Sunday, May 19, 2019

A STEM Project - Planetary Gears

Planetary Gears with Three, Four and Five Planets

Planetary gears are multiple wheels with teeth that rotate together to change the speed, torque (turning force on an object), and the direction of a power source. The center gear is called the sun and the outer gears are called the planets.  This assembly of the sun and planets are held together by a carrier. This carrier rotates around a ring gear.  If you would like to see a simulation of a planetary gear.  Use the following simulator, http://www.thecatalystis.com/gears

I designed the gears using the following program. http://output.jsbin.com/oresos/latest After I learned how to make the planetary gears, I decided to design my own.  See the previous blog post.https://papercraftetc.blogspot.com/2019/05/a-stem-project-how-to-make-gears-using.html

I used 110 lb. card stock from Michaels. Here is the PDF.
https://drive.google.com/file/d/1tZmzTg2fjFUfOCeEF7JVjeqPF1SjXibj/view?usp=sharing

Here is the .Studio file.
https://drive.google.com/file/d/1wGbAhgS7GHvgfN_XIxL0tLcTqIN-jp6-/view?usp=sharing

Precise gluing and allowing the glue to dry is a must for this model. I highly recommend using a Darice quilling glue bottle with an ultra fine tip applicator filled with Aileen's Quick Dry Tacky glue. These items can be found at a craft store or online.

Ring Gear
Glue five layers together to form the ring gear.  Make sure that they are aligned when gluing.

Glue the ring gear to the base.

Glue the two carrier layers together. A rivet is shown at the bottom of the above photo.
Make the planetary rivets by gluing four circles on top of one another for each planetary gear. Don't be messy with the glue and get glue on the edges of the circle.  If you do, the rivets will not fit into the gear.  A dot is all that you need to adhere the circles. Make sure they are stacked perfectly.  The alignment needs to be exact for the gears to move smoothly. I recommend making a few extra and taking the best of the bunch to be used in the model. Allow the glue to dry sufficiently, either a few hours or overnight.  The rivets are a crucial part of the model and they need to be thoroughly dry before the model is operated.

Make the sun rivet by gluing five circles on top of one another. Allow the glue to dry.

The carrier with the rivets attached.

Assemble the planetary gears. Starting with the planets, insert a rivet into the carrier. You will hear a slight snap when the rivet is placed correctly through the hole in the carrier. Thread the planet gear to the rivet.

Put a drop of glue on the top of the rivet and gently adhere the head of the rivet which is a paper circle.  Repeat for all of the rivets.

The rivet head has been attached to all of the planets.

Attach the sun gear onto the center rivet.

Thread the sun gear rivet through the base and snap the rivet into place.  The head of the rivet should be showing as above.

Put a drop of glue on the rivet and attach the head of the rivet.

Use the circle at the center of the gears as decoration for each of the rivets. Repeat the above directions for the other models.
Video of the planetary gears moving.



A STEM Project - Learning how to Use the Silhouette Software to Make Shapes

The Silhouette software is very powerful.  In this project, you will learn how to use the software and explore the mathematics behind the creation of shapes.


Using the drawing tools (oval shape), make a circle with a diameter of one inch.  

Hold down the shift key and drag the circle until it is 1 inch.  If you can not get the measurement exact, use the transform window scale to change both the width and height to 1 inch.

Using the drawing tools (oval shape), make an oval with a height of .05 inch and width of 1 inch. 


Hold down the shift key and drag the oval until it is 1 inch.  If you can not get the measurement exact, use the transform window scale to change the height to .05 inch and width to 1 inch.


Using the drawing tools (pentagon shape), make an equilateral triangle with the length of one inch. 

Move the slider to decrease the number of sides to three.  There is a red dot in the middle of one of the sides. Grab the dot and move it downwards while holding down the shift key.  The triangle will then have one side which is parallel to the page grid if it is turned on in page setup window. In the Transform tool, go to the scale window to change the size of the triangle to one inch. The lock aspect ratio needs to be locked.  Change the width to one and apply the change. Go to the Object menu and click on the convert to path to create a compound figure.


Using the line tools, make a right triangle.

Draw a straight line with a length of one inch. Hold down the shift key to get a line which is vertical to the page grid by moving the cursor from top to bottom of the page.  In the Transform tool, go to the scale window and change the height of the line to one inch and apply the change. This forms one leg of a right triangle. In the advanced replicate window, with the line highlighted, rotate one copy 90 degrees.  Move the copy so that a right angle is formed and the points of each line meet accurately.  Zoom in to see that the lines are not crossing one another. The second leg of a right triangle is now formed. With the line that you just created, replicate another copy of the line by rotating this copy 45 degrees.  Notice that the line is not long enough.  Adjust the line so the bottom right point is touching the horizontal line. Take the upper left box and stretch the line until it meets the vertical line on top. This line is called a hypotenuse. Using the Pythagorean theorem, a2 + b2 = c2 , where a and are the legs and is the length of the hypotenuse.  Is it the same length as the one that you created empirically? If not adjust it. The hypotenuse length should be 1.41 inches if the legs are both 1 inch. Highlight the equilateral triangle, by dragging the cursor over the entire figure. Go to the Object menu, and go to make compound path. Double click your mouse and you will see red dots on the three corners. Click on each dot to make it a gray square (it goes from white to gray) to make a compound figure. 


Using the drawing tools (rectangular shape), make a square with a length of one inch.

Hold down the shift key and drag the square until it is 1 inch.  If you can not get the measurement exact, use the transform window scale to change both the width and height to 1 inch.


Using the drawing tools (rectangular shape), make a rectangle with a width of  one inch and a height of two inches.

Drag the cursor to make the correct width and height.  If you can not get the measurement exact, use the transform window scale to change both the width and height.

Using the drawing tools (pentagon shape), make a pentagon with a side length of one inch.

The Silhouette software does not give a side length measurement.  You need to calculate it using the following formula:

Tangent = Opposite
                 Adjacent

A pentagon has five sides.
If you divide 360° by 5 sides equals 72°  Each triangle formed in the center, has an angle measure of 72°. When dividing the triangle to make a right triangle.  The measure of the angle at the center becomes 1/2 of 72° which is 36°.

Using the Tangent formula:

tan(36°) =  .5   Where h is the height
                  h

h = .688 in.  (This measure is called the apothem. It can not be doubled here because this is the radius of the incircle.)


To find the height of the rest of the pentagon, you need to use the Pythagorean theorem.
a2 + b2 = c2 

a2    +    b2     =    c2
(.5)2 + (.688)2   =    c2
.25  +  .473    =   c2 
           .723    =   c2 
          .85 in   =   c

Adding the two measurements, you will have the height of the pentagon
.688 + .85 = 1.538 in

A regular pentagon with a side length of 1 will have a height of 1.538 inches


Using the drawing tools (pentagon shape) and adjusting the slider to 6, make a hexagon  with a side length of one inch.

The Silhouette software does not give a side length measurement.  You need to calculate it using the same Tangent formula as above substituting six sides. The only difference is that you do not have to use the Pythagorean theorem because the apothem can be doubled here.   

A hexagon has six sides.
If you divide 360° by 6 sides equals 60°  Each triangle formed in the center, has an angle measure of 60°. When dividing the triangle to make a right triangle.  The measure of the angle at the center becomes 1/2 of 60° which is 30°.

Using the Tangent formula:

tan(30°) = ,5  Where h is the height
                 h

h = .867 in. 

.867 + .867 = 1.734 in.


A regular hexagon with a side length of 1 will have a height of 1.734 inches

Repeat the calculations for a heptagon, octagon and decagon.  When the number of sides is odd, you need to use the Pythagorean theorem equation in addition to the Tangent formula to add the two values together to get the height of the regular polygon. When the number of sides is even, the apothem can be doubled to obtain the height of the regular polygon.

Save all of these shapes in your Silhouette library.  This will become a valuable resource in the future and save you a lot of time when you are designing models.  This is similar to a carpenter who has a tool box. It makes designing easier.  These are basic shapes which will be used over and over again because they are exactly one inch.  They can be combined easily with one another to create a compound model. Don't worry that the size is too small.  Make it small and then enlarge the entire model as a whole to make it the correct size once completed.

 Disclaimer: there might be instances when enlarging a model will not work.  For instance, slice forms need slits that are exactly the thickness of a piece of paper and can not be enlarged.  They need to be designed with the correct thickness. In this instance, enlarge the shapes to the correct size and then work on the design.




Saturday, May 18, 2019

A STEM Project : How to Make Gears Using the Silhouette Software

Making paper gears are an excellent way to see how gears function.  It's easy to make different toothed gears with the Silhouette software using the Replicate function. I suggest following my examples first and then making your own with your calculations.

Here is the .Studio file.  I am not including a PDF version as these directions are specific to the Silhouette software.
https://drive.google.com/file/d/1GzE_-z23Hcckukm5FLZdk635w5ykpcnq/view?usp=sharing

The first thing that you need to do is determine the shape of the tooth.  I have included three different styles of teeth. The next thing you need to decide is how many teeth that you want in the gear. I am going to make two gears, one with nine teeth and the other with twelve teeth.  The gears need to have the same teeth and distance between the teeth to mesh correctly.  My first example will have teeth that are .25 inches wide.  Since there are nine teeth, there will be nine spaces in between the teeth. The spaces in between the teeth are also .25 inches wide to accommodate the other gear meshing with this gear. Calculate the circumference of the smaller circle by multiplying the width of the teeth by the number of spaces and teeth.  .25 x  (9 + 9) = 4.5 inches. The diameter of the circle can be obtained by using the circumference formula.

C = πd   
4.5 inches = πd  
d = 1.433 inches

The diameter of the circle for the nine toothed gear needs to be 1.433 inches.

Calculate the circumference of the larger circle by multiplying the width of the teeth by the number of spaces and teeth.  .25 x  (12 + 12) = 6 inches. The diameter of the circle can be obtained by using the circumference formula,.

C = πd   
6 inches = πd  
d = 1.91 inches

The diameter of the circle for the twelve toothed gear needs to be 1.91 inches.

I have included two circles with the correct measurements in my .Studio file. In the file, there are three tooth designs with a line that protrudes on the left side of the tooth.  This appendage is necessary to use the Replicate "grab handle".  Highlight the tooth that you want to replicate, in the Replicate window go to the Object on Path window.  Click on the "Show Grab Handle".  You will see that the circle with the dot is place on the point where the tooth will be placed on the circle. Move the tooth to the top of the circle that is 1.433 inches in diameter. Perpendicular and number of repeats should be checked in the Replicate window.  Increase or decrease the number of repeats to 9 for the smaller gear. You will notice that the teeth are not sitting on the circle correctly.  Increase the value of the Perpendicular Start Angle until all of the teeth are touching the circle.  I had to Zoom in to see that I had to increase the Start Angle to 11. Highlight the gear and the circle. In the Object window, click on the Convert to Path.  The grab handle will disappear and the circle will no longer be bold.  Highlight the gear and use the Offset window to .01 and then apply. Go to the Object window to release the compound path.  Select the outer line which looks like your nine toothed gear and highlight it to Offset the image with an Internal Offset of .01. Discard the outer image by deleting it.  The inner image is the nine toothed gear.

Repeat the above instructions for the twelve toothed gear. After you have made the twelve toothed gear, see if you can make your own gears with different number of teeth.  Remember, you need to calculate the diameter of the circle because each toothed gear will have different measurements. I have included a tooth with a width of .5 so that you can have different width option too.

Please note: The center of the gear might be skewed a little because of the location of the teeth.  I always save the circle that was used to make the gear.  Using this circle will allow you to center the axle hole correctly.  Once the axle hole is centered in the circle, ungroup both images. Manually move the gear image to center it in this circle with the axle hole. Delete the outer circle leaving the axle hole behind with the gear. Group these two images together to complete the process of making a gear.

Wednesday, May 8, 2019

Mother's Day Lily Flower Box

Lily box for Mother's Day

I created this cute little Lily flower box to give to the ladies at my mother's assisted living residence for Mother's Day. The box holds one Hershey kiss.  It is a 1 1/2 inch square box.  This box could be used as a favor at a wedding or a shower.  The box and flower are not hard to put together.  It is time consuming to make the flower.  I do recommend waiting for the glue to dry as it makes it easier to bring the curved flower surface together,  The stamen in the middle of the flower is rolled into a circle and glued. The color of the stamen is one shade darker than the flower petals.

I assembled the boxes first and then added the leaves and flowers.  I glued one petal at a time and went to the next flower.  The glue was dry when I went to do the next petal on the first flower.

Here is the PDF.  I used 65 lb. cardstock.
https://drive.google.com/file/d/1vurs3lw4QQhrVLSpSfDg6x8F6pULVsbl/view?usp=sharing

Here is the .Studio file.
https://drive.google.com/file/d/1aJ3ng1VhZWgg1iHB7pcJ7KsYasHdNNYJ/view?usp=sharing

I made 15 little boxes.  I know the residents enjoyed receiving them.