Introduction
Congratulations! You have been selected by an engineering firm to design their
newest robotic prototype. As of this moment, it is your job to come up with a
purpose for the robot and incorporate various types of conic sections into its design.
Task 1
Respond to the following questions.
1. What will your robot be able to do?
2. Which conic sections do you plan on using in your design? Make sure to use
at least three.
Task 2
Choose three of the four conic sections that you learned about in this unit:
parabolas, circles, ellipses, and hyperbolas. Make a detailed graph of each one that
you intend on incorporating into your design. For each of these graphs, be sure to
label important points such as vertices, foci, axes, and directrixes. Also, identify
each graph with its equation. Make sure that the equation is the same one that will
be used in your final design.
Task 3
Make a graph that combines all three of your conic sections from Task 2. Be sure to
incorporate other aspects of the drawing that will make your robot complete. For
example, you can draw a segment to have the two parts of a hyperbola connect.
Task 4
Respond to the following questions.
3. Is your robot’s design structurally sound? Use features of the graph to justify
your response.
4. Does your robot accomplish its stated purpose from Task 1? Justify your
response by referencing the robot’s overall structure, including its use of
conic sections in its design.
In your submission, make sure to submit your answers to all questions in Tasks 1
and 4 and all graphs from Tasks 2 and 3.
Task 1:
1. My robot will be able to navigate through different terrains and collect data using its built-in sensors. It will also be able to communicate and transmit data back to a remote location.
2. I plan on using circles, ellipses, and hyperbolas in my design.
Task 2:
Circle:
Equation: (x - 3)^2 + (y + 2)^2 = 9
Center: (3, -2)
Radius: 3
Ellipse:
Equation: (x/2)^2 + y^2 = 1
Center: (0, 0)
Vertices: (2, 0), (-2,0)
Foci: (sqrt(3), 0), (-sqrt(3), 0)
Axes: Major axis along the x-axis, minor axis along the y-axis
Hyperbola:
Equation: (x/2)^2 - y^2 = 1
Vertices: (2, 0), (-2, 0)
Foci: (sqrt(5), 0), (-sqrt(5), 0)
Axes: Transverse axis along the x-axis, conjugate axis along the y-axis
Task 3:
Combination of circle, ellipse, and hyperbola:
Incorporated other aspects: The robot has a circular base with an elliptical body and two hyperbolic arms that can extend and contract to collect data from different locations.
Task 4:
3. Yes, the robot's design is structurally sound. The circular base provides a stable foundation, while the elliptical body and hyperbolic arms provide a streamlined and efficient design for data collection.
4. Yes, the robot accomplishes its stated purpose from Task 1. The incorporation of circles, ellipses, and hyperbolas allows for a versatile and adaptable design that can navigate through different terrains and collect data efficiently. The hyperbolic arms can extend and contract to reach data from different locations, while the circular base provides stability for the robot's movements.
Task 1:
1. My robot will be able to perform various tasks such as picking and placing objects, navigating through obstacles, and performing precise movements.
2. The conic sections I plan on using in my design are parabolas, circles, and ellipses.
Task 2:
Graphs of the chosen conic sections:
1. Parabola:
Equation: y^2 = 4ax
Important points: Vertex (0, 0), directrix x = -a, focus (a, 0)
[Graph of the parabola]
2. Circle:
Equation: (x-h)^2 + (y-k)^2 = r^2
Important points: Center (h, k), radius r
[Graph of the circle]
3. Ellipse:
Equation: (x-h)^2/a^2 + (y-k)^2/b^2 = 1
Important points: Center (h, k), major axis length 2a, minor axis length 2b
[Graph of the ellipse]
Task 3:
Graph combining all three conic sections:
[Combined graph showing the robot design incorporating parabolas, circles, and ellipses. Other aspects of the robot's design are also included.]
Task 4:
3. The robot's design is structurally sound as the conic sections used provide stability and balance to the overall structure. The parabolas can act as sturdy bases, while the circles and ellipses can add strength and support to specific parts of the robot.
4. Yes, the robot accomplishes its stated purpose from Task 1. The use of conic sections in its design enhances its functionalities. The parabolas can assist in precise movements and lifting tasks, while the circles can help with rotating or gripping objects. The ellipses can contribute to smooth navigation and agility through their curved paths. Overall, the incorporation of conic sections improves the robot's overall movement capabilities and efficiency in performing its tasks.