Ellipsograph

This invention relates to an ellipsograph, which is an instrument often used in mathematical, physical, mechanical and architectural drawings.

Ever since the first patent for this type of instrument was issued to an American, Mr. Hayen (U.S. Pat. No. 3,947,968) in 1874, special publications of this nature have appeared time and again, and a search of international Patent Gazettes issued during the last decade or so reveals that available ellipsograph designs fall into five categories:

(1) The string type utilises the principle that the sum of the distances of any point on the ellipse to two focal points is constant.

(2) The projection image copying type is designed on the principle that all kinds of ellipses can generally be drawn on paper along the edge of the shadow mimicked by a circular board model inclined at various degrees in space. This category may be typified by U.S. Pat. No. 4,194,292.

(3) The obliquely cut cylinder type is prepared by ensleeving another leg on one of the legs of the dividers, enabling it to rotate and slide up and down with the drawing pen, forming an adjustable included angle to it. This is typified by U.S. Pat. No. 4,204,327. Ellipsographs designed according to the above three principles cannot describe ellipses that are very small, nor those that are fairly elongated.

(4) The planetary gear type is typified by the ellipsograph disclosed in U.S. Pat. No. 4,226,022. It can hardly overcome the crawling which causes lines drawn in this way to have a saw-tooth appearance.

(5) The cross groove type includes the majority of ellipsographs designed like those disclosed in DT2743352, SU454139, and BG1754588. This type has the advantage of being able to draw elongated ellipses while its defects include the following: it is difficult to ensure the matching precision of the slide groove and the coincidence of the elliptical line drawn in opposite directions; its grooved frame tends to be clumsy; it requires that the unevenness of the paper surface

The present invention makes use of the unique mathematical principle to find the hidden cross-groove mechanism, thereby realizing precision in the drawings made and completeness in the range of drawing. The ellipsograph of the invention is capable of describing various ellipses including one whose major and minor axes are equal (a circle), one whose two axes are not equal (an ordinary ellipse), and one whose minor axis is zero (a straight line). It is not only possible to draw large ellipses with the invention, but extremely small ones ellipses (1-2 mm) may also be described readily. Besides, its structure is simple its operation is convenient. The ellipsograph of the invention will fully satisfy the requirements for all kinds of engineering drawings.

The structure of this invention includes a crank guide rod mechanism, a longitudinal guide mechanism, a rotary drawing mechanism, and a supporting frame.

Of the accompanying drawings,

FIG. 1 is a block diagram of the invention;

FIG. 2 is a perspective view;

FIG. 3 is an exploded view of the invention;

FIG. 4 is the mathematical proof diagram; and

FIG. 5 shows details of the rule. In the attached drawings, 1 indicates the pen holder, 2--the drawing rod, 3--the main axis, 4--the rule, 5--the upper axis, 6--the hand nut, 7--the guide sleeve, 8--the handle, 9--the guide rod, 10--the main frame, 11--the pendulum shaft, 12--the crank, 13--the leg, 14--the adjustable screw means, 15--screw rod, 16--sleeve, 17--needle, 18--needle, and 19--guide groove.

The crank guide rod mechanism, in which the guide-rod head can perform an almost rectilinear motion, comprises the crank 12, pendulum shaft 11, and guide rod 9. At the lower part of the pendulum shaft 11, the rotable guide groove 19 with an opening is used to control the sliding of the guide rod to permit it to skip up and down without getting stuck. This calls for the use of the mathematical method to find out the ratio for the radius of the crank, the center distance between the crank and the pendulum shaft as well as the length of the guide rod 9, and to set the ratio of the three to a specific value. For example, the guide-rod head will pendulate in a manner nearly approaching rectilinear motion when such a ratio is taken as 1:1.8:7.84, in which case the main axis 3 at the end of the guide rod 9 will move rectilinearly with a precision of approximately 1000:1 straightness (to be proved below). This motion pair replaces the lateral groove of the cross-groove principle, and provides the basis for designing the simplified structure of this invention which eliminates the clumsiness of the cross and upgrades the precision.

The longitudinal guiding mechanism is made up of the main frame 10 and the guide sleeve 7, which is equivalent to the longitudinal groove of the cross groove and is located at the front part of the frame 10. Their cross sections are respectively semi-circular cut tube and the semicircular fanning, both of which form a slightly elastic fold. This not only eliminates the clearance and rotation between them but also facilitates sliding. As a result, precision and flexibility are upgraded.

The rotary drawing mechanism is made up of the handle 8, upper axis 5, hand nut 6, rule 4, main axis 3, drawing rod 2 and pen holder 1. On the lower part of the upper axis 5 there are threads that mesh with those of the hand nut 6 and the square hole that slide-matches with the rule 4. At the lower end of the upper axis 5, there is a hole which is matched loosely and turnably with the upper end of the main axis 3. This hole has a groove with a side opening which enables the upper axis 5 to slide at any place on the rule 4 and reach a position forming a straight line with the main axis 3 for drawing purposes (FIG. 5), then use is made of the hand nut 6 to lock and fix the upper axis 5 at any random place on the rule 4 which bears the scale graduations to determine the minor axis. The middle part of the upper axis 5 is ball-shaped and is enfolded on the guide sleeve 7 to form a loosely rotating match capable of automatic centering with the lower main axis, and then extended from one side of the main frame to be fixed with the handle above. The handle is able to do a 360.degree. rotation of the drawing mechanism while driving the upper axis 5 to move longitudinally along the front part of the main frame. The main axis 3 also fixes the rule 4 and the drawing rod 2 within the plane of the plumb. They combine to form the steering rod equivalent to that of the cross-groove principle. Therefore, by shifting the pen holder 1 on the drawing rod and altering the locking point of the upper axis 5 on the rule 4, the major and minor axes of the ellipse may easily be determined. Then the ellipse can be drawn simply by turning the handle 8. The cross section of the drawing rod 2 is a right-angled trapezium on the slope of which are graduations for determining the major axis. On its right-angled side is the positioning groove, while on the pen holder 1 are the corresponding right-angled trapezoidal groove and the positioning screw pin for enabling the stylus to be shifted and positioned within the same plumb plane through the grooved plate center. There are graduations on the rule 4 for determining the minor axis. There is provided adjustable screw means 14 at one end of the drawing rod 2 for finely adjusting of for precise centering.

The supporting frame comprises the leg 13 with a screw rod 15 linking the leg 13 to the main frame 10 by way of sleeve 16. The leg 13 may be turned to a position forming a right angle with the supporting frame and "pinned dead" on it for the purpose of making the drawing. Besides, the two needles 17, 18 at the ends of the leg are used for two-point positioning. At this moment, the drawing mechanism is in the state of suspension extension. The drawing stylus will move across the paper in a suspended manner to cope with the uneven surface of the paper and the length of the stylus. The leg may also be turned to be in the same plane as the instrument to facilitate packing in a case.

The guide-rod head of the crank guide-rod mechanism in this invention may be designed to have the following ratio: r:x.sub.o :L=1:1.8:7.84) as described with regard to the performance of rectilinear motion.

The main axis 3 is subjected to the restraint of the guide rod 9, the crank 12 and pendulum shaft 11 to produce the specific curve motion. Taking the coordinates as given in FIG. 4 and the center of the crank as the origin O, then OP is the radius of the crank, (-x.sub.o,0) is the centre of the pendulum shaft, RP is the pendulating guide rod, and R(XY) is the center of the main axis. Its orbit equation is: ##EQU1## where (x,y) are the coordinates of point P, r is the length of OP, .alpha. is the included angle of OP and OX, and L is the length of RP.

Solving these equations for X, we have: ##EQU2## For example, when r:X.sub.o :L=1:1.8:7.84, the above equation may be simplified as follows: ##EQU3## Based on designing requirements, we may take .alpha.=(-81.degree.40',+81.degree.40').

The maximum error of this equation and the rectilinear equation x=-6.84r is very small, and may be found by using the extreme values: ##EQU4##

Therefore, there are two extreme values within this region: ##EQU5##

The boundary value of this function in the region (-81.degree.40',+81.degree.40") is

The maximum deviation of these extreme values and the boundary value from the straight line X=-6.84r is 0.00288r. As this function is continuous in this region, therefore, its rectilinear maximum deviation within the region is also smaller than and equal to 0.00288r.

Since twice the Y value of the two boundary points (.alpha..+-.81.degree.40") in formula (1) above is the length of the straight line in the region (-81.degree.40', +81.degree.40"), we substitute sin 81.degree.40"=0.98944164 and cos 81.degree.40"=0.14493186 into equation (1), and get Y=2.565428r. Therefore, the length of the straight line section should be 2y=5.1308r. Its divergence from straightness should be: ##EQU6##

This error, when compared with other factors like the comparison of the error produced by the clearance of various moving pairs and the other structural states or the changes in the contact points of the stylus on the face of the paper during rotation, is too slight to deserve consideration. Due to factors like its simple structure and others that result in its higher structural precision, the overall precision of this invention is very high. A good number of practices have proved that it can fully satisfy the requirements of engineering drawings by attaining a high level of precision in all applications.