A STEM Project: Making a Gear and Timing Belt Assembly

A Gear and Timing Belt Assembly

In a previous blog entry, I showed how to make a gear.  https://papercraftetc.blogspot.com/2019/05/a-stem-project-how-to-make-gears-using.html  I will now explain how to incorporate this gear into a gear and timing belt assembly.

Here is the PDF.  I used 20 lb. copy paper for the timing belt and 65 lb. cardstock for everything else.
https://drive.google.com/file/d/192GzmI7ueR99EnuJzDAv-qEA5jDp4-KT/view?usp=sharing

Here is the .Studio file. The instructions for putting the model together follow after the description of how the model was made.
https://drive.google.com/file/d/1oiEHb6rDV3Wngoref_ERLFqdLUcQBRet/view?usp=sharing

Video of the gear and timing belt assembly in action

How the gear and timing belt assembly was made:

The first thing you need to understand is the shape required to make a timing belt.  With this information, the math to determine the circumference of the oval becomes easy to do.  The timing belt moves around in an oval shape. This oval shape looks like two circles that are joined by a rectangle.  See photo below.

The circumference of this oval is the circumference of one circle (two semicircles make a whole) plus the length of two sides of the rectangle. 

The next thing that you need to understand is the make up of the gear. Below is a diagram with three circles circumscribed around a gear.  The light blue circle represents the circle needed to make the gear.  The dark blue circle represents the location where the timing belt will intersect the gear when it is operating.  The green circle represents the outer edge of the gear to determine the distance between the two axles.

In the following text, the colors of the rings correspond to the diameters calculated.

To make the timing belt (dark blue circle), I wanted the distance between each of the gears segments to be one inch. A gear with ten teeth would make a ten inch circumference. Using the circumference formula I can determine its diameter:

C = πd 

10 inches = πd  

 d = 3.183 in.

The diameter of the dark blue circle is 3.183 in. With this measurement, you can now determine the diameters of the other two circles.

The height of the gear tooth is 0.4 in.  To determine the diameter of the light blue circle, subtract the height of one gear tooth (the diameter is shortened by 0.2 inches on either side of the dark blue circle). This measurement represents the diameter of the circle needed to make the gear.

3.183 - 0.4  = 2.783 in.

The green circle represents the location of the outer edge of the gear. To determine its diameter, add the height of one gear tooth (the diameter is lengthened by 0.2 inches on either side of the dark blue circle).

3.183 + 0.4 = 3.583 in.

To make a gear, use the diameter measurement of the light blue circle,  2.783 in. and the tooth design included in this file.  With the help of the gear making blog entry that I  mentioned above,  you can recreate the gear that I made.

The spacer prevents the timing belt from shifting around when it is operating.  A spacer, before it is constructed, looks like a circle with 10 tabs protruding around its edge. To make one, use the diameter of the timing belt's circle,  3.183 in. and rotate a .45 in. square ten times around the outer edge of this circle. With the help of the gear making blog entry that I  mentioned above,  you can recreate the spacer that I made.

The outer edge diameter of the gear is 3.583 inches.  This value is needed to determine the center location of the two axles. I arbitrarily decided that the distance between the two gears would be 1 inch because I did not want the gears to touch.

3.583 + 1 = 4.583 in. which is the distance between the centers of the two axles

To determine the length of the timing belt use the following formula: 

Length of timing belt =

Circumference of the dark blue circle + 2(distance between the two axles)

Length of the timing belt = 10 in. + 2(4.583 in.)

Length of the timing belt = 19.166 in.

(When I made the belt this length - 19.166 in., I determined that I needed a little wiggle room because of the thickness of the paper.  I added 0.195 inches to the length and it worked well.  I am assuming that this distance was needed to account for the thickness of the paper in all dimensions.)

Length of the timing belt with paper thickness = 19.166 in. + 0.195 = 19.361 in.

To make the timing belt, I needed to determine the size of each square inside the timing belt. I divided 19.361 in. by 19 squares to get 1.019 in. This means that each toothed segment is 1.019 in. wide. I then measured the gear tooth at the location of the timing belt.  The gear tooth was 0.357 in. wide. Given that each tooth segment is 1.019 inch wide, I subtracted 0.357 in. to get the distance 0.662 in. between each square.

Using the Silhouette to make the timing belt, I made a template with a square that was 1.019 in. I centered a .357 in. square in the middle. At the bottom edge of the square, I aligned a 1.019 in. dotted line. I then made a rectangle that was 19.361 in. long.  I aligned my square template to the the top edge of the 19.361 in. rectangle.  I deleted the 1.019 in square and used the replicate function in Silhouette on the 0.357 in. square and the 1.019 in. dotted line to make 18 more segments for the timing belt by using the number of copies custom position window. I made the Y offset 1.019 inch. I added a tab at the bottom of the rectangle by going into point edit mode and adding two points to make a trapezoid. I duplicated this strip and then removed the squares to make two strips, one with 9 squares and the other with 10 squares. I made sure everything remained aligned when I adjusted the strips.


To make the outside casing for the gears, I made a circle that had a diameter of 4.225 in. I determined this value by sight, please note that this diameter is arbitrary. I centered a 0.5 in circle for the axle in the center of this circle.I duplicated this circle within a circle. I made a rectangle with a width of 4.225 and a length of 4.583 which is the distance between the centers of the two axles. I aligned the shapes to look like the first photo above.  Using the offset window, I offset the outer edge by .01 inches. I removed the two 4.225 in. circles to make the side of the casing without tabs.  I duplicated this casing shape and added two tabs at the top and bottom to make the second side.

I used the improved square axle design from this blog post https://papercraftetc.blogspot.com/2019/06/a-stem-project-making-axle-for-gear.html because I wanted an axle that could withstand a lot of torque.




Instructions on how to put the model together:

When making this model, keep all your pieces stacked up and aligned together when taking them off your Silhouette mat.  It makes gluing the gears and spacers easier when everything is already aligned and you do not have to play with them to make sure that the teeth and center square are aligned perfectly. I also recommend using a quilling glue bottle filled with  tacky glue.  You need small amounts of glue to adhere the pieces for precision gluing.

Glue the three chipboard gear pieces together.  Make sure that you align the circle and the center square.  Repeat for the second gear.

In the picture above on the top left, sandwich the two yellow cardstock pieces on either side of the chipboard on the bottom left with glue.  Completed gear is on the bottom right.

Glue the cardstock casing together with the chipboard in the center. Do not apply too much glue to the top and bottom of the casing as this will be pulled apart to put in the tab later.

Glue the cardstock casing to the chipboard. The tabbed cardstock outer casing will be glued on later.

Bend the tabs of the spacers as shown in the photo on above left. Align the center square as shown in the middle of the photo.  Glue all of the aligned tabs together. I used tweezers to get the tabs to adhere correctly. Two completed spacers on the top right.

Bend the axle and apply glue as shown. Adhere the axle into a square. 

Insert the axle into the square.  Glue the tabs down.

The axle should be able to stand up as shown in the photo above. Repeat for the second axle.

Thread the axles through the casing which has its chipboard showing.

Thread a spacer onto each of the axles.

Thread a gear onto each of the axles.

Thread another spacer onto each of the axles.

Glue the two strips of timing belt together precisely.

Thread the timing belt onto the teeth and glue the belt precisely together.

The timing belt and gear assembly should look as shown above.

Make the knobs by sandwiching cardstock, two chipboards and another piece of cardstock together. The gear on the bottom has been glued together.

Thread the casing through the axle.  Thread the knob through the axle. Glue the tabs down onto the knob. Add a blue circle to the top of the knob(not shown in photo above).

Glue the casing with the tabs onto the chipboard. Please make sure that you do not apply any glue to the area where the axles reside.

Glue the tabs to the inside of the assembly by pulling apart the glued inner casing. Insert the tab inside the casing so that it does not show.  Repeat for the other tab.

Completed Gear and Timing Belt Assembly

A Purse Favor for a Shower Party

Purse Favor

I made this purse favor for my daughter's wedding shower a couple of years ago.  I got caught up in the whirlwind of the wedding and I just realized that I forgot to post it.

Here is the PDF. I used a pretty metallic cardstock and metallic ribbon.
https://drive.google.com/file/d/16tTjo6H2xkAMMhRPV9tdIK6HJA4vPO6B/view?usp=sharing

Here is the .Studio file.
https://drive.google.com/file/d/1fry17JG50Dh_PIVdBMkFqjfgqzNaOcnw/view?usp=sharing

The purse is easy to make by creasing the folds and gluing the bottom and side tabs.  Each handle is folded and glued together.  The tabs are inserted into the top of the purse in the slit. I added a heart charm with an initial which was hung with a gold metallic thread. When tying the bow, hold the purse upside down to get a perfect bow.

  Cut two 10 inch pieces of ribbon.

 Glue the ribbon to the inside of the purse as shown I the photos above and below.

 Four Hershey Kisses fit nicely on the bottom of the purse.

Completed purse.  

A STEM Project: Making a Planetary Model which Revolves Around the Sun

Planetary Model with a Sun and Planet that Rotates

Video of Planetary Model in Action

This planetary model uses the skills learned in the previous project, of making a square box and combines it with how a gear operates.  I purchased my tea light at Dollar Tree.  I went back a few weeks later and they did not have the tea light that I purchased in stock  They did have a different type of tea light but the height is different.  I am including the file for the height of my tea light.  With the skills you learned in the previous post, you should be able to modify the box height.

Here is the PDF.  I used 110 lb. cardstock.
https://drive.google.com/file/d/1oODKNWSrWd46mvUm7IyNSA3aB0x9_zn4/view?usp=sharing

Here is the .Studio file.
https://drive.google.com/file/d/1H-gWLuR-929OwaUfLgFxQlDj0siXHIph/view?usp=sharing

 There are three circles with slits.  The largest circle is in the middle flanked by the two smaller circles on either side.  Slide the semicircular pieces on the three circles.  Repeat until all the semicircles are attached and look like the figure below.

Bend the axle into a tube and glue. Repeat for the second axle.

 Thread the axle though the top gear (axle with an extra hole) and glue the tabs down. Thread the axle for the bottom gear (axle without an extra hole) and glue the tabs down.

Glue the ring to the carrier.

 Make the brad by gluing the four small circles together. Make sure they are aligned correctly.

 Apply glue to the center of the head and adhere the four small circles. 

Wait for the glue to dry before attaching the brad.

Make the planets by bending the circles in half.  Glue three of the circles together and repeat. Glue the two semicircle together.

Completed Planet 

 Thread the brad through the small circle in the top gear.

Thread the small planet gear onto the brad.

Using just a drop of glue, adhere the top circle to the brad.  Make sure that the planet gear rotates freely. 

Glue the two main gears together

The main gear should look like the above photo.

Make the top of the box by gluing into a square.

 Apply glue to the inner tab of the box. Adhere one of the square pieces with a hole in the center to the middle of the box form.

Turn the box top over. Glue the other square piece to the top of the box. Repeat the above instructions for the box bottom.

Using Glue Dots, place a dot in each of the four corners as shown above.

Apply two strips (blue glue) of a glue runner as shown in the above photo. Thread the bottom axle through the box top and adhere the assembly on the box top.

Apply glue to the head of the brad and adhere the planet.

Apply glue to the rim of the top axle and adhere the sun.

Thread the tea light through the axle and close the box by attaching it to the box bottom..

Completed Planetary Model.

A STEM Project: Exploring How to Make a Square Box and a Colonial House Box

 House Box

Two cube boxes and a House Box

Last September, I made 25 houses in 25 days.  Phew, what an accomplishment.  I don't want to recreate making more houses.  What I would like to do is explain how to make a simple square box with a top that slides into the bottom. Using the skills gathered here, I would like to expand your knowledge to allow you to make different types of boxes.  The concept of making a box is pretty easy.  The first thing you need to realize is how a box is made.  A simple box has two parts, a top and a bottom.  Each piece of the box is identical except the top of the box is a little larger so that it can slide easily onto the bottom of the box.

To create a simple cube box, all the side lengths will be the same. Make a square with the drawing tools, make sure to hold down the shift key to make it square. Make a copy of the box by using the Edit/Copy function.  Replicate the box in all four cardinal directions.

It should look like the above figure.

The boxes have overlapping lines at this point.  I want just the outer edge of the figure.  I use the offset window to offset the image a little bigger and then a little smaller. I do an offset of .01 with a right angle corner.  I selected the image created and then do an internal offset of .01.  Center to page this figure.  Paste a copy of the original square onto the page.  Change the straight lines to a dotted one. Center to page this square.  

The image should now look like this.

The only thing that is left to do is to make tabs for the box. The tabs are needed so that the corners of the box have a space to be glued to.  I like to make my tabs from .25 to .5 inches wide depending on how big the box will be.  

In the point editing mode, break the path for all of the red points above. The points will turn from gray to red when the points are released in the Object/Release Compound Path mode.  This will allow you to change the solid lines to dotted ones.

The image should now look like the above figure.  The box needs tabs.

Paste a copy of the original box.  In the Transform scale window, resize the box so that the width is .25 inches and apply the change.  The rectangular box needs to be open ended.  There are a number of ways to do this. Here is just one way. Double click the rectangular box, click on the bottom left point. Break the path. Pull the red dot away from the figure and then delete the red dot that is being pulled away from the figure.

Notice the red dot that is being pulled away. This is the dot that needs to be deleted. An image that looks like a bracket is created. Move this bracket to the side of the cross on the bottom right.

You might have to zoom in to see that the tab is aligned correctly.  Mirror this tab in the Replicate window to the left. Repeat for the upper cube. When completed, group the image in the Object menu so that it does not get distorted in any way.

The box template should look like the above figure. This can be the bottom or the top depending on what you choose. I chose to make it the bottom.  Duplicate the box template and drag one of the corners of the bounding box so that the entire image is bigger by approximately .2 inches. This amount is arbitrary depending on the thickness of your paper.  I recommend using scrap paper to test whether the tolerance is good enough to allow the box to be easily pulled apart but not too loose that it slips out without any resistance.

In the file you will find, a copy of the above box.  Try it out and see if you understand its construction.  I also added a different height box top to the file.   Make a copy of the the original box top and alter the height.  Each of the four sides need to be shortened.  How do you do that?  Ungroup the figure and select the top square with the two tabs. 

 In the bounding box, there are small squares, select the top square in the middle of the figure (below the green dot).  Drag the box down and you will see the height decrease.  Please note, zooming in will allow you to get very precise measurements. Repeat this process for the other three sides. A box top with shorter sides is now created.

Think about how you would make a rectangular box.  You can not just drag the image in the center of the bounding box to make it wider because the opposite sides would remain unchanged. In order to make a rectangular box, each side measure must be calculated.

Here is the PDF.  I used 65 lb. cardstock.

https://drive.google.com/file/d/1zkNAgIm3UV_iuZrUcf7EDi9sMwadSOqj/view?usp=sharing

Here is the .Studio file.

https://drive.google.com/file/d/1CmanmIpaT04hx4APKbKTo_Nguua9YpNn/view?usp=sharing

Next, cut out the house box that I made.  Do you notice the similarities and differences in the make up of this box compared with the one you made?  In the house box top, I used just one tab and I placed all of the sides together.  In the house bottom, I made it similar to the square box that you constructed. There are many configurations of the sides that will accomplish the same result.  The next time you open a box, check out its construction. It is fascinating to see all of the different ways things can be constructed.

 Box bottom on the left and House Box Top on the right.

Completed House Box

A STEM Project: Leonardo Da Vinci's Articulated Vitruvian Man and his Flying Sphere

Leonardo DaVinci's Flying Sphere and Articulated Vitruvian Man

Leonardo DaVinci's Vitruvian Man was a man drawn in pen and ink with ideal proportions inscribed inside a circle and a square. The drawing is a juxtaposition of art and mathematics.  Leonardo was using art to explain math. He drew a man with the navel as the center of the being.

Here are my working models. As you can see, the man is perfectly proportioned in both the circle and the square.  

Using the Vitruvian Man, I made a jointed front view and side view of this man. I am planning to use this articulated man in future models that require movement such as puppets and working models.

 I used paper fasteners to connect the parts

Front view and side view of Articulated Vitruvian Man

Leonardo DaVinci was also an inventor.  He described in his writings, a flying sphere.  I recreated this invention by putting Vitruvian Man inside this sphere.

 Glue the two horizontal pieces together to give strength to the piece.

 Crease the four vertical pieces at a right angle as shown

 Slide the vertical pieces into the slots on the side of the horizontal piece to create a right angle. Repeat for the other sides. Apply glue in the interior of the vertical pieces to give strength to the model.

Completed Flying Sphere 

Here is the PDF.  I used 65lb cardstock.

https://drive.google.com/file/d/1U8JiPDSx0kU05hKg1a2mtQvt3R8b_jqn/view?usp=sharing

Here is the .Studio file.

https://drive.google.com/file/d/1gnKqe6HPZFqiej85bjUeTsahyaZT8XvR/view?usp=sharing