Abstract
Disclosed is the shape of a curvature of two or more pathways for a device having moving parts that cause movement of an object along those pathways, such that the device can locate or hold the object. In the embodiment, an apparatus is described that centers and optionally locks an object at a desired location. The applications for such a device are varied and can range from chucking a workpiece of varying diameters in a lathe, to centering a drone on a landing zone, to medical and scientific devices to capture and center objects to study, to moving atomic level objects using an electromagnetic field. The scope of this disclosure is the mathematics that defines the mirrored curvatures of each curved pathway and the positioning of the curvatures relative to each other, and the relative movement of the mirrored curvatures to cause the desired effect.
Claims
1. A positioner apparatus comprising: a first Pathway Spiral Segment (PW); a second Mirrored Pathway Spiral Segment (MPW) that Intersects with the said PW; a Locating-Pin that is positioned at the said Intersect and is used to Push/Pull with a Push/Pull-Force directed along the said PW, a Rotation-Bushing to allow Relative-Rotation between the said PW and said MPW to move the said Locating-Pin either inward or outward depending on the relative direction of the rotation, and wherein the said PW, said MPW, said Locating-Pin, and said Rotation-Bushing can work together to create a Push/Pull-Force along the PW that thereby obtains the Desired Effect.
2. A positioner apparatus as in claim 1 wherein said Locating-Pin assembly is used to position, hold, or clamp a Workpiece at, along, or to a surface or forcefield.
Description
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
[0016] FIG. 1, in one embodiment, shows a top transparent view of preferred Pathway (PW) and Mirrored Pathway (MW) shapes on two approximately adjacent and aligned plates.
[0017] FIG. 2, in one embodiment, shows each plate individually.
[0018] FIG. 3, in one embodiment, demonstrates how the MPW when rotated around its origin stays perpendicular to the preferred PW in the adjacent plate at their intersection.
[0019] FIG. 4 visually shows how the curvature of prior art (Longworth chuck) can cause binding by becoming less and less perpendicular at the intersection as one plate is rotated around the other and shows that arcs on a single plate would intersect each other if extended too far limiting the length of the slotted arc.
[0020] FIG. 5 compares the preferred Pathway shape of the invention to prior art (Longworth chuck).
[0021] FIG. 6, in one embodiment, provides a numerical table for scaling the preferred Pathway.
DETAILED DESCRIPTION OF THE INVENTION
[0022] The focus of this apparatus is on the inventive stepthe curvature of the Pathway. The focus is not on the: [0023] Locating-Pin (hard or soft pin, jaw, block, teeth, clamp, spacer, threaded element, motorized device, magnet, electromagnet, plasma, force-field, or other devices used to move, locate, and/or hold a Workpiece, [0024] Rotation-Bushing (pin, bearing, bushing, sleeve, threaded element, motor, axle, gear, spindle, interior or exterior wheels/pins, magnet, electromagnet, plasma, force-field or other devices used to align and/or rotate the rotating surface to the other surface that contain the PW or MPW), [0025] Optional Lock (lock, pin, threaded element, motor, magnet, electromagnet, plasma, force-field, or other devices used to hold the Workpiece), [0026] other features that allows an apparatus to perform in a specific application.
[0027] The design and incorporation of the Locating-Pin, Rotation-Busing, Optional Lock, and other features are up to a person versed in the art and desirous of a particular use. But it is hoped that those versed in this art will see the advantage of using a curvature that is not an arc and that delivers the Desired Effect.
[0028] FIG. 1, in one embodiment, shows a twenty-four Leaf 130 apparatus called in some fields a Chuck 100 (the embodiment shows circular flat Plates 111/121 but the actual device need neither be flat nor circular as devised by someone skilled in the art). The Chuck 100 needs one (three if a perfect circular work-piece without additional locating method) or more Leaves 130. There is a limit to the number of Leaves 130 based on the fact that as Leaves 130 are added, the PW 124 or MPW 114 can weaken the Plates 111/121 or interfere with each other. Each Leaf 130 is composed of a PW 124 and MPW 114 with the PW 124 being a guide and the other MPW 114 doing the Push/Pull: [0029] MPW 114 that are in the First Plate 111. [0030] PW 124 that are in Second Plate 121. [0031] Which together, if the plates are transparent, look like a Leaves 130.
[0032] FIG. 2, in one embodiment, shows twenty-four MPW 114 on Plate 111, twenty-four PW 124 on Plate 121, and an arrow 240 showing one possible Relative Rotation 240 around the Axis 101 of both Plates 111/121. This embodiment is not meant to imply that the Workpiece, not shown, be circular as a person experienced in the art knows how to make an interface to the Workpiece by using or creating tooling. It is customary to leave enough material around each PW 124 and MPW 114 to give adequate strength to the Plates 111/121 for holding the Workpiece when slots are employed as the means for guiding a Locating Pin. Both plates can have identical slots, but if so, one is flipped during assembly so that the PW 124 and MPW 114 point in the opposite direction (in that embodiment, flipping one plate creates mirror images of the slots).
[0033] FIG. 3, in one embodiment, shows how the Relative Rotational 240 of the First Plate 111 relative to the Second Plate 121 pushes a Locating-Pin 351 inward or shows how the Relative Rotational 245 of the First Plate 111 relative to the Second Plate 121 pushes a Locating-Pin 351 outward. In the embodiment where Plate 111 is placed directly on top of Plate 121 (with the Locating-Pins and Rotation-Bushing in place), and then Plate 111 is rotated in the direction of Relative Rotation 240 (or Plate 121 rotated in the direction of Relative Rotation 240), the Locating-Pin 351 (small circle) moves inward. Starting from when both halves of a Leaf 311 Intersect 350 at the outermost slot position (where overlap occurs) in drawing labeled RR-0, the Locating-Pin 351 is at its most outward or open position. In the embodiment labeled RR-10, rotating the First Plate 111 in the direction of the Relative Rotation 240, creates a relative movement of the First Plate 111 relative to the Second Plate 121 of 10 degrees, moves the Intersect 350 and Locating-Pin 351 from the outermost position to a 10-degree position. Then in the embodiment labeled RR-20, rotating farther another 10 degrees, moves a Locating-Pin 351 to the 20-degree position; repeating from embodiment labeled RR-30 to RR-45 to RR-90 to RR-180 to RR-270 until the Locating-Pin 351 at the slot Intersect 350 moves from the outermost position to an inner most position along the curvature of PW 124 being pushed by a nearly aligned forced caused by the nearly perpendicular Opposing MPW 114 at the Intersect 350 of the slots acting upon the Locating-Pin 351; the preferred embodiment showing a shape of the two opposing pathways PW 114 and MPW 124 being perpendicular over the entire travel of the Locating-Pin 351 to minimize force of movement, prevent binding, and finally provide even and greater holding forces. It should also be noted that upon each relative rotation that the shape of the Leaf 130 remained constant but its size kept getting smaller. Also shown are two sizes of pathways measured by degrees. The embodiment in drawing RR-0 shows two mirrored 363-degree spirals that creates a large leaf 311 and a small upside-down leaf 310 around the axis 101. The embodiment in drawing RR-B shows mirrored spirals that are composed of 100 degrees or part-spiral leaf around the axis 101.
[0034] FIG. 4 shows prior artthe Longworth Chuck 400 Plates 411 & 421 with Slot 424 and Mirrored Slot 414. Longworth Chuck slots are shaped from constant radius arcs, not spirals. The arcs are Limited-in-Length 460 because they can intersect other arcs if the slots were made too long (concentric spirals do not intersect). The slots for the Longworth chuck can only practically end at approximately .sup.rd the maximum radius of the slot in compression (e.g., a 14 maximum radius Longworth Chuck will have a 4.5 minimum before serious binding occurs or the plate is weakened). Also, the Slots 414/424 are only perpendicular to each other at one location. At the other locations, the arcs deviate more and more from perpendicular that results in less and less workpiece holding-force causing chatter. As shown in the blowup 450, if the arc are taken too far, the slots will cause binding. The result is less versatility, fewer applications, less holding force, lower RPMs and/or thinner cutter depths.
[0035] FIG. 5 compares prior art 414, a constant radius Longworth arc, to one embodiment of the preferred spiral 114, showing the inventive step, and the result of that inventive step. Force 511 is created by the relative counterrotation of the MPW 114 that acts on a Locating-Pin 515 that then acts as forces 515/516 on a Workpiece. Spiral-segment 114 shows the inventive shape of a preferred PW that: [0036] Can handle a greater range of workpieces. [0037] Because the mirrored pathways are perpendicular, [0038] Binding does not occur no matter how long the spiral-segment and [0039] Clamp-up forces remain constant helping to decrease workpiece chatter. [0040] Approaches but never arrives at the origin point (0, 0). [0041] Is infinitely long as it continues to repeatedly curve around the origin/axis point. [0042] Continually decreases the radius of the curvature as it curves inward. [0043] Is Self-similar in that: [0044] As the spiral is magnified it repeats itself and [0045] It Is equiangular. [0046] The shape can be defined exactly or approximated by many equations. [0047] Mirrored curves rotated around the origin into each other: [0048] Always Intersect at a 90-degree angle. [0049] Form leaf shapes that are exactly proportional in shape to all other formed leaf shapes no matter the size.
[0050] There are many ways to express or estimate the equation for the preferred Spiral-Segment 124 that when mirrored and rotated about the origin/axis that the two Spiral-Segments are perpendicular or are nearly perpendicular. One such equation that expresses the preferred Spiral-Segment 124 is as follows:
[00001]
[0051] Where: x.sub.1, y.sub.1 can start from the scalable values (0, 1), the outer x and y coordinates [0052] for angles in degrees B.sub.n=90 to 90b [0053] b is an angle in degrees (e.g., 180), [0054] w is a weight to approximate finite calculus where w=0.498546
[0055] Or in the mathematical form of a special-case logarithmic spiral:
x.sub.n=r.sub.ncos(.sub.n+)
y.sub.n=r.sub.nsin(x.sub.n+)
r.sub.n=ck.sup..sup.n/e.sup.ln(ln(k))
[0056] Where: is an angle in radians from to [0057] r.sub.n is the radius of the spiral at (x.sub.n, y.sub.n) [0058] n is an index to the points of the spiral for angles .sub.n [0059] c is a constant to scale the spiral size [0060] is the angle of rotation of the entire spiral-segment (can be used in computer simulations to rotate a pathway) [0061] k is a number >1 [0062] and in the special case where k=e (Euler's number 2.7183 . . . ), then r=ce.sup. [0063] and when is used to scale the spiral, r=e.sup. [0064] and mirrored images are created by reversing the sign of x or y.
[0065] FIG. 6, in one preferred embodiment, provides a table of scalable values to draw a Pathway shape. This table can be used to scale and approximate the Spiral-Segment shape when an equation, like presented above is not practical.
