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Robot Motion (Episode 105) | The Robot Doctor

  Classroom Resource Information  

Title:

 Robot Motion (Episode 105) | The Robot Doctor

URL:

 https://aptv.pbslearningmedia.org/resource/episode-105-robot-motion-video/the-robot-doctor/

Content Source:

 PBS
Type: Audio/Video

Overview:

Use math to determine how a robot moves, and its future positions - given the model of the robot and the equations of motion, in this 14-minute episode. The goal of this video series is to teach the basics of Robotics: the what, why, and how—with examples—and to provide take-home problems to solve.

Robots need to move, but how do they determine how far to turn the wheels to get where they want? In this lesson we explore the equations of motion for differential drive robots. We will walk through how to derive these equations as well as talk about some of the possible wheel configurations a robot could have.

Content Standard(s):
Science
SC2015 (2015)
Grade: 9-12
Physics
1 ) Investigate and analyze, based on evidence obtained through observation or experimental design, the motion of an object using both graphical and mathematical models (e.g., creating or interpreting graphs of position, velocity, and acceleration versus time graphs for one- and two-dimensional motion; solving problems using kinematic equations for the case of constant acceleration) that may include descriptors such as position, distance traveled, displacement, speed, velocity, and acceleration.

NAEP Framework
NAEP Statement::
P12.17: The motion of an object can be described by its position and velocity as functions of time and by its average speed and average acceleration during intervals of time.

NAEP Statement::
P12.19: The motion of an object changes only when a net force is applied.

NAEP Statement::
P12.22: Gravitation is a universal attractive force that each mass exerts on any other mass. The strength of the gravitational force between two masses is proportional to the masses and inversely proportional to the square of the distance between them.

Unpacked Content
Scientific And Engineering Practices:
Planning and Carrying out Investigations
Crosscutting Concepts: Scale, Proportion, and Quantity
Disciplinary Core Idea: Motion and Stability: Forces and Interactions
Evidence Of Student Attainment:
Students:
  • Describe the motion of an object in terms of time, displacement, velocity, and acceleration in both one and two dimensions by analyzing a graph of that motion.
  • Use data obtained from observation or experimental design of an investigation to analyze and explain the motion of an object in one and two dimensions.
  • Use kinematic equations to solve for the displacement, velocity and acceleration of an object undergoing constant acceleration in both one and two dimensions using correct units.
Teacher Vocabulary:
  • model
  • graph
  • instant
  • interval
  • position
  • velocity
  • acceleration
  • displacement
  • distance
  • speed
  • average speed
  • average velocity
  • experimental design
  • kinematic equations
  • investigation
  • analyze
  • trajectory
  • projectile
  • range
  • slope
  • area under curve
  • intercepts
  • vector
  • scalar
  • coordinates
  • origin
  • magnitude
  • units of measure
  • significant figures
  • trigonometric functions
Knowledge:
Students know:
  • How to use mathematical computations to solve for the motion of an object.
  • How to analyze both linear and nonlinear graphs of motion.
  • Laboratory safety procedures.
  • Appropriate units of measure.
  • Basic trigonometric functions of sine, cosine and tangent.
  • How to determine area under a curve on a graph.
Skills:
Students are able to:
  • Manipulate kinematic equations of motion.
  • Interpret graphical data.
  • Create graphical representations of data.
  • Collect and organize experimental data.
  • Follow written and verbal instructions.
  • Make measurements of distance and time using standard units.
  • Manipulate laboratory equipment.
  • Work safely in collaborative lab groups.
Understanding:
Students understand that:
  • The motion of an object can be predicted using mathematical models and graphical models.
AMSTI Resources:
ASIM Module:
Intro to Graphing; Traveling Washer in 1D; Match the Graph; Motion of a Toy Car; Constant Velocity; Comparing Linear Speed and Circular Speed; Changing Velocity; Motion of a Falling Marble; Motion on an Incline; Motion Graphs; Treasure Hunt; Journey of a Physics Student; Tractor Pull; Projectile Motion Photo Worksheet; Horizontal Launch; Range vs. Angle; Basketball Toss; Acceleration on an Incline; Coefficient of Friction; Horizontal Circular Motion; Impulse Momentum; Collisions in 2D; Rotational Motion; Moment of Inertia; Conservation of Angular Momentum; Energy Exchange; Simple Harmonic Motion
Mathematics
MA2019 (2019)
Grade: 9-12
Geometry with Data Analysis
37. Investigate and apply relationships among inscribed angles, radii, and chords, including but not limited to: the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given circles with two points on the circle,
  • Compare the measures of the angles (with and without technology) formed by creating radii to the given points, creating chords from a third point on the circle to the given points, and creating tangents from a third point outside the circle to the given points, and conjecture about possible relationships among the angles.
  • Use logical reasoning to justify (or deny) the conjectures (in particular justify that an inscribed angle is one half the central angle cutting off the same arc, and the circumscribed angle cutting off that arc is supplementary to the central angle relating all three).


Given circles with chords from a point on the circle to the endpoints of a diameter,
  • Find the measure of the angles (with and without technology), conjecture about and explain possible relationships.
  • Use logical reasoning to justify (or deny) the conjectures (in particular justify that an inscribed angle on a diameter is a right angle).


Given a circle with a tangent and radius intersecting at a point on the circle,
  • Find the measure of the angle at the intersection point (with and without technology), conjecture about and explain possible relationships.
  • Use logical reasoning to justify (or deny) the conjectures (in particular justify that the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Teacher Vocabulary:
  • Central angles
  • Inscribed angles
  • Circumscribed angles
  • Chord
  • Circumscribed
  • Tangent
  • Perpendicular arc
Knowledge:
Students know:
  • Definitions and characteristics of central, inscribed, and circumscribed angles in a circle.
  • Techniques to find measures of angles including using technology (dynamic geometry software).
Skills:
Students are able to:
  • Explain and justify possible relationships among central, inscribed, and circumscribed angles sharing intersection points on the circle.
  • Accurately find measures of angles (including using technology (dynamic geometry software)) formed from inscribed angles, radii, chords, central angles, circumscribed angles, and tangents.
Understanding:
Students understand that:
  • Relationships that exist among inscribed angles, radii, and chords may be used to find the measures of other angles when appropriate conditions are given.
  • Identifying and justifying relationships exist in geometric figures.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
GEO.37.1: Define inscribed angles, central angles, circumscribed angles, radius, chord, tangent, secant, and diameter.
GEO.37.2: Define inscribed and circumscribed circle of a triangle.
GEO.37.3: Apply knowledge of arcs, angles and chords to solve circle related problems.
GEO.37.4: Determine angle values for all angles formed in the exterior, interior and on the circle.
GEO.37.5: Determine lengths of intersecting chords and secants.
GEO.37.6: Discuss the relationship among inscribed angles, radii, and chords.
GEO.37.7: Illustrate inscribed and circumscribed circles of a triangle and quadrilaterals inscribed in a circle.
GEO.37.8: Illustrate radii, chords, diameters, tangents to curve, central, inscribed, and circumscribed angles.

Prior Knowledge Skills:
  • Identify parts of a circle.
  • Recall how to find circumference of a circle.
  • Recall the meaning of a radius and diameter.
  • Identify all types of angles.
  • Recognize the attributes of a circle.
  • Identify and label parts of a circle.
  • Define diameter, radius, circumference, area of a circle, and formula.
Alabama Alternate Achievement Standards
AAS Standard:
M.G.AAS.10.36 Use geometric shapes to describe real-world objects.
Mathematics
MA2019 (2019)
Grade: 9-12
Mathematical Modeling
11. Plot coordinates on a three-dimensional Cartesian coordinate system and use relationships between coordinates to solve design problems.

a. Describe the features of a three-dimensional Cartesian coordinate system and use them to graph points.

b. Graph a point in space as the vertex of a right prism drawn in the appropriate octant with edges along the x, y, and z axes.

c. Find the distance between two objects in space given the coordinates of each.

Examples: Determine whether two aircraft are flying far enough apart to be safe; find how long a zipline cable would need to be to connect two platforms at different heights on two trees.

d. Find the midpoint between two objects in space given the coordinates of each.

Example: If two asteroids in space are traveling toward each other at the same speed, find where they will collide.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Can identify the x, y, and z axis on a three dimensional coordinate system.
  • Can plot coordinates on the three dimensional coordinate system.
  • Can find the distance between points in space.
  • Can find the midpoint between points in space.
Teacher Vocabulary:
  • Three Dimensional cartesian coordinate system
  • Two dimensional cartesian coordinate system
  • Points in Space
  • Vertex
  • Right Prism
  • Octant
Knowledge:
Students know:
  • how to plot points in two dimensions.
  • how to find the distance between two dimensional points.
  • how to find the midpoint between two-dimensional point.
Skills:
Students are able to:
  • Extend their knowledge of the two dimensional coordinate system to the three dimensional coordinate system.
Understanding:
Students understand that:
  • points in space are a part of the three dimensional coordinate system.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
MMOD.11.1: Define two-dimensional and three-dimensional Cartesian coordinate systems.
MMOD.11.2: Determine how to graph a point in a three-dimensional coordinate system.
MMOD.11.3: Calculate the distance between two objects in space.
MMOD.11.4: Calculate the midpoint between two objects in space.
MMOD.11.5: Compare and contrast a three-dimensional and two-dimensional Cartesian coordinate system.
MMOD.11.6: Determine how to graph a point in a two-dimensional coordinate system.
MMOD.11.7: Calculate the distance between two objects.
MMOD.11.8: Calculate the midpoint between two objects.
MMOD.11.9: Identify a diagram that shows a two-dimensional and three-dimensional coordinate system.

Prior Knowledge Skills:
  • Identify ordered pairs.
  • Recognize ordered pairs.
  • Define ordered pair and coordinate plane.
  • Create linear equations with two variables.
  • Graph linear equations on coordinate axes with labels and scales.
  • Identify an ordered pair and plot it on the coordinate plane.
Tags: angular velocity, circumference, linear velocity, speed, velocity
License Type: Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

This resource contains Lesson 5: The Robot Doctor Activity Guide.

  This resource provided by:  
Author: Kristy Lacks
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