The Pantograph and Its Applicationto Stereocompilation*

B. THOMAS HOPKINS,

U. S. Geological Survey,

Arlington, Va.

ABSTRACT: This paper presents a history of the development, by theGeological Survey, of a reduction pantograph for use with stereoplotti'nginstruments of the double-projection type. A description of the desirablefeatures of a variable-ratio pantograph for use with the Kelsh Plotter,ER-55 projectors, or Multiplex, is given. The advantages derived fromthe use of a reduction pantograph in map compilation are discussed. Abrief description of compilation techniques, insofar as they dijJer fromthose employed in compilation at model scale, is presented. Checking andcalibrating methods are discussed and a practical method utilizing rela­tively simple equipment is suggested.

HISTORY OF DEVELOPMENT

THE NEED FOR VARIABLE-RATIO

PANTOGRAPHS

realization of an instrument meeting therequired accuracy was accomplished at thecost of considerable development effort.

The desirability of compilation scalessmaller than the natural stereomodelscales, for the preraration of small- andmedium-scale topographic maps by stereo­plotting instruments, has long been recog­nized. Such scale reductions result in econ­omy during compilation and in the succes­sive steps leading to reproduction. Lack ofan adequate means of reducing the naturalmodel scale to a more desirable compila­tion scale limited the economy of opera­tion and versatility of double-projectionstereoplotters. The development of theprecision variable-ratio pantographcoupled with the techniques of compilationscribing have placed the newer double­projection stereoplotters in competitionwith the heavy plotters in many ways.

INTRODUCTION

T HE pantograph is an instrument forthe mechanical copying of diagrams,

drawings, or similar information, at ascale other than that of the original.Specifically, in its adaptation to stereo­plotting instruments, it reduces the scale ofthe stereomodel to a more desirable scalefor compilation.

The pantograph in current use in theGeological Survey, on stereoplotters of thedouble-projection type employing theanaglyphic principle, is a precision varia­ble-ratio instrument with graduated armsproviding a range of reduction ratios from1.45: to 6.5: 1 (Figure 1). It is fully sup­ported from the king-post by a cantilevermain arm, with provision in the design ofthe king-post for levelling the pantograph.Other refinements are a track providing formovement of the king-post in the y-direc­tion, low-friction bearings for easy move­ment, a magnetic pencil lift, and illumina­tion of the pencil point. Pantographs ofthis type mounted on double-projectionstereoplotters have increased the versa-tility of these instruments to a point ap- The development of a reducing panto-proaching that of the heavy plotters. graph specifically for the double-projec-

The problems involved in developing a tion type stereoplotter, employing thevariable-ratio pantograph of acceptable anaglyphic principle, was an outgrowthprecision should not be underestimated. of the introduction of the Kelsh plotterAlthough apparently simple in theory, the in the Geological Survey. Compilation at

* Presented at the 22nd Annual Meeting, American Society of Photogrammetry, Washington,D. c., March 23, 1956. Publication authorized by the Director, U. S. Geological Survey.

140

THE PANTOGRAPH AND ITS APPLICATION TO STEREOCOMPILATION 141

FIG. 1. The variable ratio pantograph.

the natural Kelsh model scale proved tobe economically impractical, and a fixed­ratio pantograph, providing a reduction of2: 1, was mounted on an auxiliary table atthe side of the instrument. This experimen tconclusively demonstrated that a panto­graph mounted on a double-projectionstereoplotter was both feasible and eco­nomically desirable. Succeeding models ofthe Kelsh plotter were designed to providea working surface beneath the pantographand a suitable mount for the king-post.Further experience indicated the desira­bility of a common compilation scale, atany given flight height, for Kelsh andMultiplex plotters so that the instrumentscould be utilized in combination.

A number of Kelsh plotters equippedwith pantographs providing a fixed ratioof 2.1:1 were put into operation in 1952.The fixed-ratio pantograph proved satis­factory for its original objectives; however,it soon became evident that this type ofpantograph limited the versatility of anystereoplotting instru men t.

During this period the technique ofcompilation by scribing on coated plasticsheets was developed. This medium provedideally suited to the compilation of fullquadrangle maps at or near publicationscales. In order to exploit this techniquefully it was evident that a need existed fora precision variable-ratio pan tograph whichcould be mounted on any of the double­projection stereoplotters in use in theGeological Survey. Much of the basic in­formation for the development of thispantograph was derived from experiencegained with the fixed-ratio pantographs.This experience, and a study of the currentand foreseeable trends in C-factors fordou ble-projection stereoplotters, indicatedthat a range of reduction ratios from 1.45: 1to 6.5 :1 would be adequate. An arm length

of 720 mm. was selected as being of suf­ficient length to reach all parts of the stereo­model and yet allow freedom of motionwithin the supporting frame of any of theplotters. This pantograph proved to bevery satisfactory for ER-55, Kelsh, andMultiplex plotters utilizing vertical pho­tography.

Experience with this pantograph in com­piling from convergent photography indi­cated that a longer pantograph to accom­modate the wider air base would be desir­able. In anticipation of the increasing useof convergent photography for stereomap­ping, current and future Geological Surveycontracts will specify a pantograph with anarm length of 840 mm.

ApPLICATION

Currently all of the Geological SurveyKelsh plotters, and many of the ER-55 andMultiplex plotters, are equipped with the720 mm. variable-ratio pantograph. A few840 mm. pantographs have been deliveredand are mounted on ER-55 plotters com­piling from convergent photography. It isintended that all double-projection stereo­plotters in the Geological Survey will ulti­mately be equipped with precision varia­ble-ratio pantographs of either the 720mm. or 840 mm. type.

A considerable amount of stereocompila­tion at or near publication scales has beenaccomplished with these pantograph­equipped plotters, and this backlog of ex­perience has indicated the many benefitsaccruing from their use. Some of the spe­cific benefits are as follows:

An increase in production rates due inpart to compiling at smaller scales, and inpart to the technique of compilation scrib­ing on dimensionally stable coated plasticbases.

The variable-ratio pantograph permits

142 PHOTOGRAMMETRIC ENGINEERING

uniform base-sheet scales, at a given flightheight, irrespective of plotting instruments.

, This uniformity simplifies base-sheet prep­aration and edge joining, and allowsgreater flexibility in apportioning projectsamong various plotters. Uniformity ofbase-sheet scales within a fairly largerange of flight heights is also possible.

Stereotemplets may be plotted, from thestereomodel, at the scale of the base, sheetthrough the medium of the variable-ratiopantograph, thus simplifying the problemof providing aerotriangulation from pho-tography at varying scales. .

The reduction of large-scale manuscnptsto suitable scales for field-completion sur­veys and for color-separation drafting,may be eliminated in many cases.

The slight but inevitable scale differencesthat accompany the mosaicing of small­scale negatives of large-scale paper manu­scripts to a quadrangle projection are elim­inated.

The insignificance of minor details on theground which may appear map-worthy atthe model scale is easily detected at the re­duced compilation scale. Greater uni­formity of topographic expression shouldresult.

CALIBRATION

The calibration of a variable-ratio panto­graph can be analyzed mathematically.!Fidelity of reproduction of a geometricfigure may also be used as a calibrationcheck. Precise calibration is possible withthese methods; however, several trialsmay be necessary to produce the desiredresults. The Geological Survey has de­veloped the straight-line calibration checkthat is relatively simple and can be per­formed by the stereocompiler on a jig atthe stereoplotting instrument.

A study of the geometry of the panto­graph reveals that the following relation­ships are required for faithful reproduction:

(1) The positions of the king-post K,the drawing point E, and the tracingpoint T, Figure 2, projected ortho­graphically onto the working sur­face, must lie in a straight line in alloperating positions, and at all ratiosettings.

(2) The ratio of KE to KT, Figure 2,

1 Knight, A. S., "An Analytical Method fortheCalibrationofa Variable-Ratio Pantograph,"PHOTOGRAMMETRIC ENGINEERING, March 1955.

King Post K

Sho" 4,,"

Vernier C

FIG. 2, Schematic drawing of pantograph.

projected onto the working surface,must be correct at all ratio settingsand in all operating positions.

The straight-line calibration check is de­signed to check these relationships in theextended as well as folded position of thepantograph.

Figure 3 shows a schematic diagram forthe s'traight-line calibration check. Astraight base-line KT is scribed on the jig,and on this base-line positions are scribedfor the tracing point of the pantograph inits extended position as well as in its foldedposition. Crosses, representing the correctpositions for the drawing point at severalselected ratios, are also scribed on thisbase-line. The diagram indicates only thepositions for the drawing point of a 720mm. pantograph at 2: 1 ratio. In practicethe jig will accommodate both the 720 mm.and 840 mm. pantographs at severalratios. The scribed arc on the jig providesa means of precisely positioning point Kof the jig on the extended axis of the king­post.

For the calibration procedure the jig isplaced beneath the pantograph and so ori-

\ -... ....... .J.. - IB' T\ I '/.r,-."......------ --..J

\ I c'\ I

~-\

FIG. 3. Schematic drawing of pantographcalibrating jig.

THE PANTOGRAPH AND ITS APPLICATION TO STEREOCOMPILATION 143

ented that point K is precisely on the pro­jected axis of the king-post. A small ob­serving microscope with a reference cross orcircle must be clamped to the short arm ofthe pantograph as an aid in achieving thisorientation. Appropriate adjustments ofthe observing microscope along the shortarm and of the jig beneath the pantographwill establish a position for the jig suchthat the arc scribed on the jig will be coin­cident with the arc described by the refer­ence point of the observing microscope, asthe short arm is rotated about the king­post. In this position point K of the jig isprecisely on the projected axis of the king­post and the jig should be clamped to theworking surface.

Pantograph scale settings which willprovide a reduction ratio consistent withthat of a group of poin ts plotted on the jigare selected and the pantograph verniersset accordingly. The pantograph pencil isreplaced with an observing microscope,having a reference cross or circle represent­ing the true position of the drawing point,and the test proceeds as follows:

With the pantograph in an extendedposition the tracing point is precisely posi­tioned and held at the extended point onthe jig, and the relationship of the drawingpoint to the base-line is observed throughthe microscope. Any deviation is correctedby adjusting the C-vernier until the draw­ing point coincides with the base-line. Withthe pantograph folded the tracing point ispositioned at the folded point on the jig,and the relationship of the drawing pointto the base-line observed as before. Anydeviation is corrected by adjusting the B­vernier.

These corrections should establish atrue parallelogram, assuming no mechani-

LARGE SCALE SURVEYS

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cal defect exists in the pantograph, yet thereduction ratio may be in error. The panto­graph is again extended and the tracingpoint positioned as before. Any deviationof the drawing point from the plotted posi­tion on the jig is corrected by equal adjust­ments of the A-, B-, and C-verniers. Withthe pantograph folded, the tracing point isappropriately positioned on the foldedpoint on the jig. The deviation of thedrawing point, as defined by the observingmicroscope, from the true plotted positionon the jig should not exceed the specifiedtolerance of 0.005 of an inch. Excessive de­viation is an indication of some mechanicaldefect existing in the pantograph.

This calibration procedure should be re­peated at the other ratios for which pointsare plotted on the jig. A convenient pro­cedure is to perform the first calibrationcheck at 2: 1 ratio and then proceed to thelarger reduction ratios.

CONCLUSIONS

The precision variable-ratio pantographdeveloped specifically for dou ble-projec­tion stereoplotters, of the anaglyphic type,has filled a long-felt need. Coupled with thetechniques of compilation scribing, theefficiency and versatility of these instru­ments have been increased to a markeddegree. Without the pantograph, compila­tion scribing with all its benefits would beimpractical with the double-projectionstereoplotters.

Although the present design of variable­ratio pantographs fulfills its major objec­tives, minor improvements may be ex­pected. Further development of scale-re­ducing devices employing electronic princi­ples can be anticipated and should bewatched with a great deal of interest.

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