Task 1
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 this robot and incorporate types of conic section into its design
Respond to the following questions
1) What will your robot be able to do
2) What conic section do you plan on using in your design? Make sure to use at least 3
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.
Task 1:
1) The robot will be able to assist in construction projects by utilizing its advanced technology to perform tasks such as welding, lifting heavy materials, and precision cutting.
2) I plan on using circles, ellipses, and hyperbolas in the design of the robot.
Task 2:
- Circle: Equation: (x-2)^2 + y^2 = 4
- Vertex: (2,0)
- Center: (2,0)
- Radius: 2
- Ellipse: Equation: x^2/9 + y^2/4 = 1
- Vertices: (-3,0) and (3,0)
- Foci: (-5,0) and (5,0)
- Major and Minor Axes: 6 and 4, respectively
- Hyperbola: Equation: x^2/9 - y^2/4 = 1
- Vertices: (-3,0) and (3,0)
- Foci: (-5,0) and (5,0)
- Asymptotes: y = 2/3x and y = -2/3x
Task 3:
I will combine the three conic sections into the design of the robot, incorporating the features of each shape in a cohesive and visually appealing manner. For example, the circles can be used for the robot's joints, the ellipses for its body shape, and the hyperbolas for its robotic arms.
Task 4:
1) The robot's design is structurally sound, as the use of conic sections such as circles, ellipses, and hyperbolas provide strength and stability to the overall structure. The vertices, foci, and axes of the conic sections help distribute weight and pressure evenly, ensuring the robot can perform its tasks effectively.
2) The robot accomplishes its stated purpose from Task 1, as the incorporation of conic sections into its design allows for efficiency and precision in construction tasks. The use of circles for joints ensures flexibility, ellipses for the body shape provide stability, and hyperbolas for the arms offer range of motion. Overall, the design elements work together to create a functional and effective robotic prototype for construction projects.