Patent Publication Number: US-3875468-A

Title: System for working cylinders along a line of intersection

Description:
United States Patent Yagi et al. 5] Apr. 1, 1975 [54] SYSTEM FOR WQRKING CYLINDERS 3,786.31 l/l974 sommeria et al 318/575 X ALONG A LINE OFINTERSECTION [75] Inventors: Takashi Yagi, lruma; Sadaaki Primary Examiner Dobifck Nanai; suuji Ouhara, both of Attorney, Agent, or FlrmFrtzpatrick, Cella, Harper Kitakyushu; Yukihiro Shirakawa, &amp; Sumo lruma, all of Japan [73] Assignee: Kahushiki Kaisha Yaskawa Denki ABSTRACT sflsakusho Fukuoka&#39;ken&#39; Japan in a system for working two cylinders (A and 8) along [22] Filed: Sept. 13, [973 a line of intersection thereof, a position (x) to which a working tool is driven in an axial direction of the cyl- [211 App! 396770 inder (A) to be worked is attained, as functions of an angle of rotation (wt) of the cylinder (A) in a direc- [30] Foreign Application Priorit Dat tion perpendicular to the axis thereof and an angle of Sept. |3 I972 Japan 47-92599 mined by shifting the angle 0f rotation (wt) to the cylinder (B), from a diameter (d) of the [52 us. Cl 318/575, 3l8/604, 266/23 .cyliflder (AL 3 diameter (D) cylinder (3) and a my Int. Cl. G05b 19/32 cmmecting (a) fmmed by axis 0f 5 ld f Search H 3 575 5 9 04. 2 23 ders (A and B) by a SlfiIiC electrical digital operation performing a servo-operation, or a feed-back compari- [56] References and son operation, of an equation d.sin wt D.sin a with UNITED STATES PATENTS the aid of digital differential analyzers.  
 3.44L8l7 4/1969 Eisengrcin ct al. H 318/575 10 Claims, l2 Drawing Figures numerical value sett mg CH&#39;CU i.  
 role of wOrkmg operutmn circuit sin all at cos wt operatio circuit Sing 6 operation CWCU it L operation circuit cos 9 cos 8 working tool driving CUlCUlDitflq section cos 9 sin 6 working tool driving 2l=d cos wi,  
 lbmnch plpe work l :mum plpe work pipe drwmq E; 2 iii 1 numerical value rate f setting circuit working d D 8 3 30 i i l 2 3 I operation circuit Sine operation circuit 6 9 wt 5&#34;] wt (:05 6  
 cos wt 6 operation circuit 8 F lmoltiplidcosw&#34; i L r f &#34;*Cntion S 9 working tool driving 5 I circ i 6l I colcuioting section L..rnoiti Iiinfriductiorfl L: who; d Cos wt 1 9 l circuit 62 ZQT COS i moltipii- Dms a i 1 C j c CD59 L 5| I c&#39; &#39;i ZHSTGOOSWHDSMCOSQ i i QL L Q l 222222 Dania i K I d 52 c&#39;rcult 4 working tool driving I i&#39; L operation circuit asm wt of Ct librunch pipe work dsin wt= D-sin (1 D&#39;NCOS a) i wt :rnoin pipe work pipe driving a y Salli 3 i]? 7 D 4 [digital F G integrator 42 register 40-- ZR R adder YtdX 4| output dX circuit Pi-fij eg&#39; te dYi r is r dY ZdY od d er Y dY adder 43 44 L register FIG. 5  
  ER R 4|- udder I output 1 dZ i circuit ID 45 j 1 hoif- .50 Y j integrator FIG. 6 r L Y all? Edy Z register dde Oddf u i 44 60 register circuit FIG. 9C  
 umeracol volue numerical value setting converter SYSTEM FOR WORKING CYLINDERS ALONG A LINE OF INTERSECTION BACKGROUND OF THE INVENTION This invention relates to a system comprising static electrical operation circuits for working cylinders along a line of intersection thereof, in which, when one of the cylinders is rotated in a direction perpendicular to the axis thereof, the line of intersection is obtained as a series of points lying in a direction of the axis by carrying out electrical operations with the aid of digital differential analyzers properly combined.  
  In this specification, the term working&#34; is defined as a process which is carried out by following the line of intersection of two cylinders. The process is for instance cutting, grinding, welding, blazing, forge welding, pressure welding and connecting of the two cylinders. The cylinder may be a cylinder made of wood or plastic material as well as a cylinder made of metal. In addition, the cylinder is not limited to a hollow cylinder like a pipe, that is, it may be a solid cylinder.  
  A system for working cylinders along a line of intersection thereof which comprises analog operation circuits with servo motors is known in the art. However, such a conventional system accompanies several difficulties as follows. An arc corresponding to an angle of rotation of one of two intersected cylinders in its axial direction increases with its diameter, the diameter being 1,000 mm or more, for instance. With increase of the are, a curve obtained by the analog operation of this conventional system is liable to become inaccurate.  
  Furthermore, since the conventional system is based on the analog operation, it suffers from drift due to the disturbance such as variation of supply voltages provided for various elements in the analog operation circuits. Accordingly, the maintenance and control of the conventional system are troublesome.  
  In addition, in the conventional system, since a servo operation is performed with the aid of motor elements, it is difficult to increase the rate of operation and accordingly the rate of working cylinders along a line of intersection thereof is obliged to be slow.  
 SUMMARY OF THE INVENTION Accordingly, it is a primary object of this invention to eliminate all of the difficulties accompanying a conventional system for working cylinders along a line of intersection thereof.  
  Another object of the invention is to provide a system for working cylinders along a line of intersection thereof in which non-linear elements such as multipliers are unnecessary for the operation of the system.  
  A further object of the invention is to provide a system for working cylinders along a line of intersection thereof in which generated functions such as a sine and cosine of an angle of rotation are not changed with time.  
  A still further object of the invention is to provide a system for working cylinders along a line of intersection thereof in which a number of cylinders having the same shape can be worked by setting numerical values only once.  
  A particular object of the invention is to provide a system for working cylinders along the line of intersection thereof in which a rate ofelectrical operation is on the order of micro-seconds.  
  The above objects and other objects of this invention have been achieved by the provision of a system for working cylinders along a line of thereof, which comprises: a numerical value setting section for setting a diameter (d) of a cylinder, a diameter (D) of another cylinder, a connecting angle (0) for connecting the two cylinders; a circuit for attaining sin 0 and cos 6; an operation circuit for attaining sin wt and cos on from an angle of rotation t fudt (where j wdt wt,  
 to 211-, and r is the time period of rotation); an operation circuit of a for carrying out servo-operation of a and D.A (cos a) so as to meet an equation d.sin w! D.sin a (where the angle of rotation wt of the first cylinder shifted on the second cylinder is represented by a); a multiplication circuit for operating d.cos wt cos 6, d.cos ml, D.cos a and D.cos d.cos 6; and a working tool driving calculating section for calculating a horizontal driving distance from the point of intersection of the axes of the two cylinders, all of the operation being electrically performed by integrators, half-integrators hereinafter referred to, register circuits and comparison circuits.  
  The nature, principle and utility of this invention will become more apparent from the following detailed description and the appended claims when read in conjunction with the accompanying drawings.  
 BRIEF DESCRIPTION OF THE DRAWINGS In the accompanying drawings:  
  FIGS. 1 and 2 are diagrams illustrating geometrical analysis of a main cylinder and a branch cylinder to be worked;  
  FIG. 3 is a block diagram illustrating the arrangement and function of a system for working cylinders along a line of intersection thereof according to this invention;  
  FIGS. 4, 5, 6 and 7 are also block diagrams respectively illustrating a digital integrator, a half-integrater hereinafter referred to, a register circuit and a comparator employed in a system for working cylinders along a line of intersection thereof according to the invention;  
  FIG. 7A is a circuit diagram illustrating in detail a comparison circuit shown in FIG. 7;  
  FIG. 8 is a graphical representation indicating a mode of a comparison output in a system for working cylinders along a line of intersection thereof according to the invention; and  
  FIGS. 9A, 9B and 9C together constitute a block diagram showing one preferred example of the system for working cylinders along a line of intersection thereof according to the invention.  
 DETAILED DESCRIPTION OF THE INVENTION As conducive to a full understanding of this invention, the following consideration of the geometrical data of a main cylinder, or main pipe, and a branch cylinder, or branch pipe, connected thereto is first presented with reference to FIGS. 1 and 2 which respectively illustrate the cases of working the branch cylinder and the main cylinder hole.  
  In FIG. 1, the axis (X) of a cylinder A to be worked makes an angle 6 with the axis of a cylinder B and an angle or rotation of the cylinder A is represented by w! (where w is the angular velocity and r is the time period of rotation). Strictly, the angle of rotation should be represented by Under these conditions, a distance or displacement it between a working point (not shown) and the origin can be represented as follows:  
 As is apparent from FIG. 1,  
 d.sinwr D.sin a and where dis the diameter of the cylinder A (with a radius r), D is the diameter of the cylinder B (with a radius R 2 r), and a is the angle of rotation obtained when the angle of rotation wt of the cylinder A is shifted to the cylinder 8, a point P being positioned on both of the cylinders A and B.  
  In FIG. 2, a main pipe is a cylinder A while a branch pipe connected to the main pipe is a cylinder B. In this case, a displacement it between a working point and the origin 0 is represented by the following equation (3).  
 cos 6 sin 6 sin 6 cos 6 sin 6 cos on D&#39; (3) sin 6 sin 0 FIG. 3 is a block diagram generally illustrating the functions of a system for working cylinders along a line of intersection thereof according to this invention, which comprises a numerical value setting section I. This section I sets numericals values such as the diameter d of the branch pipe, the diameter D of the main pipe, an angle 6 formed by the axes of the main and branch pipes and, if necessary, an offset 8 (not shown) between the main pipe and the branch pipe and produces outputs converted into serial binary numbers suitable for the operation of digital differential analyzers.  
  In this connection, it should be noted that this invention provides a system for working cylinders along a line of intersection formed by them in which the work is controlled by the operation of a digital differential analyzer. This operation is performed with the aid of clock pulses whose frequency is 1 MHz in a preferred example of the device according to the invention.  
  The system further comprises: a circuit 2 for obtaining from 6 sin 6 and cos 6 which will be used later; a circuit 3 for operating sin wt and cos cut from the angle of rotation (or by setting a rate of working with a rate of working setting device 30&#39;, a circuit 4 for carrying out the operation of equation (I) to produce its outputs D.A(cos a) and a; a circuit 5 for introducing cos 6 and cos 0=1 obtained in the circuit 2 through circuits 51 and 52 to an operation circuit 6, respectively; the operation circuit 6 performing the electrical operations of d.cos wtcos 6, d.cos wt, D.cos a and D.cos a.cos 6 in multiplication circuits 61 through 64; and switching means 7 adapted to switch the main pipe work and the branch pipe work (including the plane work).  
  The system further comprises: a section 8 for calculating the driving of a working tool, or performing the operations of addition in equations (2), (3) and (4) (hereinafter referred to as a working tool driving calculating section 8&#34;, when applicable); and an output section 9 having x pulses for (horizontally) driving the working tool and Y pulses for driving the pipes.  
  FIGS. 4 through 7 are block diagrams illustrating digital differential analyzer elements employed in this example.  
  FIG. 4 shows a digital integrator which comprises: adders 4!, 43 and 47; an R-register 42; a Y-register 44; a multiplication gate 45&#39;, and an output circuit, 46. In FIG. 4, reference symbols dY,, dY dY represent input components at the Y-register side and reference symbol Pi represents a signal for designating the scales of the input components. The multiplication gate 45 multiplies an output Y of the Y-register 44 by dx. The output circuit 46 produces as an output an overflow pulse d2 of the R-register 42.  
  Shown in FIG. 5 is a circuit 50, or a multiplication element (hereinafter referred to as a half-integrator circuit) which can be obtained by reducing the circuits relating to the Y-register from the circuits of FIG. 4. This half-integrator circuit 50 produces an output dZ =Y.dx.  
  As is apparent in comparison of FIG. 6 with FIGS. 4 and S, a register circuit shown in FIG. 6 can be obtained by reducing the circuit of FIG. 5 from that of FIG. 4.  
  Shown in FIG. 7 is a comparator comprising a comparison circuit 73. The circuit 73 operates to compare an input 71 (that is, a value in the R-register, which is positive at all times) with an input 72 (that is, a value in the Y-register) thus producing an output 74 to be applied to the output circuit 46.  
  As a result, in the output circuit 46, until an operational result in the present operation cycle (that is, in a period of time in which all the digits in the R-register and Yregister are subjected to comparison) is obtained, the operational result in the preceding operation cycle is maintained recorded and continues to produce its comparison output dZ.  
  The comparison circuit 73 described above is illustrated in detail in FIG. 7a, which comprises: AND (logical product) circuits 731, 732, and 734 through 739&#39;, an OR (logical sum) circuit 733; flip-flops FF, through FF and a delay circuit 7D. In FIG. 7a, circular symbols O provided on the input side of the AND circuits indicate that the logic of an input signal applied thereto is inverted. Furthermore, reference symbol Pn in FIG. 7a designates a synchronous pulse (or clock pulse) corresponding to 2&#34;, or the n-th digit, when the number of operational digits is n, and no synchronous pulse is applied for the operation of the digits other than the above-mentioned digit.  
  When the input 71 is greater than the input 72, the output of the AND circuit 739 turns ON and the output 74 is therefore in a mode of l. When the input 71 is smaller than the input 72, the output of the AND circuit 738 turns ON and the output 74 is therefore in a mode of+l. When the input 71 is equal to the input 72, both of the outputs of the AND circuits 738 and 739 turn OFF and the output 74 is in a mode of 0.  
  Shown in FIG. 8 are modes of the comparison output dZ in this embodiment. When the input 71 is, for instance, +7, the following three modes of comparison output dZ appear depending on the values of the input 72.  
 a. When the input 72 +6, d2 l.  
 b. When the input 72 +7, d2 0.  
 c. When the input 72 5 +8, d2 +1.  
  With reference to FIGv 9, there is shown one example of the system according to the invention, which comprises: a power source 900 of, for instance, DC +5 volts representing a logical signal I with a ground potential representing a logical signal a numerical value setting circuit 901 for setting a diameter D of a main pipe, a diameter d of a branch pipe and an angle 6 formed by the axes of the main and branch pipes (hereinafter referred to as &#34;a connecting angle 0&#34;) and a numerical value setting circuit 902 for setting operational constants K, through K,, these two circuits 901 and 902 forming a numerical value setting section 1 in FIG. 3;  
 3 switching means 903, 904 and 905&#39;, and a delay circuit 906 for delaying a logical signal output for I second for instance.  
  In FIG. 9, symbols( 0 marked on logical elements indicate that the logic of signals applied thereto is inverted as an inverter 921a inverts its input signal.  
  The system shown in FIG. 9 further comprises: AND (logical product) circuits 907, 921, 922 and 930 through 933; OR (logical sum) circuits 908 and 923 934 and 935&#39;, and comparators 909, 914, 924 and 936 such as shown in FIG. 7. Some of the inputs of these comparators are marked by symbol 9 which indicates that signs of the numerical values of inputs applied thereto are inverted.  
  The system further comprises: integrators 911, 912, 9l6, 917, 918.925, 926 and 927 as shown in FIG. 4; half-integrators 910, 915, 919, 920, 928, 929, 937 and 938 as shown in FIG. 5&#39;, register circuits 941 and 942 as shown in FIG. 6; a variable frequency oscillator 913 to which a frequency control signal is applied by a command signal (not shown) to control a rate of generating an angle of rotation wt, that is, a pipe driving speed; and digital-analog converters 943 and 944 for producing outputs (analog data) to drive a working tool and a pipe to be worked. The driving data of the tool and pipe are negatively fed back through a synchronization circuit 940 to the respective registers by pulse tachometer generators provided on the driving means of the tool and pipe.  
  A switch 904 is operated as follows. In the case of the main pipe hole work (equation 3 the switch 904 is operated so that output terminals 9041 and 9045 are respectively connected to input terminals 9042 and 9046. In the case of the branch pipe work (equation 2), the output terminals 904] and 9045 are respectively connected to input terminals 9043 and 9047. In the case of the plane work (equation 4), the output terminals 9041 and 9045 are respectively connected to input terminals 9044 and 9048.  
  The steps of working pipes, or cylinders, by the use of the system according to this invention will be described with reference again to FIG. 9. It will be seen from the foregoing and from the drawings that the various components 1-8 of FIG. 3 are shown in greater detail in the diagram of FIGS. 9A, 9B, and 9C. Thus it will be seen from the foregoing descrigtion and from the drawings that the numerical value setting circuit 1 of FIG. 3 comprises the components 901 and 902 of FIG. 9C. The operation circuit of FIG. 3 comprises the comparator 909 and integrators 910, 911 and 912 of FIG. 9A. The operation circuit 3 of FIG. 3 comprises the oscillator 913, the comparator 914, and the inegrators 915, 916 and 917 of FIG. 9A. The operation circuit of FIG. 3 comprises the integrator 918, the comparator 924 and the integrators 925, 926 and 927 of FIG. 9B. The introduction circuit 5 of FIG. 3 comprises the AND circuits 921, 922, 930 and 931 and the OR circuits 923 and 934 of FIG. 9B. The operation circuit 6 of FIG. 3 comprises the integrators 919, 920, 928 and 929 of FIG. 9B. The switching means 7 of FIG. 3 comprises the switch 904, including its subcomponents 9042-9048 of FIG. 913. Finally, the working tool driving calculating section 8 of FIG. 3 comprises the comparator 936 of FIG. 9B and the integrators 937 and 938 of FIG. 9C.  
 Step I A switch 903 (SW-1) is thrown to the position RUN.  
 Step 2 Numerical data sin 0 and cos 6 are calculated from a connecting angle 0 in initial approximately one second. For this purpose, pulses corresponding to A0 and as many as necessary for the operation in the integrators 911 and 912 are generated by the comparator 909 and the half-integrator 910.  
  The connecting an le 0 indicated by a decimal degree in the form of CIELDEI&#34; (30.00150.00) is set in the R-register 42 in the comparator (FIG. 7) operating in a servo-mode as indicated in FIG. 8. In order to regulate the relationship between the value of the connecting angle 0 and the number of pulses corresponding to A0 (hereinafter referred to as pulses A6, when applicable), the half-integrator 910 is provided in the feed-back loop of the comparator 909, while a serial biriary number which is a coefficient (constant) k, for the conversion of a numerical value is applied through the numerical value setting section 902 to the R-register 42 of the half-integrator 910 so as to satisfy the following equation (5).  
  (51 For instance, when 6 90.00 is set in the R-register, the value of the constant k can be determined so that values of sin 6 and cos 9 turn from those when 0 0 to those when 6 In other word, in the case where the register has 16 digits, its 16th digit being provided for signs, the value of the constant k, can be determined so that a content in the register of the integrator 91] turns from Olllllllllllllll to 0000000000000000 while that in the register of the integrator 912 turns from 0000000000000000 to Olllllllllllllll.  
 Step 3 The values of cos 6 and sin 9 are calculated by the use of the pulses A6 in the integrators 911 and 912, respectively. Calculation of these values is made in advance for the purpose of using them as constant in the operation which will be described later. Accordingly, in the calculation, an output l from the delay circuit 906 is not applied to the comparators 924 and 936, the read gates (not shown) of which are therefore not opened so that an erroneous comparison operation is not carried out.  
 Step 4 Angles of rotation sin wt and cos m! are calculated in correspondence to a rotation of the branch pipe. In this connection, it should be noted that the rotation of the branch pipe represents an angle of rotation on required for the work and is not limited only to an 2n 360. The angle of rotation necessary for this operation is read in the register of the comparator 914 in advance by actually rotating the branch pipe. Then, pulses corresponding to A (wt) (hereinafter referred to as pulses Amt), when applicable) as much as necessary for sin w! and cos ml are generated by the comparator 914 and the half-integrator 915. Determination of a constant k is carried out in the same manner as in the calculation of cos 6 and sin 6 by the use of pulses A9.  
  By regulating an output frequency of the variable frequency oscillator 913, a rate of driving a working tool and that of driving a pipe can be externally controlled to change with a rate of the operation. The output of the variable frequency oscillator 913 controls a rate of generation of Atwt) pulses.  
  With the aid of the pulses A(wt) thus generated, cos wt and sin mt are calculated in the integrators 916 and 917, respectively.  
 Step 5 The following servo-operation, or feed-back comparison operation, is carried out to obtain an angle of rotation a which satisfies equation (1). A high frequency output is produced by the comparator 924 until the difference between two inputs in a digital servo circuit which is provided with the comparator 924 operating in a servo mode has become zero, that is, the difference between an output d.A(sin wt) of the integrator 918 and an output D.A(sinwt) of the integrator 927 has become zero, This high frequency output is pulses corresponding to Act (hereinafter referred as to pulses Aa, when applicable) In this operation, the diameter d of the branch pipe is written through the adders 47 and 43 into the Y register 44 in the integrator 918 and the diameter d thus written is introduced to the half-integrator 919. This is to use the half-integrator 919 as an element for storing the diameter d.  
  Similarly as described above, the diameter D of the main pipe is introduced through the integrator 927 to the half-integrator 928.  
 Step 6 With the aid of the pulses A0: thus produced, sin a and cos a are calculated by the integrators 925 and 926, respectively. The generation of the pulses Au: and the calculation of sin a and cos a are carried out whenever the output pulse d.A(sinw!) from the comparator 918 is applied to the integrator 924. The pulses A0: thus generated at high speeds carry out a servo operation so as to change a value in the Y-register 44 of the comparator 924 into zero.  
  The fact that the value in the Y-register of the comparator 924 is kept zero at all times means that an integral value of the outputs of the integrators 918 and 927 applied to the comparator 924 is zero, that is, the following relationship is established between dsincut and Dsina.  
  Therefore, d.sinmt D.sina. This is the same as equation (1 Step 7 By using an output of the integrator 917 as an input dx of the half-integrator 919, a multiplication of d.A(cosmt) is carried out. Similarly, by using an output of the integrator 926 as an input dx of the halfintegrator 928, a multiplication of D,A(cos a) is carried out.  
 Step 8 The switch 904 for changing the modes of work is actuated to set a mode of work as was described previously, whereby the inputs of the Y-registers in the halfintegrators 920 and 929 are switched through the respective logical elements (gates) and the multiplica tions necessary for the respective modes of work are carried out.  
 Table 1 Modes of Plane Branch Main work work pipe pipe work hole work Y-rcgister of half-integrator 920 cos 6 cos 6 l Y-rcgistcr of half-integrator 929 O 1 cos 6 01llllllllllllll.lncaseof0showninTable l,an input signal to the half-integrator 929 is inhibited.  
 Step 9 An operation for driving the working tool in a designated mode of work is carried out. A high frequency output is generated by the comparator 936 until the sum of three inputs of a digital servo circuit with the comparator 936 operating in a servo mode, that is, the sum of the values in a column in the following Table 2 has become zero in a mode of work designated.  
 Table 2 Modes of Plano Branch Main work work pipe pipe hole work work Outputs Output of halfdMcos wrl ddtcos on) claims ml] integrator cos 0 cos 8 920 Output Table 2-Continued Modes of Plane Branch Main work work pipe pipe hole work work Outputs of halfintegrator D&#39;A(cos a) D&#39;Atcos a) 929 cos 9 Output of lialf- Arsin 0 -A\-sin 6 Ar-sin 0 93 The product of this high frequency output and a constant k is a working tool driving command pulse Ax.  
 Step l0 The output pulse AX from the comparator 936 is mul tiplied by sin 0 in the half-integrator 937 the value of this sin 9 has been calculated in step 3 and stored in the Y-resister 44 of the integrator 912 as was described previously. This operation is carried out whenever the output from the halfintegrator 920 or 929 is applied to the comparator 936, and the output pulse Ax therefrom carries out a servo-operation so as to change the value stored in the Y-register 44 of the comparator 936 into zero.  
  The fact that the value in the Y-register 44 of the comparator 936 is thus zeroed, means that an integral value of the inputs applied to the comparator 936 from the half-integrators 920, 929 and 937 is zero. That is, in the case of the plane work in the case of the branch pipe work &#39;Mcos w t-ts a P, -A(cos 01) Am a} 0 n Sm 9 us ,and  
 in the case of the main piple hole work S Atcos m!) g- -Atcos a)-cos B At-sin 6} 0 l therefor 2.\ (1&#39; sin 9 fits to! D-cos orcot H The pulse Ax obtained by each of these operation is subjected to a numerical value conversion for the operation of the tool driving system, that is, it is multiplied by the constant k in the half-integrator 938, and the product of this multiplication is applied to the register 94].  
 Step ll On the other hand, the operation for driving the tool is carried out in a designated mode of work. The following outputs are applied, as an input d.\&#39;, to the halfintegrator 939 through the switching gate separately according to the modes of work, as indicated in Table 3.  
 Table 3 Mode of work Plane Branch Main pip work pipe work hole work Output Value Aw! Am! a Comparators from which the output 914 914 924 is produced This output is subjected to a numerical value conversion for the operation of the pipe driving system, that is, it is multiplied by a constant k, in the half-integrator 939, which produces an output pulse AY. This output pulse AY is introduced to the register 942.  
 Step 12 The output pulse Ax for driving the working tool and the output pulse AY for driving the pipe, thus produced, are respectively applied, as command signals, to the registers 941 and 942. In this operation, feed-back pulses from pulse tachometer generators connected to a working tool driving motor (not shown) and a pipe driving motor (not shown) are fed back to the registers 941 and 942 through the synchronization circuit 940. The registers 941 and 942 are difference-storing registers each of which stores a difference between a command value and a present available value. This difference in value is introduced through an output circuit for analog conversion (not shown) to the digital-analog converters 943 and 944, which produce analog difference signals. By these analog difference signals the working tool and pipe are respectively driven, thereby drawing a curve of intersection of solids so as to work the pipe as specified.  
  In addition, the rate of working a pipe can be arbitrarily regulated, according to this invention, in the following manner. The positive and negative output lines of the registers 943 and 944 are connected to the logical sum circuit 945 where the logical sum of the square roots of the squares of the pulses AX and AY are obtained. This logical sum output from the circuit 945 and an output pulse from the variable frequency generator 946 arbitrarily determining the rate of working the pipe are applied to the comparator 947, to the register (R) of which 1 has been applied in advance.  
  Under these conditions if two output pulses or more are produced by the logical sum circuit 945 during the period of the output pulse of the generator 946, the comparator 947 produces an output to stop the electrical operations in the comparators 914, 924 and 936. The next output pulse from the generator 946 causes the comparator 947 to stop producing its output whereby the electrical operation of the comparators 914, 924 and 936 is carried out again. Thus, the outputs of the registers 94] and 942 are regulated by the period of the output pulse of the generator 946.  
  As is obvious from the above detailed description, in this invention, it is unnecessary to particularly provide non-linear elements such as multipliers, and generated functions such as sin 6 and cos 0 are not changed with time. Furthermore, numerical values for controlling the work can be readily stored. Therefore, a number of pipes having the same shape can be worked by setting such numerical values only once. In addition, in this invention, a value of (accuracy) x (a rate of operation) is constant the regulation of this value depends on the number of digits in the registers built in the digital differential analyzer. However, since the rate of operation is on the order of micro-seconds, it is considerably su perior to that in the conventional device employing a servo-motor.  
 What we claim is:  
  l in a system for working along a line of intersection between first and second cylinders whose axes intersect, the combination of means adjustable to produce electrical signals (d), (D), and (6) which represent, respectively, the diameters of the first and second cylinders and the angle of intersection of their axes, means responsive to the rotation of the first cylinder about its axis to produce a corresponding electrical signal (out), an electrical oscillator operative to generate a series of accurately spaced electrical impulses, first integrator means connected to receive said electrical impulses and said electrical signal (an) and to produce delta modulation pulses representative of the values (A sin wt) and (A cos wt), second integrator means connected to receive the electrical signal (d) and the delta modulation pulses (A sin wt) and to produce delta modulation pulses (d.A sin w!) in response thereto, third integrator means connected to receive the electrical signal (D) and feedback signals, and to produce delta modulation pulses (D.A sin a), first comparator means connected to receive the delta modulation pulses (d.A sin wt) on the one hand and the delta modulation pulses (DA sin a) on the other hand, the output of said first comparator being connected to supply said feedback signals to said third integrator means for operating same in a servo mode to produce a delta modulation signal (D.A sin a) where (a) is the angle of rotation obtained when the angle of rotation (wt) of the first cylinder is shifted onto the second cylinder, second comparator means connected to receive the delta modulated signals and to produce working tool driving signals in response thereto and means for driving a working tool in response to said working tool driving signals.  
  2. A system according to claim 1 wherein said second comparator means comprises fourth integrator means comprising a third comparator connected to receive the electrical signals (6) and a comparator feedback signal, said third comparator being operative to produce delta modulated pulses (A6), a half integrator and first and second integrators, said half integrator being connected to receive said delta modulated pulses (A6) and to produce said comparator feedback signals, a feedback loop connecting the output of said half integrator to an input of said third comparator, means connecting the output of said third comparator to said first and second integrators, said second integrator being operative to produce signals corresponding to the value (sin in response to the application thereto of delta modulated pulses corresponding to (A sin 6) and (A6) and operative further to produce a feedback output comprising delta modulated pulses corresponding to the alue (-A cos 6), a feedback loop connecting the feedback output of the second integrator to the first integrator, said first integrator being operative to produce signals corresponding to the value (cos 6) in response to the application thereto of said feedback output and said delta modulated pulses corresponding to (A 6), said first integrator being operative to produce further output signals comprising delta modulated pulses corresponding to the value (A sin 6) and means for applying said further output signals from said first integrator to said second integrator.  
  3. A system according to claim 1 wherein said second comparator means comprises fourth integrator means connected to receive the electrical signals (6) and to produce signals representative of the values (sin 6) and (cos 6), fifth integrator means connected to said third integrator means to receive therefrom delta modulation pulses (D.A sin a) and to produce signals representative of the value (D. A cos a), sixth integrator means connected to said second integrator means to receive therefrom delta modulation pulses (d.A sin wt) and to produce signals representative of the value (d.A cos wt), a comparator connected to receive the outputs of said fifth and sixth integrator means and a further feedback signal and to produce a comparator output signal corresponding to the comparison of said outputs of said fifth and sixth integrator means and said further feedback signal, seventh integrator means connected to receive said comparator output signal and the signal (sin 6) from said fourth integrator means and to produce said further feedback signal, eighth integrator means also connected to receive said comparator output signal and to produce a delta modulated driving command signal, a register connected to receive said delta modulated command signal and working tool driving means connected to receive outputs from said register.  
  4. A system according to claim 3 wherein said sixth integrator means is also connected to the output of said fourth integrator means to receive signals representative of the value (cos 6) and is operable to produce output signals representative of the value (d.A cos mt cos 6) wherein said fifth integrator means is also connected to receive a signal representative of the value (l wherein there is provided a ninth integrator means con nected to receive said electrical signal (wt), said ninth integrator means being operative to produce a delta modulated driving command signal corresponding to rotation of the first cylinder.  
  5. A system according to claim 3 wherein said sixth integrator means is also connected to receive a signal representative of the value l wherein said fifth integrator means is also connected to the output of said fourth integrator means to receive signals representative of the value (cos 6) and is operable to produce signals representative of the value (D.A cos 0:. cos 6) and wherein there is provided a ninth integrator means connected to receive delta modulated outputs corresponding to the value (Act) from said first comparator and to produce a delta modulated driving command signal corresponding to rotation of the second cylinder.  
  6. A system according to claim 3 wherein said sixth integrator means is also connected to the output of said fourth integrator means to receive signals representative of the value (cos 6) and is operable to produce output signals representative of the value (d.A cos wt cos 6), wherein said fifth integrator means is also connected to receive a signal representative of the value (0) and to produce an output of value zero in response thereto, and wherein there is provided a ninth integrator means connected to receive the delta modulated electrical signals (Ami), said ninth integrator means being operative to produce a delta modulated driving command signal corresponding to rotation of the first cylinder.  
  7. A system according to claim 3 wherein there is provided an adjustable frequency oscillator operable to 8. A system according to claim 7 wherein said control comparator is connected to receive first outputs from said register.  
  9. A system according to claim 8 wherein said control comparator is connected to receive additional outputs from a further register connected to process signals corresponding to the rotation of the first cylinder about its axis.  
  10. A system according to claim 9 wherein said first and additional outputs are applied to said control comparator via a logical sum circuit.  
 Bl i