United States Patent
`Eaton
`
`19
`
`(54) METHOD AND APPARATUS FOR
`MEASURING DIRECTION
`75 Inventor: Homer L. Eaton, Balboa, Calif.
`73 Assignee: Eaton-Leonard Corporation, Santa
`Ana, Calif.
`Apr. 18, 1974
`22 Filed:
`(21) Appl. No.: 461,881
`
`(56)
`
`52 U.S. Cl...... 235/151.3; 235/61.6 R; 33/174 PC;
`33/1 M, 33/1 N
`(51) Int. Cl.’........................ G01B 3/56; G01B 7/28
`58 Field of Search......... 33/1 M, 1 N, 1 PT, 1 CC,
`33/1 MP, 174 PC; 235/151.3, 61.6A, 61.6B,
`61.6R, 151.11, 92 DN, 151.32; 250/237
`References Cited
`UNITED STATES PATENTS
`ll 1966 Lemelson.............................. 33/143
`3,226,833
`4/1966 Albrecht et al............ 235/61.6 A X
`3,246,128
`8/1966 Anderson................... 235,161.6 A X
`3,267,251
`3,346,724 10/1967 Fuhremister et al............... 235,161.6
`3,410,956
`1/1968 Grossimon et al......... 235/61.6 A X
`3,515,888
`2/1970 Lewis.............
`. 235/151.34 X
`3,531,868 - 10/1970 Stevenson............................. 33/174
`3,567,950
`3/1971
`Meyer................................... 33/1 X
`3,571,934
`3/1971
`Buck..................................... 33/174
`3,601,590
`8/1971
`Norton....................... 235/151.11 X
`3,609,322
`9/1971
`Burnett et al.................. 235/151.11
`
`3,944,798
`(11)
`(45) Mar. 16, 1976
`
`Primary Examiner-Edward J. Wise
`
`ABSTRACT
`57
`Measurement of a vector inn space is accomplished by
`an articulated five axis probe carrying a working head
`that can be moved into a measuring position that has
`a known angular relation to an object to be measured.
`A plurality of pivotally interconnected links include a
`first link pivotally mounted to a work table and an end
`link that fixedly carries a working head having a V
`groove defined by four mutually spaced electrically
`conductive contact elements. For measurements made
`upon a tube having a number of bends, the working
`head is successively positioned in contact with the sev
`eral straight portions of the bent tube and the angles
`of the several links relative to adjacent links and rela
`tive to the work table are read out for each contact.
`When the working head is properly oriented with re
`spect to the tube, the electrical contacts enable read
`out of the several angles. These collectively define
`both the direction of the working head and its coordi
`nate position with respect to a reference coordinate
`system. The measured angles, together with lengths of
`the several links, are employed to calculate direction
`angles and coordinate position of vectors coaxial with
`each tube straight portion.
`47 Claims, 17 Drawing Figures
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`Sheet 1 of 6
`Sheet 1of6
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`3,944,798
`3,944,798
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`U.S. Fatent March 16, 1976
`U.S. Patent March 16, 1976
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`

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`U.S. Patent March 16,1976
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`U.S. Patent March 16, 1976
`U.S. Patent March 16, 1976
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`Sheet 3 of 6
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`UNY. 20
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`U.S. atent March 16, 1976
`U.S. Patent March 16,1976
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`Sheet 5 of 6
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`U.S. Patent March 16, 1976
`U.S. Patent. March 16,1976
`
`Sheet 6 of 6
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`3,944,798
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`5
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`55
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`3,944,798
`3,944,798
`2
`1.
`2
`1
`the straight portions (straights) of bent tubes to obtain
`the straight portions (straights) of bent tubes to obtain
`METHOD AND APPARATUS FOR MEASURING
`METHOD AND APPARATUS FOR MEASURING
`information for computation of machine bending com
`information for computation of machine bending com-
`mands or to obtain information for making various
`DRECTION
`DIRECTION
`mands or to obtain information for making various
`corrections to the tube machine bending commands.
`corrections to the tube machine bending commands.
`BACKGROUNDOFTHE INVENTION
`BACKGROUND OF THE INVENTION
`As shown in the British Pat. No. 1,329,708 to McMur
`Asshown in the British Pat. No. 1,329,708 to McMur-
`try, for example, bent tubes or pipes are made from
`1. Field of the Invention;
`1. Field of the Invention:
`try, for example, bent tubes or pipes are made from
`previously bent master pipes, employing a three-axis
`The present invention relates to measurement of
`previously bent master pipes, employing a three-axis
`The present invention. relates to measurement. of
`positions of objects, and more particularly concerns
`coordinate point measuring gauge which measures the
`coordinate point measuring gauge which measures the
`positions of objects, and more particularly concerns
`measurement of angular relations. Methods and appa
`position of two stations on each straight portion of the
`0 position of two stations on each straight portion of the
`measurement of angular relations. Methods and appa-
`_
`ratus of this invention may be employed for measure
`10
`tube in cartesian coordinates. The working head of this
`tube in cartesian coordinates. The working headofthis
`ratus of this invention may be employed for measure-
`ments of vectors, that is, the measurement of either one
`coordinate point measuring machine, much like the
`ments of vectors, that.is, the measurementof either one
`coordinate point measuring machine, much like the
`or both of the direction and coordinate position of a
`working head of other three axis measuring machines,
`or both of the direction and coordinate position of a
`working head of other three axis measuring machines,
`vector with respect to a reference system.
`will contact a point on the object to be measured but
`vector with respect to a reference system.
`will contact a point on the: object to be measured but
`2. Description of Prior Art
`does not attain any predetermined angular position or
`2. Description of Prior. Art
`does not attain any predetermined angular position or
`Position measuring instruments are employed in a
`15
`direction with respect to the object to be measured.
`Position measuring instruments are employed in a
`direction with respect to the object to be measured.
`wide variety of manufacturing, assembly and inspection
`Therefore, it is not possible to measure a vector or
`wide variety of manufacturing, assembly and inspection
`Therefore, it is not possible to measure a vector or
`operations. Generally, one or a number of different
`operations. Generally, one or a number of different
`direction without making several measurements.
`direction without making several measurements.
`points on an object to be measured are contacted by a
`Accordingly, it is an object of the present invention
`points on an object to be measured are contacted by a
`Accordingly, it is an object of the present invention
`probe that is movable with respect to a reference coor
`probe that is movable with respect to a reference coor-
`to enable measurement of direction of a line having a
`to enable measurementofdirection of a line having a
`20
`dinate system. Most commonly, the probe is mounted
`20
`dinate system. Most commonly, the probe is mounted
`fixed angular relation with respect to an object.
`fixed angular relation with respect to an object.
`for translational motion along three coordinate axes as,
`for translational motion along three coordinate axes as,
`SUMMARYOF THE INVENTION
`SUMMARY OF THE INVENTION
`for example, in the machines shown in U.S. Pat. Nos.
`for example, in the machines shown in U.S. Pat. Nos.
`3,774,311 to Stemple and 3,774,312 to Esch. These
`3,774,311 to Stemple and. 3,774,312 to Esch. These
`In carrying out the principles of the present invention
`In carrying out the principles of the present invention
`machines are of limited application because the size of
`machinesare of limited application because the size of
`in accordance with a preferred embodiment thereof,
`in accordance with a preferred embodiment thereof,
`25
`the machine itself determines the size of the object that
`25
`the machineitself determinesthesize of the object that
`direction of a line having a known angular relation to
`direction of a line having a known angular relation to
`may be measured, and costs increase rapidly with in
`may be measured, and costs increase rapidly with in-
`an object is measured by translating and angularly dis
`an object is measured by translating and angularly dis-
`creasing size. Because of the difficulties of maintaining
`creasing size. Because ofthe difficulties of maintaining
`placing a working head from a reference direction
`placing a working head from a reference direction
`precision of position and motion in traveling over long
`precision of position and motion in traveling over long
`about a plurality of axes of rotation until the working
`abouta plurality of axes of rotation until the working
`cantilevered elements, such devices must be exceed
`cantilevered elements, such devices must be exceed-
`head attains a measuring position having a predeter
`head attains a measuring position having a predeter-
`ingly massive for required rigidity. Further, they often
`30
`ingly massive for required rigidity..Further, they often
`mined angular relation to the object, and measuring the
`mined angular relation to the object, and measuring the
`require complex techniques such as the impressed vi
`require complex techniques such as the impressed vi-
`angular displacement of the working head about each
`angular displacement ‘of the working head about each
`bratory movement of the Esch patent or unique and
`bratory movement of the Esch patent or unique and
`of the axes. In a particular embodiment of the inven
`of the axes. In a particular embodiment of the inven-
`expensive bearing structures of the Stemple patent for
`expensive bearing structures of the Stemple patent for
`tion, a working head is adapted to be moved to a num
`tion, a working head is adapted to be moved to a num-
`obtaining desired precision. Even so, such machines
`obtaining desired precision. Even so, such machines
`ber of different angular positions by means of an articu
`berof different angular positions by meansof an articu-
`measure only a point, by determining its coordinates.
`35
`measure only a point, by determining its coordinates.
`lated arm mounting the head to a support and electrical
`lated arm.mounting the head to a support andelectrical
`Therefore, two separate and independent measure
`Therefore,
`two separate and independent measure- __
`signals are generated that collectively define the angu
`signals are-generated that collectively define the angu-
`ments at spaced points are needed for measuring direc
`ments at spaced points are needed for measuring direc-
`lar position of the working head with respect to a refer
`lar position of the working head with respecttoa refer-
`tion. Further, if the angular relation of a planar surface
`tion. Further, if the angularrelation of a planar surface
`ence direction. The angles of articulation of the articu
`ence direction. The angles of articulation of the articu-
`is to be measured, as for example, in determining a
`is ‘to be. measured, as for example, in determining a
`lated arm, together with lengths of the different sec
`40
`lated arm, together with lengths of the different sec-
`normal to a surface, machines of the prior art require
`40
`normal to a ‘surface, machines of the prior art require
`tions of the arm, are employed to calculate direction
`tions of the arm, are employed to calculate direction
`three separate measurements to define the plane.
`three separate measurements to define the plane.
`cosines of the working head itself with respect to a
`cosines of the working head itself with respect to a
`The U.S. Pat. to Bower, No. 2,906,179, describes a
`The U.S. Pat. to Bower, No. 2,906,179, describes a
`reference coordinate system. The arrangement also
`reference coordinate system. The arrangement also
`coordinate position measuring gauge comprising sev
`coordinate ‘position measuring gauge comprising sev-
`enables calculation of the coordinate position of a
`enables calculation of the coordinate position of a
`eral pivotally interconnected links of adjustable length.
`eral pivotally interconnectedlinks of adjustable length.
`point on a working head with respect to such reference
`45
`point on a working head with respect to such reference
`Although the Bower gauge is illustrated in connection
`45
`Although the Bower gauge isillustrated in connection
`coordinate system, or both such coordinate position
`coordinate system, or both such. coordinate: position
`with a closed loop control system for a machining tool,
`with a closed loop control system for a machining tool,
`and direction cosines.
`and direction cosines.
`it still can provide information defining solely the coor
`it still can provide information defining solely the coor-
`dinate position of a single point for any given measure
`dinate position ofa single point for any given measure-
`BRIEF DESCRIPTION OF THE DRAWINGs
`BRIEF DESCRIPTION OF THE DRAWINGS
`ment.
`ment.
`FIG. 1 is a perspective view of a five axis measuring
`FIG. lis a perspective view of a five axis measuring
`In the prior art of measuring instruments, optical
`50
`In the prior art. of measuring instruments, optical
`instrument constructed in accordance with the princi
`instrument constructed in accordance with the princi-
`devices have been employed for alignment of parts or,
`devices have been employed for alignment ofparts or, ,
`ples of the present invention;
`ples of the present invention;
`in effect, measuring direction. Thus, an autocollinator,
`FIG.2 is a diagram illustrating mathematics involved
`in effect, measuring direction. Thus, an autocollinator,
`FIG. 2 is a diagram illustrating mathematics involved
`such as shown in U.S. Pat. No. 3,024,365 to Smith etal
`such as shown in U.S. Pat. No. 3,024,365 to Smithet al
`in defining the measured vector in terms of a reference
`in defining the measured vector in terms of a reference
`has been employed for remote measurement of the
`has been employed for remote measurement of the
`coordinate system;
`coordinate system;
`orientation of a reflective surface, as used for example,
`orientation of a reflective surface,:as used for example,
`FIG. 3 is a section taken on line 3-3 of FIG. 1;
`FIG.3 is a section taken on line 3—3 of FIG. 1;
`in the alignment of an autonavigator. However, such
`in the alignment of an autonavigator.' However, such
`FIGS. 4, 5 and 6 are sections taken on lines 4-4,
`FIGS. 4, 5 and.6 are sections taken on lines 4—4,
`optical devices, like theodolites and precision transits,
`optical devices, like theodolites and precision transits,
`5-5, and 6-6 respectively of FIG. 3;
`5—5, and 6—-6 respectively of FIG. 3;
`require careful and exact positioning or setup to
`require careful: and exact. positioning or setup to
`FIG. 7 is a line section taken on line 7-7 of FIG. 1;
`achieve a predetermined and therefore, fixed position
`FIG.7 is.a line section taken on line 7—7 of FIG. 1;
`achieve a predetermined and therefore, fixed position
`FIG. 8 is a perspective view of one form of working
`FIG.8 is a perspective view of one form of working
`of alignment. For measurement of some second or
`of alignment. For measurement of some second or
`head;
`different direction such optical measuring or alignment
`head;
`different direction such optical measuring or alignment
`FIG. 9 is a section taken on line 9-9 of FIG.8;
`FIG.9 isa section taken on line 9—-9 of FIG. 8;
`devices must be moved and the precision instrument
`devices must be moved and the precision instrument
`FIG. 10 is a block diagram of an exemplary form of
`FIG. 10 is a block diagram of.an exemplary form of
`setup carefully re-established prior to a second mea
`setup carefully re-establishedprior to a second mea-
`surement.
`readout control of the angle sensors;
`readout control of the angle sensors;
`,
`Surement.
`65
`FIG. 11 is a block diagram showing further details of
`FIG. 11 is‘a block diagram showing further details of
`65
`In various types of tube bending machines, such as in
`In various types of tube bending machines, such as in
`angle sensor readout and computation;
`angle sensor readout and computation;
`that described in the U.S. Pat. to Hill No. 3, 145,756, or
`that described in the U.S. Pat. to Hill No. 3,145,756, or
`FIG. 12 illustrates a five-axis measuring instrument
`FIG. 12 illustrates a five-axis measuring instrument
`that described in the U.S. Pat.
`to -Hautau No.
`that described in the U.S. Pat. to Hautau No.
`having an optical working head;
`3,299,681, various measurements must be made upon
`having an optical working head;
`3,299,681, various measurements must be made upon
`
`60
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`5
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`3,944,798
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`3
`3
`4
`4
`FIG. 13 illustrates a measuring instrument with a
`FIG. 13 illustrates a measuring instrument with a
`can likewise be calculated. Calculations for lengths of
`can likewise be calculated. Calculations for lengths of
`replacable working head and six axes;
`strights and total length of the bent tube may likewise
`replacable working head and six axes;
`strights and total length of the bent tube maylikewise
`FIGS. 14 and 15 show a working head specifically
`FIGS. 14 and 15 show a working head specifically
`be made, as deemed necessary or desirable, from mea
`be made, as deemed necessary or desirable, from mea-
`adapted for measuring directions of planar surfaces;
`sured directions of straights and positions of tube ends.
`adapted for measuring directions of planar surfaces;
`sured directions of straights and positions of tube ends.
`and
`and
`According to the present invention, each of the vec
`According to the present invention, each of the vec-
`FIGS. 16 and 17 illustrate still other forms of working
`FIGS.16 and 17illustratestill other forms of working
`tors that coincides with a respective one of the tube
`tors that coincides with a respective one of the tube
`heads.
`heads.
`straights is fully and completely defined by a single
`straights is fully and completely defined by a single
`measurement, or, more specifically, by a single measur
`measurement, or, more specifically, by a single measur-
`GENERAL PRINCIPLES
`GENERAL PRINCIPLES
`ing operation, made with the illustrated five-axis mea
`ing operation, made with theillustrated five-axis mea-
`10
`The method and apparatus of the present invention 10
`suring instrument.
`The method and apparatus of the present invention
`suring instrument.
`,
`are applicable to measurement in a multitude of diverse
`The measuring instrument of FIG. 1 comprises a first
`are applicable to measurementin a multitude of diverse
`The measuring instrumentof FIG. 1 comprisesa first
`applications wherein it is desired to determine the di
`applications whereinit is desired to determine the di-
`link 20 mounted upon the table 12 for rotation about a
`link 20 mounted upon the table 12 for rotation about a
`rection and/or the position of the vector. Measurement
`rection and/or the position of the vector. Measurement
`first axis A. A second link 22 is pivotally connected to
`first axis A. A secondlink 22 is pivotally connected to
`of a vector may be employed in positioning and locat
`of a vector may be employed in positioning and locat-
`the first link 20 for rotation about a second axis B,
`the first link 20 for rotation about a second axis B,
`ing parts and devices used in assembly to ensure proper 15
`ing parts and devices used in assembly to ensure proper
`which is normal to axis A. A third link 24 is pivoted to
`which is normal to axis A. A third link 24 is pivoted to
`orientation. Measurement of a vector may be employed
`orientation. Measurementof a vector may be employed
`the second link 22 for rotation about a third axis C.
`the second link 22 for rotation about a third axis C.
`to originate manufacturing data by measuring direc
`to originate manufacturing data by measuring direc-
`Rotatably mounted within the third link 24 for rotation
`Rotatably mounted within thethird link 24 for rotation
`tions and positions of a sample shape such as a sample
`tions and positions of a sample shape suchas a sample
`about a fourth axis D, normal to axis C and coincident
`about a fourth axis D, normal to axis C and coincident
`bent pipe, for example. Direction measurements may
`bent pipe, for example. Direction measurements may
`with the axis of the third link 24, is a fourth link 26 (see
`with the axis of the third link 24,is a fourth link 26 (see
`20
`be employed for inspection of completed parts and may 20
`be employedfor inspection of completed parts and may
`FIG. 3). The fourth link 26 carries a fifth link 28 for
`FIG. 3). The fourth link 26 carries a fifth link 28 for
`be employed for making measurements on parts of
`be employed for making measurements on parts of
`rotation about a fifth axis E which is perpendicular to
`rotation about a fifth axis E which is perpendicular to
`varying linear, curved and planar shapes, and for com
`varying linear, curved and planar shapes, and for com-
`the fourth-axis D. Each of the second, third and fifth
`the fourth-axis D. Each of the second, third and fifth
`paring such measurements with pre-described mea
`paring such measurements with pre-described mea-
`links has nearly 360° of rotation relative to its adjacent
`links has nearly 360° ofrotation relative to its adjacent
`surements contained in a drawing or other computa
`link. The first link 22 is capable of a full 360° of rota
`surements contained in a drawing or other computa-
`link. The first link 22 is capable of a full 360° ofrota-
`25
`tion.
`tion with respect to the support and the fourth link is
`tion.
`25
`tion with respect to the support and the fourth link is
`An important application of the present invention, an
`also capable of a full 360° of rotation with respect to
`Animportant application of the present invention, an
`also capable of a full 360° of rotation with respect to
`application for which a working embodiment has been
`the third link, whereby an instrument of relatively small
`application for which a working embodimenthas been
`the third link, whereby aninstrumentofrelatively small
`initially employed, is the measurement of a sample bent
`initially employed, is the measurementof a sample bent
`dimensions is able to make measurements on objects of
`dimensionsis able to make measurements on objects of
`tube for the purpose of deriving data to enable the
`considerably greater dimensions.
`tube for the purpose of deriving data to enable the
`considerably greater dimensions.
`30
`subsequent bending of other tubes conforming to the 30
`subsequent bending of other tubes conforming to the
`Carried in a fixed orientation relative to and by the
`Carried in a fixed orientation relative to and by the
`sample. Accordingly, the invention will be described as
`fifth link 28 is a working head 30. The working head 30
`sample. Accordingly, the invention will be described as
`fifth link 28 is a working head 30. The working head 30
`embodied in this initial mechanization although it will
`is formed with a V-shaped groove that will readily
`embodied in this initial mechanization although it will
`is formed with a V-shaped groove that will readily
`be readily appreciated that principles of the invention
`straddle portions of the tube 10 to thereby define a
`be readily appreciated that principles of the invention
`straddle portions of the tube 10 to thereby define a
`may be readily employed in any of a number of applica
`predetermined angular relation between the working
`may be readily employed in any of a numberof applica-
`predetermined angular relation between the working
`tions whether or not specifically mentioned herein.
`tions whetheror not specifically mentioned herein.
`head and the direction that is to be measured. Thus, the
`head and thedirection that is to be measured. Thus, the
`Referring to FIG. 1, a sample bent tube 10 is fixedly
`working head 30, or more specifically, the tube engag
`Referring to FIG. 1, a sample bent tube 10 is fixedly
`working head 30, or more specifically, the tube engag-
`mounted to a support or work table 12 by means of a
`ing V-shaped groove thereof has a fixed orientation
`mounted to a support or. work table 12 by meansof a
`ing V-shaped groove thereof has a fixed orientation
`pair of clamps 14, 16 which are detachably but firmly
`pair of clamps 14, 16 which are detachably but firmly
`with respect to the fifth link 28 and when in contact
`with respect to the fifth link 28 and when in contact
`secured as by suction devices or the like (not shown) to
`secured as by suction devicesorthe like (not shown)to
`with the tube of which the direction is to be measured
`with the tube of which the direction is to be measured
`40
`any desired points on the table 12. Thus, the tube 10 40
`will extend in a direction that is precisely parallel to the
`any desired. points on the table 12. Thus, the tube 10
`will extend in a direction that is precisely parallel to the
`may be firmly mounted to the table in any one of a
`direction that is to be measured. The V-shaped groove
`may be firmly mounted to the table in any one of a
`direction that is to be measured. The V-shaped groove
`number of desired positions or orientations. For many
`numberof desired positions or orientations. For many
`may be said to define a direction axis of the head 30.
`may besaid to define a direction axis of the head 30.
`purposes, including inspection and manufacture, it is
`This direction axis is positioned at a predetermined
`purposes, including inspection and manufacture, it is
`This direction axis is positioned at. a predetermined
`desired to measure significant parameters of the tube
`desired to measure significant parameters of the tube
`angular relation to the direction that is to be measured
`angular relation to the direction that is to be measured
`45
`10. These parameters include the lengths of each tube 45
`for making a measurement of direction.
`10. These parameters include the lengths of each tube
`for making a measurementofdirection.
`straight portion (straight) S1, S2, S3, S4 and Ss, the angle
`straight portion (straight) S,, S., Ss, S, and S,, the angle
`For a complete set of measurements of the illustrated
`For a complete set of measurements oftheillustrated
`between adjacent straights, the total length of the tube
`tube 10, the working head 30 is moved manually into
`between adjacentstraights, the total length of the tube
`tube 10, the working head 30 is moved manually into
`from end to end, and the plane of each of the tube
`from end to end, and the plane of each of the tube
`five successive positions of contact with the tube
`five successive positions of contact with the tube
`bends B1, B, Ba and B. These parameters, after correc
`wherein the V-shaped groove straddles and is in
`bends B,, Bz, B; and B,. These parameters,after correc-
`wherein the V-shaped groove straddles and is.
`in
`50
`tion for various types of springback and other factors, 50
`tion for various types of springback and otherfactors,
`contact with the tube. Only one contact and one mea
`‘contact with the tube. Only one contact and one mea-
`may be employed to calculate commands for an auto
`may be employed to calculate commandsfor an auto-
`surement need be made on each stright. A first contact
`surement need be made oneachstright. A first contact
`matic tube bending machine (such as described in the
`is made with the working head straddling stright S at
`matic tube bending machine (such as described in the
`is made with the working head straddling stright S, at
`above mentioned patents) or may be fed to a computer
`its end. Merely positioning the working head in contact
`above mentioned patents) or may be fed to a computer
`its end. Merely positioning the working head in contact
`to check the accuracy of manufactured devices.
`with the tube automatically aligns the working head
`to check the accuracy of manufactured devices.
`with the tube automatically aligns the working head
`55
`According to principles of the present invention, 55
`direction axis parallel to the tube axis, and the direction
`According to principles of the present invention,
`direction axis parallel to the tube axis, and the direction
`information for these calculations may be acquired
`measurement is completed. The working head is then
`information for these calculations may be acquired
`measurement is completed. The working head is then
`accurately, rapidly, simply and with minimum possibil
`moved from the straight S and into contact succes
`accurately, rapidly, simply and with minimum possibil-
`moved from the straight S, and into contact succes-
`ity of error by means of a five axis measuring instru
`sively with any intermediate portion of the respective
`ity of error by means of a five axis measuring instru-
`sively with any intermediate portion of the respective
`mentillustrated in FIG. 1. It is known that the various
`ment illustrated in FIG. 1. It is known that the various
`straights S2, Sa and S4. The final measurement is contact
`straights S., S; and S,. The final measurementis contact
`60
`parameters desired to be defined in connection with 60
`with and alignment of the working head direction axis
`parameters desired to be defined in connection with
`with and alignment of the working head direction axis
`the sample tube 10, may be calculated from informa
`with the final straight Ss at the end portion thereof. For
`the sample tube 10, may be calculated from informa-
`with the final straight S, at the end portion thereof. For
`tion defining the direction of each tube straight S1, S2,
`measurement of the straights S2, S3 and S4, coordinate
`tion defining the direction of each tubestraight S,, S.,
`measurement of the straights S., S; and S,, coordinate
`Sa, S, Ss, and the position of the respective ends of the
`position of any point on the straight may be measured,
`S3, S4, Ss, and the position of the respective ends of the
`position of any point on the straight may be measured,.
`tube. For example, given data defining vectors coincid
`since only the direction of the tube axis and position of
`tube. For example, given data defining vectors coincid-
`since only the direction of the tube axis and position of
`65
`ing with the axes of the several tube strights, the angle 65
`a point on the axis are of interest or required for the
`ing with the axes of the several tube strights, the angle
`a point on the axis are of interest or required for the
`between adjacent ones of such vectors can readily be
`between adjacent ones of such vectors can readily be
`calculations. However, for measurements on the
`calculations. However,
`for measurements on the
`calculated in accordance with known principles of
`calculated in accordance with known principles of
`straights S and S2, both the direction of the axis of the
`straights S, and S., both the direction