@TecQulpment Ltd 1999
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photocopy, recording or any information storage and retrieval
systemwithout the expresspermissionof TecQuipmentlimited.
All due care has been taken to ensurethat the contentsof this
manualare accwrateand up to date. However,if any errorsare
discoveredpleaseinform TecQuipmentso the problem may be
rectified.
A Packing Contents list is supplied with the equipment.
Carefullycheckthe contentsof the package(s)againstthe list. If
any items are missing or damaged, contact your local
TecQuipmentagentor TecQuipmentLtd immediately.
Educational
PRODUCTS
KEEP FOR FUTURE REFHKBNCE
Safety and Operation Information
PRODUCT: TMI04 GYROSCOPEAPPARATUS
In compliancewith the EC directive on Safety of Machinery, the following
information should be noted:
This equipment is only to be used in accordancewith instructions in the
manual. Studentsusing the equipment must be adequately supervised.Local
regulations regarding the use of electricity, gasoline, diesel oil, kerosene,
mercury must be observedin using this apparatus.
Foreseenuse of apparatus
Demonstrationof gyroscopiceffects
Installation and assembly instructions
The apparatus is supplied fully assembled.Before use, remove the perspex
cover and take off the red transit bracketwhich holds the torque arm in place.
Replacethe cover.
The apparatus is designed to operate with the following TecQuipment
supplied units:
2xE67SpeedControl Units
lxE64 TachometerUnit
Refer to separateliterature for safety and operation information about these
units.
Operating Instru cti 0os
The perspexcover of the apparatusis fitted with an interlock so that neither
of the two motors will operateunlessthe cover is fitted securely.Connectthe
two E67 units and the EM to the electrical supply. Connect the output
terminals on the E67s to the input terminals on the TMI04 using 4mm
connectors.Connectthe tachometeroutput on the TMI04 to the input on the
EM using the single lead provided. Switch on the electrical supply. The two
E67s control the speed of rotor rotation and the precession speed. The
tachometermeasuresrotor rotation speed.A stopwatch is necessaryto time
the speedof precessionof the apparatus.
The equipment must be used within its operating limits (see operating
conditions).
Maintenance and inspection
Periodically inspect elecbical leads and connectionsfor wear. Periodically
checkthat all warning labelsare in position and legible.
Handling instructions
Net weight 22kg.
Ensure the correct proceduresfor handling the above weight are used when
moving this apparatus.
Operating Conditions
~hoDi1cr
-
TMI04
Seeserial number plate
+SOC to +4OOC
~
~
Safeopera~
relative humidity ran~
~
to 9s-.!o (In\~ens~)
Noise Level
The measuredsound pressurelevel of this apparatusis lessthan 70 dB(A).
Spares
Refer to Packing Contents List for any consumablesto cover the warranty
period supplied with the apparatus.Refer to manufacturer or importer for
any other sparesrequired.
-~~
1.
INTRmUCTION
Gyroscopic
action
change
direction.
its
axis
of
acts
a
axis,
to
remain
on the
a torque
plane
at
whenever
the
The angular
rotation
couple
the
occurs
in
system.
momentum
the
is
angles
to
plane
This
torque
reaction,
or
"gyroscopic
from
attempting
to
the
direction
action
is
The study
of
vehicle
can often
vehicles.
couple
overturn
the
the
vehicle.
gyroscopic
causes
the
produced
swing
couple
aircraft
by
a
due
to
turbine
calculate
the
causes
so long
as
the
is
which
axes of
a pitching
gyroscopic
the
the
In a similar
and thus
tends
of
com-
stability
a bend,
the
tends
direction,
the
engine
way,
the
couple
to make the
for
to
of
can enable
allow
body.
field
wheels
components
action
the
changing
ship
results
the
round
in
acts.
by rotating
affect
an aircraft
in
in
travels
the
rotor
called,
of
to
axis
couple
momentum
rotating
reactions
it
the
applied
the
applied
produced
vehicle
is
turn
important
effects
case of
to
the
made to
as no external
couple
tends
couple
up or down.
torque
body
particularly
to
of
a rotating
angular
pitch
A knowlege
sideways.
of
which
of
by turning
In the
is
couple"
when a road
produced
body
a turning
in
to undesirable
example,
a rotating
which
The gyroscopic
lead
for
gyroscopic
to
gyroscopic
engineering.
ponents
of
alter
if
produced
the
of
same direction
However,
reaction
right
axis
the
ship
designer
any undesirable
effects.
Gyroscopic
effects
can also
and
gyroscopic
stabilisers
position,
sist
a
undesirable
Successful
where
In
of
gyroscope
of
the
always
on the
of
a gyroscope
aligned
earth's
the
in
If
provide
in
rolling
of
in
horizontal
the
gravity
direction,
case of
in
a suitable
of
in
ships
have been obtained.
used to
plane
re-
stabilisation.
has been achieved
is
gyro-
can be used to
means
amplitudes
effect
the
mounted
disc
a
stabilisation
a north-south
produce
such
that
irrespective
rotation
the
of
its
axis
is
position
surface.
TecQuipment TMl04
scopic
effects
couple
and
axis
as in
of a rotating
so
reductions
gyro-compass,
axis
and
gyroscopic
significant
the
instruments.
consisting
motion
use
be used to advantage
the
and
to
direction
to be determined
Gyroscope
is
enable
the
of
rotation
designed
relationship
or
to demonstrate
between
"precession"
of
the
the
the
gyro-
gyroscopic
gyroscope
-2-
y
x
Fig 2.1 Principle of Gyroscopic Action
-3-
2.
THEORY
Gyroscopic
If
we
have
mounted
in
about
a
stationary
a trunion
an
shaft
Couple
axis,
then
to move in
Now consider
the
with
rotating
in
plane
and Ob after
a short
the
screw
axis
of
when
rule).
momentum, as represented
be
produced
is
equal
given
by the
to
the
it
rate
of
the
system
free
to
rotate
will
cause
the
disc
is
w, and the axis of spin simultaneously
lOX
with
angluar
velocity
ct.
is
on a shaft
couple.
interval
by the
action
to the
I,
but
by the
in
2.1
supported
can be represented
rotation,
viewed
rrom rig
is
inertia
rig 2.1, where the flywheel
plane
instant,
clockwise
applied
horizontal
the disc
is
couple
velocity
momentum of
along
it
of application
angular
lies
such that
any
angular
the
of moment of
case shown in
the
spinn inaJ
frame
flywheel,
of time
in
the
a direction
direction
clear
vector
ab.
This
of change of
in
the
angular
is
The
Oa at
one
The momentum vector
of the
there
of a couple
vector
such that
that
w.
p
the
rotation
vector
(right
a change
in
change
disc.
in
hand
angular
momentum must
The applied
momentum, so the
couple
torque
is
by:
or = tS(lw)
~ t
The
change
can
write
axis
of
angular
momentum is
6 (100) = ab = Oa.60
spin
rotates
in
time
represented
where 66
by the
limit
T
is the angle through
w
when
so we
which the
~t:'..+ o~
de =
= Iw "dt"
. . . . 2.1
!(A)-.OO
is
the
"precession"
w is
the
angular
is
the
moment
p
I
ab,
6t.
P
where:
vector
= Os cSe = Ioo 6e
"&
~
,.
In the
of
velocity
velocity
of
inertia
in
rad/s
of
the
disc
in
rad/s
of
the
disc
in
kgm
-4-
Mg
Fig 2.2
B1f11ar Suspension
-5From
06
Fig
is
2.1
the
vector
very
small,
its
perpendicular
to
the
the
axis
fore
about
act
its
in
sense
direction
must
the
when viewed in the direction
applied
the
disc
rotating
the
disc
therefore
ion
to
axis.
couple
couple
applied
This
is
were
would
ion
the
about
2.2
In
Moment
order
result
of
is
If
the
rotated
couple
lies
couple
the
right
the
direction
that
required
By rotating
a couple
which
is
rotor
~
in
tipping
the
axis
in
must there-
that
is
to keep the
axis
of
axis
the
of
Thus,
the
in
axis
the
the
opposite
of
if
disc,
direct-
about
the
OZ
no restoring
the
disc
anti-clockwise
in
the
direct-
validity
inertia
is
of
the
the
equation
the
tension
in
angleeabout
produced
rotor
each wire
its
force
it
is
rotor.
are
is
due to
length
axis,
both
the
for
~ = dti/2L
~
4L
The restoring
Mgde.d
4l
couple
is
thus:
we obtain
the
restoring
experi-
If
L and disthe
then
angles
tension
are
in
= Mg#2 (for small ~ )
Mg sin ~/2
to
as shown in rig
Mg/2.
vertical
If
of
necessary
In the
on two wires
wires
at the wires.
The restoring
2.1
gyroscope
of mass M and the
a small
is
of
is:
-
rule,
abn,
anti-clockwise
couple.
to rotate
the
then
L~ = del2.
Substituting
along
hand screw
the
acts
to say,
the gyroscopic
done by suspending
through
may write
vector
to say,
Inertia
apart,
displacement
is
when
OZ axis.
this
d
in
any attempt
the moment of
2.2.
tance
termed
the
XOZ plane.
couple,
to investigate
determine
ment,
the
applied,
XOZ plane
when viewed
the
applied
with
limit
to Oa, that
of
so the
the
OZ.
produces
the
and in
perpendicular
acts,
represents
in
XOZ plane
To conform
be clockwise
The
the
The direction
couple
XOV plane.
in
is
XOV plane.
which
the
ab lies
force
as,
rotor
is
an angular
small,
we
each wire
-6-
I~
-
=
~~ 4L
Re-arranging thia
e+~
This
is therefore:
of motion
The equation
4IL
equation we have:
e
= 0
simple
represents
harmonic
motion
in which
the
periodic
time
T is
gi ven by,
T
The moment
I
2
=
of
fijF; 4IL
1fMg"'dT
inertia
~g~
16'"'
L
I
is
therefore:
. . . . 2.2
-7-
3.
APPARATUS
The apparatus (see fig
shaft
of
frame
(C).
3.1
consiats of a rotor disc (A) mounted on the
a small variable
speed motor (B) which is carried
in a gimbal
This assembly can be rotated about the vertical
axis by a
speed geared motor housed inside the base of the appsecond variable
Attached to one end of the rotor motor is a torque arm which
aratus.
a mass (0) at its end to balance the motor and rotor
carries
A
balance weight (H) is also fitted to the torque srm to balsnce
assembly in its static unloaded condition.
The motor pivots in the
movable
the
disc.
!
gimbal frame such that it csn rotate in the vertical plsne. A retsining
plate (E) is fitted over the torque arm to limit the angular movementof
the motor assembly. Additional masses (f) can be attached to the end of
the
torque arm to bslance the gyroscopic couple produced when the rotor
disc is spinning and the gyroscope is being rotated (precessed) about
the vertical
axis.
A removable, but electrically
interlocked transparant safety cover is fitted over the complete rotating assembly. Removing this cover automatically
stops both motors.
The
fitted
rotor
picks
motor
up from
The distance
factory
via
also
assembly
the
four
between
a slip
ring
provides
Electronic
a
whilst
disc
(J)
0
the
the
with
and the
tape
optical
path
from
supplied
optical
to
up (G) which
rotor
up is
the base of the
the
pick
on the
pick
Power is
at
signal
an opt{cal
reflective
mounted
Tachometer.
mQunted in
of
be adjuated.
unit
The apparatua is
independant
control
between
strips
thia
and must not
is
disc
pre-set
the
gimbal
(A).
at
the
rotor
motor
frame,
which
sensor
to
the E64
-
designed to operate from two E67 units, which allow
over the rotor motor and the geared precession motor
base.,'
When in operstion;
the rotor
speed, vsrisble
and 3000 rpm, is measured on the E64 Electronic
precession
rate,
vsriable
rotor
and armature
Tachometer,
between 0 and 40 rpm, is measured
using a stop-watch.
An additional
gyroscope
with
fold-out
a aimple
apparatus.
mined
The
by
oscillations
bifilar
moment of
suspending
it
suspension
inertia
from
assembly
provided
arm mounted on the
of the
the
is
arm
rotor
and
assembly
timing
together
base of
the
can be deterthe
torsional
~
8.
b.
o. 5 M~
~
2.0~M
View of Main Gyroscope Components
View of Gyroscope with
rig
3.1
Trsnsit
Brscket
Gyroscope Assembly
in Position
-
-9-
4.
EXPERIMENTALPROCEDURE
AND RESULTS
Installation
Remove
the
free
of
the
red
safety
one
of
cover
the
transit
retaining
bracket
rigidly
to
the
frame.
voltage
supplies
which
These
operate
connection
from
The
2.
(Fig
3.lb,
cover
and lift
item
K),
The apparatus
are provided
a mains
input
sideways
cover
away.
which
holds
the
TQ [67
rim
torque
arm
variable
Speed Control
are
Units.
provided
on the TM104 unit.
.
the [64
and the
is
Remove
two 12 V d.c.
and two 4mm terminals
inputs
the
the
requires
by the
until
for
connections:
mains
Control
the
blocks
to the respective
Make the following
1.
by pushing
input
supply
to
Tachometer
[67
Speed
~its.
The output
terminals
of the [67
units
to the
TMl04 to
the
input
terminals
on the
TMlO4 unit.
J.
The
tachometer
signal
The
lead
is
cover.
now
Switch
Investigstion
Ensure that
safety
no
weights
knurled
Check
retaining
balance
and re-fit
the
motors
direction
Tachometer
using
the
of
is
running.
precession
operation.
end of
the
retaining
on the
correctly
Note the
of
the
plate.
torque
balanced
balanced,
safety
the
switched
is
to obtain
the
are
assembly
the
satisfactorily
cover
for
Re-fit
the
Direction
unit
rotor
screw
weight
screw
that
the
marks on the
is
precession
the
the
assembly
taining
to the
the mass at
to
and ready
Couple
added
en
rotor
Gyroscopic
that
the
[64
the units.
and check
between
position
up
power supplies
arm lies
the
wired
on all
of
the
cover
on the
provided.
apparatus
safety
output
OFF.
balanced,
Remove the
so that
torque
arm,
the
If
necessary,
arm balance
torque
slack-
weight
condition.
re-tighten
with
and
When the
the
knurled
re-
cover.
in
position,
direction
gyroscope
then
of
set
rotation
and whether
the
rotor
of the
the
and
rotor,
torque
arm
-11-
rises
or
falls.
front
panel,
combination
The
determine
of rotor
results
gyroscopic
an
which
axes.
and
is
the
exsmple,
in
gyroscopic
Notice
disgram
the
bifilar
spare
Use
a
mass
twist
the
of
it
by weighing
These
measurements
correct
in
its
the
tip
for
each
as
the
the
rotor
be seen that
slways
gyroscope
on the
couple
leading
It will
gyroscope
the
the
inertia
and rotor
Hang the
about
the
time,
L of
rotor
value
moment of
both
arm.
to
length
the
to
armature
stop-watch
Measure
the
couple
on the
and
directions
always
leading
edge
rotor
is
of
acts
edge
to
of
moving
acts
about
precess-
precession
tip
the
the
the
gyro-
rotor.
downwsrds
ror
and
the
downwards.
of Momenton I~tia
support
then
(s)
scts
petermination
the
direction
connections
gyroscope
4.1.
depends
that
input
directions.
to
direction
same
of the
by precessing
perpendicular
couple
Lift
direction
ss shown in rig
produced
rotation.
in
4.2,
be
The couple
rotor
scope
the
the motor
and precession
should
couple
axis
ion
By interchanging
say,
provide
and the
is
on suitable
the
then
fold
the
and fold
out
arm as shown in Fig
by about
loa
and release
the
rotor
of
1.09
scales
information
2.2.
clips
from the
distance
nominally
I from equation
readings,
axis
its
50 oscillations
the wires
assembly
from
assembly
vertical
assembly
the
aasembly
d between
kg.
if
required
Check that
assembly.
them.
You can check
you wish
to
to calculate
the
rotor
The
this
do so.
you have recorded
arm away and replace
it.
the
the
assembly
clips.
Typical
resulta
Length
a8 follows
of wires
Distance
~ss
are
=
l
between wires
of rotor
0.073
M
1.09 kg
47.5
8
0.95
8
50 oscillations
t
Periodic
time
T
valuea
these
=
in equation 2.2 givea the moment of inertia
8S:
I
Therefore
1.09
x 9.81
x 0.0731
16 x-"-
I
=
6.14
m
m
d
Time for
Substituting
0.53
X 0.952
xO.53
x 10-"
kg m2
-12-
Fig 4.2
Bifilar
Suspension
-
-l~-
Magnitude
The
object
of
relationship
rotor
of Gyroscopic
this
between
and
the
necessary
Couple
psrt
the
of
the
the
sets
of
tests
validity
conditions:-
velocity,
and
the
discrete
values
=
the
balance
1.
precession
mass.
Screw
that
the
.J.
Connect
gyroscopic
obtained
at
at
connections
of
the
be set
a constant
the
dsta
of
rotor
mass on the
This
rotor
two
velocity.
number of
torque
involves
speeds
for
precession
at a limited
has to be used.
a range
couple
a constant
by the balance
ar~),
measur-
and values
of
as follows:
the
couple
under
the
is
gyroscopic
50 g mass onto the end of the torque
dome.
electrical
is
provide
that
veocity
can only
for
The procedure
a
results
velocity
velocity
results
the
precession
procedure
investigate
p
rotor
couple
to
angulsr
2.1,
measuring
(as determined
different
safety
2.
varying
equation
is
the
The
Iw w
varying
gyroscopic
so a slightly
of
involve
(i)
(ii)
However,
ing
would
couple,
velocity.
Gyroscopic couple, T
Ideally
experiment
gyroscopic
precession
to check
the
rotor
will
and precession
raise
section
4.2
to achieve
this.
to
the
arm and replace
motor
the
supplies
torque
arm.
determine
the
so
Use the
correct
Vary the precession
velocity
until
the torque
to a level
at which the scribed
line
on the
arm rises
arm lines
up with the indicating
strips
on the bracket
'E' in Figure 3.1 page 8). This is the point
at which the gyroscopic
couple
is equal to
produced by the mass on the torque arm.
(shown by
of balance
the moment
At this
condition,
measure the
precession
speed by
timing
a suitable
number of revolutions
of the assembly
using a stop-watch.
The number of revolutions
you will
need to time depends on the test
condition.
To obtain
good accuracy,
always use a timed period
seconds. Record the exact value of rotor
of at
speed.
least
30
-15-
4.
Decreaae the rotor
speed in steps of 500 rev/min and determine the
precession speed at the
speed down to 500 rev/min.
5.
Add
additional
results
50g
to
masses to the
for
each value
increments
in
value
350g.
a
of
to use values
A typical
of
set
balance
the
of
result,
results
the
the
couple
T =
0.05
equation
mass, so giving
However,
is
torque
which
x 9.81
for
lines.
it
can
arm
gyroscopic
be seen that
which
demonstrates
the
rotor
velocity.
Fig
precession
velocity
2.5
(l/w
4.1
is
for
results
for
of
results
is
sufficient
it
four
calculated
for
different
from
up
values
the
example,
the results
mass
for
the
and
firat
4.4
lie
the
the
couple
previous
velocity
in this
the
influence
shows
values
a constant
of
of
on straight
gyroscopic
velocity
couple
velocity
line
can be calculated
of
through
uaing
example,
4.3,
and
plotted
300 rad/sthe
the
at
from
lines
shown in Fig
preceasion
rotor
For
(w) should be
way in Fig 4.3,
reaults
on a straight
section.
graphs of the recip-
do indeed lie
from
independent
results
of
against rotor
)
p
are plotted
for
in
origin.
moment of
a precession
rad/a:-
6.14 x 10~" x 300 x 2.5
0.4608 ~
values are shown to agree with
experimental
to within
Table
couple suggests that
velocity
values
of
T
The
the
found
of
~
can be constructed
inertial
limited
sets
x 0.14
The results
graphs
Theoretical
to obtain
of 7 sets
is
(O.l4m).
Two further
expected,
time
couple
the origin.
As
best
a total
if
in
which pass through
against
is
similar
and 350g.
given
rocal of precession velocity
straight
It
rotor
is:
0.0687
The
arm and obtain
of mass.
The gyroscopic
of
point for each different
torque
of 50,150,250
mass.
length
balance
about
3~.
the theoretical
values
-19-
REFERENCES
1.
Morrison, J. L. M. and Crossland, B.
"~chanics
of Machines" p. 30 - 32.
2.
J. M. Prentis.
3.
Inglis,
"Applied
4.
Sir
Longmans
"Dynamics of Mechanical
Systems11. Longmans
Charles.
Mechanics
Swanson,S. A. V.
for
Engineers"
"Engineering
Chapter
XX p.380-404.
Dynamics".
Dover.