Machine tools abstract
A new generation of hybrid form multi-axis machine tools is described.
The hybrid machine tools comprise a position mechanism and an orientation
mechanism. Both mechanisms are three-DOF parallel mechanisms that
can be connected either in series to form a hybrid parallel-serial
manipulator, or in parallel to form a cooperating machine. The position
mechanism is used for manipulating the position and the orientation
mechanism is used for manipulating the orientation of an object.
Six-axes machining of a workpiece is achieved by coordinating the
motions of the position and orientation mechanisms. This approach
has several important advantages. First of all, a high stiffness,
low inertia, and high speed machine tool is realized by using the
parallel construction. Secondly, its direct and inverse kinematic
solutions could be solved in closed forms which would greatly simplify
the control and path planning problems. Thirdly, it has a relatively
large workspace in comparison to fully parallel platform manipulators.
Fourthly, its position and orientation are completely decoupled.
Lastly, it utilizes mostly revolute joints which can be precisely
made at low cost.
Machine tools claims
The embodiments of the invention in which an exclusive property
or privilege is claimed are defined as follows:
1. A multi-degree-of-freedom hybrid machine tool comprising:
a position mechanism having a translation platform movably connected
to a fixed base by several limbs for manipulating the position but
not the orientation of said translation platform;
an orientation mechanism having a rotation platform movably connected
to a base member by several legs for manipulating the orientation
but not the position of said rotation platform;
said base member of said orientation mechanism rigidly attached
to said fixed base of said position mechanism;
a spindle attached to said translation platform of said position
mechanism for mounting a cutting tool; and
a gripping mechanism attached to said rotation platform of said
orientation mechanism for mounting a workpiece.
2. The device of claim 1 wherein the attachment points of said
spindle and said gripping mechanism are interchanged.
3. A multi-degree-of-freedom hybrid machine tool comprising:
a position mechanism having a translation platform movably connected
to a fixed base by several limbs for manipulating the position but
not the orientation of said translation platform;
an orientation mechanism having a rotation platform movably connected
to a base member by several legs for manipulating the orientation
but not the position of said rotation platform;
said base member of said orientation mechanism rigidly attached
to said translation platform of said position mechanism;
a spindle attached to said rotation platform of said orientation
mechanism for mounting a cutting tool; and
a gripping mechanism attached to said fixed base of said position
mechanism for mounting a workpiece.
4. The device of claim 3 wherein the attachment points of said
spindle and said gripping mechanism are interchanged.
5. A three-degree-of-freedom position mechanism comprising:
three limbs each having an upper arm and a forearm;
each said upper arm of said limbs comprising a planar four-bar
parallelogram;
each said planar four-bar parallelogram of said upper arm having
a first link, a second link, a third link, and a fourth link movably
connected in a closed loop;
said first link of each said planar four-bar parallelogram movably
attached to a translation platform by a first revolute joint at
non-collinear points on said translation platform;
each said forearm of said limbs having a first end and a second
and;
said third link of each said planar parallelogram movably attached
to said first end of said forearm by a second revolute joint;
said second end of each said forearm movably connected to a fixed
base by a third revolute joint at non-collinear points on said fixed
base;
said first, second, and third revolute joints being parallel to
one another and perpendicular to the rotation axes of said planar
four-bar parallelogram;
driver means affixed to said fixed base and movably attached to
each said second end of said forearm for providing rotation to each
said forearm thereby manipulating the position of said translation
platform; and said translation platform of said position mechanism
having a constant orientation with respect to said fixed base.
6. A three-degree-of-freedom position mechanism comprising:
three limbs each having an upper arm and a forearm;
each said upper arm of said limbs having a first end and a second
end;
each said forearm of said limbs having a first end and a second
end;
said first end of said upper arm movably attached to a translation
platform by a cylindrical joint at non-collinear points on said
translation platform;
said first end of said forearm movably attached to said second
end of said upper arm by a first revolute joint;
said second end of said forearm movably attached to a fixed base
by a second revolute joint at non-collinear points on said fixed
base;
said cylindrical joint, first revolute joint, and second revolute
joint being parallel to one another;
driver means affixed to said fixed base and movably attached to
each said second end of said forearm for providing rotation to each
said forearm thereby manipulating the position of said translation
platform; and
said translation platform of said position mechanism having a constant
orientation with respect to said fixed base.
7. The device of claim 6 wherein said cylindrical joint and said
first revolute joint are interchanged.
8. The device of claim 6 wherein said cylindrical joint and said
second revolute joint are interchanged.
9. The device of claim 6 wherein said cylindrical joint is substituted
by a revolute joint and a prismatic joint with an added intermediate
member.
10. The device of claim 7 wherein said cylindrical joint is substituted
by a revolute joint and a prismatic joint with an added intermediate
member.
11. The device of claim 8 wherein said cylindrical joint is substituted
by a revolute joint and a prismatic joint with an added intermediate
member.
12. A three-degree-of-freedom orientation mechanism comprising:
three legs each having an upper member and a lower member;
each said upper member of said legs having a first end and a second
end;
each said lower member of said legs having a first end and a second
end;
said first end of said upper member movably attached to a rotation
platform by a first revolute joint at non-collinear points on said
rotation platform;
said first end of said lower member movably attached to said second
end of said upper member by a second revolute joint;
said second end of said lower member movably attached to a base
member by a third revolute joint at non-collinear points on said
base member;
said rotation platform movably attached to said base member by
a spherical joint;
said first, second, and third revolute joints intersecting at the
center of said spherical joint;
driver means affixed to said base member and movably attached to
each said lower member of said legs for providing rotation to each
said lower member thereby manipulating the orientation of said rotation
platform; and
said rotation platform of said orientation mechanism having a point
fixed on said base member.
Machine tools description
TECHNICAL FIELD
This invention relates in general to multiple degree-of-freedom
(DOF) hybrid manipulators and in particular to low inertia, high
stiffness, and high speed machine tools for multi-axis machining.
BACKGROUND ART
Conventional machine tools typically use a linear x-y table for
mounting a workpiece and a z-axis for mounting a spindle. The x-y
table is usually very heavy, and its operating speed is relatively
slow. The machining capability of such a conventional machine tool
is often limited to straight lines or simple two-dimensional contours.
It is essential that non-conventional machine tools be developed
for free-form three-dimensional machining of general shapes.
The Stewart platform has been studied extensively for use as a
flight simulator and as a parallel manipulator (Stewart, D. 1965
"A Platform with Six Degrees of Freedom," Proc. Institute
of Mechanical Engr., London, England, Vol. 180 pp. 371-386). Other
variations of the Stewart platform have also been proposed. Kohli
et al. studied several six-DOF parallel manipulators which are driven
by base-mounted rotary-linear actuators (Kohli, D., Lee, S. H.,
Tsai, K. Y., and Sandor, G. N., 1988 "Manipulator Configurations
Based on Rotary-Linear (R-L) Actuators and Their Direct and Inverse
Kinematics," ASME Journal of Mechanisms, Transmissions, and
Automation in Design, Vol. 110 pp. 397-404). Hudgens and Tesar
introduced a six-DOF parallel micromanipulator (Hudgens, J. C.,
and Tesar, D., 1988 "A Fully-Parallel Six Degree-of-Freedom
Micromanipulator: Kinematic Analysis and Dynamic Model," Trends
and Developments in Mechanisms, Machines, and Robotics, Proc. of
the 20th ASME Biennial Mechanisms Conference, DE-Vol. 15-3 pp.
29-37). Pierrot, et al. studied a parallel manipulator using spatial
parallelograms (Pierrot, F., Reynaud, and Fournier, A., 1990 "DELTA:
A Simple and Efficient Parallel Robot," Robotica, Vol. 8 pp.
105-109). Pierrot, et al. introduced a high-speed six-DOF parallel
manipulator (Pierrot, F., Fournier, A., and Dauchez, P., 1991 "Toward
a Fully Parallel 6 DOF Robot for High-Speed Applications,"
Proc. of the 1991 IEEE International Conference on Robotics and
Automation, pp. 1288-1293). Most of these six-DOF parallel manipulators
consist of six limbs connecting a moving platform to a fixed base
by spherical joints. These six-limbed manipulators suffer the following
disadvantages:
1. Their direct kinematics are very difficult to solve.
2. Position and orientation of the moving platform are coupled.
3. Their workspace is relatively small.
4. Spherical joint is difficult to manufacture with high precision.
Note that the only six-limbed, six-DOF parallel manipulators for
which closed-form direct kinematic solutions have been reported
in the literature are special forms of the Stewart platform (Nanua.
P., Waldron, K. J., and Murthy, V., 1990 "Direct Kinematic
Solution of a Stewart Platform," IEEE Transactions on Robotics
and Automation, Vol. 6 pp. 438-444; Grffis, M., and Duffy, J.,
1989 "A Forward Displacement Analysis of a Class of Stewart
Platforms," Journal of Robotic Systems, Vol. 6 pp. 703-720;
Innocenti, C., and Parenti-Castelli, V., 1990 "Direct Position
Analysis of the Stewart Platform Mechanism," Mechanism and
Machine Theory, Vol. 25 pp. 611-612). In these special forms, pairs
of spherical joints are concentric on either just the platform or
both the base and the platform. However, as mentioned by Griffs
and Duffy, pairs of concentric spherical joints may present design
problems. As to the general Stewart platform, researchers have to
resort to numerical techniques for the solutions. Innocenti and
Parenti-Castelli developed an exhaustive search algorithm to solve
the direct kinematics problem of the general Stewart platform (Innocenti,
C., and Parenti-Castelli, V., 1993 "Forward Kinematics of
the General 6--6 Fully Parallel Mechanism: An Exhaustive Numerical
Approach Via a Mono-Dimensional Search Algorithm," ASME Journal
of Mechanical Design, Vol. 115 pp. 932-937). Raghavan applied the
continuation method and found that the general Stewart platform
has 40 direct kinematics solutions (Raghavan, M., 1993 "The
Stewart Platform of General Geometry Has 40 Configurations,"
ASME Journal of Mechanical Design, Vol. 115 pp. 277-282).
Although parallel manipulators have been studied thoroughly, most
of the studies have concentrated on their applications as a robot
manipulator. Recently, Giddings and Lewis (1995) introduced a machine
tool called the "VARIAX Machining Center" utilizing the
Stewart platform construction. Six legs connect a moving platform
to a base. The upper and lower ends of each leg are connected to
the moving platform and the base by gimbals. A spindle is mounted
on the moving platform to cut the workpiece. Each of the six legs
houses a ball screw. Individual servo motors drive the ball screws.
Extending and retracting of the legs controls the position and orientation
of the spindle making 6-axis machining feasible. This machine represents
a revolutionary design in the machine tool industry. However, since
the machine tool utilizes the Stewart platform construction, it
suffers all the problems mentioned above. Although the minimanipulator
introduced by Tahmasebi and Tsai (Tahmasebi, F., and Tsai, L. W.,
1994 U.S. Pat. No. 5279176) contains only three limbs, it was
designed for manipulating an object in a relatively small workspace.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a light weight,
high speed, and high stiffness hybrid machine tool for multi-axis
machining.
Another object of the invention is to provide a machine tool with
a decoupled position and orientation characteristic.
Still another object of the invention is to provide a multi-DOF
machine tool with closed-form kinematics solutions.
A further object of the invention is to provide a large workspace
for a machine tool.
A still further object of the invention is to utilize mostly revolute
joints to increase the precision and to reduce the manufacturing
cost of a machine tool.
These objects are achieved by providing a hybrid form machine tool
with a position mechanism and an independently controlled orientation
mechanism. Both mechanisms are three-DOF parallel mechanisms that
can be connected in series to form a hybrid parallel-serial manipulator,
or in parallel to form a cooperating machine. Multi-axis machining
of a workpiece is achieved by coordinating the translation of the
position mechanism and the rotation of the orientation mechanism.
These and other features of the invention will become more fully
understood from the following description of certain preferred embodiments
taken together with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic representation of a position mechanism formed
in accordance with the invention.
FIG. 2 is a schematic representation of a limb comprising a forearm
and a planar four-bar parallelogram.
FIG. 3 is the top view of the position mechanism shown in FIG.
1.
FIG. 4 is a schematic illustration of a three-DOF orientation mechanism
in accordance to the invention.
FIG. 5 is a schematic illustration of a six-DOF cooperating machine
tool.
FIG. 6 is an alternative construction of a limb which connects
a translation platform to a fixed base by a cylindrical joint followed
by a first revolute joint and a second revolute joint.
FIG. 7 is another alternative construction of a limb which connects
a translation platform to a fixed base by a first revolute joint
followed by a cylindrical joint and then a second revolute joint.
FIG. 8 is still another alternative construction of a limb which
connects a translation platform to a fixed base by a first revolute
followed by a second revolute joint and then a cylindrical joint.
FIG. 9 is still another alternative construction of a limb obtained
by replacing the cylindrical joint in FIG. 8 by a revolute joint
and a prismatic joint with an added intermediate member.
FIG. 10 is a schematic representation of an alternative three-DOF
spherical mechanism incorporating spherical and prismatic joints.
DETAILED DESCRIPTION
The Stewart platform and other variations of the Stewart platform
contain six limbs (Stewart, Hudgens and Tesar, Pierrot et al., Giddings
and Lewis, etc.). As a result, the inverse kinematics of these mechanisms
is fairly straight forward while the direct kinematics becomes a
very difficult problem. Furthermore, the position and orientation
of the moving platform are strongly coupled which makes the motion
control and path planning a very complicated task.
For the reasons mentioned in the section entitled "Background
Art," the present invention divides a six-DOF manipulator into
two decoupled three-DOF mechanisms, one for manipulating the position
and the other for manipulating the orientation. These two three-DOF
mechanisms can be connected either in series to form a hybrid parallel-serial
manipulator or in parallel to form a cooperating machine. Each of
the three-DOF mechanisms utilizes the parallel construction with
three limbs to achieve light weight, high stiffness and high speed
capabilities. In what follows, the preferred embodiments of a three-DOF
position mechanism and a three-DOF orientation mechanism will be
described. Then, how such mechanisms can be attached together to
form a multi-DOF machine tool or a general purpose robot manipulator
will be described.
Referring to FIGS. 1 through 3 in detail, numeral 0 generally indicates
a fixed base and numeral 16 a moving platform. There are three identical
limbs connecting the moving platform 16 to the fixed base 0. The
moving platform 16 of a position mechanism is called the translation
platform. Each limb consists of an upper arm and a forearm. Each
forearm is a single link denoted by the numerals 1 2 and 3 respectively.
Each upper arm comprises a planar four-bar parallelogram: links
4 7 10 and 13 for the first limb; 5 8 11 and 14 for the second
limb; and 6 9 12 and 15 for the third limb. The axes of rotation
of each parallelogram are parallel to one another while the lengths
of its opposite links are equal to each other. The parallelogram
and the forearm are connected to each other and to the translation
platform 16 and the fixed base 0 by three parallel revolute joints,
with their axes of rotation DE, FG, and QR perpendicular to the
axes of the four-bar parallelogram. A revolute joint permits two
connected members to rotate freely with respect to one another.
The axes of rotation of the parallelogram do not necessarily intersect
the axes DE and FG as depicted in FIG. 3. Note that when two revolute
joint axes intersect at a common point, it is kinematically equivalent
to a universal joint. The three limbs are preferably, but not necessarily,
separated by 120 degrees at the points of connection with the translation
platform 16 and with the fixed base 0 as illustrated in FIG. 3.
A spindle 17 as shown in FIG. 1 is attached to the translation platform
16 for mounting a cutting tool 18.
Let F be the degrees of freedom of a mechanism, n the number of
links, j the number of joints, f.sub.i the degrees of freedom associated
with the i.sup.th joint, and .lambda. the motion parameter (.lambda.=6
for spatial mechanisms and .lambda.=3 for planar and spherical mechanisms).
Then, the degrees of freedom of a mechanism is generally governed
by the following equation: ##EQU1##
For the position mechanism shown in FIG. 1 n=17 j=21 and f.sub.i
=1 for i=1 2 . . . 21. Hence,
That is the mechanism is an over constrained mechanism. However,
due to the ingenious arrangement of the links and joints, many of
the constraints imposed by the joints are redundant and the resulting
mechanism does have three degrees of freedom. More importantly,
the translation platform performs pure translation with respect
to the fixed base. Thus the translation platform will never change
its orientation while its position is being varied. This unique
characteristic is very useful in many applications such as an x-y-z
position device.
Due to the nature of the link arrangement, the useful workspace
of the present invention is generally larger than that of fully
parallel manipulators discussed in the section entitled "Background
Art." The housings of three actuators 51 52 and 53 are attached
on the base platform to drive the lower members (links 1 2 and
3) or on the translation platform to drive the upper members (links
13 14 and 15) of the mechanism. In fact, the translation platform
and the fixed base can be interchanged at will.
As mentioned above the present invention incorporates a three-DOF
position mechanism and a three-DOF orientation mechanism. Three-DOF
orientation mechanisms have been used as wrist mechanisms in serial
robots. Cincinnati Milacron designed a three-roll wrist mechanism
using bevel-gear trains for power transmission (Stackhouse, T.,
1979 "A New Concept in Wrist Flexibility," Proceedings
of the 9th International Symposium on Industrial Robots, Washington,
DC, pp. 589-599). Bendix Corporation designed a roll-bend-roll bevel-gear
wrist mechanism (Anonymous, 1982 "Bevel Gears Make Robot's
Wrist More Flexible," Machine Design, Vol. 54 No. 18 pp.
55). Chang and Tsai developed a systematic methodology for the enumeration
of geared robotic mechanisms (Chang, S. L., and Tsai, L. W., 1990
"Topological Synthesis of Articulated Gear Mechanisms,"
IEEE Transactions on Robotics and Automation, Vol. 6 No. 1 pp.
97-103). This type of orientation mechanisms may be incorporated
in the present invention. However, one major disadvantage for this
type of mechanisms is their limited load capacity. This invention
improves load capacity by using parallel construction similar to
the position mechanism described above.
Referring to the orientation mechanism shown in FIG. 4 in detail,
numeral 30 indicates a base platform and 37 a moving platform. The
moving platform 37 of an orientation mechanism is called the rotation
platform. The rotation platform 37 is directly connected to the
base platform 30 by a spherical joint centered at point Q. A spherical
joint consists of a ball and socket. In addition, the rotation platform
37 is also connected to the base platform 30 by three legs of similar
kinematic structure. Each leg consists of two links: an upper member
and a lower member. The upper member 34 of the first leg is connected
to the rotation platform by a revolute joint denoted as M1; the
lower member 31 is connected to the upper member 34 by a second
revolute joint R1; furthermore the lower member 31 is connected
to the base 30 by a third revolute joint B1. The other two legs
are constructed similarly. All the joint axes intersect at the center
of the spherical joint Q as depicted in FIG. 4. Since all the joint
axes intersect at a common point Q, the mechanism is a spherical
mechanism. Applying the above degree-of-freedom equation, yields
##EQU2##
Hence, the mechanism is a three-DOF spherical mechanism which can
be used for controlling the orientation of an object. The housings
of three actuators 41 42 and 43 are attached to the base platform
to drive the lower members (links 31 32 and 33) of the mechanism.
A gripping mechanism 39 is attached to the rotation platform 37
for the purpose of holding a workpiece. Note that when the spherical
joint at point Q is removed, the mechanism remains as a three-DOF
spherical mechanism which is the more commonly known spherical mechanism
(Gosselin, C., and Angeles, J., 1989 "The Optimum Kinematic
Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator,"
ASME Journal of Mechanisms, Transmissions, and Automation in Design,
Vol. 111 pp. 202-207; Gosselin, C., and Hamel, J., 1994 "The
Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting
Device," IEEE International Conference on Robotics and Automation,
pp. 781-786). The addition of the redundant spherical joint at point
Q increases the stiffness of the mechanism without sacrificing its
useful workspace.
An alternative construction of a three-DOF orientation mechanism
is shown in FIG. 10 wherein three legs are movably connected to
a moving platform 27 and a base platform 20 by spherical joints
denoted as M1 M2 M3 and B1 B2 B3 respectively, and wherein
each leg is comprised of two members constrained by a prismatic
joint. Furthermore, the moving platform 27 is connected to the base
platform 20 by a spherical joint at point Q. Rotation of the moving
platform is controlled by extending or retracting the prismatic
joints. This mechanism was reported by Gosselin and Sefrioui (Gosselin,
C., and Sefrioui, J., 1992 "Determination of Singularity Loci
of Spherical Three-Degree-of-Freedom Parallel Manipulators,"
ASME Mechanisms Conference, DE-Vol. 45 Robotics, Spatial Mechanisms,
and Mechanical Systems, pp. 329-335). This present invention incorporates
mostly revolute joints and one spherical joint to eliminate the
disadvantages associated with spherical joints.
A hybrid cooperating machine tool is formed by mounting the base
platform 30 of the orientation mechanism on the fixed base 0 of
the position mechanism as depicted in FIG. 5. A spindle 17 is attached
to the translation platform 16 for holding a cutting tool 18 while
a gripping mechanism 39 is attached to the rotation platform 37
for holding a workpiece. This invention makes three dimensional
free-form cutting of a workpiece possible. Because of the hybrid
parallel construction, the present invention has the following advantages:
1. It has closed-form direct and inverse kinematics solutions.
2. The position and orientation problems are completely decoupled.
3. Its workspace is substantially larger than the prior art.
4. Revolute joints can be precisely made at low cost.
Note that none of the existing parallel manipulators has the decoupled
position and orientation characteristic of the present invention.
ALTERNATIVE EMBODIMENTS OF THE INVENTION
A hybrid parallel-serial machine tool can be formed by attaching
the base platform 30 of the orientation mechanism to the translation
platform 16 of the position mechanism. In this case, the spindle
or an end-effector will be attached to the rotation platform 37
of the orientation mechanism to perform six-axis machining or manipulation
of an object. Since manipulation of the position is independent
of the orientation, the position and orientation problems are completely
decoupled. All the advantages of a hybrid coordinating machine tool
still apply to this design.
Other potential applications include: (a) a five-DOF hybrid parallel-serial
manipulator constructed by mounting a two-DOF rotation mechanism
on the translation platform 16 of the three-DOF position mechanism,
(b) a five-DOF hybrid cooperating machine constructed by mounting
the base platform of a two-DOF orientation mechanism on the fixed
base 0 of the three-DOF position mechanism, and (c) a four-DOF manipulator
constructed by mounting a one-DOF wrist on the translation platform
16 of the position mechanism.
The parallelogram depicted in the preferred embodiment illustrated
in FIG. 2 can be substituted by a single link 18 as illustrated
in FIGS. 6 through 8 with one of the three parallel revolute joints
located at DE, FG, and QR replaced by a cylindrical joint. A cylindrical
joint permits two connected members to rotate and translate with
respect to each other about a common joint axis. Additionally, a
cylindrical joint can be replaced by two parallel revolute and prismatic
joints. A prismatic joint permits only translational motion between
two connected members. FIG. 9 demonstrates one such alternation.
For the alternative limb constructions illustrated in FIG. 6 through
9 a linear actuator can be used to control the translation of a
cylindrical joint or a prismatic joint. However, it should be noted
that only two of the three translational degrees-of-freedom can
be controlled independently.
Although the position mechanism illustrated in FIG. 1 has three
limbs, theoretically any number of limbs that is greater than one
can be employed to achieve the same purpose. When only two limbs
are used, it will be necessary to incorporate two actuators in one
of the limbs. When four or more limbs are used, only three of the
limbs need to be actuated while the others simply provide extra
rigidity to the mechanism without changing its mobility. It should
be noted that the placement of actuators can be arbitrarily so long
as they comply with the mobility criteria of the mechanism. Both
rotary and linear actuators can be incorporated into the mechanisms.
For example, a linear ball screw or hydraulic actuator can be installed
between the fixed base 0 and the link 1 of the position mechanism
shown in FIG. 1 to control the rotation of link 1.
While the invention has been described by reference to certain
specific embodiments and configurations, it should be understood
that various changes could be made without departing from the spirit
and scope of the inventive concepts described. Accordingly, it is
intended that the invention not be limited to the described embodiments
but that it has the full scope permitted by the language of the
following claims.
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