Kinematic mount

Abstract

A kinematic mount with more than three mating elements. To function properly, the sum total of DOFs constrained by the mating elements is six. Mounts that have four mating elementsfor example a Pivot and three Spacers, or two Sliders and two Spacers, are beneficial. Conditions are shown under which the four-legged mounts are kinematic, stable and can be assembled from one direction, kinematic mount connecting two subassemblies along a mating direction, comprised of four mating elements, each mating element having two components, each attached to a different subassembly, two of said mating elements being Slider mating elements each having a Slide Axis and constraining two degrees of motion, and the other two of said mating elements each being a Spacer mating element each having a Spacer Axis and constraining a single degree of motion, said mating elements configured to jointly constrain six independent degrees of motion.

Claims

1. A kinematic mount for connecting two subassemblies along a mating direction and constraining exactly all of possible degrees of freedom (DOFs) between the two subassemblies, the kinematic mount comprised of at least three mating elements, characterized in that: at least one of said three mating elements comprises: a pair of adjacent Spheroid bodies configured to be fixed to one of the subassemblies, a common Spheroid body configured to be fixed to the other subassembly, and a pair of Collar bodies each having two Conoid surfaces, configured such that said common Spheroid body contacts one Conoid surface of each of the pair of Collar bodies, and each remaining Conoid surface, one belonging to each Collar body, contacts one of said pair of adjacent Spheroid bodies; wherein at least one of the pair of adjacent Spheroid bodies and the common Spheroid body comprises a truncated sphere.

2. The kinematic mount of claim 1, wherein each of the pair of Collar bodies allows the common Spheroid to move in two DOFs around one of the pair of adjacent Spheroid bodies, thereby describing a spherical surface around it and a combined motion of both of the pair of Collar bodies allow the common Spheroid to move only along a one-dimensional arc.

3. The kinematic mount of claim 1, wherein each Conoid surface is tangent to a corresponding Spheroid along a line of contact between the Conoid surface and the corresponding Spheroid.

4. The kinematic mount of claim 1, further comprising at least one retainer configured to hold one of the pair of Collar bodies, allowing the Collar body to slide on one of the pair of adjacent Spheroid bodies.

5. The kinematic mount of claim 1, wherein each of the pair of Collar bodies is made from a material having a lower yield point from the material of the pair of adjacent Spheroid bodies and the common Spheroid body.

6. The kinematic mount of claim 1, wherein each of the pair of Collar bodies has a lower elastic modulus than that of the pair of adjacent Spheroid bodies and the common Spheroid body.

7. The kinematic mount of claim 1, further comprising a fastening plate, and wherein the pair of adjacent Spheroid is fastened to the fastening plate.

8. The kinematic mount of claim 7, wherein the pair of adjacent Spheroid comprises a pair of spheres that are press-fitted into the fastening plate.

9. The kinematic mount of claim 1, further configured to allow the two Conoid surfaces belonging to two different Collar bodies to detach along the mating direction from the Spheroid bodies that they contact.

10. The kinematic mount of claim 1, wherein at least one of the pair of Collar bodies comprises an adjustable collar whose effective length is adjustable.

11. The kinematic mount of claim 10, wherein the adjustable collar comprises an electrically controlled actuator.

12. The kinematic mount of claim 1, wherein each of the Conoid surfaces is generated by revolving a concave curve.

13. The kinematic mount of claim 1, wherein each of the pair of Collar bodies constrains to a fixed value a distance between centers of the common Spheroid and a corresponding one of the pair of Spheroids.

14. A kinematic mount for connecting two subassemblies along a mating direction and constraining exactly all of possible degrees of freedom (DOFs) between the two subassemblies, the kinematic mount comprised of at least three mating elements, characterized in that: at least one of said three mating elements comprises a first Spheroid body configured to be fixed to one of the subassemblies, a second spheroid body configured to be fixed to the other subassembly, and a Collar body having two Conoid surfaces, configured such that said first Spheroid body contacts one Conoid surface of said Collar body, said second Spheroid body contacts opposite one Conoid surface of said Collar body, and wherein each Conoid surface is tangent to a corresponding Spheroid along a line of contact between the Conoid surface and the corresponding Spheroid; wherein at least one of the first Spheriod body and the second Spheriod body comprises a truncated sphere.

15. The kinematic mount of claim 14, further comprising a retainer configured to hold the Collar body to one of the first and second spheroid bodies.

16. The kinematic mount of claim 15, wherein one of the two Conoid surfaces is configured to detach from one of the first and second spheroid bodies along the mating direction.

17. The kinematic mount of claim 14, further comprising a fastening plate, and wherein one of the first and second spheroid bodies is fastened to the fastening plate.

18. The kinematic mount of claim 14, wherein the Collar body comprises an adjustable collar whose effective length is adjustable.

19. The kinematic mount of claim 14, wherein each of the Conoid surfaces is generated by revolving a concave curve.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The accompanying drawings, which are incorporated in and constitute a part of this specification, exemplify the embodiments of the present invention and, together with the description, serve to explain and illustrate principles of the invention. The drawings are intended to illustrate major features of the exemplary embodiments in a diagrammatic manner. The drawings are not intended to depict every feature of actual embodiments nor relative dimensions of the depicted elements, and are not drawn to scale.

(2) FIGS. 1A and 1B: Cone-V-Groove mount (Prior art)

(3) FIGS. 2A and 2B: 3-groove mount (Prior art)

(4) FIG. 3: CS pair (Prior art)

(5) FIG. 4: Spherolinder mating element (Prior art)

(6) FIG. 5: Bead mating element (Prior art)

(7) FIGS. 6A-6E: Spacer geometries (Prior art)

(8) FIGS. 7A-7D: Spacer implementations (Prior art)

(9) FIGS. 8A-8C: 3-1-1-1 mount using CS and Pill mating elements

(10) FIG. 9A-9B: 3-1-1-1 mount using CS and BiSphere mating elements

(11) FIGS. 1, 10A and 10B: 3-1-1-1 mount using CS and Collar mating elements

(12) FIGS. 11A-11C: 2-2-1-1 mount using Bead and Collar mating elements

(13) FIGS. 12A-12C: 2-1-2-1 mount using Bead and Collar mating elements

(14) FIGS. 13A-13C: 2-2-1-1 mount using Sphere-in-groove and Pill mating elements

(15) FIGS. 14A-14C: 2-2-1-1 mount using Sphere-in-groove and Pill mating elements (parallel)

(16) FIGS. 15A-15C: 2-2-1-1 mount using Sphere-in-groove and Pill mating elements (diagonal)

(17) FIG. 16: Collar mating element

(18) FIG. 17: BiCollar mating element

(19) FIG. 18: Cross-section of BiCollar mating element

(20) FIGS. 19 and 19A: BiCollar mating element with retainer

(21) FIGS. 20 and 20A: Complete sphere and clip ring

(22) FIG. 21: BiCollar mount using complete spheres

(23) FIG. 22: BiCollar mount using complete spheres, with retainer

(24) FIGS. 23A-23B: Complete 3-BiCollar mount

(25) FIGS. 24A and 24B: Mechanically adjustable collar

(26) FIG. 25: Electrically adjustable collar

DETAILED DESCRIPTION

(27) 4-Point

(28) Aspects of this invention include kinematic mounts comprising four mating elements (four-legged). In order to function properly, the sum total of DOFs constrained by the mating elements must be six. Divided among four mating elements, there are only two options to do this: a Pivot and three Spacers, or two Sliders and two Spacers. However, this is only a necessary condition, not a sufficient one, and any attempt to build a four-legged kinematic mount based only on these necessary conditions would failwhich is why current art only has three-legged kinematic mounts.

(29) Conditions are shown under which the four-legged mounts are kinematic, stable and can be assembled from one direction.

(30) As explained above, in order to have a kinematic mount that uses four mating elements, it is required that the in-plane (X-Y-Theta) and out-of-plane (Z-tip-tilt) DOFs are considered together and not separately, or else the problem becomes similar to the four-legged restaurant table.

(31) Before describing embodiments of the invention, we first enumerate the conditions that are levied on the mount.

(32) The underlying condition for a kinematic mount is that the mathematical equations describing the mechanical constraints resulting from the mating elements must form a set of six independent equations. Usually, when taking a linear approximation of the equations, this results in six directional vectors representing the constraints, which must then form a linear mutually-independent set. (independent is used in the linear (vector) algebra sense)

(33) Additionally, it must be guaranteed that the mating elements are able to mate properly when the mount is assembled along the Mating Axis, which means there's no mechanical interference during the assembly process.

(34) Finally the mount needs to be structurally efficient in countering both Axial loads and Side loads.

(35) When considering a CS pair (as in the case of the Pivot, FIG. 3), it is clear that the load carrying capacity of the mount is related to the half-angle of the cone. A very flat cone (approximating a flat plate) only contacts the sphere along a very small circle at the top. A very narrow cone (approximating a cylinder) contacts the sphere along a circle near its equator, at an angle that can hardly transmit any force in the direction of the axis of the cone. The optimal half-angle for the cone from this perspective is 45 (a right-angle cone), but any half-angle between 30 and 60 is still close enough to be able to hold most of the load that the right angle cone can.

(36) When considering a Spacer (e.g. the Collar of FIG. 6D), it is also clear that if it has a non-zero Tilt Angle, its Axial load capacity is further diminished (relative to that of the CS pair) by a factor of the Cosine of the Tilt Angle, and a Side load of magnitude the Sine of the Tilt Angle is generated by it. Tilt Angles of over 45 are impractical, since they generate Side forces that are too large. Tilt Angles of under 15 are also impractical since they bring the Spacers too close to parallel, which interferes with the functionality of the mount, as explained below. Tilt Angles in the range of 15 to 45 are practical, with the best results between 20 and 30.

(37) Also, the requirement that the Collar can be assembled in the Mating direction means that the Tilt Angle must be smaller than the half-angle of the cone of the Collar. Similar logic applies to the Pill, Lens, and Hat geometries.

(38) Embodiments of this invention can use elements described in prior art to implement the Pivot, Sliders, and the Spacers, or potentially use novel mechanical mating elements that perform the same functions. Since the requirements on the mating elements largely pertain to their locations and to the direction of their axes, the mating element embodiments are largely interchangeable. That is, the Pivot can be equivalently embodied as a CS Pair or any other Pivot type, each of the Sliders can be equivalently embodied as a Spherolinder, Bead, or other Slider type, and each of the Spacers can be equivalently embodied as a BiSphere, Collar, Pill, or any of the Spacer types.

(39) 4-Point3-1-1-1

(40) FIG. 8-FIG. 10 depict embodiments of the invention in which the kinematic mounts use one Pivot and three Spacer mating elements, together constraining exactly six DOFs. In order to function correctly, there are numerous requirements imposed on the location and orientation of the mating elements. The Mating Axis is perpendicular to the flat subassemblies as depicted in the drawings.

(41) The description below applies to all three figures. A detailed per-figure description follows.

(42) The Pivot [82, 91, 102] serves as a reference and is located in an arbitrary position. Since the Pivot is isotropic, there are no constraints on its orientation, other than that it be able to assemble along the Mating Axis. In the case of a CS Pair, this is trivial since the Conoid can be placed so its axis is parallel the Mating Axis.

(43) Once engaged, the pivot eliminates three translational DOFs, allowing the top subassembly only to rotate in the mating plane, tip, and tilt.

(44) These three remaining unconstrained rotational DOFs are now constrained, simultaneously, by properly positioning the Spacers [83, 92, 103] in relation to the Pivot. Each Spacer can apply a force only along its Spacer Axis, and so can only apply a torque relative to the Pivot in the direction which is the vector cross product of its own Spacer Axis and the line connecting its position with the pivot.

(45) It is convenient to describe the direction of the Spacers in terms of the Tilt Angle and Azimuth Angle (measured around the Mating Axis).

(46) To function kinematically, the three torque vectors must form a linearly independent set of vectors. For example, if all three Spacer Axes are parallel the Mating Axis, then all three torques directions will be co-planar and thus linearly dependent, and the mount will fail. Similarly, if two torque axes are parallel, they are linearly dependent, and again the mount will fail. These conditions must be avoided when positioning and orienting the Spacers.

(47) Therefore a Tilt Angle of at least 15 is desired, and a set of Azimuth angles that ensure that the Spacer Axes are at least 20 from each other (and preferably 30), so that the Spacer Axes are sufficiently far from being parallel to each other.

(48) Further, as explained above, the Tilt Angle should be no larger than 45, in order to effectively support Axial loads, and the cone half-angle must be larger than the Tilt Angle in order to allow unobstructed assembly along the Mating Direction.

(49) Therefore a Tilt angle in the range of 3015 is an acceptable design range, with cone half-angle in the range of 4515, and still having the cone half-angle larger than the Tilt Angle.

(50) Note that these conditions preclude the use of Spacers that are aligned in the vertical (or near vertical) direction, as is intuitive to do. The Spacers must be tilted quite significantly (though not too much), and angled relative to each other.

(51) FIG. 8 shows an embodiment of the invention in which the Pivot is implemented as a CS pair (FIG. 3), and the three Spacers as Pill mating elements. (FIG. 6B and FIG. 7A). The mount connects subassembly A [80] and subassembly B [81]. The Pivot is embodied as a single CS interface [82a, 82b] (the protrusion is solidly attached to subassembly A [80]). Each Spacer is embodied as a Pill type Spacer, where the Conoids [84] are machined into subassemblies A and B, and the mediating Pill bodies [83a, 83b, 83c] are simply placed between them. The Spacer Axes are shown as dash-dot lines, and lines between them and the Pivot are shown as dashed lines.

(52) Further, to keep the Spacers in compression, they are oriented so that the torques they apply act in opposing directions. That is, in top view (FIG. 8C), the diagonal Spacer [83b], exerting a torque clockwise, counters the two orthogonal Spacers [83a, 83c] that exert a torque counterclockwise.

(53) FIG. 9 shows an embodiment of the kinematic mount in which the Spacers are implemented using the BiSphere Spacer mating element. The Spacers therefore utilize point contacts, and subsequently this design has a lower load capacity.

(54) As before, it is not the BiSphere Spacer implementation that is the core of the invention, but the configuration of the Pivot mating element [91] and the three Spacers [92], with their Force Axes oriented so as to have a significant force component in the Axial load direction, and applying mutually-independent torques so as to make the mount kinematic. The Spacer Axes are shown as dash-dot lines, and lines between them and the Pivot are shown as dashed lines.

(55) FIG. 10 shows an embodiment of the kinematic mount using Collar Spacer mating elements (FIG. 6D, FIG. 7C). Just like the Pill, the Collar mimics the BiSphere mating element, keeping the distance between the centers of the balls constant, but replaces the point contact with annular line contacts, as facilitated by the annular double-cone mediating body of the element. The Collar element is more compact, however. The mount connects subassembly A [100] with subassembly B [101], using one CS pair Pivot mating element [102] and three Collar-type Spacer mating elements [103]

(56) The embodiments of the individual Pivot and Spacers, in and of themselves, are not at the core of this invention. It is the specific combination of a Pivot mating elements and three Spacer mating elements, and their locations and orientations that underlie this embodiment of the invention. The orientation and placement of the mating elements is independent of their embodiment, and the considerations for selecting them remain the same across embodiments.

(57) 4-Point2-2-1-1

(58) FIG. 11-FIG. 15 depict embodiments of this invention in which the kinematic mounts use two Sliders and two Spacer mating elements, together constraining exactly six DOFs. In order to function correctly, there are numerous requirements imposed on the location and orientation of the mating elements. The Mating Axis is perpendicular to the flat subassemblies as depicted in the drawings.

(59) The description below applies to all five figures. A detailed per-figure description follows.

(60) The geometry of the mount is best explained by first considering the two Slider mating elements [110, 120, 131, 141, 151]. Once engaged, since each Slider constrains two DOFs, in all but degenerate cases, only two DOFs between the two subassemblies remain unconstrainedan out-of-plane rotation, and an in-plane motion.

(61) The out-of-plane rotation occurs around the line connecting the two Sliders [112, 122, 133, 143, 153].

(62) The in-plane motion is determined by the relative orientation of the Slide Axes of the Sliders, and can be either a rotation or a translation.

(63) In the general case, the Slide Axes are not parallel, and the in-plane motion is a rotation around a point defined by the intersection of two mid normal lines [115, 135], each emerging from the center of each of the Sliders and perpendicular to the projection of the Slider's Slide Axis on that plane. The center of rotation is marked as [111, 121, 134].

(64) If the Slide Axes are collinear, however, then effectively the center of rotation for in-plane motion is at infinity, and the in-plane motion becomes translation, along the shared line [143, 153]

(65) The two remaining unconstrained DOFs are then constrained, simultaneously, using two properly located and oriented Spacer mating elements [114, 124, 132, 142, 152].

(66) As before, it is convenient to describe the direction of the Spacers in terms of the Tilt Angle and the Azimuth Angle.

(67) The two Spacers solve the two last DOFs simultaneouslyeach of the Spacer Axes has force components that constrain a linear combination both of the DOFs, and so (as was the case with the three Spacers in previous embodiments) their torque vectors must be linearly independent.

(68) To constrain the out-of-plane rotation DOF effectively, both Spacer elements must have Tilt Angle less than 45, to ensure that they have a large enough force component in the Mating Axis direction to support the load without generating too large of a Side load. As explained above, they also need to have a Tilt Angle of more than 15, and have an angle between them of over 20 (and preferably over 30) in order for them not to be too close to parallel to each other. As before, best results are achieved with Tilt Angles between 20 and 30.

(69) To constrain the in-plane motion effectively, both Spacer elements must apply a force perpendicular to the arm between them and the center of rotation (in the first case) or parallel the direction of translation (in the second care), and must act in opposite directions. Thus their Tilt Angles must be large enough to have a significant in-plane force component, which effectively means at least 15.

(70) Finally, to ensure they assemble along the Mating direction, the Tilt Angles should be smaller than the half-angle of the Conoids of any CS pairs used in the Spacers.

(71) FIG. 11 shows an embodiment of the invention in which the elements are roughly planar, and the two Sliders [110] are placed on adjacent corners of the quadrangle. FIG. 12 shows an embodiment of the invention in which the elements are roughly planar, and the two Sliders [120] are placed on opposite corners of the quadrangle. In both these embodiment, the Sliders are implemented as Beads, and the Spacers [114, 124] are implemented as Collars.

(72) The Sliders [110, 120] are located so that their Slide Axes [113, 123] lie in said Mating Plane, and are not collinear (A minimum angle of 30 is used). The two remaining unconstrained DOFs are shown: the out-of-plane rotation axes [112, 122] and in-plane rotation axes [111, 121].

(73) In the embodiment shown in FIG. 11 the center of in-plane rotation [111] is located approximately at the center of the mount, whereas in the embodiment shown in FIG. 12 the center of in-plane rotation [121] is collocated with one of the Sliders. In FIG. 12, the line between the Sliders [123] is collinear with the Slide Axis of one Slider.

(74) The two Spacers [114, 124] are positioned based on the orientation of the sliders. The Tilt Angles of the Spacers are best illustrated in FIG. 11A, FIG. 11B, FIG. 12A, and FIG. 12B. As can be seen, the Tilt Angles are about 3015, as was explained above, allowing the Conoids to assemble and extract from the Spheroids with no interference, and giving the Spacers enough of force component in the Mating direction to support Axial loads, while still being able to support Side loads.

(75) The azimuth angles are best illustrated in FIG. 11C and FIG. 12C. They are chosen to maximize the torque provided by the Spacers around the axis of in-plane rotation. Therefore in FIG. 11 the Spacers are oriented at 45 to the edges of the plate, so that the projection of their Axes on the Mating plane are each perpendicular to a line between them and the center of rotation at the center of the plate, but in FIG. 12 the Spacers are oriented parallel the edges, since the center of rotation is at a corner of the plate. As before, deviating from this angle does not immediately break the functionality of the mount. However, if a Spacer were to be rotated so that the projection of its Spacer Axes on the Mating plane intersects (or nearly intersects) the axis of rotation, it would be applying zero (or close to zero) torque, and would not be generating an independent equation.

(76) Further, to keep the Spacers in compression, they are oriented so that the torques they apply counter-act each other.

(77) The torques applied by the Spacers are shown as double-lined arrows.

(78) FIG. 13 shows another embodiment of the mount, similar in geometry to the embodiment shown in FIG. 11, but using ball-in-V-groove Sliders [131], and Pill Spacers [132].

(79) FIG. 14 shows another embodiment of the mount, using ball-in-V-groove Sliders [141], and Pill Spacers [142]. In this embodiment, the Slide Axes of the Sliders are collinear [143], and the Sliders located on adjacent corners. The Spacer Axes are therefore parallel to this common Axis, and counter act each other. This is best illustrated in the top view [14C]. The torques applied by the Pill Spacers are shown as arrows.

(80) FIG. 15 shows another embodiment of the mount, using ball-in-V-groove Sliders [151], and Pill Spacers [152]. In this embodiment, the Slide Axes of the Sliders are collinear [83], and the Sliders are located on opposing corners. The Spacer Axes are parallel to this common axis, and counter acting. This is best illustrated in the top view [15C]. The torques applied by the Pill Spacers are shown as arrows.

(81) As stated above, the embodiments of the individual Spacers and Sliders, in and of themselves, are not at the core of this invention. It is the specific combination of two Sliders mating elements and two Spacer mating elements, and their placements and orientations that underlie the invention. The orientation and placement of the mating elements is independent of their embodiment, and the considerations for selecting them remain the same across embodiments.

(82) BiColar

(83) Aspects of this invention include a BiCollar Slider mating element that constrains two DOFs between mated subassemblies. A BiCollar mating element consists of two Collar mating elements (FIG. 6D, FIG. 7C) sharing one of their spherical bodies. The shared body, whose center's distances from the centers of the other two spherical bodies is thus constrained to move along an arc. Since the Collar (which serves as the building block for the BiCollar mating element) consists of simple bodies of revolution, it is easy to fabricate and provides a high load capacity.

(84) The BiCollar Slider is a drop-in replacement to the other Slider mating elements mentioned abovethe BiSphere, the Spherolinder, and the Bead. Like the latter two, the BiCollar has a much higher load capacity than the BiSphere, but because it uses CS interfaces exclusively, it has lower friction than them, and is cheaper to fabricate.

(85) A detailed look at an embodiment of a Collar element is shown in FIG. 16. The two Spheroids [161], [162] are fabricated as short cylinders with spherical caps, the Spherical caps also having flat faces in the direction of the Collar [163] in order to allow the Spheroids to be placed closer together. The top Spheroid [161] has a retainer disc [164] attached to it, and this ring keeps the Collar [163] captive to the upper Spheroid (so the ring does not fall off), but still able to move in all directions, since the disc is fitted loosely around the bolt [165] that's holding it in place. An air path leads from an inlet [166] through the body of the Spheroid to the retaining disc, to allow a burst of compressed air to ensure the mating element is clean of particulate contamination just before mating.

(86) Note that the Spheroids do not rotate relative to the mating subassembliesit is the sliding of the Conoid around the static Spheroid surface that creates the motion. However, from the point of view of the CS Pair, the motion is equivalent to a Spheroid rotating inside a Conoid.

(87) An embodiment of a BiCollar mating element is depicted in FIG. 17, achieves functionality practically equivalent to existing Slider mating elements by using the combined rotations of two Collar mating elements. Such motion is much preferred over linear sliding motion since the Conoid is tangent to the Spheroid along the line of contact between itself and the Spheroid, so that if the leading point experiences friction, at the micro level, the cone climbs over it by virtue of its shape.

(88) The base part of the BiCollar mating element, equivalent to a traditional v groove, comprises a fastening plate [170], two truncated spheres [171], and two Collars [172]. The Collar on the right is shown in cross-section. The truncated spheres are press-fitted into the fastening plate, so cannot move in its plane. They transfer vertical load through their flat surface directly to the subassembly attached to the fastening plate. The truncated spheres cannot rotate because their flat faces are pressed against the parent subassembly [176].

(89) The top part of the mating element comprises a fastening plate [173] and a truncated sphere [174] acting as the common Spheroid. Here too, the flat face of the truncated sphere is pressed against the parent subassembly [175].

(90) Both the fastening plates are bolted to the parent subassemblies that are to be mated kinematically [175, 176]. These subassemblies are represented in this depiction by flat plates, though this is not essential. In the full kinematic mounts, multiple mating elements (typically three or four) are connected between the two subassemblies to create the mount.

(91) The Collars present one conic face towards each sphere such that the conic faces are tangent to their respective spheres. This constrains the distance between the centers of the two Spheroids touching the Collar to be a fixed value. In effect, the mating element would have functioned the same if the Collars were removed and the Spheroids were allowed to contact each other directly, except that the load carrying capacity would have been reduced due to the point contact.

(92) The Spheroids and Collars are typically made from high-strength stainless steel, and it is advantageous to have the Collars made from a material with a lower yield point, so that if the yield stress is exceeded, the plastic deformation occurs at the collar and is spherical in shape. Similarly, it is advantageous if the Collar has a lower elastic modulus, since then any elastic deformations are primarily confined to the collar and are spherical in shape. Spherical deformations present less of a hindrance to rotational motion.

(93) In other embodiments, the elements can be made from other metals including aluminum, copper or bronze as dictated by design requirements, or from non-metals ranging from plastics to ceramics.

(94) In some embodiment, anti-friction coatings, lubricants, or other treatments are applied to the contact surfaces of the Conoids or the Spheroids in order to reduce friction.

(95) The fastening plates function as a method to attach the Spheroids to the subassemblies in a robust manner. In different embodiments, the truncated spheres can be fastened directly to their respective subassemblies as is done in the Collar mating element shown in FIG. 16, welded, glued, or otherwise connected.

(96) The simplest way to combine to Collar mating elements into a BiCollar mating elements is by using two dedicated Spheroids in one component of the mating element and one common Spheroid on the other component, the latter Spheroid being shared by both Collar mating elements. However, in some embodiments it is also possible to simply place two Collar mating elements in close proximity to each other (still having the Collars in the same directions), thus using a total of four Spheroids.

(97) In this embodiment, the Spheroids are made of material that is more rigid than the Conoid, so elastic deformations occur primarily in the Conoid, and the contact line continues to slide over a spherical object. Additionally, the Spheroids are made of a material that is stronger than the Conoid, so even in the case of plastic deformation, they occur on the Conoid, and just re-shape it into a Sphere, which can continue to slide over the Spheroid. These properties reduce the resistance of the mating element to motion under load.

(98) An analogy to a sphere in a v-groove is very instructive to understand the operation of the BiCollar mating element. The sphere touched the v-groove in two points, one on each face. Each point can move on its respective face in two dimensions, but the combined constrain allows the sphere to move within the v-groove only in one dimension. Similarly, each Collar allows the common Spheroid to move in two DOFs around its dedicated Spheroid, describing a spherical surface around it. The combined motion of both Collars allow the common Spheroid to move only along a one-dimensional arc, as depicted in FIG. 18 and explained further below.

(99) FIG. 18 shows the same embodiment in cross-section. The dashed arc [180] shows the path that the center of the top Spheroid [181] can take, as long as it is in contact with both Collars [182], which are themselves in contact with their respective bottom Spheroids [183] (Only one of each is visible in the cross-section). The path is an arc perpendicular to and centered around the line between the centers [184] of the bottom Spheroids, the top of which is horizontal, and so for small motions, approximates the straight line motion of a sphere in a v-block.

(100) Even for larger motions, however, this mating element functions well in a kinematic mount, since there is no requirement that the Slider move along a straight line. Motion along a well defined arc is equally one-dimensional.

(101) The Slider Axis for the BiCollar element is defined as the projection of the arc of motion of the top Spheroid on the mating plane.

(102) The embodiment shown in FIG. 17 can only withstand compression loads, as if the bottom subassembly is on the floor, and the load is simply a gravity load. If on the other hand the assembly was on a tip-tilt table, or the upper subassembly was pulled upwards, the mating element would simply separate. This is very similar to the situation in a standard sphere-in-v-groove mating element, which also can only support compressive loads. The standard mitigation is to create a preload between the subassemblies, and the best way to do this is using a tensile retaining fastener that acts through the center of the common Spheroid and pulls the two halves of the mating element towards each other. Ideally, such a retainer does not change its length if the four unconstrained DOFs (one translational DOF and three rotational) are exercised.

(103) FIG. 19 shows an embodiment of the invention depicting a number of additional elements.

(104) A retainer bolt [190], in conjunction with a captive non-rotating nut [191], are used to fasten the subassembly attached to the top component [199] of the mating element to the bottom component. As explained, such retainers are necessary if the mate is to be used in an assembly that might be expected to operate upside-down, or under dynamic conditions. The nut [191] has a curved top surface, whose center lies on the line between the centers of the bottom Spheroids [197], so that if the top component were to follow its prescribed arc of motion, the retainer bolt would rotate around the same center without having to change length. An O-ring and a washer [194] are used in this embodiment to give the head of the bolt the ability to tip and tilt, while maintain a certain force preload. In other embodiments, other flexible elements such as springs or spring washer can perform the same function.

(105) Additionally, a small retainer pin [192] in conjunction with a retainer disc [193] are used to loosely locate the Collars near their nominal position so that they self-align when the two components of the mating element are mated. The hole at the center of the retainer disc is larger than the diameter of the neck of the pin, so disc is able to move a small amount in any direction perpendicular to the axis of the pin.

(106) In another embodiment, the retainer disc is attached to the pin, but is elastic, made from a material such as silicon, providing the same functionality. The pin is friction fit into a hole drilled in the Spheroid, in the direction of the nominal position of the Collar.

(107) In another embodiment, the Collar-Spheroid pair is encapsulated by an elastomeric shell that retains the Collar near its nominal position.

(108) The two base plates [192] that belong to the two subassemblies that are being mated kinematically are shown, though they are not part of the invention and only have to interface correctly with the mating bolt holes [193].

(109) FIG. 20 shows an alternative embodiment of the top component of the mating element. Rather than using a truncated sphere that transfers the vertical forces through its flat surface, the Spheroid used here is a complete sphere [200] into which two circumferential notches [201] were ground, on either side of an equatorial belt [202]. This Belted Sphere is then sandwiches between a stepped edge [204] of the mounting bracket [203], and a press-fitted ring [205] that is pushed in and welded in place. In this embodiment, lateral loads on the sphere are transferred through the walls of the hole in the mounting bracket.

(110) FIG. 21 depicts an exploded view of a similar embodiment of the invention. Instead of using a Belted Sphere as the Spheroid, in this embodiment the Spheroid is implemented as a Ringed Spherea full sphere [211] into which a perimeter slot has been cut, and mated with a thin retainer ring [212] which can be press-fitted into the slot, soldered, or glued. The ring of the Ringed Sphere is in turn trapped between a mounting plate [213] and the load bearing surface of one of the mating subassemblies [214]. The mating subassembly has a hole [215] into which the Ringed Sphere is press-fitted when the mounting plate [213] is tightened into place.

(111) In this embodiment, a similar mechanism is manifested at the bottom component, where each of the two Spheroids [216] is implemented as a Ringed Sphere, and both are attached to the mating subassembly using a shared mounting plate [217], and located using its own press fitted hole.

(112) The Conoid contact surfaces [218] of the Collars in this embodiment are slightly concave to increase their load carrying capacity in comparison to that of straight conic Collars. This concaveness can be fabricated, for example, when machining the Collar, or it can be formed into a straight-conical Collar by pushing a hard spherical tool into it.

(113) As is the case in previous embodiments, the Spheroids do not rotate relative to the mated Subassemblies.

(114) FIG. 22 depicts another embodiment of the invention, building on the embodiment shown in FIG. 21. In this embodiment, a retainer plate [220], retainer bolts [221] and retainer nuts [222] are added to the assembly to secure the two halves together against any force that tries to separate the mated subassembliesa situation that can occur, for example, if the assembly is tilted, flipped, jolted, or vibrated. The retainer nuts [222] are cylindrical, allowing the retaining mechanism to follow the motion of the Collars on the Spheroids. The axes of the retainer nuts are at the same height as the line between the two bottom Spheroids. The retainer nuts are kept captive by channels [223] in the bottom mounting plate [224]. Two additional cylindrical adapters [225] allows the top of the retainer screws [221] to rotate with the motion of the Collars without having to have a flexible element under them. The retainer plate [220] pushes against the top Spheroid [227] using a conical feature [226] which allows the retainer plate to tip, tilt, and swivel around the top Spheroid [227] in response to motions of the top subassembly. The retainer mechanism therefore perform a similar function to that of the retainer bolt [190] in FIG. 19.

(115) BiCollar mating elements can be used wherever Slider elements are used in the context of a kinematic mount, such as in the two-Slider two-Spacer mounts described above.

(116) FIG. 23A shows a schematic representation of a three-Slider geometry using the BiCollar mating elements [230] arranged around a common center [231] with their Slide Axes [232] offset from the common centroid by a small amount.

(117) FIG. 23B depicts an embodiment of this geometry. The embodiment is shown before mating occurs, with a gap still existing between the two subassemblies being mated along the mating axis.

(118) This mount is functionally equivalent to a 3-groove mount, but has a much higher load carrying capacity, and exhibits less friction due to the properties of the CS interface. As with a 3-groove mount, there's no requirement for the axes of the mating elements to intersect exactly at a common point.

(119) FIGS. 24A and 24B depict an embodiment of a Collar whose effective length (the distance between the centers of the Spheroids touching it) is adjustable (an Adjustable Collar). The length adjustment is achieved by turning the two threaded bodies [240,241] relative to each other, causing them to move relative to each other along their axes of rotation. As they do so, they control the opening angle of flexible Conoid bodies [242,243], which are made flexible by cutting slots into them. The two flexible Conoid bodies are press fitted onto an inner tube [246] to enable assembly around the pair of threaded bodies. The contact line between the threaded bodies and the flexible Conoids is adjacent the contact line between the Conoids and their Spheroids, indicated by the dashed line [244,245]. (The Spheroids are not shown). As the opening angle of the Conoids changes, this line will invariably move, and so the amount of adjustment is limited, since once it moves a certain distance away, the flexibility of the Conoid will mean it will no longer be able to carry the load. However, in many optical system, adjustments in the <100 um range are all that is required. The Conoids do not rotate during the adjustment process.

(120) When considering a BiCollar mating element that uses two adjustable collars, it is clear that a lengthening (or shortening) of both Collars by the same amount results in a vertical motion with no sideways motion component, and vice-versa (for small motions) a lengthening of one Collar and a shortening of the other by the same amount results in a sideways motion with no vertical motion.

(121) An adjustable BiCollar therefore has the ability to neatly either lift/lower the top Spheroid, or move it from side to side.

(122) Therefore, when considering a 3-Slider kinematic mount that uses three adjustable BiCollars, it is relatively easy to adjust the out-of-plane motions of Tip, Tilt and Z-motion by adjusting each of the mating elements only in the vertical direction. Rotation of the mount in-plane is achieved by moving all three mating elements sideways (either clockwise or counter-clockwise), and motion in the X-Y direction (in-plane) is achieved by calculating the vector sum of three sideways motions of the mating elements.

(123) In other embodiments, the threaded pair [240, 241] is controlled by an electrically controlled actuator such as a servo motor.

(124) FIG. 25 depicts another embodiment of an Adjustable Collar comprises two Conoid bodies [250] separated by a piezo electric stack [251], achieving highly controlled adjustment of the distance between the two Conoids, without any relative motion between the Conoids and the Spheroids, other than that results from the shift in position of the entire kinematic mount.

(125) In other embodiments, the piezo electric stack can be replaced by other forms of linear actuators such as piston or lead screws.

(126) The present invention has been described in relation to particular examples, which are intended in all respects to be illustrative rather than restrictive. Those skilled in the art will appreciate that many different combinations of hardware, software, and firmware will be suitable for practicing the present invention. Moreover, other implementations of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.