Marrinan
~ Elite 1000 Member ~
http://i355.photobucket.com/albums/...n Centerring Fixture/proportionaldividers.jpg
Notes that were used in presentation are imbedded in the text. Fred
PROPORTIONAL DIVIDERS are used for transferring measurements from one scale to another. This capability is necessary when drawings are to be made to a larger or smaller scale. Most of you probably use the computer to do this now however. It can also be accomplished using a Plexiglas grid and graph paper Show grid with line drawing mounted . I would like to share an old system that works very well and is very quick and easy. They can also be used to divide lines or circles into equal parts.
Proportional dividers set 2:1 consist of two legs of equal length Show divider open, pointed at each end Show, and held together by a movable pivot Show. By varying the position of the pivot, you can adjust the lengths of the legs on opposite sides of the pivot so that the ratio between them is equal to the ratio between two scales Show setting 2:1 open to three inches, six inches. Therefore, a distance spanned by the points of one set of legs has the same relationship to the distance spanned by the points of the other set Set 3:1 Show by opening to 3 inches, 6 inches and 14 inches read measurement on drafting ½ inch scale State that we really don’t need to read the scale for and we don’t have to calculate Open 5/8 at 3:1 = .208333 or just shy greater than 7/64. On the proportional dividers, a thumb nut moves the pivot in a rack-and-gear arrangement. When the desired setting is reached, a thumb-nut clamp on the opposite side of the instrument locks the pivot in place. A scale and vernier are provided on one leg to facilitate accurate setting.
Setting is done with the legs closed show alignment pin. In this position, with the slider screw loosened, the slider can be moved up or down the longitudinal slot. Set the slider mark at the number of the ratio desired. Tighten the slider screw. Open the legs to the original measurement. The opposite end of the dividers will indicate the desired proportion. The slider does not have to be positioned at one of the pre-engraved marks. This is useful if you are working from a drawing that has been printed from a computer on an ink-jet or laser printer. Often the drawings will print at a slightly different size than desired. This is due to the difference in calibration between the scanner/CPU/printer. The same is true for the color you are able to produce. As long as there is a scale on the drawing or a known dimension to use as a starting point, it is a simple matter to set the dividers to the correct ratio for the scale you are working in. It is a good idea to scan the part to be engraved at the same time the drawing is scanned to establish a common scale. They save a tremendous amount of work with a calculator which is a real bonus for the mathematically challenged or challenged with the calibration of the electronic devises.
On less expensive models, the movable pivot is not on a rack and gear, and there is no vernier. The dividers may be set by reference to the table of settings that is furnished with each pair; they will accommodate varying ranges of scales from 1:1 to 1:10. However, it is better not to depend entirely on the table of settings. You can check the adjustment by drawing lines representing the desired proportionate lengths, and then applying the points of the instrument to them in turn until, by trial and error, the correct adjustment is reached.
Feet to Meters and other Scale Conversions
To use proportional dividers to transfer measurements from feet to meters, draw a line 1 unit long and another line 3.28 units long and set the dividers by trial and error accordingly. You can do the same for other conversions with the appropriate multiplier. D Drafting scale can be used for this as well. Show scale
Measuring Life Models
You can measure life models more accurately with a pair of proportional dividers.
Hold the tool at arm's length and use the large arms to take an optical measurement.
The small arms will produce short measurements in direct proportion to the large measurements. You can transfer those small measurements to your paper.
By sliding the fulcrum, you can adjust the reduction ratio to better suit the scale of your drawing.
For example, when using the points on the long end to measure the width of a mouth, the short end of the dividers will automatically open to a distance exactly proportional to the width of that mouth. If the width of the mouth in the photo is ¼ inch and the dividers are set at 4-to-1, you can then use them to check whether you enlarged the mouth to 1 inch wide.
Duplicating an Oval or any Picture
To enlarge or reduce a picture or geometric shape, an oval for example, Draw a horizon line outside the original. Draw a data line outside the original and finally draw a centerline through the original. Does not need to be dead center. Show picture behind Plexiglas and on drafting paper. Point out lines. In oval example show how the enlarged oval needs to fit the floor plate. Demonstrate how to arrive at the ratio when it is not on the scale. You probably use a scanner and computer to accomplish this now. If so, be sure to include a scan of the part or a scale in the same scan.
Dividing a line into equal parts
To divide a line into equal parts, set the divider to a ratio of 1 to the number of parts desired on the Line scale which is marked Lines. For instance, to divide a line into three parts, set the scale at 3. Measure off the length with points of the longer end. The span of the points at the opposite ends will be equal to one-third the measured length. Show finding the center without measuring. Show laying out the grid on the centering fixture plate. Show side plate and discuss number of scrolls and issues with staying within space while maintaining correct size. Discuss bracelets, rings and other things with repeated pattern spacing.
Dividing Circles
An additional scale on the proportional dividers makes it easy to divide the circumference of a circle into even segments. First, with the dividers closed, loosen the thumb screw and move the pivot until the scribed line aligns with the number on the Circle scale which corresponds to the number of segments required. Next, set the long legs to the diameter of the circle. The distance between the short legs transferred to the circumference divides the circle into the required number of segments. Describe issues with even vs. odd segments. Show protractor and show how it is divided. Discuss using paper to get circumference then dividing line and transferring back to circle.
How I use the proportional divider in my engraving layout: Recap
The Proportional Divider can of course be used to change the ratio of a design. This is the traditional use . They can serve as a tool in our engraving in many other ways that I find very useful. I, for example, use them to locate the center line by setting them at 2:1 -Spread them to the distance between borders and then use the other end to mark the center line.* The same thing can be used to layout a 3:1 (or any other ratio) and divide the surface into ay number of equal parts.** The scale is normally up to a 10:1 but can be used for higher ratios by like 20:1 by laying out 10:1 then divide one of the sections into half then use this new mark to divide each section in half. ***
Another very useful function is to layout things like scroll spacing on a bracelet or the spacing of scrolls down a border. **** As an example, say you are laying out a batwing border and need to establish the length of each wing. By setting the dividers at the distance of the total length of the border and establishing a ratio (say 10:1) you can mark the length of each wing by ticking off the length using the opposite end of the proportional divider.*****
The Proportional Divider can also be used to divide the circumference of a circle into equal parts, on a rosette for example. While dividing a circle into 4 part is very easy 9 parts is another story. Using the Proportional Divider you simply set 9 on the circle scale, use the large end to measure the diameter and walk the divider around the edge.******
Final Note:
+++The points of the dividers are of hardened steel, and if they are handled carefully, these points will retain their sharpness during long use. If they are damaged, they may be sharpened and the table of settings that come with a new pair will still be usable, but the scale on the instrument will no longer be accurate. Most of the fine drawing instrument manufactures have replacement points available. Some dividers have adjustable points like the ones in the illustration, mine do not. There is a trade off. The adjustable type are pins and easily damaged mine are half round blades and are not as easily damaged.
One source
http://www.micromark.com/PROPORTIONAL-DIVIDER,6494.html
Check eBay or drafting supply houses. They are not cheap but used with care they will last a life time.
Notes that were used in presentation are imbedded in the text. Fred
PROPORTIONAL DIVIDERS are used for transferring measurements from one scale to another. This capability is necessary when drawings are to be made to a larger or smaller scale. Most of you probably use the computer to do this now however. It can also be accomplished using a Plexiglas grid and graph paper Show grid with line drawing mounted . I would like to share an old system that works very well and is very quick and easy. They can also be used to divide lines or circles into equal parts.
Proportional dividers set 2:1 consist of two legs of equal length Show divider open, pointed at each end Show, and held together by a movable pivot Show. By varying the position of the pivot, you can adjust the lengths of the legs on opposite sides of the pivot so that the ratio between them is equal to the ratio between two scales Show setting 2:1 open to three inches, six inches. Therefore, a distance spanned by the points of one set of legs has the same relationship to the distance spanned by the points of the other set Set 3:1 Show by opening to 3 inches, 6 inches and 14 inches read measurement on drafting ½ inch scale State that we really don’t need to read the scale for and we don’t have to calculate Open 5/8 at 3:1 = .208333 or just shy greater than 7/64. On the proportional dividers, a thumb nut moves the pivot in a rack-and-gear arrangement. When the desired setting is reached, a thumb-nut clamp on the opposite side of the instrument locks the pivot in place. A scale and vernier are provided on one leg to facilitate accurate setting.
Setting is done with the legs closed show alignment pin. In this position, with the slider screw loosened, the slider can be moved up or down the longitudinal slot. Set the slider mark at the number of the ratio desired. Tighten the slider screw. Open the legs to the original measurement. The opposite end of the dividers will indicate the desired proportion. The slider does not have to be positioned at one of the pre-engraved marks. This is useful if you are working from a drawing that has been printed from a computer on an ink-jet or laser printer. Often the drawings will print at a slightly different size than desired. This is due to the difference in calibration between the scanner/CPU/printer. The same is true for the color you are able to produce. As long as there is a scale on the drawing or a known dimension to use as a starting point, it is a simple matter to set the dividers to the correct ratio for the scale you are working in. It is a good idea to scan the part to be engraved at the same time the drawing is scanned to establish a common scale. They save a tremendous amount of work with a calculator which is a real bonus for the mathematically challenged or challenged with the calibration of the electronic devises.
On less expensive models, the movable pivot is not on a rack and gear, and there is no vernier. The dividers may be set by reference to the table of settings that is furnished with each pair; they will accommodate varying ranges of scales from 1:1 to 1:10. However, it is better not to depend entirely on the table of settings. You can check the adjustment by drawing lines representing the desired proportionate lengths, and then applying the points of the instrument to them in turn until, by trial and error, the correct adjustment is reached.
Feet to Meters and other Scale Conversions
To use proportional dividers to transfer measurements from feet to meters, draw a line 1 unit long and another line 3.28 units long and set the dividers by trial and error accordingly. You can do the same for other conversions with the appropriate multiplier. D Drafting scale can be used for this as well. Show scale
Measuring Life Models
You can measure life models more accurately with a pair of proportional dividers.
Hold the tool at arm's length and use the large arms to take an optical measurement.
The small arms will produce short measurements in direct proportion to the large measurements. You can transfer those small measurements to your paper.
By sliding the fulcrum, you can adjust the reduction ratio to better suit the scale of your drawing.
For example, when using the points on the long end to measure the width of a mouth, the short end of the dividers will automatically open to a distance exactly proportional to the width of that mouth. If the width of the mouth in the photo is ¼ inch and the dividers are set at 4-to-1, you can then use them to check whether you enlarged the mouth to 1 inch wide.
Duplicating an Oval or any Picture
To enlarge or reduce a picture or geometric shape, an oval for example, Draw a horizon line outside the original. Draw a data line outside the original and finally draw a centerline through the original. Does not need to be dead center. Show picture behind Plexiglas and on drafting paper. Point out lines. In oval example show how the enlarged oval needs to fit the floor plate. Demonstrate how to arrive at the ratio when it is not on the scale. You probably use a scanner and computer to accomplish this now. If so, be sure to include a scan of the part or a scale in the same scan.
Dividing a line into equal parts
To divide a line into equal parts, set the divider to a ratio of 1 to the number of parts desired on the Line scale which is marked Lines. For instance, to divide a line into three parts, set the scale at 3. Measure off the length with points of the longer end. The span of the points at the opposite ends will be equal to one-third the measured length. Show finding the center without measuring. Show laying out the grid on the centering fixture plate. Show side plate and discuss number of scrolls and issues with staying within space while maintaining correct size. Discuss bracelets, rings and other things with repeated pattern spacing.
Dividing Circles
An additional scale on the proportional dividers makes it easy to divide the circumference of a circle into even segments. First, with the dividers closed, loosen the thumb screw and move the pivot until the scribed line aligns with the number on the Circle scale which corresponds to the number of segments required. Next, set the long legs to the diameter of the circle. The distance between the short legs transferred to the circumference divides the circle into the required number of segments. Describe issues with even vs. odd segments. Show protractor and show how it is divided. Discuss using paper to get circumference then dividing line and transferring back to circle.
How I use the proportional divider in my engraving layout: Recap
The Proportional Divider can of course be used to change the ratio of a design. This is the traditional use . They can serve as a tool in our engraving in many other ways that I find very useful. I, for example, use them to locate the center line by setting them at 2:1 -Spread them to the distance between borders and then use the other end to mark the center line.* The same thing can be used to layout a 3:1 (or any other ratio) and divide the surface into ay number of equal parts.** The scale is normally up to a 10:1 but can be used for higher ratios by like 20:1 by laying out 10:1 then divide one of the sections into half then use this new mark to divide each section in half. ***
Another very useful function is to layout things like scroll spacing on a bracelet or the spacing of scrolls down a border. **** As an example, say you are laying out a batwing border and need to establish the length of each wing. By setting the dividers at the distance of the total length of the border and establishing a ratio (say 10:1) you can mark the length of each wing by ticking off the length using the opposite end of the proportional divider.*****
The Proportional Divider can also be used to divide the circumference of a circle into equal parts, on a rosette for example. While dividing a circle into 4 part is very easy 9 parts is another story. Using the Proportional Divider you simply set 9 on the circle scale, use the large end to measure the diameter and walk the divider around the edge.******
Final Note:
+++The points of the dividers are of hardened steel, and if they are handled carefully, these points will retain their sharpness during long use. If they are damaged, they may be sharpened and the table of settings that come with a new pair will still be usable, but the scale on the instrument will no longer be accurate. Most of the fine drawing instrument manufactures have replacement points available. Some dividers have adjustable points like the ones in the illustration, mine do not. There is a trade off. The adjustable type are pins and easily damaged mine are half round blades and are not as easily damaged.
One source
http://www.micromark.com/PROPORTIONAL-DIVIDER,6494.html
Check eBay or drafting supply houses. They are not cheap but used with care they will last a life time.
