Design and development of random function tracer for obtaining coordinates of points on contour map

Eskew, M. H., Jr.

Fuhrmeister, P. F.

English

NASA Technical Reports Server

REPLY TO 
ATTN OF: GP 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
WASHINGTON, D.C. 20546 
March 27, 1971 
TO : USI/Scientific & Technical Information Division 
Attention: Miss Winnie M. Morgan 
FROM r GP/Qffice of Assistant General 
Counsel for Patent Matters 
SUBJECT: Announcement of NASA-Owned 
U.S. Patents in STAR 
In accordance with the procedures contained in the Code GP 
to Code US1 memorandum on this subject, dated June 8 ,  1970, 
the attached NASA-owned U . S .  patent is being forwarded for 
abstracting and announcement in NASA STAR. 
The following information is provided: 
U.S. Patent No. : 3,346,724 
Corporate Source : Lanqley Research Center 
Supplementary 
Corporate Source 
NASA Patent Case No.: XLA-01401 
Gayle Parker 
Enclosure: 
Copy of Patent 
N 
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5 
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t I 
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5 (NASA CR OR TMX OR AD NUMBER) (CATEGORY) 
NASA-HQ 
https://ntrs.nasa.gov/search.jsp?R=19710011704 2020-03-17T02:56:04+00:00Z
Oct. 10, 1967 P. F. FUHRMEISTER ETAL 3,346,724 
FIG. 1 
24 
FIG. 2 
FIG. 5 
BY 
INVENTORS 
PAUL F. FUHRMEISTER 
MILNER H. ESKEW, JR. 
q.tt,.-q 
W & # K  
A T O R  T EYS
Oct. 10, 1967 P. F. FUHRMEISTER ETAL 3 ~ 3 ~ 6 , ~ ~ ~  
RANDOM FUNCTION TRACER 
Filed J u l y  15, 1964 2 Sheets-Sheet 2 
16 
FIG. 4 
BY 
INVENTORS 
PAUL F. FUHRMEISTER 
MILNER H. ESKEW, JR. 
3,346,724 United States Patent Office Patented Oct. 1967 
1 
3,346,724 
RANDOM FUNCTION TRACER 
Pad F. Fuhnneister, Wdliamsburg, and Milner H. Eskew, 
Jr., Hampton, Va., assignors to the United States of 
America as represented by the Administrator of the  
National Aeronautics and Space Administration 
Filed July 15, 1964, Ser. No. 382,976 
8 Claims. (CL 235-61.6) 
The invention described herein m>ay be manufactured 
and used by or for the Government of the United States 
of America for governmental purposes without the pay- 
ment of any royalties thereon or therefor. 
The invention relates generally to a random function 
tracer and more particularly concerns a device for obtain- 
ing indigital form the Cartesian coordinates of points on 
contour maps. 
The only method known by the inventors, at the time 
this invention was made, of obtaining Cartesian coordi- 
nates from contour maps was a method used with a stand- 
ard film reading device. This method is laborious and 
time-consuming. The present invention provides a random 
function tracer which utilizes a fast and simple method 
of obtaining Cartesian coordinates from contour maps. 
The tracer consists essentially of a tracing device, a digi- 
tizing and recording system, and a computer. The tracing 
device is similar to a standard drafting machine. It con- 
sists of a first arm with one of its end rotatably mounted 
on a table; a second arm with one of its ends rotatably 
attached to the other end of the first arm; a stylus at- 
tached to the free end of the second arm; a first potenti- 
ometer attached to the table and to the first arm to vary 
in accordance with the angle sweep of the first arm; and 
a second potentiometer attached to the first and second 
arms to vary in accordance with the angle of sweep of 
the second arm. The potentiometers are connected across 
a voltage source so that their outputs are voltages that 
are proportional to the angles of sweep of the two arms. 
The voltage outputs of the two potentiometers are applied 
to the digitizing and recording system which converts the 
voltages to digital form and then records them. The re- 
cordings are then applied to a computer which converts the 
recordings to Cartesian coordinates. 
It is therefore an object of this invention to provide a 
device for converting points on maps into Cartesian co- 
ordinates. 
Another object of this invention is to provide a device 
for tracing lines on a map and for converting these trac- 
ings into Cartesian coordinates. 
A further object of this invention is to provide a tnacing 
device that is more flexible than previous tracing devices. 
A still further object of this invention is to  provide a 
tracing device that utilizes certain features of a standard 
drafting machine. 
Other objects and [advantages of th is  invention will 
further become apparent hereinafter and in the drawings, 
in which: 
FIG. 1 is a plan view of the tracking device used by 
this invention; 
FIG. 2 is a side view of the tracing device shown in 
FIG. 1; 
FIG. 3 is a schematic and block diagram of the elec- 
trical components of this invention; 
FIG. 4 is a diagram used for the purpose of explaining 
how Cartesian coordinates are calculated from the outputs 
of the potentiometers in FIG. 1; land 
FIG. 5 is a diagram used for the purpose of explaining 
how an axis rotation may be performed in the computing 
operation. 
In describing the preferred embodiment of the invention 
illustrated in the drawings, specific terminology will be 
2 
resorted to for the sake of clarity. However, it is not in- 
tended to be limited to the specific terms so selected, and 
it is to be understood that oath specific term includes 
all technical equivalents which operate in a similar man- 
5 ner to accomplish a similar purpose. 
Turning now to the specific embodiment of the inven- 
tion selected for illustration in the drawings, the number 
11 in FIGS. 1 and 2 designates generally the tracing de- 
vice of this invention. Tracing device 11 consists essen- 
10 tially of a drafting table 12, a potentiometer 13, an arm 
14, a potentiometer 15, an (arm 16 and a stylus 17, Po- 
tentiometers 13 land 15 are high-precision single-turn 
potentiometers. In addition to producing outputs propor- 
tional to the angles through which the potentiometers are 
15 turned, potentiometers 13 and 15 also provide the pivot 
bearings for the tracer. Potentiometers 13 and 15 each 
consists of two sections that #are rotatable with respect 
to each other. The output of each potentiometer is pro- 
portional to the angle that one of its sections has been 
20 rotated with respect to its other section. Potentiometers 
13 and 15 are connected in an electrical circuit shown in 
FIG. 3. The electrical output of potentiometer 13 is across 
wires 18 and 19, and the electrical output of potentiom- 
eter 15 is ,across wires 20 and 21. 
The lower section of potentiometer 13 is attached to 
table 12 by any suitable means 22. Arm 14 is attached 
betwen the upper section of potentiometer 13 and the 
upper section of potentiometer 15 and is supported by a 
roller support 23. Arm 16 has one of its ends attached 
30 to the lower section of potentiometer 15 with a stylus 17 
(attached to its other end. The free end of arm 16 is slid- 
ably supported by a support 24. 
Arms 14 and 16 are each twenty-four inches long; 
however, they can be any length without departing from 
36 the scope of this invention. In operation potentiometer 
15 is free to  move and describe a first arc about potenti- 
ometer 13, and stylus 17 is free to move and describe B 
second arc about potentiometer 15. As stylus 17 traces 
lines on any map placed on table 12, potentiometer 13 
40 produces across wires 18 and 19 a voltage output directly 
proportional to the angle between arm 14 and the back 
of table 12, and potentiometer 15 produces across wires 
20 and 21 a voltage output directly proportional to the 
angle between arm 14 and arm 16. These two voltage out- 
45 puts are used to oalculate the Cartesian coordinates of 
points on the lines traced by istylus 17. 
Referring now to FIG. 3 there is shown the electrical 
components of this invention. Potentiometers 13 and 15 
5o are connected across a DC voltage source 25. Two equal 
resistom 26 and 27 are connected in series across poten- 
tiometer 13, and two equal resistors 28 and 29 are con- 
nected in series across potentiometer 15. The slider of PO- 
tentiometer 13 is connected through wire 18 to a digitizing 
and recording system 30, and the junction of resistors 
55 26 and 27 is connected through wire 19 to recorder 30. 
Recorder 31) is a digitizing and recording system, such as 
the Beckman 210 digitizing and recording system, which 
provides outputs in the form of digital magnetic tape. 
6o Consequently, the voltage between wires 18 and 19 is 
converted to digital readings on magnetic tape by re- 
corder 30. The slider of potentiometer 15 is connected 
through wire 20 to recorder 30, and the junction of resis- 
tors 28 and 29 is connected through wire 21 to recorder 30. 
The voltage between wires 20 and 21 is converted to digital 
65 readings on magnetic tape by recorder 30. The purpose 
of resistors 26-29 is to enable the sliders of potentiom- 
eters 13 and 15 to  produce negative as well as positive 
voltage outputs. 
The digital magnetic tape produced by recorder 30 is 
70 applied to  a computer 31 where the Cartesian coardi- 
nates are computed. Computer 31 can be a general pur- 
26 
3,346,724 
3 4 
pose computer such as the IBM 7070 or it can be a com- Random function tracers constructed in accordance with 
puter designed for this specific application. this invention may use synchros or shaft encoders to 
Since the digital magnetic tape produced by recorder replace the potentiometers for better precision and reli- 
30 contains data of angular measurements, geometric con- ability. Also the recording step done by recorder 30 could 
version are performed in computer 31 to convert angles 5 be eliminated by connecting digital shaft encoders directly 
to X-Y coordinates. The manner in which these conver- to  the computer. 
sions are made can best be understood by referring to the What is claimed is: 
diagram in FIG. 4. The arm 14 makes an angle G1 with 1. A random function tracer for tracing lines on a 
the back of table 12 and arm 16 makes an angle $2 with map and converting the tracings into Cartesian coordi- 
arm 14. The vector sum of arms 14 and 16 is a vector 32. nates comprising: a table with said map on the surface 
The angle between vector 32 and the back of table 12 is of the table; a first arm with one of its ends rotatably 
G ~ .  From the law of cosines: mounted to said table; a second arm with one of its 
C=(Aa+B2--AB cos $Iz) ?h ends rotatably attached to the other end of said first arm; means attached to the other end of said second 
Where A is the length of arm 14, B is the length of arm 15 arm for tracing Iines on said map; means for producing 
16, and C is the length of vector 32. The components of a first voltage proportional to the angle of rotation of 
vector 32 relative to table 12 may be calculated as said first arm; means for producing a second voltage 
follows: proportional to the angle of rotation of said second arm; 
and means for computing from said first and second 
20 voltages the Cartesian coordinates of points on the lines 
traced by said tracing means. 
2. A random function tracer in aocordance with claim 
1 wherein said means for producing a first voltage in- 
eludes a first potentiometer attached to said table and The x-y coordinates thus obtained may be 25 to said one end of said first arm such that the slider of to a map’s origin by subtracting the calculated x-y co- said first potentiometer varies as said first arm rotates ordinates of the origin from the calculated coordinates of 
all other locations. 
To eliminate the necessity of accurately aligning a map 
tracing operation with two ,recorded points on the base 
line of map 33. Assuming that the coordinates of these 
two points are XI, Y1, and Xz, Yz, then the angle align- 
ment error “a” of map 33 with respect to table 12 is: 
Y2 - Y1 a = tan-1 XZ-XI 
on said table, 
3. A random function tracer in accordance with claim 
wherein said for producing a second voltage 
arm such that the &der of said second potentiometer 
varies as said second arm rotates about the said other 
end of said first arm. 
lines on a 
map and converting the tracings into Cartesian coordi- 
nates comprising: a table with said map on the surface 
of the table: a first arm with one of its ends rotatable 
mounted to said table; a second arm with one of its ends 
means attached to the other end of said second arm for 
tracing lines on said map; means for producing a first 
voltage proportional to the angle of rotation of said 
first arm; means for producing a second voltage pro- 
45 portional to the angle of rotation of said second arm; 
means for digitizing and recording said first and second 
voltages and digital computing means for computing 
Thus all points on a tracing result in true x-y Cartesian coordinates from said recording. 
nates with respect to the map origin and base line. 5. A random function tracer for tracing lines and 
The operation of the invention will now be described 5o Converting the tracings into Cartesian coordinates COm- 
while referring to ~ G S .  1-3. A map that is to be traced prising: a table; a first arm with one of its ends rotatably 
is aligned and attached to the top surface of table 12. mounted to said table; a second arm with one of its ends 
Then the operator takes stylus 17 and traces the lines on rotatably attached to the other end of said first arm; 
the map, As &hese lines are traced potentiometers 13 and attached to the other end of said second arm 
15 vary causing the voltages produced between wires 18 55 for tracing lines on maps or drawings Placed on said 
and 19, and between wires 20 and 21 to vary. These volt. table: means for producing a first voltage proportional 
ages are applied to  recorder 30 where they are converted to the angle Of rotation of said first arm frorn a first 
into readings on digital magnetic tape. This tape is then reference Point; means for producing a second voltage 
to computer 31 w ~ c h  computes the Cartesian proportional to the angle Of rotation of said second arm 
wordinates of p i n t s  on the lines traced by stylus 17. 60 from a second reference point; and means connected 
me primary advantage of h i s  sandom function tracer to receive said first and second voltages for computing 
is the with which an osrator can trace lines on a Cartesian coordinates whereby said computing means 
map. It is possible to have a tracer whose stylus is free produces the Cartesian coordinates Of points on the l i e s  
to move in either of two mutually perpendicular direc- traced by said tracing means- 
tions. However, such a tracer would not be nearly 6. A random function tracer for tracing lines and pro- 
flexible as the tracer used in this invention. ducing electrical outputs indicative of the lines traced 
Pt is to  be understood that the form of the invention comprising: a table; a first arm with one Of its ends 
herewith shown and described i s  to be taken as a prefepred rotatably mounted to said table: a second arm with one 
embodiment. Various changes may be ma& in the shape, of its ends rotatably attached to the other end of said 
size and arrangement of parts. For example, equivalent 70 first arm; means attached to the other end of said second 
elements may be substituted for those illustrated and de- arm for tracing lines on maps or drawings placed on 
scribed herein, parts may be reversed, and certain features said table: means for producing a first electrical output 
of the invention may be utilized independently of the use proportional to the angle of rotation of said first arm; 
of other features, all without depamrting from the spirit or and means for producing an electrical output proportional 
scope of the invention as defined in the subjoined claims. 75 to the angle of rotation of said second arm whereby said 
337 in FIG. 5, with respect to 12, an 
axis rotation may be performed by preceding 30 includes a second potentiometer attached to said other end of said first arm and to said one end of said second 
35 4. A random function tracer for 
The components of veotor 32 relative to table B2 tal- 
ment error “a” to previously derived equations for X and 
Y as shown below: 
above may be corrected by the 40 rotatably attached to the other end of said first arm; 
65 
3,346,724 
5 6 
first and second electrical outputs are indicative of the 
lines traced by said tracing means. 
7. A random function tracer in accordance with claim 
6 wherein said means for oroducing a first electrical 
ometer varies as said second arm rotates about the said 
other end of said first arm. 
References Cited 
output includes a first potekiometer attached to said 6 
table and to said one end of said first arm such that the 
slider of said first potentiometer varies as said first arm 
rotates on said table. 
UNITED STATES PATENTS 
2,889,627 6/1959 Culpepper et al. _ _ _ _  178-18 X 
2,989,238 6/1961 Ford _ _ _ _ _ _ _ _ _ _ _ _ _ _  235-184 
8. A random function tracer in accordance claim 3,126,541 311964 Kern et -------- 178-18 x 
6 wherein said means for producing a second electrical 
output includes a second potentiometer attached to said 
other end of said first arm and to said one end of said 
second arm such that the slider of said second potenti- 
MALCOLM A. MORRISON, 
T. J. PAINTER, Assisllnnt Examiner. 


Random function tracer Patent

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