The present invention relates to kinematic couplings to enable the location and manipulation of objects with improved repeatability and accuracy.
The present invention is directed to kinematic couplings, particularly to such couplings comprising surfaces to exactly constrain the six degrees of freedom of a rigid body. It is also directed at kinematic couplings that need to constrain a body in fewer than six degrees of freedom. The understanding of kinematic couplings has been developed since the 1800s. The topic is fully explained in D. L. Blanding, Principles of Exact Constraint Mechanical Design, Eastman Kodak Co., 1992.
Previously, there existed two general types of kinematic couplings. Both types use three spheres or balls attached to one part which come to rest on six surfaces on the mating part. This gives nearly ideal kinematics but suffers from very high localized stresses. The first of these two types of kinematic couplings is commonly called a Kelvin Clamp. In this coupling, the three balls rest respectively in a tetrahedral socket, a vee-groove aligned to the socket, and a flat plane. The load capability of the Kelvin Clamp is typically limited by high localized stresses.
The second type of kinematic coupling is sometimes referred to as the Maxwell clamp. The reference mechanism comprises three balls sitting into three grooves. This is shown in
In U.S. Pat. No. 6,065,898 Hale discloses a coupling that utilizes a three tooth arrangement where mating surfaces contact at a three theoretical line contacts formed by mating teeth rather than six theoretical point contacts. This is an example of what is termed a quasi-kinematic coupling. As two points form a line, conceptually, this remains close to the theoretical requirement of six constraining points, but provides a higher load capacity than six point Hertzian support. The inventor discloses that this gives, an increased load capacity analogous to the increased load capacity of a roller bearing compared to that of a ball bearing.
U.S. Pat. No. 6,193,430 discloses another quasi kinematic coupling where the mating contacts comprise a ball seating in a truncated conical hole. The contact area is greater than in the case of Hertzian point loading, and so has a high load capacity, though its repeatability is somewhat reduced as the object is over-constrained.
Repeatability in the submicron range has been reported in the laboratory for kinematic couplings. However, an ongoing problem in achieving such repeatability is that the uncertainty regarding the magnitude and direction of the sliding friction between the contacting surfaces causes the kinematic coupling to be statically indeterminate below a certain range. This range appears to be of the order of one micron. In prior art designs, the repeatability of the kinematic coupling is limited by sliding friction. Attempts to overcome this have relied on flexural bearings comprising a single degree of freedom. In U.S. Pat. No. 5,678,944 Slocum discloses a coupling where the mating contacts are mounted on a flexural bearing which can flex in the direction normal to the contact plane i.e. the axis or the single degree of freedom is normal to the contact plane. The coupling first constrains the mating surfaces in the X and Y planes, while allowing them to move in the Z direction. This is a single degree of freedom flexure with its single compliant direction normal to the contact surface of the mating elements. Another design disclosed by Schouten et al. in Precision Engineering 20, p 46-52, 1997 similarly uses a single degree of freedom flexure, but oriented in a direction orthogonal to the contact surface. This however is insufficient to give the repeatability required of modem kinematic couplings.
U.S. Pat. No. 6,746,172 discloses an adjustable kinematic coupling, where the desired accuracy is achieved by adjusting the three mating eccentric balls relative to the three grooves in which they locate. However, as there are only three means of adjustment, the object cannot be controllably moved in all six degrees of freedom.
All of the above prior art has sought to provide repeatable location to close tolerances, while accommodating high loads. However, the repeatability is limited by the impact of sliding friction, and use of a single degree of freedom flexure mounts does not overcome the problem. Therefore, there still exists a need for a kinematic coupling with improved repeatability, and with a capability of adjustment in the nanometer range in all six degrees of freedom.
It is an object of the present invention to provide an improved kinematic coupling with improved repeatability.
Another object of the invention is to provide a kinematic coupling with increased area of contact, reduced localized stress points, and increased stiffness and load capacity.
Another object of the invention is to provide a kinematic coupling comprising a means of controllably adjusting the location of the object in each of Its constrained degrees of freedom.
Other objects and advantages of the present invention will become apparent from the following description and accompanying drawings. The kinematic coupling of this invention can be beneficially used in various applications such as in precision fixturing for tools or workpieces, and in industries such as precision machining and metrology, optics, and semiconductor industries.
The accompanying drawings, which are incorporated into and form a part of the disclosure, illustrate an embodiment of the invention and, together with the description, serve to explain the principles of the invention.
a is a coupling of prior art.
a illustrates an embodiment of one half of a coupling for constraining an object in six degrees of freedom using a 3-2-1 configuration.
a
4
b & 4c illustrate three coupling elements with suitable contact surfaces.
a, 5b, 5c & 5d illustrate four examples of five degree of freedom flexures
a is an isometric view of a coupling element.
The kinematic couplings of this invention conform to the rules of kinematic design which are summarized as follows: By definition, an unconstrained object has 6 degrees of freedom. It has a translational degree of freedom along each of three reference orthogonal axes. It also has a rotational degree of freedom about each of the same three axes. For an object to be kinematically constrained, each degree of freedom must be exactly constrained. To effect this, the object must be constrained at exactly six points, and no constraining point may be redundant. If the body is constrained at more than six points, then it is over-constrained. The rules governing redundancy are simple and well understood by those skilled in the art: for instance, no three points may lie in a single line, and no four or more points may lie in a plane. Combinations of constraints are similarly restricted. They can be best understood by examining the planes of contact at each contact surface.
The points of contact restrict the six degrees of freedom of a rigid body in two basic configurations. The first is hereby termed a plane-line-point or 3-2-1 configuration. The second is hereby termed a line-line-line or 2-2-2 configuration. In the 3-2-1 configuration, the contact planes at three points form a first reference plane, the contact planes at two points form a second reference plane orthogonal to the first, and the final point forms a third reference plane, orthogonal to the other two. It should be understood that a component of the contact planes of three points may form the above reference planes, rather than the contact planes themselves. The difference between the two configurations is only absolute when the contact planes themselves are parallel to the orthogonal reference planes derived above. It is readily understood from the above, that only 3-2-1 and 2-2-2 configurations satisfy the conditions that (a) the total number of constraints must add to six, and (b) no plane may have more than three constraints, and (c) each plane must have at least one constraint. All kinematic couplings conform to the above rules, as do the embodiments of this invention. For the following invention, a coupling will be treated as kinematic if it satisfies the above design rules, even if the area of contact at each location is greater than that of a single theoretical point.
Earlier designs of kinematic couplings have contact planes that are not orthogonal. The prior art coupling shown in
Referring now to
The essential design feature of this invention is that each contact surface supports the opposing surface with high rigidity only in the direction normal to its canted surface, and in contrast, is designed to be relatively compliant in the orthogonal directions, and about all rotational axes. Hereinafter, the direction normal to the contact surface shall be referred to as the coupling element's axial or Z direction, and directions orthogonal to it are hereinafter called the coupling element's X and Y axes. Thus, compared with its Z axis, the coupling elements contact surface is relatively free to move translationally in the X and Y directions, and rotationally about the X, Y and Z axes. This relative compliance is provided by a flexure with five degrees of freedom.
With reference to a 2-2-2 configuration shown in
One can understand how the coupling operates by examining the operation of a single coupling element half 10a with its mating half 10b. At the point where they mate, there will be what is hereinafter caned a placement error in the X and Y directions. The Z axis is however fixed with a high degree of precision. When coupling element halves 13a and 13b similarly mate, the coupling is referenced translationally in the Z axis, and rotationally about the Y axis. It is still relatively free to translate in the X and Y directions. The contact surface planes are also relatively free to rotate about the X and Y axes in order to orient to be fully parallel with each other.
When coupling element halves 11a and 14a mate with their corresponding halves 11b and 14b, the coupling is referenced translationally in the X axis, and rotationally about the Z axis. When coupling element halves 12a and 15a mate with their corresponding halves 12b and 15b, the coupling is similarly referenced translationally in the Y axis, and rotationally about the X axis. The coupling is then fully coupled in all six degrees of freedom.
A number of different designs of five degree of freedom flexures exist. The simplest form is a rod where the length is greater than its diameter. Such flexures are commonly referred to as wire flexures. This term is not used in this application as it may imply that the flexure has low axial stiffness and is thus unsuitable for use in compression, which is not the case. Instead, the five degree of freedom flexures used in this invention are referred to hereinafter as studs. Four different embodiments of studs are illustrated in
White rotationally symmetric designs are common, other shaped designs can also be employed.
Two five degree of freedom flexures when mounted in series, with their axes collinear, combine to be a five degree of freedom flexure.
The relative difference in the stiffness of the stud in the axial direction compared with the orthogonal directions is designed to suit the application. For instance, for a cylindrical stud with a length 10 times greater than its diameter, the stiffness ratio of X to Z direction stiffness is about 1 to 133. Where a contact element is mounted on the stud this ratio is increased. For instance, if the contact element is the same length as the stud, the stiffness ratio is increased to about 1 to 300, or 0.3%. This is hereby termed an orthogonal resistance factor. Those skilled in the art will recognise that this is equivalent to the friction factor in a coupling limited by sliding friction. Sliding friction values of prior art couplings are typically in the range of 10% to 20% or higher. A variation in the axial load on the stud leads to a variation in the axial strain of the coupling interface of that coupling element, and thus to a variation in the location of the coupled object. An important influence on the repeatability of this invented coupling is that most of the axial load at each coupling interface is carried axially by that supporting stud, and that this amount should not vary except within allowable tolerance. Only a small proportion, of consistent magnitude, of that load is carried by shear or torsional loading of any of the other orthogonal studs. The stiffness of the stud and the mating procedure is designed to achieve this. This invention provides for the reduction in the orthogonal resistance factor by two orders of magnitude or more, with a resulting significant improvement in the coupling's repeatability.
The dimensions of the stud can be designed according to normal engineering principles. Many applications require couplings with a high torsional stiffness as well as linear stiffness. To maximise the torsional stiffness of this invention the studs are placed at the maximum distance from the centre of gravity. For dynamic applications, the coupling design can be optimized to provide a high resonant frequency using shorter shaft studs with smaller diameters. Finite Element Analysis is particularly useful for estimating the numerous design parameters that need to be considered such as the normal load that the stud can accommodate, the factor of safety relating to any given loads or deflections, the stresses induced by any given deflection, and the stiffness of the stud in all directions. It should also be noted that the stud of this invention can be designed to be used in tension as well as compression, as required by the particular application, and that each of the six studs need not be of the same design. The couplings may be subject to different types of loads with some in tension, and others in compression, as is the case where the coupling is used to support an overhanging load. The location of the coupling elements and the orientation of their axes can be adapted to optimally couple parts subject to off-centre loads, torque loads, or overhanging loads. In general, for maximum three dimensional repeatability it is desirable to design the coupling elements' location and orientation to support the loads evenly across the six coupling elements. As with all product design, other design objectives and restrictions influence the coupling design.
The contact surface geometries of kinematic couplings known to date are typically composed of balls or cylinders mating to suitable flat or curved surfaces. One such prior art coupling is shown in
For mating contact of two flat surfaces, it is instructive to refer to the use of gauge blocks. Reference gauge blocks are lapped to high flatness and surface roughness standards, and are brought together in a process known as ‘wringing’. The length of a gauge block is taken as the length of the material plus the length of this wringing layer. The wringing layer is typically about 25 nm, and is generally stable to within a few nanometers under controlled conditions. In this invention, the dimensional stability and repeatability of each mating contact surface to the other is the key limitation on the repeatability of the coupling. As shown by the case of gauge blocks, this can be as low as a few nanometers under controlled conditions. It should be noted that this is two to three orders of magnitude lower than the locating repeatability of contact surfaces which are subjected to sliding friction.
While the above-mentioned gauge blocks are rectangular in shape and may be used, generally rotationally symmetric designs are preferred for this invention because of their ease of manufacture and symmetric stress distribution profiles. Preferred materials used for the contact surfaces are stainless steels and ceramics and superhard materials such as polycrystalline diamond. Ceramic faucet (tap) washers are similar in dimension and machining tolerance to the contact surfaces of this invention, and are manufactured in high volumes and at low cost. Similar materials and production processes may be used to manufacture the contact surface elements of this invention. In some applications the materials used for coupling may be restricted. For instance, inver or Super inver may be required due to their low co-efficient of thermal expansion and may be used in this invention.
The stud typically incorporates a wider section at either end. The wider ends may be used to attach the stud to one of the objects or to attach a separate contact surface element. This is the case where the stud is constructed from metal, such as stainless steel or aluminium, and the contact areas are constructed from ceramic, such as silicon nitride. Normal engineering means may be employed to attach the stud to objects and to the Contact surface element. Adhesive means can be used, as the thin layer has very little impact on the total axial rigidity of the stud.
It is preferred to have a controlled method of clamping of the two opposing surfaces of each coupling element. In some cases, gravity loading is sufficient, but vacuum clamping may also be usefully used.
The distance between the point where each coupling surface initially seats with its partner and the point where it is fully supported influences the repeatability of the coupling. With careful placement, all six couplings will seat substantially simultaneously. However, for maximum repeatability, the invention shown in
c shows a surface element 62b with two porous regions 63b and 63c, along with a ceramic contact surface 66b and all adhesively bonded into a steel casing 64b. Air is supplied to porous region 63b via symmetric through hole 65b, and air supplied to 63c via symmetric through hole 65c. This design gives added control over the mating process for light weight parts or where gravity acts to oppose coupling, as positive air pressure can be applied in one porous region while simultaneously applying vacuum to the other. Reducing the relative force from the air pressure causes the coupling surfaces to mate. Because of the high modulus of the ceramic, it carries practically the entire load of the coupling. Typically when polished as a single assembly, the surface of the softer graphite regions are marginally recessed under the ceramic surface, but this is not a detriment to the operation of the bearing.
The above air bearing, and their design and manufacture are well understood by those skilled in the art. If using a porous material as shown, porous graphite with 10 to 20% open porosity is highly suitable. Alternative designs do not use a porous material but instead use one or more holes and channels to provide the air flow. White air is referenced here as the fluid of choice, it should be noted that applying a liquid such as water or oil to the opposing surfaces prior to mating provides a temporary fluid bearing and can be advantageously used in certain applications. Those skilled in the art will also recognise that a permanent magnets can be replace one of the porous regions to good effect.
There can be a need to adjust the location of objects even when placed to nanometer accuracy. The advantage of this invention is that the length of each stud may be readily adjusted in a controlled manner, and by doing so controllably moves an object in six degrees of freedom. Several linear actuators with sub-nanometer resolution are known to those skilled in the art, are suitable for the task. They are described in Foundations of Ultraprecision Mechanism Design by S. T. Smith & D. G. Chetwynd p 202, CRC Press, 1992. As each coupling element acts in a single axis only, a linear actuator can be easily integrated with each element to give adjustability in six degrees of freedom.
Modem piezoelectric transducers are well suited to this task. A piezoelectric transducer is mounted in series with each stud, with its axis of action collinear with the eats of the stud, and a voltage applied to it. The desired adjustment can be made with resolutions of less then one nanometer. Poisson ratio actuators may be used and integrated into the coupling element. For instance, referring to
Referring to
Referring to
It has thus been shown that the present invention provides an improved kinematic coupling which increases the repeatability over the prior known couplings. White particular embodiments of the invention have been illustrated, they are not intended to be limiting. Modifications and changes may become apparent to those skilled in the art, and it is intended that the invention be limited only by the scope of the appended claims.