# Archives

## Graphing with Finch

You have learned to use the Finch sensors to move a sprite on the screen. In this activity, you will use the commands on the Pen menu to graph the value of a sensor over time.

Start by writing a program that uses the block below to move the sprite on the screen. What numbers do you need to put in the blanks so that the sprite moves all the way to the top and the bottom of the screen

Now you want to record the path of the sprite on the screen. Explore the commands under the Pen menu. Start with the pen down block; you can think about this block as placing a pen on the “paper” of the screen. How can you change the color of the sprite’s path?

You have a program that tracks the value of the light sensor. To create a graph, you need to start with the sprite on the left side of the screen and gradually increase the x-coordinate as you change the y-coordinate. At the very beginning of your script, add a command that will make the sprite start at (-240, 0).

Within your loop, add a block that will increase the value of the x-coordinate by one pixel each time through the loop. When you run your program, you should see a graph that looks something like the one shown below.

Extension: Can you add axes to your graph? Can you graph the light value for exactly 30 seconds?

## Mechanisms: Cable-Driven Robots

In this lesson, you will be building a cable-driven robot. Watch this video to see what it will look like.

The mechanism includes the following parts:

• Links are connected by rotating joints.
• A hollow guide is attached to each link.
• A cable passes through all the guides. This cable is attached to a motor.

The motor pulls on the cable to move the links. As the motor pulls the cable, the guides become closer together, which makes the links rotate about the joints. Note that the cable can only move the mechanism in one direction, to bend the linkage at the joints.

#### Materials Needed

##### Paper Templates (See Teacher Materials)

When printing the templates, be sure to print them the actual size (no scaling) on 8.5” x 11” paper. You will use the templates to cut cardboard as shown in the instructions below. Be sure to use cardboard that is less than ⅛” thick.

• Servo Unit
• Box Unit
##### Other Materials
• servo motor with bag of accessories
• straws cut into 2” pieces (12 pieces)
• yarn or cord
• optional: Tapestry needle

#### Building a Cable-Driven Robot

1. Use this video to assemble the servo motor unit.
2. Attach the servo motor to your Hummingbird board and set it to 0°.
3. Next, assemble the cable-driven mechanism using the video below. You may find it helpful to use a tapestry needle to thread the cable through the straws.
4. Reattach the servo to the Hummingbird board. Gradually increase the angle of the servo and observe the movement of the links.
5. Continue to increase the servo angle until the links stop moving. This is the maximum angle that you should use with your mechanism. Record this angle.
6. Write a program to move the servo back and forth between 0° and the maximum angle.
7. The motor acts to bend the linkage. What provides the energy to straighten the linkage? How could you use another servo to straighten the linkage?
8. We used a cable-driven mechanism to create this giraffe. What are some other ways that you might use this mechanism in a robot?

#### How the Mechanism Operates

You can use geometry to investigate how moving the cable causes the cable-driven linkage to bend at the joints.

1. The diagram below shows one joint of the cable-driven robot. We can approximate this as the triangle JAB. Assuming that the joint is midway between the two guides, what type of triangle is JAB?
2. Use your mechanism to measure the length of line segments JA and JB. Do these measurements support your answer to (1)? Explain.
3. Angle AJB in the diagram measures 110°. Draw a scaled version of triangle JAB using the measurements that you have taken so far and this angle. Lengths in the scaled version should be 10 times larger than the real-world lengths.
4. Measure the scaled length of line segment AB. What real-world length does this correspond to?
5. When the motor pulls on the cable, it acts to shorten the line segment AB. Suppose that the length of AB decreases by 20%. What is the new scaled length of this line segment?
6. Construct a new scaled version of triangle JAB using the decreased length. Measure angle AJB.
7. How has the change in cable length affected angle AJB? Explain what this means for a cable-driven robot.

You can create a cable-driven robot with multiple linkages. In this part of the lesson, you will connect two linkages to your servo motor unit. Examples with even more linkages are shown below.

1. Make sure your servo motor is set to 0°.
2. Use this video to modify your cable-driven mechanism to include two linkages. You will need a second cardboard box as a spacer. You may have one from a previous lesson, or you can make a second box using the instructions and paper template above. Alternatively, you can team up with a neighbor for this section!
3. Reattach the servo to the Hummingbird board. Gradually increase the angle of the servo and observe the movement of the links.
4. Continue to increase the servo angle until the links stop moving. This is the maximum angle that you should use with your mechanism. Record this angle.
5. Write a program to move the servo back and forth between 0° and the maximum angle.
7. We used two cable-driven linkages to create this bird. What are some other ways that you might use this mechanism in a robot?

#### Creating Cable-Driven Robots

You have already seen the giraffe and bird examples, but the you can create many other cable-driven robots! This video shows a cable-driven robotic hand.

In this lesson, the linkages were created from cardboard, but you can use other materials. This blooming flower was created with stiffened felt.

Now it is time to create your own cable-driven robot! How many linkages will you need? Will you connect them to the same servo or to different servos?

## Mechanisms: Gear Trains

In this lesson, you will be building mechanisms with gears. Watch this video to see an example.

A gear train is a mechanism that consists of two or more gears. Gears are disks with teeth that mesh together. The diagram below shows a gear train with two gears. This mechanism has the following parts:

• The drive gear is rotated by a motor.
• The teeth of the drive gear mesh with those of the driven gear.

As the drive gear rotates, its teeth turn the driven gear. How fast the driven gear rotates depends on the number of teeth it has relative to the number of teeth of the drive gear.

### Materials Needed

#### Paper Templates (See Teacher Materials)

When printing the templates, be sure to print them the actual size (no scaling) on 8.5” x 11” paper. You will use the templates to cut cardboard as shown in the instructions below. Be sure to use cardboard that is less than ⅛” thick.

• Motor Unit
• Box Unit

#### Other Materials

##### Building the Gear Train Mechanism
• Gear motor plus plastic brick adapter
• Pipe cleaner
• 3 Technic friction axle pegs
• 1 Technic 13M beam
• 2 Technic gears with 40 teeth
• 1 3M Technic axle
• 1 Technic bushing
##### Additional Materials for Investigating the Gear Ratio
• Pipe cleaner
• 1 Technic gear with 24 teeth
• 1 Technic gear with 8 teeth
• Stopwatch
##### Additional Materials for Extending the Gear Train
• More axles, bushings, and gears

#### Building the Gear Train Mechanism

1. You will need a motor unit for this lesson. You may have already built one. If not, you can use these instructions to assemble the motor unit.
2. Next, use this video to assemble your gear train mechanism.
3. Attach the motor to motor port 1 on your Hummingbird board. Write a simple program to turn on the motor. Observe the movement of the gears.
4. Does the drive gear rotate clockwise or counterclockwise? Does the driven gear rotate clockwise or counterclockwise?

#### Investigating the Gear Ratio

1. Glue a small piece of pipe cleaner to the bushing, as shown in the picture below.
2. Set the motor speed to 40 and measure the amount of time that it takes the driven gear to make ten rotations.
1. Start the stopwatch when the pipe cleaner passes the black beam.
2. Stop the stopwatch when the pipe cleaner has made ten complete rotations. The pipe cleaner should be in the same position that it was when you started the stopwatch.
3. Enter your measurement in the table below and compute the time required for one rotation of the driven gear.
3. What is the time required for one rotation of the drive gear? Explain your answer.
4. Replace the driven gear with a gear with 24 teeth. This video will show you how. Make sure that the teeth of the drive gear mesh with the teeth of the new driven gear.
5. Set the motor speed to 40 and measure the amount of time that it takes the driven gear to make ten rotations.
1. Enter your measurement in the table and compute the time required for one rotation of the driven gear.
6. Replace the driven gear with a gear with eight teeth. Make sure that the teeth of the drive gear mesh with the teeth of the new driven gear.
7. Set the motor speed to 40 and measure the amount of time that it takes the driven gear to make ten rotations.
1. Enter your measurement in the table and compute the time required for one rotation of the driven gear.
8. The gear ratio is defined as the proportion that relates the number of teeth on the driven gear to the number of teeth on the drive gear.
1. Compute gear ratio for each driven gear and enter it in the table.
9. Based on your data, write an equation that predicts the time for one rotation of the driven gear based on the gear ratio and the time for one rotation of the drive gear. You should be able to defend your equation.

#### Extending the Gear Train

A gear train can include more than two gears. Gears in between the drive gear and the driven gear are called passive gears. For example, the picture below shows a gear train with three gears. The 24-tooth gear in the middle is a passive gear.

Try building different gear trains. How does the number of gears in the train influence the direction of rotation of the driven gear?

In this lesson, the gear ratio was always greater than or equal to 1. However, this is not a requirement. Try using a smaller gear as the drive gear!

#### Using Gears to Create Robots

Gears are used in a robot design to increase or decrease the speed of a motor. Increasing the speed of the motor decreases the torque that it can apply; this means that the motor cannot apply as much force to rotate an object. Decreasing the rotation speed of the motor increases the amount of torque that it can apply. If you need your robot to rotate something heavy, you will need to use gears to decrease the rotation speed.

Gear trains are often used to in vehicles; for example, this video shows how gears are used in a car. However, gears can also be used in many other ways. The video below shows how gears were used to create a robotic Etch-A-Sketch and ballerinas that rotate at different speeds.

Now it is time to use gears to create your own robot! Do you want to increase or decrease the rotation speed of the motor? How many gears do you need in your gear train?

###### News

In the last two lessons, you learned to make mechanisms with cranks, rods, and pistons. These mechanisms are special cases of a more general type of mechanism called a linkage. In this lesson, you will explore other types of linkages. Watch this video for an example.

The diagram below shows a four-bar linkage. This mechanism has the following parts:

• Four links that are connected by four rotating joints.
• Three of the links can move, but the fourth is fixed in position. This link is called the ground link.
• One of the moving links is a crank that is rotated by a motor.

As the crank rotates, it causes two other links to move while the ground link remains fixed in position. Varying the lengths of the links produces different patterns of movement.

#### Materials Needed

##### Paper Templates (See Teacher Materials)

When printing the templates, be sure to print them the actual size (no scaling) on 8.5” x 11” paper. You will use the templates to cut cardboard as shown in the instructions below. Be sure to use cardboard that is less than ⅛” thick.

• Motor Unit
• Box Unit
##### Other Materials
###### Building the Four-Bar Linkage Mechanism
• motor unit with gear motor plus plastic brick adapter
• pipe cleaner
• 5 Technic friction axle pegs
• 4 Technic beams, two 5M and two 13M
• 11 Technic friction pegs
• 4 Technic 13M beams
• 2 Technic 5M beams
• 2 Technic 3M beams
• 1 Technic 9M beam
• motor unit with gear motor and plastic brick adapter
• small box
• pipe cleaner
• marker

#### Building the Four-Bar Linkage Mechanism

1. You should complete the crank lesson prior to this one. If you have not already completed the crank lesson, do that first. This lesson will use the motor unit from the crank lesson.
3. Attach the motor to motor port 1 on your Hummingbird board. Write a simple program to turn on the motor. Observe the movement of the four-bar linkage.

#### Grashof Condition

Not every set of link lengths will produce a working four-bar linkage. The lengths must satisfy an equation known as the Grashof condition. This equation is defined in terms of the following variables:

• s is the length of the shortest link
• l is the length of the longest link
• p is the length of one of the intermediate links
• q is the length of the other intermediate link

1. Measure the lengths of all four of the links in your mechanism (including the ground link). Which links are s and l?
2. You have seen that your linkage can move, so you know that it should satisfy the Grashof condition. Use your measurements to show that it does.
3. Next, move the pin that connects the two 13M beams. Place this pin so that it is in the center hole for both of these beams. You may have to rotate the crank to reconnect the two beams.
4. How have the link lengths changed for your mechanism? Does the linkage still meet the Grashof condition? Predict whether or not the linkage will be able to move.
6. Again, move the pin that connects the two 13M beams. Place this pin so that it is in at the end of one beam and in the fifth hole of the other (close to the joint of the ground link). You may have to rotate the crank to reconnect the two beams.
7. How have the link lengths changed for your mechanism? Does the linkage still meet the Grashof condition? Predict whether or not the linkage will be able to move.

1. Use this video to transform your four-bar linkage into a scissor linkage. You will need four more 13M beams and six more connecting pins.
2. This mechanism is based on a four-bar linkage, but it uses additional links to increase the amount of movement produced by the linkage.
3. The picture below shows a scissor linkage at two different positions.
1. As the red point on the linkage moves from height h1 to height h2, how far does the top of the linkage move? Defend your answer using congruent triangles.
4. We used the scissor linkage to animate a fish leaping out of the water. What are some other ways that you might use a scissor linkage in a robot?

1. For the next part of this lesson, you will need two motor units. You can use these instructions to assemble a second one, or you can team up with a neighbor!
2. Use the two motor units to create a new linkage for drawing. You will need a small box, a pipe cleaner, paper, a marker, two 5 M beams, two 13 M beams, two 3M beams, one 9M beam, and 11 connecting pins.
3. Attach the motors to motor ports 1 and 2 on your Hummingbird board. Write a program to turn on the motors. What does your robot draw?
4. Vary the speeds of the motor. Use a different piece of paper for each speed combination and label it with the speeds you used. This will enable you to compare your drawings more easily.
5. How do the speeds of the two motors affect what your robot draws?
6. What does the robot draw when the two speeds are equal? How is this different from the drawings when the speeds are different?
7. Your drawing robot is a five-bar linkage. Draw a picture of it and label the five links (don’t forget the ground link!).
8. A five-bar linkage can move in more different ways than a four-bar linkage. That is why you can use two cranks to make two of the links rotate independently. What would happen if you tried to attach motors to two of the links in the four-bar linkage?

#### Using Linkages to Create Robots

In this lesson, you have used different kinds of linkages to create several different robots, but there are so many more possibilities! Theo Jansen even uses linkages to create enormous works of art!

As examples, this video shows a linkage that was used to make the wings of a penguin flap, and the video below shows a robot arm that incorporates a number of linkages. How would you describe the linkages shown in these videos?

Now it is time to use linkages to create your own robot! How can you modify the linkages you used in this lesson to make something new?

## Mechanisms: Cranks with Pistons

In this lesson, you will be extending your crank mechanism to create a crank and piston mechanism. Watch this video to see what it will look like.

This mechanism has four parts:

• The crank is attached to a motor that rotates it.
• The rod is attached to the crank and the piston at joints that are free to rotate.
• The guide is fixed in place; its purpose is to make the piston move in a line. The piston is free to move up and down in a line but cannot rotate.

As the crank rotates, the piston moves up and down in a linear reciprocating motion. A crank and piston system transforms rotational motion into linear motion. The linear motion can be vertical or horizontal (or in another direction), depending upon the orientation of the guide.

#### Materials Needed

##### Paper Template (See Teacher Materials)

When printing the template, be sure to print it the actual size (no scaling) on 8.5” x 11” paper. You will use the template to cut cardboard as shown in the instructions below. Be sure to use cardboard that is less than ⅛” thick.

• Piston Unit
##### Other Materials
• crank mechanism (from crank lesson)
• 1 Technic friction axle peg
• 1 Technic 13M beam
• pipe cleaner
• ruler or tape measure
• stopwatch

#### Building the Crank and Piston Mechanism

1. You will need a crank mechanism for this lesson. If you have not already completed the crank lesson, do that first.
2. Next, use this video to assemble your crank and piston mechanism.
3. Attach the motor to motor port 1 on your Hummingbird board. Write a simple program to turn on the motor. Observe the movement of the mechanism.

#### Graphing the Position of the Piston

Think about starting a timer when you turn on the motor. As the seconds pass, the crank rotates and the piston moves up and down. We could make a graph with time on the x-axis and the position of the piston on the y-axis. This graph would look something like the curve shown below.

The figure above shows only a single rotation of the crank. As the crank rotates again and again, this curve would be repeated. This type of periodic motion is called a wave.

1. The highest point of a wave is called the peak, and the lowest point is called the trough. Label one peak and one trough on the graph above.
2. The distance between the peak and the trough is called the wave height. Label the wave height on the graph above.
3. How can you find the wave height for the piston? Measure this value and then compare your method and answer with your classmates.
4. A wave is often described by its amplitude instead of its wave height. The amplitude is half of the wave height. Find the amplitude of the piston wave.

#### Changing the Length of the Crank

Now you will investigate how you can change the piston wave by changing the length of the crank. You can change the length of the crank by using the other holes along the length of the crank.

1. Move the connecting pin at the end of the crank to the neighboring hole.
2. Measure the amplitude of the piston wave.
3. Change the length of the crank again. This time, place the connecting pin between the two connecting pins that connect the crank to the motor adapter.
4. Measure the amplitude of the piston wave.
5. How is the amplitude of the piston wave related to the length of the crank?
6. Can the rod ever be shorter than the crank? Why or why not?

#### Period of the Piston Wave

The time period between one peak and the next is called the period of a wave.

1. Set the speed of the motor to 20.
2. Use a stopwatch to measure how long it take the crank to rotate 10 times.
3. What is the period of the wave?
4. Complete the table below.
5. How is the period of the wave related to the speed of the motor? Predict the period for a speed of 50 and give evidence for your answer.

#### Using Cranks and Pistons to Create Robots

Crank and piston mechanisms are used in robots to produce linear movement in a particular direction. For example, this video shows a project in which a piston is used to move a character up and down. Can you identify the parts of the mechanism in the video? This robotic turtle also uses a crank and piston. What might be inside the turtle’s shell?

Now try it out in your own robot! How far do you want to move the piston? How long do the crank and connecting rod need to be to make this happen? Remember, the piston does not have to move only vertically or horizontally. It can move along a straight line in any direction!

• Crank and Slider Mechanism: This website animates the movement of a crank and piston mechanism and describes its parts.
• Diesel Engine: This video shows how a diesel engine uses a crank and piston mechanism in a car or truck. In this case, the explosion of the fuel produces the linear motion of the piston, and the mechanism transforms this motion to rotate the wheels of the vehicle.

## Mechanisms: Cranks

In this lesson, you will be building a crank mechanism. Watch this video to see what it will look like.

This mechanism has three parts:

• The crank is attached to a motor that rotates it.
• The rod is attached to the crank using a connecting pin. The rod is free to rotate about this pin.
• The guide is fixed in place; its purpose is to keep the rod in place horizontally. The rod is free to rotate and move vertically.

As the crank rotates, the rod moves back and forth. This type of back and forth motion is called reciprocating motion.

#### Materials Needed

##### Paper Templates (See Teacher Materials)

When printing the templates, be sure to print them the actual size (no scaling) on 8.5” x 11” paper. You will use the templates to cut cardboard as shown in the instructions below. Be sure to use cardboard that is less than ⅛” thick.

• Motor Unit
• Box Unit
##### Other Materials
• Gear motor plus plastic brick adapter
• 3 Technic friction axle pegs
• 2 Technic beams: 5M and 13M
• Pipe cleaner
• Cardboard
• Construction paper
• Pencil

#### Building the Crank Mechanism

1. You will need a motor unit for this lesson. You may have already built one. If not, you can use these instructions to assemble the motor unit.
2. Next, use this video to assemble your crank mechanism.
3. Attach the motor to motor port 1 on your Hummingbird board. Write a simple program to turn on the motor. Observe the movement of the crank and the rod.
4. Change the speed of the motor. How does this change the movement of the rod?

#### Calculating How Far the Crank Moves

You can use geometry to calculate how far the crank will move horizontally and vertically.

1. This diagram shows an idealized version of the crank mechanism. The length of the crank is c, and r is the length of the rod. G is the point where the guide keeps the rod in place. The rod must always pass through this point.
2. Draw the crank and guide when the rod is at its highest point. What are the coordinates of the top of the rod in terms of c and r?
3. Draw the crank and guide when the rod is at its lowest point. What are the coordinates of the top of the rod in terms of c and r?
4. In terms of c and r, what is the vertical distance that the top of the rod moves between its highest and lowest points?
5. Measure c and r for your crank mechanism. The length of the rod should be measured from the center of the connecting pin to the center of the hole at the end of the rod. The length of the crank should be measured from the center of the motor to the center of the connecting pin at the end of the crank, as shown in the picture below.
6. Use your measurements to calculate the vertical distance that the rod moves.
7. Next, you will find the horizontal distance that the rod moves as it travels. The crank mechanism is shown below with the crank lying along the x-axis. The distance h is the maximum distance that the top of the rod moves to the left of the y-axis.
8. What similar triangles can you find in the diagram above? Use the properties of similar triangles to fill in the blanks in the equation below.
9. Consider the triangle below point G. We will call the height of this triangle a. Measure the value of a for your crank mechanism by measuring the vertical distance from the center of the motor to the guide.
10. Now that you have values for a and c, find the length of the third side of the triangle in the diagram above.
11. Now you have enough information to find h! Use your equation from (8) to solve for h. What is the total horizontal distance that the end of the rod moves?

#### Finding the Path of the Rod

Next, you will trace the path of the end of the rod. This way, you can get a better idea of the type of movement caused by a crank. This process is shown in this video and described below.

1. Tape a piece of paper onto a piece of cardboard about the same size. Place this behind the end of the rod.
2. Place a pencil through the top hole of the rod.
3. As the rod moves, use the pencil to trace its path. Try not to affect the motion of the rod; just follow it with the pencil.
4. Remove the paper and the pencil. Darken the path you traced and measure its maximum width and height.
5. How do these values compare with the ones that you calculated above?

#### Changing the Length of the Crank

Now you will investigate how you can change the motion of the mechanism by changing the length of the crank. You can change the length of the crank by using the other two holes along the length of the crank.

1. Use this video to change the length of the crank. Move the connecting pin to the next hole on the crank.
2. Trace the path of the rod. Measure the maximum width and height of the new path.
3. Change the length of the crank again. This time, place the connecting pin between the two pins that connect the crank to the motor adapter.
4. Trace the path of the rod. Measure the maximum width and height of the new path.
5. How does changing the length of the crank affect the path of the rod?

#### Using Cranks to Create Robots

Cranks can be incorporated into a robot design in many different ways. Two examples are shown in this video. Can you identify the parts of the mechanisms in this video? In the fish example, how has the crank mechanism been modified?

Now it is time to use a crank to create your own robot! How can you use reciprocating motion to make make something interesting? Do you need to modify the crank, rod, or guide for your design?

• Crank: This website animates the movement of a crank mechanism and describes its parts.
• Karakuri: How to Make Mechanical Paper Models that Move by Keisuke Saka: This book describes a number of mechanisms. It comes with paper models of different mechanisms and examples of how they can be used in fun ways.

## Laser Cut Mechanisms: Cable-Driven Robots

In this lesson, you will be building a cable-driven robot. Watch this video to see what it will look like.

The mechanism includes the following parts:

• Links are connected by rotating joints.
• A hollow guide is attached to each link.
• A cable passes through all the guides. This cable is attached to a motor.

The motor pulls on the cable to move the links. As the motor pulls the cable, the guides become closer together, which makes the links rotate about the joints. Note that the cable can only move the mechanism in one direction, to bend the linkage at the joints.

#### Materials Needed:

• servo motor with bag of accessories
• straws cut into 2” pieces (12 pieces)
• yarn or cord
• optional: Tapestry needle
• Laser Cut Servo & Cable Driven Unit (see Teacher Materials)

#### Building a Cable-Driven Robot

1. Use this video to assemble the servo motor unit.
2. Attach the servo motor to your Hummingbird board and set it to 0°.
3. Next, assemble the cable-driven mechanism using the video below. You may find it helpful to use a tapestry needle to thread the cable through the straws.
4. Reattach the servo to the Hummingbird board. Gradually increase the angle of the servo and observe the movement of the links.
5. Continue to increase the servo angle until the links stop moving. This is the maximum angle that you should use with your mechanism. Record this angle.
6. Write a program to move the servo back and forth between 0° and the maximum angle.
7. The motor acts to bend the linkage. What provides the energy to straighten the linkage? How could you use another servo to straighten the linkage?
8. We used a cable-driven mechanism to create this giraffe. What are some other ways that you might use this mechanism in a robot?

#### How the Mechanism Operates

You can use geometry to investigate how moving the cable causes the cable-driven linkage to bend at the joints.

1. The diagram below shows one joint of the cable-driven robot. We can approximate this as the triangle JAB. Assuming that the joint is midway between the two guides, what type of triangle is JAB?
2. Use your mechanism to measure the length of line segments JA and JB. Do these measurements support your answer to (1)? Explain.
3. Angle AJB in the diagram measures 110°. Draw a scaled version of triangle JAB using the measurements that you have taken so far and this angle. Lengths in the scaled version should be 10 times larger than the real-world lengths.
4. Measure the scaled length of line segment AB. What real-world length does this correspond to?
5. When the motor pulls on the cable, it acts to shorten the line segment AB. Suppose that the length of AB decreases by 20%. What is the new scaled length of this line segment?
6. Construct a new scaled version of triangle JAB using the decreased length. Measure angle AJB.
7. How has the change in cable length affected angle AJB? Explain what this means for a cable-driven robot.

You can create a cable-driven robot with multiple linkages. In this part of the lesson, you will connect two linkages to your servo motor unit. Examples with even more linkages are shown below.

1. Make sure your servo motor is set to 0°.
2. Use this video to modify your cable-driven mechanism to include two linkages. You will need a second cardboard box as a spacer. You may have one from a previous lesson, or you can make a second box using the instructions and laser cutter file above. Alternatively, you can team up with a neighbor for this section!
3. Reattach the servo to the Hummingbird board. Gradually increase the angle of the servo and observe the movement of the links.
4. Continue to increase the servo angle until the links stop moving. This is the maximum angle that you should use with your mechanism. Record this angle.
5. Write a program to move the servo back and forth between 0° and the maximum angle.
7. We used two cable-driven linkages to create this bird. What are some other ways that you might use this mechanism in a robot?

#### Creating Cable-Driven Robots

You have already seen the giraffe and bird examples, but the you can create many other cable-driven robots! This video shows a cable-driven robotic hand.

In this lesson, the linkages were created from cardboard, but you can use other materials. This blooming flower was created with stiffened felt.

Now it is time to create your own cable-driven robot! How many linkages will you need? Will you connect them to the same servo or to different servos?

## Laser Cut Mechanisms: Cams

In this lesson, you will be building a cam mechanism. Watch this video to see what it will look like. The rotating disk makes the post move up and down.

This mechanism has three main parts:

• A cam is a flat disk that is rotated by a motor.
• The cam follower sits on top of the cam. It moves up and down as the cam rotates.
• The guide is fixed in place; its purpose is to keep the cam follower positioned above the cam.

The cam follower moves loosely in the guide. The cam pushes the follower up, and gravity pulls it down. This means that a cam mechanism transforms rotation into vertical motion.

#### Materials Needed

• Gear motor plus plastic brick adapter
• 2 Technic friction axle pegs
• ¼” dowel rod approximately 6” long
• 2 pennies
• Craft stick (popsicle stick)
• Rubber band
• Laser Cut Cam & Motor Unit (see Teacher Materials)

#### Building the Cam Mechanism

1. You will need a motor unit for this lesson. You may have already built one. If not, you can use these instructions to assemble the motor unit kit.
2. Next, use this video to assemble the parts in your cam mechanism kit. There are a lot of parts, so take your time and be sure to follow the directions carefully.
3. Attach the motor to motor port 1 on your Hummingbird board. Write a simple program to turn on the motor. Observe the movement of the cam and cam follower. Important Note: You will need to hold the motor unit and cam assembly in place.
4. Change the speed of the motor. How does this change the movement of the cam follower?

The first entry in the table below shows the cam pointing to the right and the cam follower on top of it. Imagine that the cam rotates clockwise.

1. Where will it be after it rotates 90°? Draw that position in the table.
2. Draw the position of the cam after it rotates 180°, 270°, and 360°.
3. For each angle, draw the position of the cam follower.
4. At what angle will the follower be at its highest point?
5. At approximately what angle will the follower be at its lowest point?
6. How can you find the distance that the cam follower travels between its highest and lower points?
##### Second Oval Cam

Consider the second oval cam, which is shown in the table below. Imagine that the cam rotates clockwise. Draw the position of the cam for each angle in the table below, and then draw the position of the cam follower.

1. At what angle will the follower be at its highest point?
2. At approximately what angle will the follower be at its lowest point?
3. What distance does the cam follower travel between its highest and lower points?
4. Watch this video to learn how to remove a cam and change it for a different one. Put the second oval cam on the dowel rod. Turn on the motor and observe the movement of the cam mechanism.
5. Does its movement match your predictions? How does the movement differ from what you observed with the first cam?
6. Make the motor speed negative to turn the cam in the opposite direction. How does this affect the movement of the cam follower?
7. At what position(s) of the cam does the cam follower move most quickly? Where does it move slowly?
##### Snail Cam

Complete the table below for the third cam, which is called a snail cam. For the table, assume that the cam rotates clockwise.

1. What do you think will happen when the cam rotates counterclockwise? After you complete the table, test your predictions.
##### Heart Cam

The last cam is the heart cam. Consider its shape.

1. When will the cam follower be at its highest point?
2. When will the cam follower be at its lowest point?
3. At what position(s) of the cam will the cam follower move most quickly? Where will it move slowly?
4. Test your predictions. Is there anything you did not expect about how this cam moves?

#### Using Cams to Create Robots

This video shows just two of the many possible ways that you might use cam mechanisms to make robots. Can you identify the parts of the mechanisms in this video?

Now that you have explored how cams work, you are ready to use them in your own creation! Design a robot that uses at least one cam. Maybe you even want to include multiple cams or design your own cam shape!

• Cam Mechanisms: This website animates the movements that results from different cam shapes.
• Cams and Followers: You used a cam follower with a flat bottom in this lesson, but you can learn about other choices for the cam follower here.
• Karakuri: How to Make Mechanical Paper Models that Move by Keisuke Saka: This book describes a number of mechanisms. It comes with paper models of different mechanisms and examples of how they can be used in fun ways.

## Laser Cut Mechanisms: Winches

In this lesson, you will be building a winch mechanism. Watch this video to see what it will look like.

This mechanism has three parts:

• The winch is a cylinder attached to a motor that rotates it.
• The cable is wound around the winch. It is flexible and can be made of string, cord, or wire.
• The mass is attached to the end of the cable.

When the winch shown below rotates counterclockwise, it winds more of the cable around itself, and the mass moves upward. When the winch rotates clockwise, it releases more of the cable, and the mass moves downward. This mechanism transforms rotation into vertical motion in a straight line.

#### Materials Needed

##### Building the Winch Mechanism
• gear motor plus plastic brick adapter
• ¼” dowel rod
• 2 Technic friction axle pegs
• string
• quarter
• Laser Cut Winch & Motor Unit (see Teacher Materials)
##### Additional Materials for Using Two Winches
• gear motor plus plastic brick adapter
• 2 Technic friction axle pegs
• string
• object to move (small plastic animal or similar)

#### Building the Winch Mechanism

1. You will need a motor unit for this lesson. You may have already built one. If not, you can use these instructions to assemble the motor unit kit.
2. Next, use this video to assemble the parts in your winch mechanism kit.
3. Attach the motor to motor port 1 on your Hummingbird board. Write a simple program to turn on the motor. Observe the movement of the winch and mass.
1. Which direction of motor rotation (positive or negative) moves the mass upward?
2. Which direction of motor rotation moves the mass downward?

#### Drawing a Free-Body Diagram

A free-body diagram is a drawing of all the forces acting on an object. Each force is shown as acting at the center of mass of the object (in this case, the center of the quarter).

1. Draw a free-body diagram of the mass. What force pulls the quarter upward? What force pulls the quarter downward?
2. Which force is larger when the mass moves upward?
3. Which force is larger when the mass moves downward?

#### Using Two Winches

You can use a single winch to raise and lower a mass in the vertical direction. You can also use winches to move objects horizontally. This requires two winches.

1. For the next part of this lesson, you will need two motor units with winches. You can make another winch mechanism, or you can team up with a neighbor!
2. Connect the two winch mechanisms to motor ports 1 and 2 on your Hummingbird board.
3. To move an object horizontally, one winch will need to release cable while the other winch retrieves cable. For example, for the snail in the video below to move to the left, the left winch must retrieve (wind up) cable while the right winch releases (winds out) cable.
4. Use a table like the one below to record whether positive or negative motor speed makes each winch retrieve or release cable.
5. Tape the winch mechanisms to the table. Tie each cable to one end of a piece of cardboard. This forms a platform that you can use to move a small object back and forth.
6. Write a program that moves the platform slowly to the left by retrieving cable from one winch while simultaneously releasing it from the other.
7. Write a program that moves the platform slowly to the right.
8. Use a knob sensor to control whether the platform moves to the left or right.

#### Using Winches to Create Robots

A single winch can be used to move an object up and down, but a single winch can also move an object along an inclined plane. This video shows a model of Pittsburgh with a cable car moving up and down a hill.

Two winches were used to create this biomechanical model of the knee. One winch represents the muscles that bend (flex) the knee, and the other represents the muscles that straighten (extend) the knee. To bend the knee, the flexor muscles muscles shorten while the extensor muscles lengthen. This is represented by the flexor winch retrieving cable while the extensor winch releases cable.

Now it is time to use winches to create your own robot! What linear movement do you want to create? How many winches do you need?

• Winch: This website gives some nice real-world examples of winches.
###### News

In the last two lessons, you learned to make mechanisms with cranks, rods, and pistons. These mechanisms are special cases of a more general type of mechanism called a linkage. In this lesson, you will explore other types of linkages. Watch this video for an example.

The diagram below shows a four-bar linkage. This mechanism has the following parts:

• Four links that are connected by four rotating joints.
• Three of the links can move, but the fourth is fixed in position. This link is called the ground link.
• One of the moving links is a crank that is rotated by a motor.

As the crank rotates, it causes two other links to move while the ground link remains fixed in position. Varying the lengths of the links produces different patterns of movement.

#### Materials Needed

##### Building the Four-Bar Linkage Mechanism
• motor unit with gear motor plus plastic brick adapter
• pipe cleaner
• 5 Technic friction axle pegs
• Laser Cut Motor & Linkage Unit (see Teacher Materials)
• 7 Technic friction pegs
• motor unit with gear motor and plastic brick adapter
• small box
• pipe cleaner
• marker

#### Building the Four-Bar Linkage Mechanism

1. You should complete the crank lesson prior to this one. If you have not already completed the crank lesson, do that first. This lesson will use the motor unit from the crank lesson.
3. Attach the motor to motor port 1 on your Hummingbird board. Write a simple program to turn on the motor. Observe the movement of the four-bar linkage.

#### Grashof Condition

Not every set of link lengths will produce a working four-bar linkage. The lengths must satisfy an equation known as the Grashof condition. This equation is defined in terms of the following variables:

• s is the length of the shortest link
• l is the length of the longest link
• p is the length of one of the intermediate links
• q is the length of the other intermediate link

1. Measure the lengths of all four of the links in your mechanism (including the ground link). Which links are s and l?
2. You have seen that your linkage can move, so you know that it should satisfy the Grashof condition. Use your measurements to show that it does.
3. Next, move the pin that connects the two long links. Place this pin so that it is in the center hole for both of these links. You may have to rotate the crank to reconnect the two links.
4. How have the link lengths changed for your mechanism? Does the linkage still meet the Grashof condition? Predict whether or not the linkage will be able to move.
6. Again, move the pin that connects the two long links. Place this pin so that it is in at the end of one link and the middle of the other. You may have to rotate the crank to reconnect the two links.
7. How have the link lengths changed for your mechanism? Does the linkage still meet the Grashof condition? Predict whether or not the linkage will be able to move.

1. Use this video to transform your four-bar linkage into a scissor linkage. You will need six more connecting pins and the cardboard parts that you set aside earlier.
2. This mechanism is based on a four-bar linkage, but it uses additional links to increase the amount of movement produced by the linkage.
3. The picture below shows a scissor linkage at two different positions.
1. As the red point on the linkage moves from height h1 to height h2, how far does the top of the linkage move? Defend your answer using congruent triangles.
4. We used a scissor linkage to animate a fish leaping out of the water. What are some other ways that you might use a scissor linkage in a robot?

1. For the next part of this lesson, you will need two motor units. You can use these instructions to assemble one, or you can team up with a neighbor!
2. Use the two motor units to create a new linkage for drawing. You will need a small box, a pipe cleaner, paper, a marker, and 7 connecting pins.
3. Attach the motors to motor ports 1 and 2 on your Hummingbird board. Write a program to turn on the motors. What does your robot draw?
4. Vary the speeds of the motor. Use a different piece of paper for each speed combination and label it with the speeds you used. This will enable you to compare your drawings more easily.
5. How do the speeds of the two motors affect what your robot draws?
6. What does the robot draw when the two speeds are equal? How is this different from the drawings when the speeds are different?
7. Your drawing robot is a five-bar linkage. Draw a picture of it and label the five links (don’t forget the ground link!).
8. A five-bar linkage can move in more different ways than a four-bar linkage. That is why you can use two cranks to make two of the links rotate independently. What would happen if you tried to attach motors to two of the links in a four-bar linkage?

#### Using Linkages to Create Robots

In this lesson, you have used different kinds of linkages to create several different robots, but there are so many more possibilities! Theo Jansen even uses linkages to create enormous works of art!

As examples, this video shows a linkage that was used to make the wings of a penguin flap, and the video below shows a robot arm that incorporates a number of linkages. How would you describe the linkages shown in these videos?

Now it is time to use linkages to create your own robot! How can you modify the linkages you used in this lesson to make something new?