US2264910A - Integrator for circular ordinates - Google Patents

Description

Dec. 2, 1941. w. H. KLIEVER 2,264,910v INTEGRATOR FOR CIRCULAR ORDINATES Filed "March 1, 1941 WALDo H. KLIEYER, uvwvrox By 2 ATTORNEYS Patented Dec. 2, 1941 QFFICE INTEGRATOR FOR CIRCULAR ORDINATES Waldo H. Kliever, Minneapolis, Minn; dedicated to. the free use of the People in the territory of the United States Application March 1, 1941, Serial No; 381,275

(Granted under the act of March 3, 1883, as amended April 30, 1928; 370 G. 757) 3 Claims.

This application is made under the act of March 3, 1883, as amended by the act of April 30, 1928, and the invention herein described and claimed, if patented, may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment to me of any royalty thereon.

I hereby dedicate the invention herein described to the free use of the People in the territory of the United States to take effect on the granting of a patent to me.

This invention rel-ates to integrators, and comprises an integrator for use on charts obtained with recording instruments which use a continuous ruled band of paper upon which the pen or pencil of the recording instrument swings in an arc in recording data. These charts are general- 1y referred to as circular ordinate charts.

The curve obtained by this method of recording renders it extremely difficult to calculate the time integral of the quantity measured, since this integral is not equal to the area below the curve, and the ordinary use of a planimeter or other conventional integrator cannot be made.

An object of this invention is the provision of an instrument which can be used to integrate circular ordinate charts.

Another object of this invention is the provision of such an instrument which is simple to construct and which is convenient and rapid to use.

The following description, considered together with the accompanying drawing, will disclose this invention more fully, and further objects and advantages thereof will be apparent.

In the drawing:

Figure 1 is a plan view partly in section of a preferred embodiment of this invention, illustrating the method of using it; and

Figure 2 is a section on the line 22 of Figure 1.

Referring with more particularity to the drawing, in which like numerals designate like parts, the embodiment illustrated comprises a guide rod it], which is adapted to be placed over a plane surf-ace H, such as the top of a table, along one edge thereof, substantially as shown. A carriage I2 is provided with grooved rollers I3 and I4 which travel on the guide rod Ill. A trunnion roller I5 is mounted on the carriage l2 to support said carriage on the plane surface ll, thereby permitting the carriage to be moved along the guide rod it with ease. A rod i6 is mounted on the carriage l2 and is slidable thereover in a direction perpendicular to the guide rod l0 and is disposed through aperture 9 and a bracket 8 fixed to the carriage l2. Adjacent to rod Hi there is rotatably mounted a drum I'I. Generally, the drum I! will be circular, but other shapes may be used for special cases. The drum l1 and the rod I6 are operatively connected by any suitable means. The means illustrated comprise a pair of flexible bands l8 and I9, one end of each of which is secured to the drum I! at 20 and 2|, respectively; The other ends, 22 and 23, respectively, of said bands extend tangentially from said drum, being secured to the rod H3 substantially as illustrated. Other means of operatively connecting the drum 1! and the rod It may be employed, such as rack and pinion means, but the means illustrated is preferred since it produces a smooth tangent motion without backlash.

. There is radially secured to the drum I! a tracing arm 24 having a common pivot with said drum IT at one end, the other end carrying a tracer 25. The tracer 25 may be of any suitable design, but the type illustrated is preferred and comprises a transparent plate 26 supported on the bottom of a ring 21. The plate 26 is provided with a reference mark 30, which may be etched, embossed, or otherwise. inscribed, and is preferably a small circle, so that in tracing a curve the operator, looking directly through the transparent plate 26, simply maintains the curve diametrically through the circuit. This type of tracer provides full visibility and makes it easy for the operator to trace a curve. The distance between the axis of the drum I1 and the center of the mark 30 must be equal to the radius of curvature of the circular ordinates of the chart to be integrated. The polar arm 28 of a planimeter 29 is fixed on the'carriage l2 parallel to the rod It by means of a small indentation (not shown) in the carriage I2 to receive the pivot point 3| of the polar arm, and adjustable abutment screws 32 and 33, carried by brackets 34 and 35, respectively, laterally straddling said polar arm. The tracing arm 36 of the planimeter is attached to the rod it. This attachment may be accomplished by securing a lug 31 on the rod IS with a groove 38 parallel to the guide rod l0 and placing the tracing point 39 of the arm 36 in the groove 38. However, any other suitable arrangement may be used for the purpose. If desired, the polar arm 28 may be omitted entirely by pivoting one end of the arm 36 to the carriage 12. This is, in efiect, what is accomplished by fixing the polar arm as illustrated, since the polar arm in this position simply becomes an extension of the carriage 12 with vertical freedom of motion. The integrating wheel 40 carried by the arm 36 is disposed so as to contact the plane surface H. The illustrated method of mounting the polar arm 28 is preferred since it insures the fact that the integrating wheel 40 will rest on the table surface with uniform pressure under the weight of the planimeter.

To use this device the chart 4| to be integrated is placed on the plane surface II and the guide rod l0 clamped thereon parallel to the time axis of the chart and such that the tracing arm 24 occupies the same relative position with respect to the chart that was occupied by the recording arm of the recording instrument, and so that when the tracer follows the o-abscissa, no reading is accumulated on the integrating wheel of the planimeter. The tracer 25 is then placed on the curve 32 at the initial position and the reading of the integrating wheel 40 is recorded. The curve 42 is then traced out with the tracer 25, during which the carriage [2 moves along the time axis with the tracer. to rest at the end of each measurement on the same abscissa of the chart on which the measurement was begun. The o-abscissa will generally be selected for this purpose. At the completion of the tracing operation the integrating wheel is again read. From this reading the recorded initial reading is subtracted, the difference being proportional to the area under the curve.

The principle of operation of this invention is as follows: The usual type of integrator records the area under the curve of a chart as jydx where y is the distance straight across the chart and x is distance along the time axis. The problem solved by the present invention is that of providing an instrument with an integrating wheel which converts the angle A which the pen arm of the recording instrument makes with its zero position into y, or into the sin B where B is the angle which the axis of the integrating wheel makes with its zero position, that is, the position where the integrating wheel will not rotate when the carriage is moved along the time axis.

If the tracer arm 24 has an effective length 10 equal to the pen arm of the recording instrument upon Which the integrated curve was made, and

the pivot point of the tracing arm 24 moves along the chart parallel to the time axis in the same relative position as the pen arm of the recording instrument, then, if the zero position of the chart is taken to correspond to the position of zero angle of the tracer arm, the angular position of the tracing arm for any point on the curve will be the same as that originally assumed by the recording pen arm at that point, which is generally proportional to the quantity being measured, such as watts. Assuming that the wheel IT has a radius r, and that the eifective length of The tracer must come Since 1/ equals TA, where A is measured in radians, therefore,

sin B== sin B= Since the reading of the integrating wheel is proportional to the sin B and to distance along the time axis, it is, therefore, from Equation 2 also proportional to A. Therefore, the integrating wheel gives fsin Bdat, which is proportional to Mali". 1*, i, and p, being constant, they can be varied to give any proportion of the integral quantity.

Having thus described my invention, I claim:

1. An integrator comprising a carriage movable over a plane surface, means for guiding said carriage in a straight line, a rod slidably mounted on said carriage, said rod being slidable on said carriage in the direction perpendiculan to the movement of said carriage, means including a drum rotatably mounted on said carriage to slidably actuate said rod, tracing means radially secured to said drum, an arm having one end pivoted to said carriage and the other end comovable with said rod, and an integrating wheel on said arm, said integrating wheel being disposed so as to contact the plane surface.

2. An integrator comprising a carriage movable over a plane surface, means for guiding said carriage in a straight line, a rod slidably mounted on said carriage, said rod being slidable on said carriage in the direction perpendicular to the movement of said carriage, means including a drum rotatably mounted on said carriage to slidably actuate said rod, tracing means radially secured to said drum, and a polar planimeter having its polar arm secured to said carriage and having the end of its tracing arm comovable with said rod, the integrating wheel of said planimeter being disposed so as to contact the plane surface.

3. An integrator comprising a carriage movable over a plane surface, means for guiding said carriage in a straight line, a rod slidably mounted on said carriage, said rod being slidable on said carriage in the direction perpendicular to the movement of said carriage, a drum rotatably ounted on said carriage, a pair of flexible links disposed about the periphery of said drum in opposite directions, one end of each of said links being secured to said drum, the other ends of said links extending tangentially over said drum and being secured to said rod, tracing means radially secured to said drum, an arm having one end pivoted to said carriage and having its other end comovable with said rod, and an integrating Wheel on said arm disposed so as to contact the plane surface.

WALDO H. KLIEVER.

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