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The present invention involves the production of linear πeasureirents from the interconversions of linear and rotary motions, and utilizes a thin, cross-sectionally curved drive member.
Many measuring devices exist, such as large calipers or bow micrometers, having "resolution" factors or that are "graduated" to read .001 inches or less when extended to the lengths described. No assurances, however, are iirplied that the dimensions will actually be as read. For example, two scales, having indicia produced by different companies, may be meshed and visiably witnessed that every indicant does not align. When such indicia are then aligned with others, and used to facilitate vernier measurements, there exists no common denominator to determine the accuracy of the measurements. Other devices incorporate geared or sliding members linked with dials indicating the measurements. Especially at extended distances, and with devices produced by different means, the finite increments of measurements will vary from those shewn and indicated by the dials. Again, there being no comα denominator with which to deteirnine correctness.
The above conditions have always plagued machinists, few of who will trust such finite measurements made with the devices described. Other means are employed to match-fit components, and many machinists will not accept such jobs. Because of these conditions, it is well knewn among design engineers, machining operations requiring finite measurements will entail additional expense. Therefore, wide latitude is afforded to avoid such problematic designs. Despite preferences to obtain accuracy, it has become custom to design around a problem.
Computer aided design and drafting are technologies with which the measurement digitizer of this invention may be used. With these sciences, the measurement problems indiciated have thus far been avoided using other techniques. A popular technique uses a surface beneath which a printed circuit, liaving vertical and horizontal

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wires spaced about .010 inches apart, are embedded. Through electrical induction with a pen-like instrument slid among the surface, analogous cross hair lines are displayed by a CRT. Other data entry mechanisms are the typewriter-like keyboard, light pen, cursor arm, track ball, joystick, thuπbwheel, laser scanner and more, all dependent upon CRT definition of the reference point entered.
Although many systems for interconversions of linear and rotary motions have been taught, and so used to measure linear distanced increments, to applicant's knowledge, no prior art exists employing a perforated rack, curved in cross section, and catenated with a sprocket wheel coupling in the manner described and claimed with this application. U.S. Patent Nos. 2,824,374 and 3,526,890 teaches a conversion method with a flat tape held straight, somewhat similar to a rack and pinion, and well known for backlash characteristics.
U.S. Patent Nos. 3,271,564 and 3,780,440 technically teach a flat tape contai ing no perforations. U.S. Patent Nos. 3,145,070, 3,182,399, 3,500,379, 3,553,681, and 3,553,842 teach other types of rotary and linear conversion methods not utilizing a rack type member and dissimilar to that taught here.
Heretofore, little significance has been attached to finite measurements made from systems interconverting linear and rotary motions. A major reason for this is the inherent backlash and hysteresis characteristics that have always made repeatability impossible. Consequentially, there has always existed a need for a conversion system having none. It is recognized that the total absence of hysteresis is analogous to either a perfect straight line or circle and thereby only possible with theory. Urgently needed, however, is a system for interconverting linear and rotary motions whereby hysteresis, for practicable purposes, does not exist; one wherein hysteresis is neg-lible in terms of reality. It is an object of this invention to meet such requirements.
Briefly, and in general terms, the measurement device comprises an elongated, flexible rack which is thin and normally curved in cross-section to define opposite concave and convex surfaces. The

OMFI rack is characterized by a plurality of perforations longitudinally disposed adjacent at least one of its edges. While the rack is normally straight, it may be radially bent toward either said concave or convex surface, the rack then tending to spring back to its normally straight orientation. A rotatably mounted sprocket wheel assembly having sprockets for engaging the perforations in the rack and a cylindrical surface for receiving the rack convex surface radially bent thereagainst is provided. As the perforations engage the sprockets the convex surface is normally deformed laterally flat. A position encoder is coupled with said sprocket wheel assembly.
Figure 1 is an isometric view depicting the measurement digitizer in an operable position and showing its linear and angular measurement functions.
Figure 2 is a section view taken from Figure 1, and depicts the linear and angular apparatus' internal operating characteristics.
Figure 3 is a section view taken from Figure 2, and shows the rack holder of the linear measuring apparatus.
Figure 4 is a isometric view.of the rack holder, and depicts ts connections with the perforated rack.
Figure 5 is a section view taken from Figure 4, and shows the method of electrical conductivity through the rack holder.
Figure 6 is a section view taken from Figure 2, and depicts the sprocket wheel coupling and rack guide of the linear Treasuring apparatus.
Figure 7 is an enlarged view, taken from Figure 6, illustrating the principal used for the interconversions of linear and rotary motions.
Figure 8 is a section view taken from Figure 7, and in-dicates motions of the perforated tack when catenating with sprockets of the sprocket wheel coupling.
Figure 9 is an enlarged detail of actions that occur when interconverting linear and rotary motions.
Figure 10 is a section view taken from Figure 1, and depicts details of the cursor assembly holding a scribe, and attached to the

own end of the perforated rack.
Figure 11 is an alternative to Figure 10, and depicts the cursor assembly containing a mechanical pencil representative of a marker.
Figure 12 is a semL-schematic view, and indicates the number of polar coordinates capable of being digitized en a normal working or drafting table.
Figure 13 is a sectionalized view, similar to Figure 3, illustrating the rack holder without the requirement of electricity being conducted therethrough.
Figure 14 is a sectional view of a cursor assembly used with machining operations when digitizing distances between surfaces.
Figure 15 is a sectional view of a cursor assembly used with machining operations when digitizing the distances between hole centerlines.
Figure 16 is an electrical schematic representation illustrating the electrical conductivity of the measuring digitizer.
Figure 17 is a plan view of the punches and.dies used to process the perforations in the perforated rack.
Figure 18 is a sectional view, taken from Figure 17, showing the method for eliminating tolerances from the linear spacing of the rack perforations.
Figure 19 is a section view, taken from Figure 17, showing the mechanics to adjust the flattened width of the rack being per-forated.
Figure 20 is a section view taken from Figure 17, and illustrates the manner with which the rack is aligned and perforated.
Polar coordinates of a point on a plane may be visualized as a twofold fix of "linear" (radius vertex) and "angular" (polar angle) measurements. The radius vertex is a linear measurement along a pivotal axis from its vertex to the point. The polar angle is an angula measurement between the pivotal axis and another fixed axis with the same vertex. Together, they form the polar coordinates relative to their common vertex. Thus, a measurement system capable of digitizing polar coordinates must incorporate functions to digitize both kinds of measurements; linear and angular.
The measurement digitizer of this invention, including linear and angular measurement digitizing functions, is generally illustrated in Figure 1. Therein, the digitizer, identified by the numeral 10 incorporates linear measuring apparatus 12, angular measuring apparatus 14, a cover 16 "(shown with reference lines for clarification) , and a cursor assembly 18. Although digitizer 10 may operate from any direction, the arrangement shown best illustrates its features. For clarification, "forward" is the direction of cursor assembly 18 looking from angular apparatus 14.
Digitizer 10 is attached to the upper rear edge of table 20 and centrally located frcm its sides. Table 20 represents any drawing, drafting, or working table. Affixed with tape or the like (not shown) is document 22 representing any drawing, reproduction, paper, map, or record of any relative size. Surface 24 of document 22 represents a two-dimensional plane on which points may be or are recorded. Polar coordinates of such points may be digitized by this invention.
Linear apparatus 12 involves the bidirectional interconversion of linear and rotary motions. It will be shown and described how these interconversions are accomplished whereby hysteresis and backlash, for practicable purposes, are non-existent. Forward and reverse linear motions represented by arrows 26 and 28, of perforated flexible rack 30, are measured by the bidirectional rotational movements within encoder 32 made by its shaft 34. Thus flexible rack 30 may somewhat be compared with a rack of a conventional rack and pinion arrangement in taht the two are used for interconverting linear and rotary motions. With a conventional rack, however, backlash generally becomes inherent while with the new flexible rack backlash is eliminated.
Wien extended rack 30 is always rigidly straight and perpendicular to shaft 34. The rack often' embodies two parallel rows of holes equally spaced along its length. It is thin, normally curved in cross section, coilable and usually made of metal. It may,
however, be made of plastic. Rack 30 possesses considerable strength and rigidity being cross-sectionally curved.

"wii-α" Linear apparatus 12 embodies vertical walls 36 and 38 held parallel with bottom plate 40 and top plate 42 with pins and
Though encoder 32 may be mounted upon either wall because it is bidirectional, it is shown mounted to the outside of wall 36 with its shaft 34 secured by hardware in wall 38. Perpendicular to the shaft and emerging frc cleaner assembly 52 attached with screws 54, rack 30 has its distal end 56 sandwiched in cursor assembly 18. Cleaner assembly 52 consists of top and bottom grooved segments each containing wiper strips between which rack 30 extends and retracts. In this manner, dust and other particles are prevented from entering the inner the inner workings of digitizer 10.
Linear apparatus 12 may be used separately since components to digitize linear measurements are integral with it. When so used, it may be mounted for lateral rotatability, or mounted using mounting holes 58. If mounted flat, provisions should be considered to extend and retract rack 30 in a straight line because the rack will not bend or curve sideways. If mounted for rotatability, the shaft of the vertically mounted encoder (to be described) may appropriately be replaced with a short shaft.
Angular apparatus 14 measures, with electrical pulses, the angl made by linear apparatus 12 when rotated about vertical axis 60.
Any angle so measured is a polar angle. Then, any linear measurement made by linear apparatus 12 is a radius vector. To-gether, the polar angles and radius vectors form the polar coordinates of points on surface 24.
Angular apparatus 14 is shown configured with top plate 62 and base plate 64 held parallel with a semicircular wall 66. The rear of the top plate, semi-circular to match the wall, is aligned to it with taper pins 68 used to relocate and reposition the top plate when linear apparatus 12 is assembled into angular apparatus 14. When aligned, top plate 62 is appropriately secured to wall 66.
Base plate 64 is alwo shown circular with the exception of a bottom lip 72 that tapers to front edge 74 designed to lie parallel with the edge of table 20 when digitizer 10 is aligned -7- into its operable position (to be explained) . The bottom lip serves as a base upon which cover 16 rests and edge 74 serves as an
alignment edge against which document 22 may be abutted. Base
plate 64 is attached to wall 66 (from below) with countersunk screws (not shown) .
Top plate 62 is spotfaced to accept a second encoder
mounted flat thereupon. The frontal sides are tapered to abutment edges 76 and 78 whose surfaces are in a line slightly beyond the
vertex 80 of top plate 62.
A bidirectional encoder 82 with shaft 84 is mounted, coaxial with vertical axis 60, with a plurality of mounting cleats
with screws. The shaft penetrates ball bearing 90 mounted within top plate 62 and terminates within top plate 42 where it is retained (not shown) . At the lower extremity of vertical axis 60, a thrust ball bearing 92 is -secured within bottom plate 40. A tri-diameter shaft 94, its top end shown penetrating ball bearing 92, is retained within base plate 64. The principal of rotation is shown whereby linear apparatus 12, integral with shaft 84, rotates laterally about axis 60 between ball bearing 90 and thrust ball bearing 92.
Cover 16 allows rack 30 to rotate from side to side.
Although it may be of any appropriate shape, a spherical shape was selected because of the inherent strength of a sphere. Dome 96 is joined to circular base 98 attached to wall 66 with thread forming screws 100 (one only shown) . Circular base 98 extends below the sur-face of table 20 whereby the edges, as edge 102, are abutted against table 20. In this manner, digitizer 10 is aligned into its operable position.
Cover 16 made of plastic, may be conventionally fabricated.
From side to side and around the front is a slot 104 allowing rack
30 to rotate. The sides extend beyond the centerline of circular
base 98 so its edges, as edge 106 (one edge only shown) , give
sufficient clearance to rack 30 when rotated. Also, behild edge
106, semi-circular cuts, as cut 108, are machined drcm each end of circular wall 66-also allowing rack 30 its full rotational swing.
Stop bracket 110, preventing rack 30 from striking the

edges of the slot or semi-circular cuts, is mounted with screws
112 against the front of linear apparatus 12. The screws
penetrate through a dust cover 114 and into wall 38. (Dust covers
114, 116 and 118 protect the inner workings of linear apparatus 12.) Stop bracket 110 has an upper extremity centered between walls 36 and 38 and jutted forward whereby when an abutment edge 76 or 78
is struck by it, sufficient clearance for rack 30 is afforded to
edge 106 and cut 108.
A cursor holder 120 is attached with screws 122 to the edge of wall 66. A ball plunger 124 is threaded upward frcm the base
of the holder and penetrates into a bifurcation designed to receive and lock cursor assembly 18 into a preset position. From this
position the electronics of digitizer 10 are set. Ball plunger 124 is cαrcnercially available consisting of a steel ball partly pene-trating an aperture and backed by a disk which is backed by a compression spring. The steel ball, when depressed, will always exhibit a reverse force caused by the spring.
Vertical centerline 126 of the ball pluriber bisects
horizontal fixed axis 128 having a vertex 130 on ertical axis 60.
From this axis polar angles are determined. An extension of it
(shown dashed) represents the extent to which polar angles are made.
This extent is 180 degrees represented by polar angle arrows 132
and 134 on polar angle line 136.
Cursor holder 120 has a U-shaped cut 138 permitting slot
140, in the base cover 16, to fit over the cut. In this manner, cursor holder 120 may be attached inside of the cover and its main body will extend outside.
The inside height of the cursor holder's bifurcation is designed to receive the assembled height of cursor 142 having top and bottom segments between which rack 30 is sandwiched. When sandwiched, the centerlines of the rack and cursor are aligned, indicated by centerline 144 bisecting vertical axis 60. Centerline 144 is
also represented on surface 24 by the radius vertex 146 bisecting vertical axis 60 at vertex 130. Thus, the vertex is coirmon to both fixed axis 128 and radius' vertex 146.

Wu A vertical axis 148, of cursor assembly 18, is made
perpendicular to surface 24 with a hand operated cursor guide
150. The guide may be rotated 360 degrees, indicated by arrows
152 and 154, about insert 156 through which a scribe 158 is
coaxially penetrated. A mechanical pencil 158a, shown referenced, may alwo be used because the cursor is machined to accept either.
Cursor guide 150 is tripodaled by scribe 158 with its tip 160
(or by the mechanical pencil lead or marker) touching surface 24.
With adjustment screw 162, sliding balls 164 and 166 may be ad- justed (to be shown and explained) up or down to contact surface
24. With that adjustment, axis 148 is made perpendicular to the surface and the cursor guide is allowed to rotate.
The bottom of cursor 142 embodies a hole 168 the centerline (not shown) of which is perpendicular to centerline 144. Hole 168 is designed to mate with the ball in ball plunger 124 and has a diameter slightly less than the diameter of the aperture, within ball plunger 124, that retains the ball. In this manner, when the edge of hole 168 depresses the ball, the ball will exhibit a reverse force against it.
A wall 170 is provided on the lower branch of the bifurcation. The wall, top, bottom," and rear of the bifurcation then all serve as a nesting area for cursor 142. For easy insertion
of the cursor, the bifurcation's branches are usually chamfered.
It may now be visualized that while holding cursor guide 150, as the corner 172 of cursor 142 is gently pushed toward corner 174 in the cursor holder, the ball in ball plunger 124 will depress allowing the cursor to enter the bifurcation. When the ball begins to penetrate hole 168, and cursor guide 150 is released, cursor
142 will automatically be centered by ball plunger 124. It will
always be centered in an identical position because the ball in the ball plunger is ring fitted therein. This position of scribe tip
160 is synchronized (to be explained) with the electronics of
digitizer 10. When inserted, the fit is designed so tip 160 is
slightly lifted from table 20. The sponge-like, upper wiper strip in cleaner assembly 52 allows rack 30 to be lifted to that extent

< i"> Thereby, tip 160 is prevented from striking the surface of the table and possibly being misaligned.
Although they may be located anywhere, cursor holder 120 is shown incorporating the digitizer on-off switch and a light lit with the switch in the "on" position. The wiring for the switch 176 and light 178 is fed, from inside of cover 16, through a hole (not shown) in cursor holder 120. With this arrangement, cover 16 may be removed and replaced without disturbing the wiring.
A wire bundle 180 (from encoder 32) has branched frαrt it another wire bundle 182 carrying electricity conducted to a push button switch located on cursor assembly 18. An alternative method of conducting electricity to the switch is through wire bundle 182a (shown dashed) . The switch, for signaling the positions indicated by encoders 32 and 82, may also be located separately, fed by wire bundle 182b (also shown dashed) .
Wire bundle 180 is attached with tape or ties 184 to the upper extremity of stop bracket 110 so the bundle or ties will not interfere with the stopping action of the bracket. Bundle 180 is hung in a loose coil 186 captured by a gronmet 188 within bracket 190. Bracket 190 is attached with screws 192 to top plate 62 and employs a cutout 194 adapted with plug 196 attached to encoder 82. In this way, linear apparatus 12 may be rotated from side to side and coil 186 will exert minimum resistance.
Frcm gronmet 188, wire bundle 180 parallels wire bundle 198 from encoder 82. The bundles are fed through hole 200, in top plate 62. and extend to receptacle 202 attached appropriately to base plate 64. Wire bundle 204, ccntaining wires from switch 176 and light 178, may be seen extending from cursor holder 120 and joins bundles 180 and 198 at receptacle 202.
Outputs of encoders 32 and 82 may vary depending upon the application of digitizer 10 and are generally predicated upon input requirements of electronic equipment to which digitizer 10 is connected, signal manipulability of such equipment, and the end use of signals produced. Example, if digitizer 10 is eonnected with a main computer having functions to manipulate signals; encoders generating pulses would be appropriate. If connected directly with a polar to rectangular converter; encoders generating binary coded decimal signals may be required. If digitizer 10 is used to locate and store addressable points, such as on a map; encoders having binary coded signals may be used, or encoders generating only pulses may be used if connected with a digital pulse counter.
Although any type of shaft position, signal generating device may be employed, an example is used to show and describe measuring functions. Adequate encoders are those such as produced by Litton Industries. These are the shaft position encoders of the optical, bidirectional incremental -type utilizing gallium arsenide light emitting diodes as an illumination source, and generating square waved electrical pulses. These are operable within a temperature range of 32 to 185 degrees Fahrenheit, and each encoder enploys two outputs; data A and data B. One output is energized when emitting pulses for a forward direction as the encoder's shaft is rotated clockwise. The other output is energized when emitting pulses for a reversed direction as the shaft is rotated counterclockwise. Such encoders are available each having specific numbers of pulses per revolution of its shaft. Exaπple, encoders that will generate 86,400 pulses per revolution, clockwise or counterclockwise, are not uncxnraon.
With the new system for interconverting linear and rotary motions (to be described and explained) encoders generating any number of pulses per revolution may be used with each pulse representing a converted linear distance. Therefore, depending upon the incremental distance desired, a suitable encoder may be chosen. Example, with the science of computer graphics, .010 inches is the tolerance generally required when digitizing coordinates of a point upon a plane. To digitize within the example of .010 inches, an encoder generating 1,000 pulses per shaft revolution may be used.
The above is explained whereby rack 30 can be configured to move linearly approximately 3.60 inches with each rotation of shaft 34. Therefore, with encoder 32 chosen to generate 1,000 pulses per revolution, rack 30 will move approximately .0036 inches per pulse generated (3.60 inches divided by 1,000 pulses). The .0036 inches is then within the .010 inches tolerance required when digitizing with the science of computer graphics.
For the example outlined, the number of pulses generated by encoder 82 sould be chosen by determining the longest radius vertex to be used by digitizer 10. The longest being the distance from vertical axis 60 to a lower corner of surface 24 not shown in Figure 1 but apprcadmately 52.38 inches long. The circumference of a circle having that radius is 329.1132 inches (2 times pi times 52.38 inches) . That circumference, divided by an example of 36,000 pulses chosen for encoder 82, equates to a movement per pulse of .0091 inches. With encoders 32 and 82, then the polar coordinates' maximum tolerance window of .0036 inches by .0091 inches would fall within the .010 inches by .010 inches tolerance indicated when digitizing with computer graphics.
Although encoders used are usually digital, analog encoders may also be used. Example, encoder 32 could be a 20 turn, serve-mount potentiometer. With digital encoders, one rotation may be divided into more than 86,400 increments. With an analog potentiometer type of encoder 86,400 parts equate to 15 seconds of a degree ([360 times 60 times 60] divided by 15 equals 86,400) requiring a potentiometer not as available as the digital type nonrtally used.
Since the exact linear movement of rack 30 per rotation of shaft 34 cannot be predetermined because of obvious irachiiiing limitations , a measuring beam 208 is utilized to determine that distance. The beam (shown broken to fit within Figure 1, is given the designations 208a and 208b. With its explanation it will be obvious, for linear measurements only, it may be abutted anywhere against linear apparatus 12 and not synchronized to vertex 130 indicated here with polar requirements.
Measuring beam 208 incorporates finite dimensions originated at^the U.S. Department of Dimensional Metrology (U.S.D.D.M.) The beam, penetrating slot 210 in the cover's circular base 98, is slid along the circular floor and abutted against the tri-diameter shaft 94 (to be shown with Figure 2) . From its centerline at the abutment end, precise measurements are made by U.S.D.D.M. to the centers of scribe holes 212 and 214. Where abutted, the radius of tri- diameter shaft 94 is added to the measurements obtained. In this manner, the precise radius vertexes to the centerlines of holes
212 and 214 are then known.
With Figure 6 it will be described how, using measuring beam 208, centerline 144 is aligned to bisect vertical axis 60.
When aligned, with encoder 32 connected to a standard digital pulse counter, tip 160 of scribe 158 is inserted into one measuring beam hole and then the other with the pulse count between determined.
Because the precise distance between the holes is known, the "pulse count" from vertex 130 to the centerline of hole 212 may proportionally be determined because that "measurement" is known. With tip 160 then inserted in hole 212, the pulse counter may be zeroed back to vertex 130 by subtracting the number of pulses determined for that distance. Measuring beam 208 is then withdrawn and set aside.
Cursor 142 is inserted into its "locked" position within cursor holder 120. The pulse count there may then be read from the pulse counter. That count and its proportional distance is then recorded and may be used with any electronic equipment to which
digitizer 10 may be attached. It may now be visualized each time c.
cursor assembly 18 is withdrawn from cursor holder 120, and tip
160 placed anywhere on surface 24, the distance (radius vertex)
from vertex 130 may always be determined because it is relative
to the additional pulses, from centerline 126, emitted by encoder
The above conditions should be accomplished within an
environment having humidity and temperature equal with those (stamped on measuring beam 208) when the beam was measured at U.S.D.D.M.
Thereafter, the using environment is dependent upon the material of rack 30, and also the small'extent to which measurements are
A low carbon steel has thermal change (expansion or
contraction) of approximately .0000065 inches per inch per degree of temperature change (Fahrenheit) . By contrast, a material such as Invar, a nichol allo developed for uses requiring π nimum

OMPI thermal change, will vary approximately .0000014 inches per inch per degree of temperature change (Fahrenheit) . If rack 30 is made from either of these materials, its thermal changes should be considered if linear apparatus 12 is used to produce extremely small measure-ments.
For encoder 82, synchronization of its electrical pulses with the polar angle is made with cursor assembly 18 "locked" within cursor holder 120. There, tip 160 is resting upon fixed axis 128 where the polar angle of encoder 82 is 0/360 degrees. Polar angles, with conventional electronic technologies, are usually determined counterclockwise from a fixed axis- at that position.
With encoder 82 also connected to a standard digital pulse counter, then with using a standard polar to rectangular convertor, the polar coordinates may be converted to Cartesian coordinates. Thus, with digitizer 10 the polar angles, along polar angle line 136 from polar arrow 134 counterclockwise to polar arrow 132, are representative of polar angles from 180 degrees to 360 degrees. The
radius vertexes are as described.
Wires, embedded within rack 30, lead to push button switch 216 shown on cursor 142. When cursor assembly 18 is extended or retracted to any position on surface 24, switch 216 may be depressed signaling the shaft positions of the encoders relative to the position of tip 160; linearly frcm vertex 130 and angularly from fixed axis
128. Together, the two dimensions are the polar coordinates. When not advisable to contain the switch in cursor 142, switch 216 (shown dashed in moved position) may be contained in switch holder 217.
Switches 216a and 216b are alternative switches to signal the positions of the individual encoders.
Figure 2, sectionalized, shows digitizer 10 attached to table 20 by one of two clamping assemblies. Though the lower protrusion of the circular base may be eliminated and the entire base plate 64 fitted flat upon table 20 (whereby the clamping arrangement would penetrate through table 20) , the configuration shown is desired for use with standard drafting tables. As such, large drawings or drawing paper may be affixed to the table in front of the digitizer.

OMPI Edge 218 and edge 102 (Fig. 1) protect the table frcm being marred by the threaded shafts of the clamping assemblies. Threaded shaft 220, hex nut 222, a conventional clamp 224, and wing nut 226 are one of two such assemblies positioned equidistant from the center of digitizer 10. In this manner, hex nuts 222 will not interfere with linear apparatus 12 when rotated from side to side. The shafts are threaded through tapped holes (not shown) in base plate 64 and the nex nuts lock the shafts. The wing nuts secure the clamps with table 20.
Encoder 82 has its flange 232 mounted upon spotfaced top plate 62. The plate has a countersunk area within which base 234 is extended. Two additional countersinks are provided. One contains shim spacer 236 retaining the outer race of ball bearing 90 slightly press-fitted into top plate 62. Shim spacer 236 prevents ball bearing 90 from riding up on shaft 84 where the inner race of the bearing might gall with base 234. The other countersink retains the flange of ball bearing 90. A spring washer 238, its minor diameter contacting the lower extremity of ball bearing 90's inner race and its major diameter retained by a countersink in top plate 42, applies a spring loaded force to the inner race of the bearing, thereby, eliminating its radial play. Shaft 84 penetrates the above and is secured within top plate 42 by set screw 240.
At the opposite extremity of axis 60, thrust ball bearing 92 is slightly press-fitted into bottom plate 40 that retains the bearing's outer race. The inner- race is mounted on one diameter and retained by another diameter of tri-diameter shaft 94 also separating bottom plate 40 from base plate 64. There, tri-diameter shaft 94 is reduced to yet another diameter designed so binding head screw 242, when tightened, will press fit shaft 94 with base plate 64. The countersink for screw 242 allcws base plate 64 to fit flush with the table.
When linear apparatus 12 is assembled into angular apparatus 14, top plate 62 is removed to allow ball bearing 92 (assembled within linear apparatus 12) to be fitted upon the flange of the tri-diameter shaft. Top plate 62 is then realigned and attached. When securing the encoder, the preloading force of spring washer 238 is also introduced into thrust ball bearing 92, thereby eliminating all radial play of linear apparatus 12 in relation to angular
apparatus 14.
To circumvent possible doubts concerning side bending or torque of rack 30 when extended maximum distances and rotated from side to side, shaft 84 of encoder 82 exhibits only one inch-ounce of torque when rotated. In actual praetice, a person may blow lightly against a side wall of linear apparatus 12 and that slight force is all required to rotate it from one side to the other.
Dust covers 114, 116, and 118 are attached for easy
removal. Covers 114 and 118 are inserted into slots provided along the length of top plate 42. As such, the covers need only be secured at the front and rear of the side walls. A similar slot provided along the top rear edge of cleaner assembly 52 assures a tight seal when the cleaner assembly is vertically adjusted. Cover 116 for easy removal is secured with screws 254. A fourth dust cover 256 is attached to the top of bottom plate 40, thereby, protecting thrust ball bearing 92.
Perforated rack 30 is coiled against its concave side about a rack holder assembly 260. Then rack 30 is reversed in direction and catenated, against its convex side, with sprocket wheel coupling 262 mace integral with shaft 34. When reversed, rack 30 is sandwiched between the sprocket wheel coupling and rack guide assembly 264, then fed through cleaner assembly 52 and slot 104 of cover 16.
Rack holder assembly 260 involves some basic principals often utilized with conventional push-pull, tape measuring rules. These principals are as follows: Shaft 266 has a central slot through which the proximal end of negator spring 268 is inserted and secured with a counterclockwise wrap. The opposite end is then wrapped tightly, counterclockwise, and its distal end interlocked with the proximal end of rack 30. Two disks, as disk 270 (shown broken for clarity) , usually -made of teflon are aligned one on each side of negator
spring 268. As rack 30, wider than the spacing of the disks, is fed over the two disks, it is concentrically coiled around the disk's edges

- as they rotate about shaft 266 as negator spring 268 unwinds from it's tightly wrapped position.
Separate from the above principals, rack holder 260
generally embodies other advantages such as a rotatable shaft and also elements to conduct electrical power to and from push button switch 216 (Fig. 1) . These new advantages, and also new mechanics of circular disk holders, as teflon disk holder 272 (one side only shown) will be shown more in detail and described with relation to Figures 3 - 5. Each disk holder, usually containing three teflon alignmen disks 274, 276, and 278, is attached to the inside of a housing vertical wall with screws 280, 282, and 284 the ends of which may be secured in disk holder 272. The functions of the disks are for initial alignment of rack 30 fully described and explained with Figure 6.
Wire bundle 182 is secured with grαrmet 286 in wall 36.
Inside the wall, the covering of the bundle is stripped and its two pairs of wires 288 and 290 are attached to spring backed terminal brushes contained within the teflon (electrically insulative) disk holders. The pair of wires 288 has each wire connected to a separate terminal brush, as brush 292 (one only shown) , and the pair of wires 290 (sectionalized) has each wire similarly connected to a terminal brush contained within the opposite and opposing disk holder.
Two pairs of wires, as the wire pair 294, are embedded in the concaved side of rack 30. They lie between two flexible, insulative, thermoplastic coatings 296 and 298. These coatings may be of materials such as polyvinyl chloride of fluorcaxbon TEE. The wires generally run in a zig zag pattern to prevent their breakage when stretched and contracted as rack 30 is extended and retracted.
Sprocket wheel assembly or coupling 262 has three circular segments coaxial with shaft 34. The central segment, center-wheel 300 (sectionalized) , has a somewhat friction type surface as that made with acrylonitrile butadiene styrene (ABS) . The centerwheel is located whereby the centerline of its width is coaxial with centerline 144 (Fig. 1) of rack 30. It may be retained with a set screw 302 usually silver tipped to prevent marring shaft 34. The diameter of the centerwheel determines how far rack 30 will move with

- θREΛ
OMPI όne rotation of shaft 34. The diameter, plus the thickness of rack

30', times pi (3.1415926654 ) , will equate to the distance rack

30 will move.
Sprocket wheels, usually made from stainless steel, are aligned one on each side of centerwheel 300. Seen in Figure 2 are a plurality of sprockets 304 held by one of the sprocket wheels. The sprockets mate exactly, as will become apparent with this specification, with the perforations of rack 30 where radially bent about centerwheel 300. To be described and explained, the diameter of center-wheel 300 is approximately equal with the diameters of the sprockets where their straight sides are tangent to the spherical radiused extremeties leading to their tips.
When rack 30 is extended or retracted, the perforations at the radial bend fall with the deformation of the rack straightened laterally when reversed in direction. Then the perforations rise with the rack again assuming its cross-sectionally curved shape after being reversed. When the perforations fall they do not abut the sprockets. Rather, they fall upon the sprockets and firmly adhere to them. It may be visualized each perforation in the entire length of the rack is mated with only one individual sprocket. It will be explained how no tolerance exists when catenation takes place. Though various numbers of sprockets may be used, of the 36 total sprockets indicated (one side only shown) , 20 to 22 of these are at all times in constant engagement with perforations of rack 30.
The torque required to rotate shaft 34 is one inch-ounce. This torque is easily overpowered when extending or retracting rack 30 whereby 20 to 22 perforations are ring fitted with the sprockets, and also whereby frictional engagement takes place between rack 30 and centerwheel 300. When moving rack 30 relative to shaft 34 being rotated, or when rotating shaft 34 relative to rack 30 being moved, the slightest linear micrαmovement, simultaneously, will be reflective between the shaft and rack, regardless of where cursor assembly 18 may be extended on surface 24 (Fig. 1) .
As a point of interest, rack 30 in digitizer 10 was tested for durability. The rack was violently extended and retracted at speeds to and exceeding 1,750 rpm and to distance of more than five feet, while simultaneously twisting it and skewing it from side to side and up and down. The purpose of the test was to introduce "wear" into the perforations and also to ascertain conditions re- quired to tear the rack. More than 5,500 such extensions and retractions (in excess of 11,000 total mating times of each perforated hole with its sprocket) were required with such violent actions to purposefully tear the rack. It finally tore from a perforation to its adjacent side of the rack.
The rack was then disassembled from digitizer 10, and the perforated holes were carefully examined with a fifty power microscope calibrated to measure less than .0005 inches. Absolutely no wear of the perforated holes (or the sprockets) could be determined. Measured before and after the test, the holes, still, were exactly the same diameters as the sprockets.
Guide assembly 264 embodies two guide wheels 306 and 308 centrally molded upon their respective shafts 310 and 312. The wheels, usually made from a urethane casting elastomer having a duro- rreter hardness of approximately 6Θ Shore A, when cured undergo an approximate three percent shrinkage factor. The shafts are roughened where the wheels are molded to them, thereby, creating a tight, non-slip fit when the wheels are cured. Shafts 310 abd 312 rotate freely within bearings (not shown' in Figure 2) retained within the parallel sidewalls of bifurcated bracket 314. The bracket is slide-ably adjusted along centerline 316 bisecting the center of shaft 34.
Plate 318 is attached with screws (not shown in Figure 2) to chamfers at the lower rear corners of wall 36 and wall 38 (Fig. 1) . Centrally located within the plate is a threaded hole, coaxial with centerline 316, mated with a hand adjustment screw 320 pene-trating into an in-line hole at the base of bracket 314. When the adjustment screw is tightened, guide wheels 306 and 308, in turn, equally impinge upon rack 30 and sandwich it between the wheels and centerwheel 300.
When rack 30 is retracted into linear apparatus 12, it is catenated with sprocket assembly 262 then rotating counterclockwise. Negator spring 268, wanting to unwind, is consistently pulling rack 30 about the disks as disk 270. If rack 30, however, should inadventently be pushed at a speed faster than the "pulling" capability of the negator spring, then guide wheel 306 will prevent rack 30 from being "pushed off" from sprocket assembly 262, and also aid to push the rack against rack holder assembly 260.
In this manner, negator spring 268 is assisted and allowed
to rapidly uncoil, assuring rack 30 is consistently coiled tightly around the disks. When extending or retracting rack 30 by hand, no slackness exists in relation to its position as shown in Figure 2.
Parallel with centerline 316, two slots 322 and 324,
respectively, are provided in wall 36 and wall 38 (Fig. 1) .
Two shafts 326 and 328, each threaded on both ends, penetrate
through and are secured in the base of bracket 314. The shafts extend through the slots to the outsides of the walls where they are provided with hex nuts (not shown in Figure 2) to lock the
guide assembly 264 following its adjustment. Because the slots are slightly larger than the shafts slidable within them, wheels 306 and 308 find their own equally balanced impingement points when
sandwiching rack 30 against centerwheel 300.
Catenation of rack 30 with sprocket assembly 262 is
not dependent upon rack holder assembly 260 or guide assembly 264.
Many types of rack holders and guide assemblies may be employed
or under various circumstances not even utilized. Example, rack
30 shown dashed (and also broken for clarification) is extended
horizontally from the top of sprocket assembly 262 and the rack
there given the designations 30a and 30b. In that fashion the catenation of the rack with sprocket assembly 262 is equally effective when alternately retracting the ends of the rack.
Another pair of disk holders, as the rectangular disk
holder 330 attached with screws 332, are aligned on each side of rack 30 and each is attached to a vertical wall. These holders each contain a disk 334 also slideably adjustable as the disks held by the circular disk holders above them. With disks 334, however, each has machined across its center a V-groove 336.used to retain

OMPI an edge of rack 30 slid in it during alignment (to be explained) .
Here with Figure 2 the centerline of measuring beam
208 (shown sectionalized) may be seen resting upon the circular floor of base plate 64 and abutting tri-diameter shaft 94.
Advancing to Figure 3, please notice that its section taken along line 3-3 in Figure 2, indicated here with arrows 338 and 340, is for clarity extended as though taken from a whole view. Shaft 266, interference fitted with walls 36 and 38, abuts the inside of wall 36 and is there threaded to receive locking nuts 342 used to lock the shaft in any position. Opposite a pin 344 secures a hand knob to the shaft.
The major: purpose of the arrangement described is to adjust tension of negator spring 268 whereby rack 30, when extended and released, will not creep forward or backward. With locknuts 342 loosened turning knob 346 counterclockwise tightens the coil made fcy the negator spring. Then, after rack 30 is extended, the negator spring wanting to uncoil will pull back rack 30. Turning knob 346 clockwise will uncoil the negator spring thereby giving it less ability to pull back rack 30. By extending rack 30 while adjusting knob 346, a balanced position may be attained whereby rack 30 ( (especially with the weight of cursor assembly 18 (Fig. 1) attached) ) will remain motionless when placed anywhere on surface 24 (Fig. 1) . At that position, locknuts 342 are tightened to retain the shaft.
Another purpose for selective rotatability of shaft 266 is initial coiling of the long negator spring that, otherwise, would be a time consuming effort. Also, as explained, the negator spring is depended upon to pull and wrap rack 30 around the disks. Knob 346 is used to complete this task. The negator spring is usually not as wide as the rack because the pulling force of a wide spring is not required. As such, it has been found while using a narrower negator spring, a more comprehensive "balancing" position may be attained when adjusting the rack to remain motionless when extended and released.
Spool 348, usually made of a lubricious plastic material as delrin, embodies a central slot, extending through its two axial «
-22- walls, and equal dimensionally with the slot in shaft 266. The
spool is interference fitted with the shaft. The proximal end
of the negator spring is secured through the aligned slots, and its
remaining length coiled ccainterclockwise about spool 348. Through

5 the slots is not a singular method of securing the spring. It
could, as well, be secured with a screw through the spool and into
the shaft.
Each outside surface of the spool's flanges has two
embossed surfaces 350 and 352. The surfaces, being lubricious,
10 align disks 270 and 354 rotatable about shaft 266. Each disk (made
with electrically non-conductive material, like teflon) has molded
in it two electrically conductive rings 356 and 358. The rings conduct electricity from terminal brushes, as brushes 292 and 360, each backed by compression springs as springs 362 and 364. When rack 30 is

15 installed around disks 270 and 354, the disks are adjusted against
embossed surfaces 350 and 352, assuring the brushes make good contact with the rings. The electricity from the pair of wires 288 to terminal brushes 292 and 360 'is conducted through the rings within disk
270. The pair of wires 290 conducts electricity through the rings

20 within disks 354. That electricity is then fed to the conductions in rack 30.
The fashion with which disk holders 272 and 366 are attached may be seen with screws 280 and 368. Each screw penetrates a hole in a vertical wall and draws the disk holder tightly against it. Disks

25 278 and 370 are adjusted with screws 372 each having a locking nut
374. The rectangular disk holders are attached, with disks, likewise.
Figure 4 shews rack 30 (broken for clarityX interlocking
with negator spring 268. Also, the manner in which electrical power is conducted to. the rack is shown. The distal end of the spring is

30 fitted over the rack where the spring's side notches are interlocked with a triangular cutout in the rack. This standard procedure is
referenced to illustrate how the spring holds rack 30 tightly against disks 270 and 354. With wrapping the rack about the disks, the
• - grip of the rack becomes more firm with each wrap until peeled off

35 in the direction of arrows 376 and 378.

OMPI When coiled, the proximal end of the rack is pulled clockwise while its distal end is subjected to being pulled counterclockwise. The result is that the rack is wrapped tightly.
It will not slip about the disks because of friction whereby
5 seizure takes place. With this manner, each wire of the pair
of wires 294 is inserted into terminals 382 and 384 (the wire
to terminal 382 is shown not yet attached) and there soldered in the standard manner. The pair of wires 380 are similarly installed within terminals 386 and 388. The first few wraps of the rack about 10 the disks are generally guided by hand. Then, the negator spring, with the final, assistance of hand knob 346 turned in the direction of arrow 390 (about centerline 392) , completes the coiling. Once coiled, the rack will not slip about the disks , an action that could break the wires.
15 Figure 5 is typical of each disk. Conductive rings 394 and 396 incorporate notches to hold them firm. Molded with disk
354 is a metal strip 398 solder connected to ring 394 and terminal
386. Similarly, a metal strip 400 connects ring 396 with terminal
388. These metal strips complete the electrical power conductivity 20 between receptacle 202 and push button switch 216 (Fig. 1) .
Figure 6 taken along line 6 - 6 of Figure 2 shown here
with arrows 402 and 404, is also for clarity extended as though taken from a whole view. In this manner, encoder 32 may be seen "float mounted" whereby an open tolerance is left around its hub 406 per- 25 mitting the encoder to be centered where shaft 34 penetrates ball bearing 408 retained with the heads of binding head screws (shown in Figure 1) in wall 38. The encoder is conventionally secured
against the spotfaced wall 36. Radial play is eliminated from
bearing 408 by gently applying pressure against its inner race with 30 the chamfered end of collar.414 appropriately secured. Prior to the adjustment described, centerwheel 300 and two sprocket wheels 418 are slid onto the encoder shaft. The centerwheel is retained with screw 302 and the two sprocket wheels are retained with screws 420 after the rack is aligned.
,~3-5 Guide wheel 306 maybe seen abutted against rack 30. On each side of the guide wheels are laminated shim spacers 422. Shaft spacers 424 generally separatethe shim spacers from oil-impregnated bearings 426 retained with binding head screws 428. In this manner, shafts 310 and 312 (Fig. 2) are allowed to rotate freely. Here also may be seen screws 430 securing plate 318; retaining screws 432 retaining shaft 326; and lock washers 434 with hex nuts 436 securing sjiaft 326.
Mating perforated holes of rack 30 with sprcckers 304, where no appreciable tolerance between them exists, is accomplished simply and rapidly. In practice, the holes are punched having slightly smaller diameters than the sprockets. Also, the holes are punched whereby no appreciable tolerances exist between the holes along the length of the rack. This process is described with Figures 17 - 20.
As such, the holes are rapidly "worn" to the diameters of the sprockets during an initial alignment procedure.
Alignment is accomplished by initially assuring that retaining screw 302 and the two retaining screws 420 are loosened whereby centerwheel 300 and the two sprocket wheels 418, although snug, may rotate about shaft 34. Hex nuts 436 on shaft 326 and shaft 328 (Fig. 2) are loosened and guide assembly 264 is backed from sprocket wheel coupling 262. Then, the distal end of the rack is radially bent about the sprocket wheel coupling (in the direction shown by Figure 2) .
The tips of sprockets 304 will then only partially penetrate the smaller holes punched in the rack.
With the rack positioned as described, the three alignment disks in disk holders 272 and 366 (Fig. 3) , are adjusted inward to forceably square the coiled sides of rack 30 (the disks in this position are shown dashed with Figure 3) . The disks are then adjusted to slightly touch the squared sides and locked in that position by tightening hex nuts 374 (Fig. 3) against walls 36 and 38. The alignment disks in the lower disk holders, as disk 334 in disk holder 330 (Fig. 2) , are adjusted also having no tolerance and locked with the sides of rack 30 inserted into the V-grooves machined across the ends of the disks. During this adjustment, it is assured rack 30 is centered between walls 36 and 38.

-25- Guide assembly 264 is adjusted with screw 320 so the guide wheels touch rack 30. With the cleaner assembly removed, the rack is extended 5 to 6 feet and returned. This process is repeated 8 to 10 times with the adjustment screw consecutively tightened until rack 30 is snugly sandwiched between the guide wheels and centerwheel 300. When the rack is so extended and retracted, it is usually grasped between the thumb and forefinger with the hand slid along the surface and the rack maintained level with the V-grooves. Any lateral movement of the hand will be compensated by lateral rotation of linear apparatus 12.
As the alignment disks, at each radially bent end of the rack, firmly guide it in a non-deviating, linear path (rack 30 between them will not move laterally) , the rack's perforations will align the sprocket wheel coupling on its shaft. Also, any slight di- mensional descrepancies of the individual sprockets (tolerances with fabrication limitations) will be nullified because the perforations will rapidly "wear" to fit them (each perforation being mated with only a singular sprocket) . The sprocket wheels' retaining screws 420 and the centerwheel's retaining screw 302 are secured at that time.
When aligned as described, the functions to guide the rack in a non-deviating linear path are transferred from the alignment disks to the sprockets. This is significant and may be compared with the guiding functions of any steel bar guided in a linear path. The comparison is analogous because rack 30, in fact, is a steel bar. As with any bar having its sides supported whereby it will move only linearly, any slight deviation to that direction will deform its shape. Rack 30 has threse identical characteristics but is unique in that with the manner described, many such supports (in the form of sprockets) are used to guide its linear movement. As such, it cannot deviate from its linear path because, as with any bar, it will not bend sideways.
Following alignment, the disks in the four disk holders are backed from the rack and adjusted flush with the inside surfaces of the disk holders. The disks need not be used again unless rack 30 might eventually be replaced. Also, as a precaution if the rack should require future removal, it is extended a maximum length
and two sprockets (one on each side of the centerwheel) together with their mated sprocket holes are marked with a scribe or
dabs of paint. Without such markings, extreme difficulty would
be encountered to again align the perforations with their respective sprockets.
With Figures 6 and 1, the procedure may be visualized
where it is assured rack centerline 144 (Fig. 1) bisects vertical axis 60 (Fig. 1) . Looking first at Figure 1, encoder 80 is connected with a standard digital pulse counter and a pulse count (any count) read with tip 160 inserted coaxial into measuring beam hole
212. Tip 160 is then extended and inserted coaxial into hole 214 where the pulse count reading should be identical (the holes lie upon the same radius vertex pivotable axis) . If not the same,
sprocket wheel coupling 262 (Fig. 6) is adjusted on shaft 34 (to the left or right) and secured, with retaining screws 302 and
420, when the pulse count readings are identical. It is then
assured the rack centerline and vertical axis bisect.
With the above procedure, the distal portion of rack
30, around disks 270 and 354 (Fig. 3) , will be circumnutated.
This condition is corrected by extending rack 30 to where interlocked with negator spring 268 (Fig. 4) . With rack 30 again
retracted, sprocket wheel coupling 262, in its adjusted position, will circumferentially realign rack 30 around the disks. Again
looking at Figure 1, cursor assembly 18 is then inserted into cursor holder 120 at which position encoder 80 is synchronized with the electronics of 0/360 degrees.
Figures 7, 8 and 9 show the catenation, enlarged for
clarification, of rack 30 with the sprocket wheel coupling. Figure 7 depicts how the sprockets 304 do not abut with the perforated
holes, identified with the numeral 438, as the holes engage them.
Also, it shows that the base radii 440, do not interfere with the catenation of the holes and sprockets.
An area of possible confusion is clarified here by observing Figure 7 and also Figure 8. It has been described, when aligning rack 30, the adjustment screw is consecutively tightened


WIPO until the rack is snugly sandwiched between the guide wheels and the centerwheel. It should not be visualized, during that process, that the edges of the rack might flare upward whereby full catenation might not take place. When rack 30 is radially bent it is laterally straight (illustrated with the sectional view of
rack 30 shown in Figure 8) . If the edges of the rack flared
upward, they would either rip or become permanently deformed.
With Figure 8, gaps between centersheel 300 and the
sprocket wheels 418 may be seen. Each sprocket wheel independently allows its sprockets 304 to find the most applicable mating arrangement with its related row of holes in the rack. Here also, it
may be visualized that sprocket wheels 418 need not be limited
to two. Additional rows of holes in the sides of the rack can be perforated whereby additional sprocket wheels may be utilized with them. Also, the holes in one row need not be laterally parallel with the holes in another row. And, if desired, only one row of holes may catenate with the sprockets of only one sprocket wheel.
Various combinations may be used for sprocket and hole engagements. Example, two rows of engagements are used with digi-tizer 10 because rack 30 is rotated from side to side and the perforations are therefore subject to lateral wear. If linear apparatus 12 is used only for linear measurements, only one row of catenations may be sufficient. Again, if the sprockets are used to drive the rack, such as where measurements may be taken in a
dangerous environment, two or more rows might be used. Also, a
sprocket wheel might contain one or a number of sprocket rows and have sprockets of various shapes such as round, square, rectangular, oblong, and more. With digitizer 10, circular shaped sprockets
are shown because less machining costs are involved when ring fit-ting them with their respective holes.
Rack 30 in its normally curved position is indicated
with dashed lines. When the rack is reversed in direction and
radially bent about the centersheel, its sides deform and fall in the direction of lines with arrows 442 and 444 to the straight
position shown sectionalized. Because of the elliptical geometry

OMPI involved, the closer rack 30 assumes the straight position the more vertically the sides fall. Because of this phenomenon, there exists no perceptible galling between Hie sides of holes 438 with sprockets 304.
The curvature of the rack may be even more pronounced.
The greater the curvature the longer the length may be extended without sagging. Also, the width may vary. By varying the curvature and the width, and even the thickness, the rack may be made to encompass wide varieties of measurement capabilities.
When bending metals, it is well known that calculations of

"developed lengths" are based upon centerline lengths. Lateral centerline 446 is illustrated to describe this principal. When flat
(shown sectionalized) the widths of the rack along the top, centerline, and bottom are all equal. However, when the rack assumes its normally curved position (shown dashed) , the developed width of its top surface is slightly reduced, the developed width of its centerline remains constant, and the developed width along the bottom
surface is slightly increased.
The above principal is utilized when mating the holes
with sprockets. When mating, at the last instant, the bottom 448 of each hole will close and fit tightly to the sprocket. Con-- versely, when leaving the sprocket, at the first instant, the
bottom 448 of the hole will open and release from the sprocket
allowing rack 30 to assume its nornal cross-sectionally curved
At times, other diciplines have taught holes produced
along the longitudinal centerline of a member such as rack 30.
The center is the "working" portion of the rack. With a row of
holes punched along the centerline, the rack would soon split
into two lengths if radially bent as with rack 30.
Figure 9 shows a typical sprocket 304 and its spherical radius taken from a c iman tangency point 450. Ideally, because
tolerances must be considered, centerline 446 is designed to bisect point 450. Then, as hole 438 is "lifted" in the direction of the line with arrow 452, the bottom sides of the hole will open as the

/ IO top 454 of the hole slides from the spherical radius. Rack 30, when extended, retracted, and rotated is always moved having
no perceptible backlash, sidelash, or hysteresis with relation to sprocket wheel coupling 262. This is significant for repeatability. If tolerances existed even though slight, one reading would be indicated when extending the rack and another indicated when the rack was retracted.
With Figure 10, cursor guide 150 has a Z-shaped bracket
456 tongue and grooved wit T-shaped bracket 458 pivotal about
adjustment screw 162. Bracket 456 supports a handle 460 held by screws 462, and bracket 458 is supported by teflon sliding balls
164 and 166 (Fig. 1) secured with threaded shafts 464. Bracket 458 may pivot up and down about screw 162 and cursor guide 150 is so adjusted whereby vertical axis 148 is made perpendicular to surface 24, thereby, assuring the edges of rack 30 are parallel to the table.
Scribe 158 is threaded through cursor 142. Insert 156, usually made of a lubricious thermoplastic such as teflon or molybdenum disulfide (MDS) filled nylon, is penetrated through bracket 456 with a no tolerance, yet, swivel fit, and whereby the length penetrating bracket 456 is slightly longer than the thickness of the bracket. Spacer 466, usually of the same material as insert
156, is slipped onto scribe 158. Insert 156, penetrating bracket
456, is interference fitted with scribe 158. This arrangement,
locked together with tip 160 (usually nylon) threaded onto scribe 158, allows cursor guide 150 to rotate about the spool made by insert 156 and spacer 466. Also, when rack 30 is extended and retracted, no backlash exists with tip 160 in relation to movement of rack 30.
Cursor 142 embodies upper segment 468 and a lower segment 468a. The upper segment has a concave cut and the lower segment a convex cut. These cuts sandwich the rack and each cut has a radius equal with that of centerline 446 (Fig. 8) with rack 30 curved in its normally cross-sectional state. In this manner, when the rack is sandwiched, its sides are initially pinned between the cuts, thereby automatically aligning the centerline of cursor 142 with the rack's centerline 144 (Fig. 1) .- Also, only one screw is required to

_ OM?I
V V//11 OO sandwich the rack.
Positioning the rack between the segments is accomplished with a hole, through the centerline of the rack, interference fitted with dowel pin 470 press fitted into lower segment 468a. The hole with which the pin is fitted is hole 168, used to align cursor assembly 18 with cursor holder 120 (Fig. 1) . The pair of wires 380 are attached to push button switch 216. The pair of wires 294 are. shown sectionalized. Upper segment 468 and lower segment 468a contain the switch. The assembly, with rack 30 sandwiched therein, is held together with screw 474.
Figure 11 depicts how mechanical pencil 158a, rather than scribe 158 (Fig. 10) , may be fitted with cursor 142. The mechanical pencil, prior to machining, is usually a cctmercially available pencil normally used in an upright vertical position. Its tip 476 has a barrel 478 through which lead 480 is fed. An ink marker, as well as a pencil marker, may be used and fitted similarly.
The shaft of the pencil is threaded to match those of cursor 142, and the lower portion is machined to mate with insert 156, and is secured with cursor 142 in the same manner as is scribe 158 (Fig. 10) with tip 476 used rather than tip 160 (Fig. 10) . ϊfechanical pencil 158a has the added capability of drawing or marking-on the surface.
Figure 12 is a semi-schematic drawing illustrative of typical point location coverage by tip 160 on surface 24. Digitizer 10 is centrally located on table 20 and abutted by document 22 having a borderline 482 upon its surface. Figure 12 is referenced to the example explained with Figure 1. There, the example was described whereby encoder 32 emitted a pulse for each .0036 inches of linear movement by rack 30, and encoder 82 emitted a pulse for each .0091 inches of rotational movement of rack 30 extended to a distance of 52.38 inches.
Tip 160, schematically shown, is depicted at three different distances from vertical axis 60. Distance 484, 52.38 inches, is representative of the longest radius, vertex described. Distance 486, 5.41 inches, is the shortest radius.-~vertex used on that surface.

-31- Distance 488, 28.895 inches, is a radius vertex distance equal to one half the distance between distances 484 and 486.
The linear distance, per pulse, moved by tip 160 is
constant. However, when tip 160 is rotated from fixed axis 128, the circumferential distance traveled by tip 160, between consecutive pulses, varies. That distance is equal with the radius vertex of tip 160 times two times pi (3.14159 ) divided by 36,000 pulses (example given) per revolution of encoder 82. The circumferential distance traveled per pulse, by tip 160 at distance 484 is .0091 inches. At distance 486 it is .0009 inches and at distance 488 it is .005 inches.
The average tolerance "window" then, made along polar angle line 490, is .0036 inches by .005 inches. Therefore, it may be roughly calculated that tip 160 will indicate an average 55.555 separate "window" addresses per square inch on surface 24 ( (1.00 inch divided by .005 inches) times (1.00 inch divided by .0036 inches)) Because surface 24, inside of borderline 482, is approximately 34.00 inches by 69.00 inches (2,346 square inches) , approximately 130 million location addresses (2,346 square inches times 55,555 address-es per square inch) may be indicated with digitizer 10 inside of borderline 482. If four times that many addresses were desired, the pulse counts of encoders 32 and 82 would be doubled.
Figure 14 depicts rack holder arranged without the
requirement for electricity to be conducted therethrough. Negator spiring 268 is inserted through the slot in shaft 266, reverse wrapped, and its distal end wound around shaft 266 rather than spool 348 (Fig. 3) . Two collars 494 with set screws 496 at times secure disks without rings 492 between the collars and negator spring 268. It has been found that the collars, although not necessary, aid when assembling rack 30 to the negator spring. A pair of disk holders 498 without springs and brushes are attached and contain the disks.
Figures 14 and 15 illustrate additional cursor assembly arrangements when this invention is used with machining functions.
Significant uses are for marking where machining operations are to be performed, and when inspecting operations produced. Although many devices may be designed to fit with the end of the rack, basic
cursors are shown.
Figure 14 depicts cursor assembly 500, primarily used
when measuring between two surfaces, such as the opposite ends of plate 502 contacted by the lower extremity of shaft 504 when turning knob 506. A teflon or nylon rod, line-bored to form bearing 508, is molded into circular handle 510 usually made using an acrylic thermoplastic having good optical qualities. In this manner,
maximum vision is afforded so care may be exercised that the con-tact point does not become unduly chipped or scratched. The upper extremity of the handle is threaded through cursor 511. Handle top 512 is threaded to handle 510, securing it with the"cursor.
Shaft 504 is inserted through the handle assembly having no tolerance between it and bearing 508. The shaft's lower extremity is abutted against handle 510. Knob 506 is secured with set screw 514. The bottom of shaft 504 at times embodies a 90 degree cutout, extending to the shaft's centerline 516, used to fit around an upper comer of the work measured. When marking dimensions where machining operations are to be performed, a marking scribe may be used along the cutout's lower horizontal surface at centerline 516. Another method of measuring the length between surfaces is with the spherically radiused ring 518. Its diameter is -appropriately added or subtracted from the. measurement taken.
Figure 15 shows cursor assembly 520 primarily used when marking or measuring hole locations. It is shown measuring the center distances between holes, as hole 522 in plate 524 on table 20. When marking, shaft 526 is depressed with finger knob 528.compressing spring 530 with retaining ring 532. The tip of the shaft may then be used for marking work painted with paint such as steel blue marking fluid.
When the centerlines between holes are ireasured, the bottom of the transparent handle 534 is usually slid along the work assuring the cursor assembly's perpendicularity. When a hole is approximately centered, knob 528 is depressed allowing the shaft's tapered, self centering bottom to align with the centerline of the hole.

sA,. w.?o Bearing 538 is molded onto handle 534 and shaft 526 is inserted with no tolerance through the bearing. Handle top 540 sandwiches cursor 511 between the top and handle. Top 540 is also a stop for retaining ring 532. Finger knob 528, when depressed, maintains centerline 536 perpendicular with cursor 511.
Figure 16 is an electrical schematic of digitizer 10.
The wiring leads to receptical 202 a connector having multiple pins. The remaining pins (not shown) are used as spares so other equipment, such as a counter, convertor, microprocesser, or the like, may be located inside the digitizer cover.
Pins 4 and 5 are connected across a voltage source (not shown) . Pin: 4, though on-off switch 176, is the cαπmon feed to the encoders and light 178 (usually a light emitting diode) . The common return is pin 5. Encoders 32 and 82 (each employing a case ground) show the case ground pins connected with pin 3. Pins 1 and 2 carry the data A and data B signals from encoder 32, and pins 6 and 7 carry the data A and B signals from encoder 82.
Wire bundle 182 carries the pair of wires 288 and 290 to diskc 270 and 354. The pair of wires 294 and 380 (embedded in rack 30) continue the elctrical conductivity between the disks and push button switch 216 located in cursor 142. When the pairs of wires 294 and 380 are not carried by rack 30, they are fed (shown dashed) through grαπ et 542 and carried by wire bundle 182a to the push button switch located in the cursor. When convenient to locate the switch away from the cursor, this condition is shown with the pairs of wires 294 and 380 carried in bundle 182b to the switch located in push button switch holder 217.
The conductors used to signal polar positions are connected to pins 9 and 10, and their returns are connected to pins 8 and 11. As shown, these conductors are usually isolated from the conductors to and from the encoders. The reason is to accomodate various types of equipment possibly used with the digitizer. Exaπple, if connected with pulse counters that, in turn, are connected with a polar to rectangular coordinate convertor, the output from the convertor may then be tapped and connected through pins 8 and 9 or 10 and 11. Then, the push button would be used to signal the converted Cartesian coordinate signals from the convertor. Another exaπple, if digitizer
10 is connected with a main-stage computer, the signals to the push
button switch would be conducted from the ccmputer.
5 With the arrangement shown, pins 1 and 2 supply pulse indications for the radius vertexes, and pins 6 and 7 supply those for
the polar angles. The radius vertexes and polar angles thereby
constituting the polar coordinates. Or, if desired, the user may
utilize only one encoder or each encoder separately. When.used as
10 such, they are signaled fcy switches 216a and 216b, not shown in
Figure 16 but depicted with Figure 1. In effect, the user has the
capability of signaling the electronics of digitizer 10 from any
desired location.
Figure 17 is a top view of the rack processor 544 used
15 to produce rack 30. It incorporates a lower die 546 and upper die
548. The dies sandwich, in a flattened manner, the cross-sectionally curved, stock material of rack 30 inserted therebetween and shown
emerging, perforated, as rack 30. Also incorporated are: A U-shaped guide 550" attached with dowel pins 552 to the upper die; a U-shaped

20 die guide 554 made adjustable with socket head screws 556 threaded
to the upper die; two die aligning taper pins 558; two die fastening
socket head screws 560; two die. separating socket head screws 562;
two punches 564 and 566; and a pivot pin 568 pivotable about axis
570 with a punch striking assembly (not shown in Figure 17) that is

25. rocked back and forth parallel with axis 572. The four holes 574
are to mount the processor.
The upper die is machined along the bottom length with a
convex cut having a radius equal with that of centerwheel 300 (Fig.
2) . The lower die is machined along the top length with a con- 30 cave cut having the same radius as the centerwheel plus the thickness of rack 30. The dies, guides, punches, and stop pin and cam body (to be explained) are all fabricated from tool steel and
The two U-shaped guides 550 and 554 align the stock material

35 milled die straight and usually hot rolled. Because minor width

CM?I_ discrepancies may exist with batches milled, U-shaped guide 554 mέy be adjusted so that each of the material's edges slide along a guide. In this manner, the material is guided in a straight line perpendicular to the dies. The material will not slide
through the dies unless the width is perfectly consistent and the material perfectly straight.
Figure 18 is a sectional view showing the arrangement for stop pin 576. The pin is generally positioned in the lower die and extends into a recess, provided in the upper die, preventing the pin from becoming damaged. When perforations are made by the punches, and the rack is advanced, the hold made by punch 564 is placed around the pin, and the hole's edge is abutted against it- Though stop pin 576 is press fitted, set screw 578 assures consistent positioning of the pin. The angle 580, between the centerline of punch 564 and that of the stop pin, corresponds with 360 degrees divided by the number of sprockets on the sprocket wheel used. It is noted that the angle described, although correct mathematically, is purely theoretical and for machining would be dependent upon no-tolerance conditions, impossible with reality.
From the example previously given with Figure 1, whereby rack 30 moves 3.60 inches per rotation of encoder shaft 34, the 3.60 inches would contain 18 perforations if the sprocket wheel shown in Figure 2 were used (18 sprockets) . With that example, the distance between hole centerlines would be .20 inches (3.60 inches divided by 18 holes) . Also, with the exaπple shown by Figure 12, whereby distance 484 can be 52.38 inches, the total length of rack 30 can easily be 8 feet (96.00 inches). With these examples, the number of perforations, in one row along a 96.00 inch rack, would be 480 holes (96.00 inches divided by .20 inches).
As with the above exaπple, 480 holes can be processed whereby no build-up of tolerances, for practical purposes, will exist between the first and last of the 480 holes consecutively punched. This is accomplished with stop pin 576 being removable and having a smaller tip as shown. In this manner, the distance between perforations is adjusted by removing the pin and honing,

OMPI lapping, and polishing its hardened radial abuttment surface. This procedure is continued until, when the pin is used, the first to last of the total perforations exhibit no elongation or tolerance when catenated with the sprockets. Usually, longer rack lengths are perforated. Then, with no tolerance fits in the longer lengths, the racks are cut into the lengths required with no tolerance fits being assured.
It may be visualized that different stop pins are used with rack processor 544. The various pins being adjusted for the various surface finish combinations of the rack. Example, where electrical conductors are embedded within the finishes of the fack additional finishes are required. Although each finish usually requires only about .0005 inches more thickness per side, the thickness is significant when processing the perforations to match the sprockets, therefore, an additional pin is required.
Figure 19. is a sectional view showing haw the U-shaped guide 554 is slid along the upper die and adjusted against the side of the material to be perforated. The upper and lower dies are machined with stepped, convex and concave cuts allowing the guides to abut the sides of the rack material, thereby, assuring the
material will not slip under the guides. Also, when U-shaped guide 554 is slid against the material, and screws 556 are tightened, because of the semi-circular sliding surface, the abutting edge of the guide will always remain perpendicular to the surface against which it is slid.
Figure 20 shows the alignment of the rack processor's components whereby their operational characteristics may be visualized. The top central portion.of upper die 548 is machined with a structure supporting the punch striking assembly generally indicated with the numeral 582, and machined with two bifurcations supporting the punches 564 and 566. Each punch is ring fitted with in-line holes vertically bored through upper die 548, and the punches are machined with ring grooves to fit with retaining rings 584. Compression springs 586 are placed within the bifurcations, the punches are inserted through, and retaining rings 584 are snapped into the ring grooves. Each tims a punch is depressed and released, it is returned by the pushing force of the spring.
Cam body 588 contains a bifurcation (only one side shown because of the sectional view) the branches of which extend on each side of the uppermost structure 582 machined with a hole to accept pivot pin 568. The bifurcation bracketed branches are machined with in-line matching holes. Pivot pin 568 is inserted therethrough and retained with screw 590. Striking assembly 582 is then pivotable about axis 570 (Fig. 17) to strike and depress the punches to a depth made adjustable by stop screws 592 locked with locking nuts 594 and pivoting on a line indicated with the numeral 598.
Each punch is tapered at its lower extremity and ring fitted with an in-line hole bored in lower die 546. The punch receiving hole in lower die 546 is opened to receive the material punched. The convex cut 600 in lower die 546 permits wires, embedded within the rack finishes, to pass therethrough.
Now, glancing at Figures 17, 18, 19 and 20, it may be visualized how rack 30 is processed. With upper die 548 removed, the material is radially bent toward its normally convex side around the convex surface of the upper die. The edges of the material are abutted with the U-shaped guides by adjusting guide 554. The material, upper die, and guides are oiled for lubricity, and the material length is slid between the guides, assuring a snug, sliding fit.
It is also assured the edges of the material are perfectly straight and its width is consistent.
The upper and lower dies are loosely connected with screws 560, leaving a space permitting the material to be inserted between the guides and radially bent around the upper die's convex surface.
Using wire snippers, a small punch, or the like, a V-cut or any
appropriate hole is made into the material, and the cut or hole is placed around stop pin 576. The dies are closed, using taper pins 558 for positioning, and held closed with screws 560 being tightened. The material is punched by alternately rocking back and forth handle 596 stopped by screws 592 adjusted to permit each punch to slightly penetrate into the lower die.

Die fastening screws 560 are then unthreaded and the dies ape separated. Experience has taught that mounting the rack processor upon a surface having cutouts, whereby the bottom of the taper pins 558 may gently be tapped, is best to effectively release the pins, in turn, separating the dies. In this manner, any wear, in the surfaces where the pins and dies contact, will be distributed evenly, therefore, the pins will always locate the dies closed in exactly the same position. The die .separating screws 562 are then threaded into the upper die and against the lower die, separ-ating them sufficiently to lift rack 30 from pin 576. The hole previously punched is placed around the pin and the edge abutted against the pin. The dies are again fastened, as previously described, and consecutive holes are punched, with the process explained, the length of the rack.
As outlined in this specification, if desired, only one row of perforations may be processed by using only one punch. Also, it may be visualized that cam body 588 may be fabricated to strike multiple punches arranged within the punch holding structure of the upper die. Also, if desired, similar rack processors may be pro-duced having punches separated by various distances and stop pins set at various degrees, thereby, making possible any combination of perforations within the rack.
The convex cut 600 may be, as well, a concave cut machined in upper die 548. Although the processing of rack 30 is preferred as described, the rack may be processed while being radially bent toward its concave surface. If processed as such, the resulting slight taper of the perforations will disappear with the "wearing" of the holes when mated with the sprockets.