) and would be wound in the opposite or negative 
sense around poles 3, 7 and 11. Similarly, winding W2 would be wound 
positively around poles 2, 6 and 10, and would be wound in the opposite or 
negative sense around poles 4, 8 and 12. The result of this choice of 
windings is that the windings for poles 1-12 have the orientations W1+, 
W2+, W1-, W2-, W1+, W2+, W1-, W2-, W1+, W2+, W1-, W2-, respectively. When 
a direct current is caused to flow in winding W1, this induces a vector 
magnetic field B1 that is directed as shown in FIG. 2 in the stator poles 
1, 3, 5, 7, 9 and 11. Note that the direction of the magnetic field B1 
alternates between being directed outwardly and being directed inwardly as 
one proceeds from one pole in this group of six to the next pole in the 
group. In one embodiment, during the time that direct current flows in the 
winding W1, no current flows in the winding W2. After a predetermined time 
interval .DELTA.t.sub.w, the direct current in winding W1 is terminated 
and the direct current of equal magnitude is established in the winding 
W2; this produces the vector magnetic field B2, also directed, in each of 
the stator poles 2, 4, 6, 8, 10 and 12. Note that the magnetic field 
direction also alternates from one pole in this group of six to the next 
pole in the group. Direct current flows alternatingly or simultaneously in 
the windings W1 and W2. 
The rotor includes one or more sets of uniformly spaced rotor teeth, with 
each set being arranged in a circular pattern and lying in a plane, where 
the two planes are parallel but spaced apart from each other. Viewed along 
the rotor axis that is perpendicular to these two planes, the sets of 
rotor teeth are offset from one another by an angle that is one-half the 
rotor pitch angle, as illustrated in FIG. 3. Thus, if the rotor teeth in 
one of these sets are out of alignment with corresponding stator teeth by 
one-half the pitch angle, the rotor teeth in the other set are aligned 
with the corresponding stator teeth, and conversely. 
Assume that current is flowing only in winding W1 in a particular time 
interval of length .DELTA.t.sub.w and that certain rotor teeth adjacent to 
poles 1, 5 and 9 (43a, 43e, and 43i, respectively in FIG. 2) are 
approximately aligned with the corresponding stator pole teeth in those 
three poles. The rotor 45 (FIG. 3) is free to rotate, and it will attempt 
to rotate to a position that minimizes the reluctance S=L/.mu.A for the 
magnetic circuit involving the winding W1 shown in FIG. 2, where L, A and 
.mu. are the length, area and magnetic permeability for a component of the 
circuit. The reluctance of all components of this circuit except the air 
gap component are substantially unchanged for any angular position of the 
rotor 45. Thus, a first set of rotor teeth will attempt to rotate to a 
position that minimizes the reluctance associated with the air gap 
component of the magnetic circuit in FIG. 2; and this will occur when a 
maximum number m of consecutive rotor teeth in that set, shown in FIG. 1, 
are precisely aligned with m stator pole teeth for each of the poles 1, 5 
and 9 shown in FIG. 2. At this point, m consecutive rotor teeth that are 
adjacent to the stator pole teeth for each of the poles 3, 7 and 11 will 
be one-half pitch angle or 1.8.degree. out of alignment for the first 
rotor teeth set; but the poles 3, 7 and 11 of the second set of rotor 
teeth will be aligned, and the poles 1, 5 and 9 of this second set of 
rotor teeth will be out of alignment by one-half the pitch angle. Keeping 
in mind the effects of the angular offset of one set of rotor teeth 
relative to the other set of rotor teeth, attention is focused on only one 
of the two sets of rotor teeth. The reluctance associated with the 
magnetic flux circuit that includes the rotor teeth for poles 3, 7 and 11 
of the first set is less effective than the reluctance associated with the 
magnetic flux circuit that includes rotor teeth from the first set for 
poles 1, 5 and 9; and, in a first approximation, the rotor alignment force 
for the rotor teeth adjacent to poles 1, 5 and 9 is the factor initially 
considered here. 
During a second time interval of length .DELTA.t.sub.w, the current in 
winding W1 is terminated and the current in winding W2 is established. The 
inertia of the rotor, which is moving clockwise in this embodiment, plus 
the alignment force associated with the m motor teeth that are adjacent to 
each of stator poles 2, 6 and 10, cause the teeth of the rotor 45 to 
rotate clockwise by one-quarter of the pitch angle or 0.9.degree., so that 
these rotor teeth are now perfectly aligned with the m stator teeth for 
each of the poles 2, 6 and 10; misalignment of the rotor teeth of either 
set adjacent to stator poles 4, 8 and 12 is ignored, to a first 
approximation. This requires rotation of the teeth in each set of the 
rotor 45 by an angular amount of one-quarter of the pitch angle (say, 
0.9.degree.) during a time interval of length .DELTA.t.sub.w. The rotation 
continues during a third time interval of length .DELTA.t.sub.w, wherein 
the current in the winding W2 is terminated and current in the winding W1 
is re-established. During this third time interval of length 
.DELTA.t.sub.w, seven rotor teeth adjacent to the m stator teeth in each 
of the poles 3, 7 and 11 are now aligned therewith. During a fourth time 
interval of length .DELTA.t.sub.w, m rotor teeth that are adjacent to the 
m stator teeth in each of poles 4, 8 and 12 are aligned therewith. The 
result of this action is that the rotor moves a distance of 
4(0.9.degree.)=3.6.degree. in a time interval of 4.DELTA.t.sub.w. This 
corresponds to a rotational speed of (400.DELTA.t.sub.w).sup.-1. The 
effect is qualitatively unchanged for two stators, such as 21 and 31, that 
have a center-to-center offset of .phi..sub.12 as in FIG. 1. Thus, the 
alignment forces are qualitatively unchanged from one pole to the next 
consecutive pole. 
The embodiment illustrated in FIG. 1 allows a decrease in the effective 
step angle .phi..sub.s of the stator without requiring a decrease in 
nominal pitch angle .phi..sub.p so that current manufacturing technology 
can be used to fabricate a stepping motor that incorporates this 
invention. The angular resolution, or minimum rotation angle that can be 
controlled and sensed, of a stepping motor incorporating this invention is 
effectively reduced by a factor of two. FIG. 4 is a perspective view of a 
group of stator teeth, constructed according to the embodiment of FIG. 1, 
with eight stator laminations. 
In a second embodiment 60 of the invention, illustrated schematically in 
FIG. 5 for a hybrid stepping motor, two stator stacks and two rotors, all 
coaxial, are used to reduce the number of poles required in each stator 
stack for operation. The first rotor 61 has two rotor components 63 and 
64, the second rotor 62 has two rotor components 65 and 66, and each of 
these four rotor components has a set of K.sub.r uniformly spaced rotor 
teeth. The teeth of the rotor components 63 and 64 are angularly offset by 
an amount .DELTA..theta..sub.34 =.phi..sub.p /2=N.phi..sub.s /2 relative 
to one another, the teeth of the rotor components 65 and 66 are angularly 
offset by an amount .DELTA..theta..sub.56 =.phi..sub.p /2=N.phi..sub.s /2 
relative to one another; and the teeth of the rotor components 63 and 65 
are angularly offset from one another by an amount .DELTA..theta..sub.35 
=.phi..sub.s, where N is the number of motor phases (N&gt;1). A first stator 
67, positioned adjacent to the rotor 61, and a second stator 69, 
positioned adjacent to the second rotor 62, together form a stator stack, 
and the two stators are not angularly offset relative to one another in 
this first mode of the second embodiment. Each of the two stators 67 and 
69 has the same pitch angle as the rotor. The first stator 67 is wound or 
wired for operation with a first predetermined current phase, denoted 
"even phase", and the second stator 69 is wound or wired for operation 
with a second predetermined current phase, denoted "odd phase", that may 
be out of phase with the first stator current phase by a phase angle 
.DELTA..beta..sub.79 =360.degree./N. Assume that the teeth of the rotor 
component 63 are aligned with the teeth of the first stator 67 at a time 
t=t.sub.o. At this time, the teeth of the rotor component 65 associated 
with the second rotor 62 are misaligned with the teeth of the second 
stator 69 by the offset angle .phi..sub.s. 
If the electrical signal that drives the two stators 67 and 69 is 
sinusoidal and has a frequency f=1/T, at a time t=t.sub.o +T/2, the rotor 
teeth in the second rotor 62 will now move or rotate by the step angle 
.phi..sub.s in order to align themselves with the teeth on the second 
stator 69, in order to minimize the reluctance S.sub.2 =L.sub.2 
/.mu..sub.2 A.sub.2 of the magnetic circuit that includes the rotor 
components 65 and 66 and the second stator 69. The first rotor 61 will not 
resist this rotation, but will help promote the rotation, in order to 
minimize the reluctance S.sub.1 =L.sub.1 /.mu..sub.1 A.sub.1 of the 
magnetic circuit that includes the rotor components 63 and 64 and the 
first stator 67. At a later time t=t.sub.o +2(T/2), the positions are 
reversed, and the first and second rotors 61 and 62 will both rotate by an 
angle 2.phi..sub.s, relative to their respective positions at time 
t=t.sub.o, in reacting to the further phase change and in minimizing the 
total reluctance S=L.sub.1 /.mu..sub.1 A.sub.1 +L.sub.2 /.mu..sub.2 
A.sub.2 of the magnetic circuits. The rotational speed associated with 
this change of phase is thus 2.phi..sub.s /T=.phi..sub.r 
/T=360.degree./K.sub.r T, expressed in degrees per second, or 1/K.sub.r T, 
expressed in cycles per second. 
FIGS. 6A and 6B illustrate the winding diagram and direction of current 
flow for the "odd" and "even" phases, respectively, for a hybrid stepping 
motor constructed according to the embodiment discussed in FIG. 5. For 
example, the stator poles A.sub.1 and A.sub.1 are counter-wound so that 
their polarities are reversed relative to one another. FIG. 6C illustrates 
suitable pole polarities associated with the poles A.sub.1, A.sub.1, 
B.sub.1 and B.sub.1 for eight 6C illustrates suitable pole polarities 
associated with the poles A.sub.1, A.sub.1, B.sub.1 and B.sub.1 for eight. 
FIG. 7A illustrates the alignment of eight sets of stator teeth (A.sub.1, 
A.sub.1, A.sub.2, A.sub.2, A.sub.3, A.sub.3, A.sub.4 and A.sub.4) relative 
to adjacent rotor teeth of the first rotor components 63 and 64, when 
phase A is energized and phase B is not energized, for the hybrid motor 
illustrated in FIG. 5. FIG. 7B illustrates the misalignment of a second 
eight sets of stator teeth (B.sub.1, B.sub.1, B.sub.2, B.sub.2, B.sub.3, 
B.sub.3, B.sub.4 and B.sub.4) relative to adjacent rotor teeth of a second 
rotor components 65 and 66, when phase A is energized and phase B is not 
energized. FIGS. 7C and 7D illustrate the alignments and misalignments of 
the rotor components shown in FIGS. 7A and 7B, respectively, after one 
half step rotation of the rotor components 63 and 64, or 65 and 66, when 
both phases A and B are energized. FIGS. 5 and 7A-7D illustrate the first 
mode of the second embodiment, in which the stepping motor is a hybrid 
motor having two aligned stator stacks and two out-of-alignment rotors. 
FIG. 8 is a sectional side view of a variable reluctance ("VR") stepping 
motor constructed according to the second embodiment of the invention. In 
this embodiment, two coaxial rotors 81 and 82 and two stators 87 and 89 
are provided. Where a VR motor is to be constructed, two modes are again 
available. In a first mode of the second embodiment for a VR motor, the 
teeth of the rotors 81 and 82 are angularly offset from one another by an 
angle .DELTA..theta..sub.12 "=.phi..sub.s ; the teeth of the two stators 
87 and 89 are not angularly offset from one another; and the current 
phases of the two stators 87 and 89 are related as in the first mode of 
the second embodiment for a hybrid motor. In a second mode of the second 
embodiment for a VR motor, the teeth of the rotors 81 and 82 are not 
angularly offset from one another; the teeth of the stators 87 and 89 are 
angularly offset from one another by an angle .DELTA..beta..sub.79 
'"=.phi..sub.s ; and the current phases of the two stators 87 and 89 are 
related as in the second mode of the second embodiment for a hybrid motor. 
FIGS. 9A and 9B illustrate the winding diagram and direction of current 
flow for the "odd" and "even" phases, respectively, for a variable 
reluctance stepping motor constructed according to the embodiment 
discussed in FIG. 5. FIG. 9C illustrates suitable pole polarities 
associated with the poles A.sub.1, B.sub.1, C.sub.1 and D.sub.1 for eight 
consecutive steps S.sub.i (i=1, 2, . . . , 8) in rotation of the rotor. 
FIG. 10A illustrates the alignment and misalignment of a first set of eight 
stator teeth (A.sub.1, C.sub.1, A.sub.2, C.sub.2, A.sub.3, C.sub.3, 
A.sub.4 and C.sub.4) of a VR stepping motor relative to adjacent rotor 
teeth of the first rotor 81 in FIG. 9, when phase A is energized and phase 
B is not energized. FIG. 10B illustrates the misalignment of a second set 
of eight stator teeth (B.sub.1, D.sub.1, B.sub.2, D.sub.2, B.sub.3, 
D.sub.3, B.sub.4 and D.sub.4) relative to adjacent rotor teeth of the 
second rotor 82, when phase B is energized and phase A is not energized. 
FIG. 10C and 10D illustrate the relative alignment of the stator teeth and 
rotor teeth shown in FIGS. 10A and 10B, respectively, after one half step 
rotation of the rotors 81 and 82, when both phases A and B are energized. 
The windings for the stators have the same phase delay relative to one 
another as for the stators 87 and 89 discussed in connection with the 
first mode of the second embodiment. 
These approaches allow use of half as many poles to achieve the same 
angular resolution. For example, a four-phase motor with a step angle of 
0.9.degree., which would require a 16-pole stator with a conventional 
approach (FIG. 11), may be implemented with two 8-pole stators using the 
second embodiment illustrated in FIG. 12. A four-phase motor with a step 
angle of 0.45.degree. may be fabricated, using two 16-pole stators in the 
second embodiment, where the conventional approach would require use of a 
32-pole stator. 
FIGS. 13A and 13B illustrate the magnetic flux paths for a hybrid stepping 
motor for a single phase "on" and for two phases "on", respectively. FIGS. 
14A and 14B illustrate the magnetic flux paths for a variable reluctance 
stepping motor for a single phase "on" and for two phases "on", 
respectively, using the second embodiment. 
FIG. 15 is a sectional view of a stepping motor constructed according to a 
first mode of a third embodiment of the invention. In this mode of the 
third embodiment, one coaxial rotors, including two rotor caps 101 and 
102, and two stators 107 and 109 are provided. The teeth of the rotor caps 
101 and 102 are angularly offset from one another by a rotor step angle 
.DELTA..theta..sub.12 "=.phi..sub.s. The teeth of the two stators 107 and 
109 are not angularly offset from one another in this embodiment, and the 
current phases of the two stators 107 and 109 are related as in the first 
mode of the second embodiment for a hybrid motor. 
In a second mode of this third embodiment, the teeth of the rotor caps 101 
and 102 are not angularly offset from one another; but the teeth of the 
two stators 107 and 109 are angularly offset from one another by an angle 
.DELTA..theta..sub.79 '"=.phi..sub.s, and the current phases of these two 
stators are related as in the second mode of the second embodiment for a 
hybrid motor. 
The embodiment illustrated in FIG. 15 is similar to the embodiment 
illustrated in FIG. 5, but the two rotor pairs 63/64 and 65/66 are 
replaced by two individual rotor caps 101 and 102 in FIG. 15. The 
embodiment shown in FIG. 15 reduces the flux leakage problems that 
sometimes arise where two rotors are positioned in a side-by-side 
arrangement, as in FIG. 5. However, operations of the embodiments shown in 
FIGS. 5 and 15 are similar. The embodiment illustrated in FIG. 15 is 
suitable for operation as a hybrid motor, if the two rotor caps 101 and 
102 are spaced apart by a permanent magnet 112. The embodiment illustrated 
in FIG. 15 is suitable for operation as a VR motor if the two rotor caps 
101 and 102 are spaced apart by a magnetically conductive material 112. 
In the third embodiment illustrated in FIG. 15, the component 111 of the 
motor housing that overlies the two stators 107 and 109 should be 
constructed of a magnetically conductive material, such as iron, steel, 
nickel or cobalt to carry the magnetic flux required. 
In a fourth embodiment of the invention, illustrated in FIG. 16, a stator 
pole group 121 has a plurality of stator teeth 123A, 123B, 123C and 123D 
with a stator pitch angle .phi..sub.p, and a coaxial rotor 125 has a 
plurality of rotor teeth 127A, 127B, . . . , 127L with a rotor pitch angle 
.phi..sub.r. The stator pitch angle and the rotor pitch angle are related 
by the equation .phi..sub.p =M.phi..sub.r, where M is an integer.gtoreq.2. 
Preferably, M=2 here, as illustrated in FIG. 16, but greater values of the 
integer M are also suitable. Any two adjacent stator teeth will be 
separated by a pitch angle that is at least twice the rotor pitch angle so 
that the stator teeth in a pole group such as 121 will lie closest to 
every other rotor tooth, such as 127B, 127D, 127F, 127H and 127J. The body 
of the stator pole group 121 is fabricated from a plurality of punched 
sheets, superimposed upon one another. In a hybrid motor constructed 
according to FIG. 16, soft magnetic material in the rotor caps carries the 
magnetic flux lines of a central magnet. In a variable reluctance motor 
constructed according to FIG. 16, the rotor is unexcited and is made of 
magnetically soft iron, and the rotor teeth 127A-127J are attracted by the 
energized stator teeth 123A-123D in a stator pole group. 
FIG. 17 illustrates graphically the static holding torque developed versus 
rotor angular displacement for the configuration shown in FIG. 16 with 
M=2. With this configuration, the torque developed by angular displacement 
of the rotor will be distorted somewhat compared to torque for a 
conventional design in which the stator pitch angle and the rotor pitch 
angle are equal. Rotor angular displacement .DELTA..theta. ranges between 
A and D on the abscissa, and the useful range of rotor angular 
displacement for torque development purposes lies between the values B and 
C, where the torque curve is sinusoidal and is undistorted in shape from 
the conventional design. The peak-to-peak torque 2N.sub.0 is 
correspondingly reduced from the peak-to-peak torque for a conventional 
design. For M=2, the configuration of FIG. 16 may be realized by use of a 
hybrid motor or by use of a variable reluctance motor. The configuration 
shown in FIG. 17 also reduces the flux leakage that might otherwise be 
present with the configuration shown in FIG. 1.