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Description  |
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The present invention relates to position determining apparatus and has
application, for example, in measuring probes.
Measuring probes are known, for example from UK Patent No. 1,455,977 in
which a movable stylus carrier is supported on seats within the probe body
in a rest position, when no force acts on the stylus. In a measuring
operation the probe is moved by a machine until the stylus contacts a
workpiece to be measured whereby a force is applied to the stylus causing
the stylus to be displaced from the rest position by tilting or axial
displacement.
It is important for accurate measurement of workpieces that the stylus
carrier returns to its rest position with great precision after each
displacement so that the stylus ball, which contacts the workpiece returns
to the same position in space relative to the probe.
In a probe which uses a kinematic location for the stylus carrier the
position to which the stylus carrier returns is influenced by friction at
the seats. Thus the position of the stylus ball in space can vary after
each displacement and the so-called rest position of the stylus may not be
exactly the same prior to each measurement. A spring may be used to assist
in overcoming the frictional forces at the seats, but this has been found
not to completely solve the problem without unacceptably high spring
forces.
A similar problem occurs in a variety of pieces of apparatus particularly
in the measuring field where one member or part is to be repeatedly
mounted on and removed from another part with great accuracy. Examples of
such apparatus are robots; probe heads for mounting measuring probes, and
in machine tools which carry probes for measuring workpieces.
This problem is solved in accordance with the invention in apparatus having
a first member supported on a second member by determining in all
directions the displacement of a part of the supported member which is
caused by a change in the force applied by the supported member to a part
of the support.
This is most conveniently done by measuring the forces on sufficient parts
of the support or the supported member to enable the displacement of the
supported member in all of the required directions to be determined.
In the case of a kinematically mounted stylus carrier in a measuring probe
for example, in which six confronting support points are provided on each
of the movable stylus carrier and the fixed structures, this can be
achieved by determining the translational and rotational displacements
about three orthogonal axes of each of the support points on the stylus
carrier due to any change in the forces between the fixed and movable
structures.
In preferred embodiments of the invention this determination is made by
measuring variations in the forces on the fixed structure or the stylus
carrier using strain measuring devices adjacent the support points
thereon, although other methods are possible.
Examples of the invention will now be more particularly described with
reference to the accompanying drawings in which:
FIG. 1 is a sectional elevation of a probe according to the present
invention.
FIG. 2 is an enlarged view of one of the supports for the stylus carrier
within the probe of FIG. 1 and showing the strain measuring devices.
FIG. 3 is an electrical circuit for producing an electrical signal from the
strain measuring devices, and
FIG. 4 is a diagrammatic illustration of the electronics required for the
analysis of the signals from the strain measuring devices.
FIGS. 5a and 5b are respectively an end elevation and cross-section of an
alternative support arrangement for the stylus holder of a measuring
probe, and
FIGS. 6a and 6b are respectively an end elevation and cross-section of a
further alternative support arrangement for the stylus holder of a
measuring probe.
FIGS. 7, 7a and 7b show the nomenclature for the calculations required by
the computer.
Referring now to the drawings, a probe comprises a housing 2 which
constitutes a fixed member of the probe. The housing has an axis 2A and
which terminates in a shank 4 for connecting the probe to a machine (not
shown). The machine may be a co-ordinate measuring machine or a machine
tool. The probe includes a stylus 6 which terminates in a ball 8 for
contacting a workpiece. The stylus 6 is connected to a stylus carrier 10
which includes seating elements 12. The stylus carrier constitutes a
movable member of the probe. In this example the seating elements are in
the form of three cylindrical rods spaced at 120.degree. intervals around
the axis 2A. The seating elements 12 are supported in confronting seats 14
each of which in this example consists of a pair of hollow wedge-shaped
seating elements 16 (FIG. 2) fixed to the housing 2. The seating elements
12 are urged into contact with both wedge-shaped seating elements 16 of a
seat 14 by bias means which as shown may be a spring 18. Because in this
example three equi-angular spaced seats are used they form a kinematic
location for the stylus carrier 10. This seating arrangment provides a
so-called positive rest position for the stylus when no external force
acts on it. However, other seating arrangements may be used which are not
necessarily kinematic, and the invention may be applied to them.
The stylus is capable of being displaced from its rest position by an
external force acting on it, usually when the stylus ball 8 contacts a
workpiece being measured. The displacement may be an axial or tilting
movement which causes the seating elements 12 to be displaced from the
seats 14. Upon cessation of the external force on the stylus the seating
elements are returned to the seats 14 with the aid of the spring 18.
It has been found however, that friction at the surfaces of the seating
elements 12 and 16 can cause slight variations in the relative positions
of the seating elements 12 and 16 each time the stylus is displaced from
and returned to the rest position. This slight variation in the relative
position of the seating elements can cause a significant variation in the
position in space of the centre 0 of the stylus ball 8 relative to the
probe housing. This is particularly apparent when a long stylus is used
with the probe.
Thus the so-called rest position of the stylus has been found not to be a
fixed position relative to the housing but one which involves random
slight variations because of the friction acting at the seating elements.
Any variation in the positions of the seating elements 12 relative to the
confronting wedges 16 will cause variations in the loads applied to the
six surfaces of the wedges 16, and this will result in variations in the
strains produced in the structure of the wedges by the weight of the
stylus carrier and the pressure of the spring 18.
The invention provides measuring devices for example strain gauges 20
suitably positioned on the wedges 16 to measure the strain in the wedge
structure, whereby any variations in strain may be detected. The
electrical output of the strain gauges 20 is taken to an electrical
circuit 25 within the probe by leads 22.
By calibrating the position of the stylus ball in space relative to the
probe against the strain detected at the seats, the error in the position
of the centre of the ball in the so-called rest position at each
re-seating of the stylus carrier, can be determined and allowed for in the
next measurement. Thus the accuracy of the probe measurements can be
improved.
FIG. 3 illustrates an electrical circuit 25 which produces an output which
varies linearly with the strain gauge output. The circuit consists of a
bridge circuit having three resistors R of equal value and a strain gauge
S the resistance X of which is variable. The two mid-point connections of
the bridge C1 and C2 are connected to an operational amplifier A the
output of which is connected to the other side C3 of the strain gauge S.
Assuming a voltage V is connected at one side of the bridge circuit and the
other side is earthed, the voltage at the mid-point connections C1 and C2
will be V/2. The operational amplifier is designed to produce an output at
C3 which maintains the value of the voltage at C2 at the value V/2 as the
resistance X of the strain gauge S varies.
The output e.sub.o from the bridge can be shown to be e.sub.o =V/.sub.2 X.
As shown in FIG. 4 the six outputs from the bridge are each fed to a
multiplexing unit 30 and are sequentially read under the control of a
computer 32. The output from the multiplexing unit 30 is fed to an
analogue to digital converter 34 and from there passes to the computer 32.
The computer is programmed to handle the information from the strain gauges
in various ways depending on the information required from the probe.
First of all the computer compares each reading as it comes from the
multiplexing unit with a reference value to determine which of the
readings have changed since the last reading, and the value of the change.
The change in each reading is directly proportional to the increase or
decrease in the strain at each of the six seating elements 16. The
computer thus calculates the new strain value from which the new positions
of the rollers 12 can be determined. This in turn enables the location of
the centre of the stylus ball relative to the probe to be calculated and
this information is continuously used to update the software in the
machine which is used for calculating the measurements of the workpiece.
The method of calculation is briefly as follows:
Considering the mid-point of the centre assembly it will undergo a rotation
and a translation as any one of the rollers is moved due to a change in
force at the support.
Referring now to FIGS. 7, 7a and 7b:
the six balls are identified at a b c d e and f,
the distance of the centre of the centre assembly from each ball is R,
the three coordinate axes of the centre assembly are x, y and z,
the angular position of any ball e.g ball a is .alpha.a,
the contact angle between the balls and rollers is .theta. and,
the displacement of the roller due to change of force at any ball e.g. a is
1a, the measurement of which is determined from the strain gauge signals.
With this notation it can be shown that taking one ball a the movement dr
of a roller in the x or y directions due a movement 1a is given by
dr (z)=1a Sin .theta.
dr (x,y)=1a Cos .theta.
Considering the situation when ball a is the only one with a change in
force and therefore 1b=1c=1d=1e=1f=0 the incremental translations of the
centre of the centre assembly in each of the three coordinate directions
x,y and z due to a movement 1a of roller a are given by:
##EQU1##
the incremental rotations of the centre of the centre assembly abut the
axes x,y and z are given by:
##EQU2##
The resultant movement of the centre of the centre assembly when movements
1b 1c 1d 1e and 1f are taken into account will be the sum of six
increments of translation and rotation for all six balls.
These movements can then be used in combination with details of the stylus,
for example, length and orientation, to calculate the changes in position
of the stylus ball.
To increase the speed at which the computer can update the machine
software, a pre-programmed look-up table may be provided in the memory of
the computer 32 which contains information relating to the positions of
the centre of the stylus ball relative to the probe for a large number of
combinations of readings of strain from the six seats. A different look-up
table will be needed for each new length of stylus provided on the probe.
To take account of temperature changes affecting the strain measurement,
the strain gauges can be zeroed at appropriate intervals by driving the
probe into a workpiece in a direction such as to lift the seating elements
12 out of the seats 14. In this condition the readings of all of the
strain gauges should be the same since there is no force on the seats 14.
These readings are taken to be the zero readings.
After the seating elements 12 have been allowed to re-seat, the readings on
the strain gauges will clearly change, and from the differences in the
readings of the strain gauges it is possible to calculate where the centre
of the ball should be. By subsequently measuring the actual position of
the stylus ball relative to the probe, allowance can be made for any
deformation of the stylus. This measurement can be carried out by a
standard datuming routine, provided that the assumed position of the
stylus ball is re-calculated before each contact between the stylus ball
and a datum artefact, and any change in position allowed for in the
datuming calculations.
It can be seen that the invention provides a method of continuously
updating the knowledge in the machine computer of the position of the
centre of the stylus ball relative to the probe. The method therefore
automatically eliminates hysteresis errors due to unequal forces being
generated at the seating elements 16. The computer can also be programmed
to send a signal to the machine that the next reading will be in error, if
it detects from the strain gauges that the stylus carrier has failed to
re-seat.
The probe may use any form of signalling means to provide a signal to the
machine indicating that the stylus has contacted a workpiece. For example,
the probe may include a piezo-electric element which detects the shockwave
generated in the stylus at the instant of contact, strain gauges for
detecting strain on various elements of the probe fixed or moving parts,
or optical, pneumatic or electrical switches to detect displacement of the
seating elements 12 from the seats 14. Alternatively the contact of the
stylus with the workpiece may be used to complete an electrical circuit
through the probe to the machine. These and other methods of generating
the required signal for making measurements and to stop the machine are
known and are not described in detail.
If desired, however, in place of, or in addition, to any of the signalling
means referred to above, the computer can also be programmed to send a
trigger signal to the machine when the strain gauges indicate that a force
on the stylus ball has caused the stylus carrier to lift off one of the
seats, or that the strain on a pair of seats has decreased to a level such
that lift off is imminent. For this the computer needs to be programmed
simply to add together the signals from the two adjacent seating elements
16 forming a seat, and compare the total strain at each seat with a
pre-programmed threshold for the respective seat, and produce a signal
when the threshold is reached.
Because the invention enables the positions of the seating elements 12 to
be accurately and continuously monitored, the need for accuracy in the
formation of the seats is reduced. For example, it is no longer necessary
to use a three point kinematic location which has hitherto been required
for accurate re-positioning of the probe stylus. Depending on the capacity
of the computer, more seating positions may be introduced to reduce the
lobing characteristic of the three point location system, i.e. that
characteristic produced by the fact that different forces are required to
cause displacement of the stylus depending on the direction of the force
on the stylus.
Another example of the use of the invention in a probe application is in a
probe in which the stylus is removable to be replaced by a different type.
In such probes means are provided for clamping and unclamping the various
styli but it is important to know that each one is clamped correctly into
its rest position.
The invention is of particular use for a probe which is mounted on the end
of a horizontal arm of a machine where the effect of gravity will affect
the rest position of the styli.
The strain gauges have been shown positioned on the underside of the
seating surfaces. However the positions and numbers of the strain gauges
is a matter of experiment and choice in order to provide the optimum
response. For example, they may be positioned on top surfaces of seating
elements 16 or on the rods 12 in positions where the load on the stylus
carrier acts directly through the strain gauge. Any inaccuracy which might
result in the position of the rods 12 because of the flexibility of the
strain gauges will be automatically compensated for by the ability of the
computer to calculate their positions continuously.
FIGS. 5a, 5b, 6a and 6b show two alternative positions for the strain
measuring devices. In FIG. 5a the seat elements 16 of FIG. 2 are replaced
by a single ball 16a, and the single rod 12 forming the seat element on
the stylus carrier 10 is replaced by a pair of rods 12a. Strain gauges 20a
are placed on each of the rods at positions diametrically opposite to the
contact point between the rods and balls. In FIG. 6a the seat elements 16
of FIG. 2 are replaced by rods 16b which are partly cut away to leave a
cantilevered section (16c) on which the strain gauges 20b are positioned,
and the rod 12 is replaced by a ball 12b which rests on the rods 16b.
The term strain gauge as used throughout should be interpreted to mean any
suitable form of strain measuring device that can detect the deformation
of the support elements. Examples of such known devices, are resistance
strain gauges, piezo resistive devices photo elastic devices and load
cells. However, since deformation of the support will inevitably involve a
movement or displacement of both the supporting end members, a sensitive
optical displacement measuring system may be carried by either of the
members to determine the displacement directly.
The invention is not limited to the determination of the position of a
stylus in a probe as described above. For example the invention may be
applied to robots where it is important to know that the relative
positions of parts of the robot arms are accurately repeated during a
sequence of movements. Also in a co-ordinate measuring machine or machine
tool a probe may be mounted on an indexable head in which case it is
important to know that each time the head is moved to one of its
predetermined positions, it achieves the position accurately, or if it
does not achieve the position, by how much its position varies from the
desired position.
By measuring the strains on the supports supporting relatively movable
parts of any apparatus, including robots, probe heads machine tools or
measuring machines, the relative positions of the two parts can be
calculated after each movement.
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