Machine tools abstract
A multi-axis computer numerically controlled machine tool is provided
in which a cutting tool is movable relative to a workpiece by a
number of linear and rotary joints under the control of a programmable
control unit. The machine is programmed with a plurality of principal
programmable axes, called "hard" axes, and with at least
one synthesised additional programmable axis or "soft"
axis which enables the cutting tool to be moved linearly in the
direction of the soft axis without requiring a specific joint for
that purpose. The synthesised "soft" axis is a non-collinear,
partially redundant axis which increases the number of programmable
degrees of freedom to a greater number than the machine degrees
of freedom, i.e., the number of non-collinear joints. The principle
of synthesising "soft" axes may be extended to CNC machine
tools having four or more principal hard axes, for instance, to
produce a 5-joint CNC machine tool which has the flexibility of
a conventional 7- or 8-joint machine tool.
Machine tools claims
I claim:
1. A computer program recorded on memory or data storage means
for a multi-axis computer numerically controlled (CNC) machine having
workpiece mounting means for mounting a workpiece, a tool operable
upon said workpiece, a plurality of machine members and a plurality
of controllable joint means movable under the control of a part
program to cause relative movement between the tool and the workpiece
mounting means so as to cause the tool to move along a programmed
path relative to the workpiece mounting means, said machine having
a plurality of principal programmable axes for the machine which
axes constitute the minimum number of axes required to position
the tool relative to the workpiece mounting means, said program
recorded on said memory or data storage means synthesising at least
one additional concurrently programmable axis for the machine and
automatically controlling relative movement of said tool and said
workpiece mounting means in relation to said additional concurrently
programmable axis in accordance with said part program without physical
location of said additional concurrently programmable axis by said
joint means of the machine.
2. A computer program according to claim 1 which is arranged to
synthesise at least one additional concurrently programmable axis
which is non-collinear with said principal programmable axes.
3. A computer program according to claim 1 in which said at least
one additional concurrently programmable axis is arranged to pass
through a part of the tool and is fixed relative to the tool.
4. A computer program according to claim 1 which is arranged to
synthesise a plurality of additional concurrently programmable axes,
at least one of said synthesised additional concurrently programmable
axes being non-collinear with said principal programmable axes.
5. A computer program according to claim 4 in which at least one
of said synthesised additional concurrently programmable axes is
arranged to pass through a part of the tool and is fixed relative
to the tool.
6. A computer program according to claim 1 in which the total number
of programmable axes including said additional concurrently programmable
axis is greater than the number of joint means of the machine.
7. A computer program recorded on memory or data storage means
for a multi-axis computer numerically controlled (CNC) machine having
workpiece mounting means for mounting a workpiece, a tool operable
upon said workpiece, a plurality of machine members and a plurality
of controllable joint means movable under the control of a part
program to cause relative movement between the tool and the workpiece
mounting means, said plurality of joint means including a plurality
of linear joints and at least one rotary joint, said machine having
a plurality of programmable linear axes and at least one programmable
rotary axis which constitute the minimum number of axes required
to position the tool relative to the workpiece, said program recorded
on said memory or data storage means synthesising at least one additional
concurrently programmable axis and controlling relative movement
of the tool and said workpiece mounting means in relation to said
additional concurrently programmable axis without physical location
of said additional concurrently programmable axis by the said plurality
of joint means.
8. A computer program according to claim 7 in which the total number
of programmable axes is greater than the total number of joint means
of the machine.
9. A computer program according to claim 1 which is arranged to
generate axis position signals, each axis position signal representing
a desired position for the tool relative to the workpiece mounting
means in terms of components and co-ordinates of the principal axes
and said at least one synthesised additional concurrently programmable
axis, and which is arranged to transform said axis position signals
into joint position signals for controlling the positions of the
plurality of joint means so as to cause the tool to occupy the desired
position and orientation relative to the workpiece mounting means.
10. A computer program according to claim 9 which is arranged to
generate axis position signals, each axis position signal representing
a desired position for the tool relative to the workpiece mounting
means in terms of components and co-ordinates of the principal axes
and said at least one synthesised additional concurrently programmable
axis, and which is arranged to transform said axis position signals
into joint position signals for controlling the positions of the
plurality of joint means so as to cause the tool to occupy the desired
position and orientation relative to the workpiece mounting means.
11. A memory or data storage means including a computer program
for a multi-axis computer numerically controlled (CNC) machine having
workpiece mounting means for mounting a workpiece, a tool operable
upon said workpiece, a plurality of machine members and a plurality
of controllable joint means movable under the control of a part
program to cause relative movement between the tool and the workpiece
mounting means so as to cause the tool to move along a programmed
path relative to the workpiece mounting means, said machine having
a plurality of principal programmable axes for the machine which
axes constitute the minimum number of axes required to position
the tool relative to the workpiece mounting means, said computer
program recorded on said memory or data storage means synthesising
at least one additional concurrently programmable axis for the machine
and automatically controlling relative movement of said tool and
said workpiece mounting means in relation to said additional concurrently
programmable axis in accordance with said part program without physical
location of said additional concurrently programmable axis by the
joint means of the machine.
12. A memory or data storage means according to claim 11 in which
said at least one additional concurrently programmable axis is non-collinear
with said principal programmable axes.
13. A memory or data storage means according to claim 11 in which
said at least one additional concurrently programmable axis is arranged
to pass through a part of the tool and is fixed relative to the
tool.
14. A memory or data storage means according to claim 11 which
is programmed to synthesise a plurality of additional concurrently
programmable axes, at least one of said synthesised additional concurrently
programmable axes being non-collinear with said principal programmable
axes.
15. A memory or data storage means according to claim 14 in which
at least one of said synthesised additional concurrently programmable
axes is arranged to pass through a part of the tool and is fixed
relative to the tool.
16. A memory or data storage means including a memory computer
program for a multi-axis computer numerically controlled (CNC) machine
having workpiece mounting means for mounting a workpiece, a tool
operable upon said workpiece, a plurality of machine members and
a plurality of controllable joint means movable under the control
of a part program to cause relative movement between the tool and
the workpiece mounting means; said plurality of joint means including
a plurality of linear joints and at least one rotary joint, said
machine having a plurality of programmable linear axes and at least
one programmable rotary axis which constitute the minimum number
of axes required to position the tool relative to the workpiece,
said program recorded on said memory or data storage means synthesising
at least one additional concurrently programmable axis and controlling
relative movement of the tool and said workpiece mounting means
in relation to said additional concurrently programmable axis without
physical location of said additional concurrently programmable axis
by said plurality of joint means.
17. A memory or data storage means according to claim 16 and comprising
a co-ordinate transform module which is arranged to generate axis
position signals, each axis position signal representing a desired
position for the tool relative to the workpiece mounting means in
terms of components and co-ordinates of said principal programmable
axes and said at least one synthesised additional concurrently programmable
axis, and which is arranged to transform said axis position signals
into joint position signals for controlling the positions of the
plurality of joint means so as to cause the tool to occupy the desired
position and orientation relative to the workpiece mounting means.
18. A co-ordinate transform module for a multi-axis computer numerically
controlled (CNC) machine having workpiece mounting means for mounting
a workpiece, a tool operable upon said workpiece, a plurality of
machine members and a plurality of controllable joint means movable
under the control of a part program to cause relative movement between
the tool and the workpiece mounting means so as to cause the tool
to move along a programmed path relative to the workpiece mounting
means, said machine having a plurality of principal programmable
axes for the machine which axes constitute the minimum number of
axes required to position the tool relative to the workpiece mounting
means, said machine synthesising at least one additional concurrently
programmable axis for the machine, said co-ordinate transform module
transforming axis position signals representing a desired position
for the tool in terms of co-ordinates of said principal programmable
axes and said at least one synthesised additional concurrently programmable
axis into joint position signals for controlling the positions of
the plurality of joint means and automatically controlling relative
movement of said tool and said workpiece mounting means in relation
to said additional concurrently programmable axis in accordance
with said part program without physical location of said at least
one additional concurrently programmable axis by said joint means
of the machine.
Machine tools description
This invention relates to multi-axis computer numerically controlled
(CNC) machine tools in which a cutting tool is movable relative
to a workpiece under the control of programmable control means including
a computer program known as a "part program".
As used herein the term "cutting tool" refers to the
portion of the machine that is designed to act upon the workpiece
to perform the desired task. In the context of this invention, the
cutting tool is not restricted to standard turning or milling cutters,
but also includes all mechanical, electronic and/or electro-mechanical
devices used to modify the shape and/or properties of the workpiece.
Examples of cutting tools include: end-mills, turning tools, grinding
wheels, laser cutting beams, plasma beams and punch tools.
Multi-axis CNC machine tools conventionally include a plurality
of movable machine members and a plurality of controllable joints
movable to cause the cutting tool to move relative to a fixed frame
of reference (eg. the machine base). The workpiece may be mounted
on workpiece mounting means which is fixed relative to the machine
base. Alternatively, the workpiece may be mounted on workpiece mounting
means connected to the machine base by further movable machine members
and controllable joints.
The joints of a multi-axis machine tool may include prismatic (linear)
joints which enable a machine part to be moved in a linear direction
and rotary joints which enable a machine part to be rotated about
a rotary axis. The programmable control means of a multi-axis CNC
machine tool is conventionally programmed to control the position
and orientation of the joints to cause the cutting tool to occupy
a desired position and orientation relative to the workpiece mounting
means.
The term multi- or multiple axis control, when used in the context
of CNC machine tools, conventionally refers to a form of CNC control
in which the machine may be programmed to control one or more joints
concurrently. The development of multi-axis and multifunction machine
tools in conjunction with the development of sophisticated computer
controlled operations has facilitated the emergence of a generation
of very high speed precision machine tools capable of complex multi-step
operations from one machine.
In programming a CNC machine tool with multi-axis control a plurality
of programmable positioning directions or "axes" are chosen
which constitute the minimum number of axes required to position
the cutting tool relative to the workpiece. These programmable axes,
referred to herein as principal programmable axes may include up
to three linear orthogonal axes and one or more rotary axes.
Conventionally, a CNC machine tool has a number of programmable
axes and is controlled by part program which serially instructs
the machine to perform a sequential series of discrete operations
in a predetermined or programmed sequence.
In simple CNC machine tools, the number of joints of the machine
is often equal to the number of programmable axes. For instance,
a four axis machine tool may have three orthogonal linear or prismatic
joints providing control of movement in three orthogonal directions
(X, Y and Z), and one rotary joint providing rotation about a rotary
axis A. In programming such a four axis machine, the directions
X, Y and Z may conveniently be chosen as programmable linear axes
and the axis A chosen as a programmable rotary axis,
U.S. Pat. No. 4591771 discloses a numerical control system for
a five axis CNC machine tool of the type having three linear or
prismatic joints controlled by servo motors which provide relative
movement between the tool and the workpiece in the directions of
the X, Y and Z axes of an orthogonal co-ordinate system and two
rotary joints controlled by servo motors which provide rotary movement
in the directions of B and C axes of a spherical co-ordinate system.
In programming the five axis machine of U.S. Pat. No. 4591771
the orthogonal axes X, Y and Z and the rotary axes B and C may be
conveniently chosen as programmable axes.
The five axis CNC machine of U.S. Pat. No. 4591771 also includes
a manual pulse generator which allows the machine tool to be moved
manually in the axial direction A of the machine tool relative to
the workpiece to increase or decrease the cutting amount.
Conventional four or five axis CNC machines, such as the five axis
machine of U.S. Pat. No. 4591771 can thus be programmed to carry
out simple linear movements of the machine tools using the programmable
linear axes (X, Y and Z) and to carry out rotary movements in the
directions of the programmable rotary axes (eg. B and C) which are
located by rotary joints. However, such conventional CNC machine
tools cannot automatically move along or contour around axes other
than the four or five programmable axes without more complicated
programming using a combination of the programmable axes or unless
the other axes are located by means of further prismatic or rotary
joints under the control of the part program.
It is therefore desirable to provide a method of operating a multi-axis
CNC machine tool wherein the cutting tool can move automatically
along or contour around an axis without requiring physical location
of that axis by means of a prismatic or rotary joint.
It is also desirable to provide a multi-axis CNC tool having a
certain number of joints and which is able to control movement of
a cutting tool automatically relative to a workpiece in a plurality
of linear axis directions and around at least one rotary axis direction
without requiring at least as many joints as the number of linear
and rotary axis directions.
In accordance with one aspect of the present invention there is
provided a method of operating a multi-axis CNC machine tool having
workpiece mounting means for mounting a workpiece, a cutting tool
operable upon said workpiece, a plurality of machine members and
a plurality of controllable joint means movable under the control
of a program to cause relative movement between the cutting tool
and the workpiece mounting means,
said method comprising the steps of programming the machine with
a plurality of principal programmable positioning directions or
axes which axes constitute the minimum number of axes required to
position the cutting tool relative to the workpiece mounting means,
and programming the machine to control movement of the joint means
in accordance with a part program so as to cause the cutting tool
to move along a programmed path relative to the workpiece mounting
means,
the method being characterized by the step of programming the machine
to synthesize at least one additional programmable axis whereby
relative movement of said cutting tool and said workpiece mounting
means is automatically controllable in relation to said additional
programmable axis in accordance with said part program without physical
location of said additional programmable axis by joint means.
In accordance with another aspect of the invention there is provided
a multi-axis CNC machine tool comprising:
workpiece mounting means for mounting a workpiece thereon;
a cutting tool movable relative to the workpiece mounting means;
a plurality of machine members; and
a plurality of controllable joint means movable to cause the relative
movement between said cutting tool and said workpiece mounting means;
and
programmable control means programmed to control automatically
the position and orientation of said plurality of joint means in
accordance with a part program;
the machine tool having a plurality of principal programmable positioning
directions or axes which constitute the minimum number of programmable
axes required to position and orientate the cutting tool relative
to the workpiece mounting means;
characterized in that the machine is programmed to synthesize at
least one additional programmable axis, whereby movement of said
cutting tool or said workpiece mounting means in relation to said
at least one additional programmable axis is automatically controllable
in accordance with said part program without physical location of
said at least one synthesized additional programmable axis by joint
means.
The CNC machine may be programmed to synthesize more than one additional
programmable axis, allowing movement of the cutting tool or the
workpiece in relation to each one of the additional programmable
axes to be controlled without physical location of said synthesized
additional programmable axes. The or each synthesized additional
programmable axis may be hereinafter referred to as a "soft
axis", with the principal programmable axes being referred
to as "principal hard axes".
Preferably, at least one of said synthesized additional programmable
axes or "soft" axes is non-collinear with the principal
programmable axes. Hitherto, in programming conventional multi-axis
machine tools, such non-collinear axes would be regarded as partially
redundant axes since it is possible to describe any required position
or orientation of the cutting tool relative to the workpiece in
terms of co-ordinates of the principal "hard" axes. A
soft axis which is collinear with one of the other soft axes may
be regarded as a fully redundant axis, although it will be appreciated
that the present invention in its broadest form includes the synthesis
by electronic or computational means of any "soft" axis,
whether it is partially redundant or fully redundant.
Soft axes are fully programmable axes capable of simulating normal
axis operations such as: interpolation, contouring, splicing, offsetting,
jogging, manual positioning and live offset positioning.
Conventionally, at least one of said synthesized additional programmable
axes or soft axes is arranged to pass through a part of the cutting
tool and to remain fixed relative to the cutting tool. The synthesis
of such a soft axis enables the machine to be programmed to control
linear movement of a rotatable cutting tool either along a soft
axis coinciding with the axis of rotation of the cutting tool or
to control the cutting tool to contour around a soft rotary axis,
for instance an axis passing through a grinding point at the edge
of the cutting tool.
It will be appreciated that the synthesis of soft axes can increase
the number of programmable axes to exceed the total number of joints
in a multi-axis CNC machine. In this case it is possible, for instance,
to provide a four or five axis machine tool having four or five
joints which can function as effectively as conventional machine
tools having six or more joints.
Some preferred embodiments of the present invention will now be
described, by way of example only, with reference to the accompanying
drawings in which:
FIG. 1 is a schematic diagram of a simple prior art CNC machine
tool having four "hard" axes and four joints;
FIG. 2 is a schematic diagram of a simple CNC machine tool in accordance
with the invention having three principal "hard" axes,
a partly redundant "soft" axis and three joints;
FIG. 3 is a block diagram of a co-ordinate transform module for
a CNC machine tool in accordance with the invention having five
principal "hard" axes, two "soft" axes and five
joints;
FIG. 4 is a perspective view of the workpiece and grinding wheel
of a CNC tool grinder having five principal "hard" axes,
two "soft" axes and five joints;
FIG. 5 is a perspective view showing the joint layout for the CNC
tool grinder of FIG. 4;
FIG. 6 is a perspective view of the workpiece and grinding wheel
of a CNC cylindrical grinder having four principal "hard"
axes, two "soft" axes and four joints;
FIG. 7 is a perspective view of the laser cutter of a CNC laser
cutting machine tool having five principal "hard" axes,
three "soft" axes and five joints.
FIG. 8 is a perspective view of the workpiece and cutting tool
of a CNC milling machine having five principal "hard"
axes, three "soft" axes and five joints.
The principle of using synthesized partially redundant axes in
a CNC machine tool to reduce the number of joints required to move
a cutting tool may be described with reference to FIGS. 1 and 2
of the drawings.
The CNC machine tool illustrated schematically in FIG. 1 is a simple,
conventional machine tool comprising a programmable control unit
or PCU 1 a trajectory interpolator 2 a position controller 4
a machine base 5 having mounting means 8 for mounting a workpiece
6 thereon, a rotatable cutting tool 7 a plurality of movable machine
members L.sup.1 to L.sup.3 a plurality of joints J.sup.1 -J.sup.4
and a respective actuator 11 to 14 associated with each joint J.sup.1
-J.sup.4.
As shown schematically in FIG. 1 the first joint J.sup.1 is a
linear or prismatic joint forming a telescopic linkage between a
part of the machine base 5 and the first machine member L.sup.1
and providing movement of machine member L.sup.1 relative to the
base 5 in a horizontal direction X, the second joint J.sup.2 is
a linear or prismatic joint forming a telescopic linkage between
the first machine member L.sup.1 and the second machine member L.sup.2
and providing relative linear movement between the first and second
machine members L.sup.1 and L.sup.2 in a vertical direction Z, the
third joint J.sup.3 is a rotary joint between the second and third
machine members L.sup.2 and L.sup.3 and providing angular movement
of the third machine member L.sup.3 relative to the second machine
member L.sup.2 about a rotary axis B, and the fourth joint J.sup.4
is a linear or prismatic joint forming a telescopic linkage between
the third machine member L.sup.3 and the head of the cutting tool
7 providing linear movement of the cutting tool 7 relative to the
third machine member L.sup.3 in a direction V coinciding with the
axis of rotation of the rotatable cutting tool 7.
In conventional terms a machine tool such as that of FIG. 1 is
often referred to as a "four axis machine" because it
has four joints J.sup.1 to J.sup.4. The machine is also considered
to have four machine degrees of freedom (MDOF) because it has four
non-collinear joint axes or directions in which relative movement
between adjacent machine members or between the cutting tool and
the third machine member may take place, ie: linear axes X, Z and
V and rotary axis B. However, in the context of the present invention,
the CNC machine tool of FIG. 1 is considered to have three principal
axes, known as principal "hard" axes, ie: orthogonal linear
axes X and Z and rotary axis B. Linear axis V is known as a partially
redundant "hard" axis, since any change in linear position
of the cutting tool 7 in the V direction relative to the workpiece
6 could be expressed in terms of the change in co-ordinates of the
X and Z axes. Conventionally, in programming the CNC machine of
FIG. 1 to control movement of the cutting tool 7 in accordance with
a programmed path, the program would define the relative positions
of the joints J.sup.1 to J.sup.4 and the movable machine members
M.sup.1 to M.sup.3 relative to a point of reference on the fixed
workpiece known as the workpiece reference point in terms of coordinates
from the X, Z and B principal "hard" axes and the partially
redundant "hard axis" V. Thus, the number of programming
degrees of freedom (PDOF) in the machine of FIG. 1 is four, equal
to the number of machine degrees of freedom (MDOF), ie. the number
of joints.
The machine tool illustrated schematically in FIG. 2 is similar
to that of FIG. 1 and corresponding reference numerals have been
applied to corresponding parts. The machine tool of FIG. 2 however,
differs physically from that of FIG. 1 in that the third machine
member L.sup.3 the fourth joint J.sup.4 and its associated actuator
14 have been omitted. Also, in contrast to FIG. 1 the machine tool
of FIG. 2 includes a co-ordinate transform module 3 and, by suitable
programming of the PCU 1 and the co-ordinate transform module 3
is able to control movement of the cutting tool 7 relative to the
workpiece reference point in the same linear directions X, Z and
V and about the same rotary axes B and C as the machine tool of
FIG. 1 despite the fact that there is no physical location of linear
axis V by means of a joint since joint J.sup.4 has been omitted.
In accordance with the present invention, the three joint machine
of FIG. 2 is able to position the cutting tool relative to the workpiece
as effectively as the four joint machine of FIG. 1 because the co-ordinate
transform module 3 is programmed to synthesize a partially redundant
"soft" axis corresponding to linear axis V which passes
through the cutting tool 7. It will be appreciated that linear movement
of the cutting tool 7 in the direction V' is possible by appropriate
actuation of prismatic joints J.sup.1 and J.sup.2 without physically
locating the linear axis V by means of a corresponding joint J.sup.4.
Since the machine has only three joints, J.sup.1 J.sup.2 and J.sup.3
it only has three machine degrees of freedom (MDOF) but because
an additional partially redundant "soft" axis is synthesized,
the machine has four programming degrees of freedom (PDOF). In this
manner, the three joint or three axis machine of FIG. 2 can operate
in the same way as the four joint machine of FIG. 1.
The manner in which a CNC machine tool is programmed to synthesize
one or more "soft" axes will be described with particular
reference to FIG. 3 which shows a co-ordinate transform module 3
of a machine having five joints J.sup.1 to J.sup.5 five principal
"hard" axes and two partially redundant "soft"
axes. First, however, it is necessary to define various terms and
some axis classification rules as follows:
Definitions
Cutting Tool
The cutting tool is the portion of the machine that is designed
to act upon a workpiece to perform the desired task. In the context
of this patent, the cutting tool is not restricted to standard turning
or milling cutters, but also includes all mechanical, electronic
and/or electro-mechanical devices used to modify the shape and/or
properties of the workpiece. Examples of cutting tools include:
end-mills, turning tools, grinding wheels, laser cutting beams,
plasma beams and punch tools.
Workpiece
The workpiece is the part upon which useful work is done by the
machine tool. The principal job of the machine tool is to modify
a workpiece's shape and/or properties.
Workpiece Reference Point (WRP)
The workpiece reference point (WRP) is a point of reference, logically
attached to the workpiece. It is located as a fixed position relative
to the workpiece but this position may be programmed be means other
than using axes.
Machine Member
A machine member is an essentially rigid mechanical structure of
the machine tool or a combination of mechanical structures that
result in a mathematically constant link between 2 joints J.sup.n
and J.sup.n-1 or between the base of the machine and joint J.sup.1
or between joint J.sup.N and the cutting tool (where N is the number
of joints in the machine tool).
Last Machine Member
The last machine member is the machine member that attaches joint
J.sup.N to the cutting tool where N is the number of joints in the
machine tool.
Joint
A mechanical linkage between two machine members. A joint is controlled
by means of an actuator. The position of a joint describes the kinematic
relationship between one machine member and another. In most implementations,
each joint position maps directly and simply to the position of
one actuator. In some implementations, a simple N to N mapping occurs
between joint positions and actuator positions however, this is
rare for most normal machine tools.
Actuator
Active mechanism used to power a joint. Typical actuators are electrical
servo motors, pneumatic and hydraulic pistons.
Tool Reference Point (TRP)
The tool reference point (TRP) is a point of reference, logically
attached to the last machine member of the machine tool. It is located
as a fixed position relative to the last machine member but this
position may be programmed be means other than using axes.
Rotating Cutting Tool
A rotating cutting tool is a cutting tool designed to spin about
a particular axis, whereby useful work is done by the swept volume
of the cutting tool. This implies that the orientation of the cutting
tool is limited to 2 degrees of freedom; the third degree of freedom
(rotation about the spinning axis) has no meaning.
Spacial Degrees of Freedom (SDOF)
A machine tool can be defined as having SDOF spacial degrees of
freedom and ODOF orientation degrees of freedom. The spacial degrees
of freedom (SDOF) of a machine tool is an integral number that represents
the fundamental space that the machine tool is designed to operate
in. This space is called SDOF-Dimensional Euclidean Space which
may be defined as a rectangular coordinate system with SDOF euclidean
dimensions embedded in the workpiece at the workpiece reference
point. This reference frame and its corresponding euclidean space
are used herein as the base frame when referencing the position
and orientation of the machine tool. The number of SDOF will be
one of:
0. For a purely rotational machine (eg: carousal).
1. For a fundamentally 1 dimensional machine (eg: conveyor belt).
2. For a fundamentally 2 dimensional machine (eg: conventional
lathe).
3. For a fundamentally 3 dimensional machine (eg: conventional
knee mill).
This value must be viewed with reference to the orientation degrees
of freedom (ODOF).
SDOF is defined as the minimum number of Euclidean space dimensions
required to fully describe the set of fundamental axis direction
vectors for all linear axes and the set of fundamental axis direction
vectors for all rotary axes for all axis vector values within the
working envelope of the machine tool.
ie: If the position of the tool reference point relative to the
workpiece reference point is always constrained in 1 dimension then
SDOF=1; in 2 dimensions then SDOF=2; in 3 dimensions SDOF=3.
Orientation Degrees of Freedom (ODOF)
The orientation degrees of freedom (ODOF) of a machine tool is
an integral number that represents the fundamental degrees of freedom
that the orientation of the cutting tool may make with respect to
the workpiece.
More specifically, given that the tool reference point is in contact
with the workpiece reference point, ODOF is the number of different
direction vectors D.sup.n (maximum of 3) (each of which is orthogonal
to all other D.sup.m) about which the cutting tool may be programmed
to rotate (using the rotary axes and linear axes) for all axis vector
values within the working envelope of the machine tool for which
the tool reference point remains in contact with the workpiece reference
point.
This definition does not imply that the cutting tool cannot be
rotated about more than ODOF direction axes over the entire working
envelope. It refers to the number of degrees of rotary freedom given
a fixed position of the tool reference point with respect to the
workpiece reference point. At a different position (or in a different
programmed configuration) the cutting tool may rotate about a different
direction vector. The number of ODOF will be one of:
0. For machines where the cutting tool cannot be pivoted with respect
to the workpiece.
1. For machines where the cutting tool can be pivoted about only
one direction vector with respect to the workpiece (eg: a 4 axis
knee mill; with rotary workpiece axis).
2. For machines where the cutting tool can be pivoted about two
direction vectors with respect to the workpiece (eg: a conventional
5 axis mill).
3. For machines where the cutting tool can be pivoted about three
direction vectors with respect to the workpiece (eg: a conventional
6 axis robot). Note: a 5 axis mill has ODOF=2 even if it is fitted
with a rotary workpiece axis as this axis is not orthogonal to the
2 tool pivoting axes. To create a mill with ODOF=3 a rotary axis
parallel to the normal tool spindle rotation direction would need
to be provided (which is capable of performing useful work with
normal tooling).
NOTES:
1. A rotary axis designed to rotate the workpiece can not be used
in the calculation of ODOF and SDOF. It is counted either as an
axis used to effect principal positioning of the tool reference
point with respect to the workpiece reference point (eg: theta in
a cylindrical coordinate position system) or as an axis used to
effect principal orientation of the tool reference point with respect
to the workpiece reference point.
2. A machine with a rotating tool may have a maximum ODOF=2 since
there can be no distinction of tool orientation along the axis of
tool rotation.
Axis
In the context of this patent, an axis is a "programmable"
positioning direction. The principal means of programming a CNC
to position the machine tool to a particular position is to specify
the destination point as a set of axis positions. Typical names
for axes are: X, Y, Z, A, B, C, U, X1 X2 A3 etc. Axes may be either
linear axes or rotary axes. For descriptive purposes in this patent,
axes are represented as A.sup.n where n represents the location
of the axis in the axis vector.
Axis Position
The axis position of an axis (say A.sup.n) is the value that the
axis has been programmed to reach after all programmed transformations
have been accounted for.
Axis Vector
An axis vector (A) is a vectorial representation of the position
of the machine tool expressed as a column matrix (M+1.times.1) where
each element of the vector represents the axis position of one of
the M axes of the machine tool. The last element in the vector is
the value 1. This is used for homogeneity of the vector: ##EQU1##
where:
a.sup.I represents the position of axis i.
NOTE: Whilst A is referred to as an axis vector, it bears no direct
relationship to a normal 3-dimensional Euclidean space vector.
Position Matrix
The position matrix (P) is a representation that combines the position
of the tool reference point (TRP) in SDOF-dimensional euclidean
space (with respect to the workpiece reference point (WRP)) with
the orientation of the cutting tool (with respect to SDOF-dimensional
euclidean space). P can be represented as follows: ##EQU2## where:
N is called the normal orientation vector (see below).
O is called the orient orientation vector (see below).
A is called the approach orientation vector (see below).
P is called the position vector (see below).
The vectors N, O and A described above are called orientation vectors.
They form an orthogonal set of unit vectors, whose values (in SDOF-dimensional
euclidean space) represent the orientation of the cutting tool with
respect to the workpiece. This set of vectors can encompass up to
3 orientation degrees of freedom (which is the maximum allowed).
These vectors can be defined as follows: ##EQU3## where:
N.sub.x is the i axis position of the vector N in SDOF-dimensional
euclidean space.
N.sub.y is the j axis position of the vector N in SDOF-dimensional
euclidean space.
N.sub.z is the k axis position of the vector N in SDOF-dimensional
euclidean space.
similarly for O.sub.x, O.sub.y, O.sub.z, A.sub.x, A.sub.y and A.sub.z.
Axis Matrix
The axis matrix (A) is a symbolic 4.times.4 matrix that defines
the kinematic relationship between the position matrix (P) and the
axis position of each of the axes (a.sup.n); which are the elements
of the axis vector (A). The elements of A are expressed symbolically
in terms of a.sup.n.sub.(for n-1 . . . N) where N is the number
of axes in the machine tool. A is defined as: ##EQU4## where:
f.sub.ij (A) is a function of the components of A (a.sup.1 a.sup.2
. . . a.sup.N).
A satisfies the following equation:
for all values of A within the working envelope of the machine
tool.
Linear Axis
An axis is a linear axis if, for all current axis vector (A') values
within the working envelope of the machine tool, the following equations
are true: ##EQU5## where:
a.sup.n is the component direction of the axis vector corresponding
to A.sup.n.
.DELTA.a.sup.n is a scalar representing the displacement of axis
A.sup.n from the axis position at A'.
A' is the current axis vector.
A is the axis matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
K is a scalar constant
for all A' and all .DELTA.a.sup.n.
Rotary Axis
A rotary axis is an axis that causes the orientation of the cutting
tool (with respect to SDOF-dimensional euclidean space) to change.
A rotary axis satisfies at least one of the following criteria:
##EQU6## where:
a.sup.n is the component rotation of the axis vector corresponding
to A.sup.n.
A' is the current axis vector.
A is the axis matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
for all A' within the working envelope of the machine tool.
Collinear Axes (linear)
Two or more linear axes are defined as being collinear if they
satisfy the following criteria:
The fundamental axis direction vectors (D.sub.a.sup.n (A')) of
the axes form a collinear set of vectors for all axis vector values
within the working envelope of the machine tool. ie: A linear axis
(say A.sup.n) is collinear to another linear axis (A.sup.m) if the
direction of movement of A.sup.n always coincides with the direction
of movement of A.sup.m regardless of the position of the machine
tool. This is expressed in the following equation:
where:
K is a scalar constant.
for all current axis vector values A' within the working envelope
of the machine tool.
A third axis (A.sup.P) is collinear to A.sup.m if it is collinear
to A.sup.n. Note: This definition does not imply that the fundamental
axis direction vectors of a collinear axis set are constant. It
only relates to the relative linear dependence of the set.
Current Axis Vector
The current axis vector (A') is the value of the axis vector A
at the current position of the machine tool.
Fundamental Axis Direction Vector
The fundamental axis direction vector (D.sub.a.sup.n (A')) for
a linear axis A.sup.n is defined as the vector that relates the
rate of change of the position of the tool reference point (with
respect to the workpiece reference point) in SDOF-dimensional euclidean
space to the rate of change in the position of A.sup.n at the current
axis vector. It is represented by the solution of the partial differential
equation at the current axis vector: ##EQU7## where:
a.sup.n is the component direction of the axis vector corresponding
to A.sup.n.
A' is the current axis vector.
A is the axis matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix)
N, O and A are the orientation vectors (see the definition of position
matrix).
Collinear Axes (rotary)
Two or more rotary axes are defined as being collinear if they
satisfy the following criteria:
The fundamental axis rotation vectors (R.sub.a.sup.n (A')) of the
axes form a collinear set of vectors for all axis vector values
within the working envelope of the machine tool and the fundamental
axis rotation origin vectors (V.sub.a.sup.n (A')) of the axes are
identical for all axis vector values within the working envelope
of the machine tool. ie: A rotary axis (say A.sup.n) is collinear
to another rotary axis (A.sup.m) if the direction of rotation of
A.sup.n always coincides with the direction of rotation of A.sup.m
and the origin of rotation of A.sup.n is always the same as the
origin of rotation of A.sup.m regardless of the position of the
machine tool. This is expressed in the following equations:
where:
K is the scalar constant 1 or -1.
for all current axis vector values A' within the working envelope
of the machine tool.
A third axis (A.sup.P) is collinear to A.sup.m if it is collinear
to A.sup.n. Note: This definition does not imply that the fundamental
axis rotation vectors or fundamental axis rotation origin vectors
of a collinear axis set are constant. It only relates to the relative
linear dependence and equality of the set.
Fundamental Axis Rotation Origin Vector
The fundamental axis rotation origin vector (V.sub.a.sup.n (A'))
for the rotary axis A.sup.n defines the instantaneous location of
the axis of rotation of A.sup.n in SDOF-dimensional euclidean space
at the current axis vector (A'). It is defined by the following
equation: ##EQU8## where:
a.sup.n is the component rotation of the axis vector corresponding
to A.sup.n.
A' is the current axis vector.
A' is the axis matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
R.sub.a.sup.n (A') is the axis rotation vector for A.sup.n.
Fundamental Axis Rotation Vector
The fundamental axis rotation vector (R.sub.a.sup.n (A')) for the
rotary axis A.sup.n is defined as the unit vector that relates the
rate of change in the orientation vectors (N, O and A) (see the
definition of position matrix) to the rate of change of the axis
position of A.sup.n at the current axis vector. It defines the instantaneous
direction of rotation of A.sup.n about which, a change in the axis
position a.sup.n will cause the cutting tool to rotate. R.sub.a.sup.n
(A') is defined by following equation set: ##EQU9## where:
a.sup.n is the component rotation of the axis vector corresponding
to A.sup.n.
A' is the current axis vector.
A is the axis matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
K.sub.1 are scalar constants.
Collinear Axis Set
A set of axes, each of which is collinear to every other axis in
the set. There may be multiple collinear axis sets for a particular
machine tool.
Non-Collinear Axis
A non-collinear axis is an axis that cannot be placed in any collinear
sets of axes.
Programming Degrees of Freedom
In the context of this patent, the programming degrees of freedom
(PDOF) of a machine tool is an integral number that represents the
number of non-collinear axes plus the number of collinear axis sets.
Working Envelope
The working envelope is defined as the complete family of values
that the position matrix (P) is able to acquire for the machine
tool. This family of values will be dependent on the spacial degrees
of freedom and the orientation degrees of freedom and any limits
applied to axis positions and joint positions.
Joint Position
For prismatic joints, the joint position (j.sup.n) is expressed
as a linear displacement in units of millimeters. For rotary joints,
the joint position (j.sup.n) is expressed as an angular position
in units of radians.
The units expressed above are for definition to correspond to the
equations stated. Real applications may have units different to
these (eg: encoder counts). Appropriate scaling of the equations
is then in order.
Joint Vector
A joint vector (J) is a vectorial representation of the position
of the machine tool expressed as a column matrix(N+1.times.1) where
each element of the vector represents the joint position of one
of the N joints of the machine tool. The last element in the vector
is the value 1. This is used for homogeneity of the vector: ##EQU10##
where
j.sup.I represents the position of joint i.
NOTE: Whilst J is referred to as a joint vector, it bears no direct
relationship to a normal 3-dimensional Euclidean space vector.
Current Joint Vector
The current joint vector (J') is the value of the joint vector
J at the current position of the machine tool.
Joint Matrix
The joint matrix (J) is a symbolic 4.times.4 matrix that defines
the kinematic relationship between the position matrix (P) and the
joint position of each of the joints (j.sup.n); which are the elements
of the joint vector (J). The elements of J are expressed symbolically
in terms of j.sup.n.sub.(for n-1 . . . N) where N is the number
of joints in the machine tool. J is defined as: ##EQU11## where:
f.sub.ij (J) is a function of the components of J (j.sup.1 j.sup.2
. . . j.sup.N).
J satisfies the following equation:
for all values of J within the working envelope of the machine
tool.
Prismatic Joint
A joint is a prismatic joint if, for all current joint vector (J')
values within the working envelope of the machine tool, the following
equations are true: ##EQU12## where:
j.sup.n is the component direction of the joint vector corresponding
to J.sup.n.
.DELTA.j.sup.n is a scalar representing the displacement of joint
J.sup.n from the joint position at J'.
J' is the current joint vector.
J is the joint matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
K is a scalar constant.
for all J' and all .DELTA.j.sup.n.
Joint Displacement Vector
The joint displacement vector (D.sup.n (J')) for the prismatic
joint J.sup.n is defined as the vector that relates the rate of
change of the position of the tool reference point in SDOF-dimensional
euclidean space (with respect to the workpiece reference point)
to the rate of change in the position of J.sup.n at the current
joint vector. It is represented by the solution of the partial differential
equation at the current joint vector: ##EQU13## where:
j.sup.n is the component direction of J corresponding to J.sup.n.
J' is the current joint vector.
J is the joint matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
Rotary Joint
A rotary joint is a joint that causes the orientation of the cutting
tool (with respect to SDOF-dimensional euclidean space) to change.
A rotary joint satisfies at least one of the following criteria:
##EQU14## where:
j.sup.n is the component rotation of the joint vector corresponding
to J.sup.n.
J' is the current joint vector.
J is the joint matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
for all J' within the working envelope of the machine tool.
Joint Rotation Vector
The joint rotation vector (R.sup.n (J')) for the rotary joint J.sup.n
is defined as the unit vector that relates the rate of change in
the orientation vectors (N, 0 and A) (see the definition of position
matrix) to the rate of change of the joint position of J.sup.n at
the current joint vector. It defines the instantaneous direction
of rotation of J.sup.n about which, a change in the joint position
j.sup.n will cause the cutting tool to rotate. R.sup.n (J') is defined
by following equation set: ##EQU15## where:
j.sup.n is the component rotation of J corresponding to J.sup.n.
J' is the current joint vector.
J is the joint matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
K.sub.i are scalar constants.
Joint Rotation Origin Vector
The joint rotation origin vector (V.sup.n (J')) for the rotary
joint J.sup.n defines the instantaneous location of the axis of
rotation of J.sup.n in SDOF-dimensional euclidean space at the current
joint vector (J'). It is defined by the following equation: ##EQU16##
where:
j.sup.n is the component rotation of J corresponding to J.sup.n.
J' is the current joint vector.
J is the joint matrix.
P is the position matrix.
P is the position vector (see the definition of position matrix).
N, O and A are the orientation vectors (see the definition of position
matrix).
R.sup.n (J') is the joint rotation vector for J.sup.n.
Collinear Joints (prismatic)
Two or more prismatic joints are defined as being collinear if
they satisfy the following criteria:
The joint displacement vectors (D.sup.n (J')) of the joints form
a collinear set of vectors for all joint vector values within the
working envelope of the machine tool. ie: A prismatic joint (say
J.sup.n) is collinear to another prismatic joint (J.sup.m) if the
direction of movement of J.sup.n always coincides with the direction
of movement of J.sup.m regardless of the position of the machine
tool. This is expressed in the following equation:
where:
K is a scalar constant.
for all current joint vector values J' within the working envelope
of the machine tool.
A third joint (J.sup.P) is collinear to J.sup.m if it is collinear
to J.sup.n. Note: This definition does not imply that the joint
displacement vectors of a collinear joint set are constant. It only
relates to the relative linear dependence of the set.
Collinear Joints (rotary)
Two or more rotary joints are defined as being collinear if they
satisfy the following criteria:
The joint rotation vectors (R.sup.n (J')) of the joints form a
collinear set of vectors for all joint vector values within the
working envelope of the machine tool and the joint rotation origin
vectors (V.sup.n (J')) of the joints are identical for all joint
vector values within the working envelope of the machine tool. ie:
A rotary joint (say J.sup.n) is collinear to another rotary joint
(J.sup.m) if the direction of rotation of J.sup.n always coincides
with the direction of rotation of J.sup.m and the origin of rotation
of J.sup.n is always the same as the origin of rotation of J.sup.m
regardless of the position of the machine tool. This is expressed
in the following equations:
where:
K is the scalar constant 1 or -1.
for all current joint vector values J' within the working envelope
of the machine tool.
A third joint (J.sup.P) is collinear to J.sup.m if it is collinear
to J.sup.n. Note: This definition does not imply that the joint
rotation vectors or joint rotation origin vectors of a collinear
joint set are constant. It only relates to the relative linear dependence
and equality of the set.
Collinear Joint Set
A set of joints, each of which is collinear to every other joint
in the set. There may be multiple collinear joint sets for a particular
machine tool.
Non-Collinear Joint
A non-collinear joint is a joint that cannot be placed in any collinear
sets of joints.
Fully Redundant Joint
A fully redundant joint is a joint that can be included in a collinear
set of joints. The inclusion of a fully redundant joint in a CNC
does not add to the machine degrees of freedom (MDOF).
Machine Degrees of Freedom
In the context of this patent, the machine degrees of freedom (MDOF)
of a machine tool is an integral number that represents the number
of non-collinear joints plus the number of collinear joint sets.
Axis Classification Rules
A CNC machine tool will have at least (SDOF+ODOF) axes. These axes
can be classified as follows:
Principal Hard Axes
A selection of the machine tool's axes is made such that this set
of axes constitutes the minimum number of axes required to position
the tool reference point with respect to the workpiece reference
point to any position defined within SDOF-dimensional euclidean
space and thereafter to rotate the cutting tool about the tool reference
point in ODOF orthogonal directions. The axes in this set are called
"principal hard axes". There may be multiple sets of axes
that satisfy this criterion, however one of these sets must be chosen
in order to differentiate between hard axes and soft axes. The selection
of this set will have no bearing on the number of soft axes of a
machine tool.
Partially Redundant Axis
A linear axis (say A.sup.n) is a partially redundant axis if it
is a non-collinear axis and satisfies all of the following criteria:
1. A.sup.n is not classified as a principal hard axis under the
axis classification rules.
2. The fundamental axis direction vector of A.sup.n can be define
in SDOF-dimensional euclidean space for all axis vector values within
the working envelope of the machine tool.
A rotary axis (say A.sup.n) is a partially redundant axis if it
is a non-collinear axis, is not classified as a principal hard axis
under the axis classification rules and satisfies one of the following
criteria:
1. The fundamental axis rotation vector of A.sup.n is collinear
to the fundamental axis rotation vector of one of the rotary axes
A.sup.m classified as a principal hard axis for all axis vector
values within the working envelope of the machine tool but the fundamental
axis rotation origin vectors for A.sup.n and A.sup.m are not identical
for all axis vector values within the working envelope or the machine
tool.
2. The fundamental axis rotation vector of A.sup.n is collinear
to the axis of rotation of a rotating cutting tool for all axis
vector values within the working envelope of the machine tool.
A partially redundant axis does not add to the spacial degrees
of freedom or the orientation degrees of freedom of the machine
tool. ie: the position of the tool reference Point with respect
to the workpiece reference point or the orientation of the cutting
tool cannot be modified be means of a partially redundant axis in
a way that could not otherwise be done by utilizing the machine's
other axes. Note: this definition does not concern the axis vector
or the joint vector. It only concerns the relative position and
orientation of the cutting tool with respect to the workpiece.
Fully Redundant Axis
A fully redundant axis is an axis that can be included in a collinear
set of axes. The inclusion of a fully redundant axis in a CNC does
not add to the programming degrees of freedom (PDOF).
Fully Redundant Hard Axes
An axis of the machine tool that is a fully redundant axes and
is a collinear axis to one or more principal hard axes but is not
a principal hard axes is called a "fully redundant hard axis".
Partially Redundant Hard Axes
A selection of the machine tool's axes (called the set of "partially
redundant hard axes") that are neither principal hard axes
nor fully redundant hard axes is made such that the set of hard
axes (if no other axes were provided) would cause the programmed
degrees of freedom (PDOF) to equal the machine degrees of freedom
(MDOF) and that the number of axes in the set of partially redundant
hard axes is the maximum possible. This implies that if axis A.sup.n
is a collinear axis to A.sup.m and A.sup.m is included in this set,
then A.sup.n is also included in this set. There may be multiple
sets of axes that satisfy these criteria, however one of these sets
must be chosen in order to differentiate between partially redundant
hard axes and soft axes. The selection of this set will have no
bearing on the number of soft axes of a machine tool.
Soft Axes
An axis of the machine tool that is not a hard axis is called a
"soft axis". The set of soft axes may include partially
redundant axes and fully redundant axes. If an axis A.sup.n is a
fully redundant axis and is a collinear axes to A.sup.m and A.sup.m
is a soft axis, then A.sup.n is also a soft axis. Soft axes increase
PDOF to a number that is greater than MDOF. Given a machine tool
with N axes, if the number of hard axes is H and the number of soft
axes is S (S=N-H), the values of S, N and H do not change, regardless
of how the axes are classified according to the above rules even
though the actual axes that are assigned the classification "soft
axis" may be different depending on how the classification
sets are chosen.
Hard Axes
Hard axes are thus defined as the set of axes that includes all
of the axes classified as either; principal hard axes, fully redundant
hard axes or partially redundant hard axes via the axis classification
rules.
NOTES:
1. In this specification, the machine tool, its axes, joints, geometry
and kinematics are considered as being precisely mathematically
modelled. Misalignments and non-linearities inherent in any "real
world" implementation do not effect the fundamental definitions
and claims of this patent.
2. Axes and joints are considered within this specification as
having unlimited travel.
3. Definitions relating to spacial and orientation degrees of freedom
must be considered at axis vector and joint vector values that result
in the maximum possible values of these. The fact that some axis
vector or joint vector values correspond to a reduction in spacial
or orientation degrees of freedom due to the instantaneous alignment
of 2 or more axes (or joints) that are not part of the same collinear
set or because 1 or more axes (or joints) is restricted due to physical,
electrical or computer imposed limits is not relevant.
4. The definitions herein consider machine tools with axes and
joints designed to have one workpiece reference point and one tool
reference point. For machines designed to have multiple concurrent
workpiece reference points and/or multiple tool reference points,
these definitions should be considered for each logical pair of
workpiece reference point and tool reference point.
5. The descriptions herein of axis and joint positions and orientations
do not consider any clearance or other constraints that may be imposed
by the practical application of a machine tool to a specific job.
Referring to FIG. 2 the programmable control unit (PCU) 1 contains
a part program which determines the programmed path along which
the cutting tool 7 is programmed to move when the machine tool is
operating in automatic mode. The PCU 1 interprets the part program
and passes high level motion command signals to the trajectory interpolator
2. The trajectory interpolator 2 processes the high level motion
commands to produce axis vector values A at a rate of one axis vector
value every machine update period (on average). The trajectory interpolator
2 may also process, in known manner, feedrate specification signals
representing an automatic feedrate for the speed of movement of
the cutting tool along the programmed path. A novel form of trajectory
interpolator which also processes an MPG feed specification from
a manual pulse generator (MPG) in automatic mode is described in
our co-pending International Application entitled "Improvements
in or relating to Computer Numerically Controlled Machines",
the disclosure of which is incorporated herein by reference.
The axis vector values from the trajectory interpolator 2 are input
sequentially to the co-ordinate transform module 3 as current axis
vector values A'. The co-ordinate transform module 3 performs calculations
based on the current axis vector, the machine's axis matrix A and
the machine's joint matrix J in order to produce a joint vector
J'. This joint vector J' (called the current joint vector) is then
output as a signal from the co-ordinate transform module 3 and input
to the position controller 4. The position controller 4 then controls
the actuators 11 12 and 13 to move the joints J.sup.1 to J.sup.3
machine members L.sup.1 and L.sup.2 to cause the cutting tool 7
to occupy the desired position on the programmed path.
Referring to FIG. 3 of the drawings, there is shown a co-ordinate
transform module 3 for a CNC machine tool having five principal
"hard" axes, two partially redundant "soft"
axes, and five joints.
The co-ordinate transform module shown in FIG. 3 comprises a programmable
module 3 and includes a driver preparation module 15 a kinematic
driver module 16 and a driver debriefing module 17. The driver preparation
module 15 sequentially receives signals representing the current
axis vector A' and prepares and passes each signal to the kinematic
driver module in the form of component axis positions a.sup.1 to
a.sup.7 where a.sup.1 to a.sup.5 represent component axis positions
of the five principal "hard" axes, and a.sup.6 and a.sup.7
represent component axis positions of the two "soft" axes.
The "soft" axes, as defined above, are partially redundant
axes or fully redundant axes that have been synthesized by electronic
or computational means of the CPU, with the kinematic driver module
16 also being programmed with encoded mathematical kinematic equations
of the particular machine tool in terms of both "hard"
and "soft" axis positions. This module can be replaced
for different machine tools so that the kinematics can be customized
for each type of machine tool.
The kinematic driver module 16 may perform the transformation from
a current axis vector value A' to a joint vector value J' by means
of two procedural sections. The first section calculates a numerical
value for the position matrix P(A') at the current axis vector based
on the axis matrix A: The second section uses equations of the form:
where:
f.sub.n (P) is a function of the components of the position matrix
P,
for each component joint position j.sup.n, derived from the equation:
where:
J is the joint matrix and P is the position matrix, to calculate
the joint positions j.sup.n from the numerical value for P calculated
from the first section. These two sections may be combined into
one stage (in simple kinematic machines) where the equations can
be represented as:
where:
A is the axis vector and f.sub.n (A) is a function of the components
of A (a.sup.1 a.sup.2 . . . a.sup.M) where M is the number of axes
of the machine tool.
In the co-ordinate transform module illustrated in FIG. 3 the
kinematic driver module 16 transforms the current axis vector A'
with seven component axis positions a.sup.1 to a.sup.7 into a current
joint vector J' having five component joint positions j.sup.1 to
j.sup.5 each of which corresponds to one of the five joints J.sup.1
to J.sup.5 of the machine tool.
The current joint vector J' then passes through the driver debriefing
module 17 before being passed to the actuators for the respective
joints J.sup.1 to J.sup.5 of the machine.
It will thus be appreciated that the present invention introduces
a coordinate transform module which completely detaches the coordinate
system(s) that the programmer uses from the joint space coordinate
system that the position controller uses. This allows greater flexibility
in the equations that map the programming coordinates (axes) to
joints. In particular, the kinematic driver module allows the value
of soft axes to be included in the axis vector value passed to the
coordinate transform module. Using the axis matrix, joint matrix
and position matrix value allows the correct joint vector to be
calculated that satisfies the axis vector, even though the axis
vector contains redundant information (the soft axis position values).
The present invention also provides the significant advantage that
a CNC machine in accordance with the invention requires less joints
than a conventional machine to perform the same function as the
conventional machine. For instance, whilst this invention is not
limited to a CNC machine having a particular number of joints and
soft axes, preferred embodiments of this invention include a 7 axis
CNC tool grinder which contains 5 joints; a 6 axis CNC cylindrical
grinder which contains 4 joints; an 8 axis CNC laser cutter that
contains 5 joints and an 8 axis CNC milling machine that contains
5 joints. These preferred embodiments will be described with reference
to FIGS. 4 to 8 of the drawings.
Referring to FIGS. 4 and 5 there is shown the workhead 18 and
wheelhead 19 of a CNC tool grinder having 5 hard axes and 2 soft
axes to provide the programmability and flexibility of a full 7
axis machine with the added advantage of full contouring facilities
on all axes whist requiring only 5 joints.
In the embodiment of FIGS. 4 and 5 the workpiece 6 is rotatably
carried by the workhead 18 which itself is linearly movable in the
directions of axes X and Y by means of prismatic joints J.sup.1
and J.sup.2 which connect the workhead 18 to the base of the machine
(not shown).
The wheelhead 19 carries on one end a rotating cutting tool 7 in
the form of a grinning wheel, and the other end of the wheelhead
19 is connected to a column 20 by a prismatic joint J.sup.3 which
permits vertical movement of the wheelhead 19 relative to the column
20 in the direction of axis Z. The machine also includes two rotary
joints J.sup.4 and J.sup.5. Rotary joint J.sup.4 permits rotation
of the workpiece about a horizontal rotary axis A and rotary joint
J.sup.5 permits rotation of the column about a vertical rotary axis
C.
The axis layout in FIG. 4 of the machine may be chosen according
to the axis selection rules as:
Hard Axes
X Linear axis (left/right).
Y Linear axis (fore/aft).
Z Linear axis (up/down).
A Rotary axis (horizontal rotation of workhead)
C Rotary axis (vertical rotation of wheelhead)
Soft Axes
B Rotary axis (grind point (tool reference point: TRP) location
on grinding wheel)
V Linear axis (parallel to grinding wheel spindle axis of rotation).
The joint layout for this machine is depicted in FIG. 5:
J.sup.1 Prismatic joint (left/right linear slide)
J.sup.2 Prismatic joint (fore/aft linear slide)
J.sup.3 Prismatic joint (up/down linear slide)
J.sup.4 Rotary joint (horizontal rotation of workhead)
J.sup.5 Rotary joint (vertical rotation of column)
As can be seen from FIG. 3 the spacial degrees of freedom of this
machine SDOF=3. The orientation degrees of freedom ODOF=2. Since
this machine contains a rotating cutting tool, ODOF cannot equal
3. Axes X, Y and Z are 3 orthogonal linear axes, selected as principal
hard axes under the axis classification rules to provide the SDOF
positional degrees of freedom. None of the axes are collinear axes,
so we are free to select 2 of the 3 rotary axes as principal hard
axes. A and C are arbitrarily chosen to be principal hard axes under
the axis classification rules to provide the ODOF orientation degrees
of freedom. The remaining 2 axes B and V, thus are classified as
soft axes. The programming degrees of freedom is thus PDOF=SDOF+ODOF+2=7.
The machine degrees of freedom MDOF=number of non-collinear joints=5.
Therefore, by appropriate selection and synthesis of soft axes
B and V, the machine tool can be programmed to control relative
movement between the workpiece and cutting tool either in the direction
of linear axis V or about rotary axis B. This movement would conventionally
require a 7-axis machine with specific joints to control movement
in the direction of linear axis V or about rotary axis B.
Referring to FIG. 6 of the drawings there is shown a CNC cylindrical
grinder having 4 hard axes and 2 soft axes.
In FIG. 6 a grinding wheel 27 is carried by a wheelhead 29 which
is linearly movable in the X and Z directions by prismatic joints
J.sup.2 and J.sup.1 respectively. The wheelhead 29 is rotatable
about vertical rotary axis B by means of rotary joint J.sup.3 and
the workhead 28 is rotatable about horizontal rotary axis C by means
of rotary joint J.sup.4.
The axis layout may be chosen according to the axis selection rules
as:
Hard Axes
X Linear axis (left/right).
Z Linear axis (fore/aft).
B Rotary axis (vertical rotation of wheelhead)
C Rotary axis (horizontal rotation of workhead)
Soft Axes
V Linear axis (perpendicular to grinding wheel spindle axis of
rotation).
W Linear axis (parallel to grinding wheel spindle axis of rotation).
By the selection and synthesis of soft axes V and W, the machine
tool of FIG. 6 can be programmed to control movement of the grinding
wheel in the direction of linear axis V or linear axis W. To provide
this movement in conventional machine tools would require specific
joints.
Referring to FIG. 7 there is shown a CNC laser cutting machine
tool having 5 hard axes and 3 soft axes.
The laser cutting machine of FIG. 7 has a laser cutting tool 37
carried by a toolhead 38 which is movable in the directions of three
orthogonal axes X, Y and Z by means of prismatic joints J.sup.1
J.sup.2 and J.sup.3 respectively. The laser cutting tool 37 is rotatable
about a horizontal rotary axis B by means of rotary joint J.sup.4
and rotatable about a vertical rotary axis C by means of rotary
joint J.sup.5.
The axis layout may be chosen according to the axis selection rules
as:
Hard Axes
X Linear axis (left/right).
Y Linear axis (fore/aft).
Z Linear axis (up/down).
B Rotary axis (horizontal rotation of laser beam)
C Rotary axis (vertical rotation of laser beam)
Soft Axes
U Linear axis (perpendicular to laser beam direction and Z axis
direction)
V Linear axis (perpendicular to laser beam direction and U axis
direction)
W Linear axis (parallel to laser beam direction)
Thus, by the selection and synthesis of soft axes U, V and W, the
laser cutting machine tool can be programmed to control movement
of the laser cutting tool 37 in the direction of linear axes U,
V and W without requiring specific joints for that purpose.
Referring to FIG. 8 there is shown a CNC milling machine having
5 hard axes and 3 soft axes. The milling machine of FIG. 8 has a
cutting tool 47 carried by a toolhead 49 which is movable in the
direction of a vertical axis Z by means of prismatic joint J.sup.3.
The workpiece 46 is mounted on a workpiece holder 48 which is movable
in the directions of horizontal axes X and Y by means of prismatic
joints J.sup.1 and J.sup.2 respectively. The cutting tool 47 is
rotatable about a horizontal rotary axis B by means of rotary joint
J.sup.5 and rotatable about a vertical rotary axis C by means of
rotary joint J.sup.4.
The axis layout may be chosen according to the axis selection rules
as:
Hard Axes
X Linear axis (left/right).
Y Linear axis (fore/aft).
Z Linear axis (up/down).
B Rotary axis (horizontal rotation of cutting tool)
C Rotary axis (vertical rotation of cutting tool)
Soft Axes
U Linear axis (perpendicular to cutting tool spindle axis of rotation
and Z axis direction)
V Linear axis (perpendicular to cutting tool spindle axis of rotation
and U axis direction)
W Linear axis (parallel to cutting tool spindle axis of rotation)
Once again, by the selection and synthesis of soft axes U, V and
W, the cutting tool 47 of the milling machine can be programmed
to control movement of the cutting tool 47 in the direction of linear
axes U, V and W without requiring specific joints for that purpose.
|