Embedded Files
Mathematical Modeling
Understand how varying two joint angles determines the end-effector’s location, and visually map the robot’s reachable workspace.
Make sure the robot’s “home” position is arms straight out (if possible). Label this as (θ₁ = 90°, θ₂ = 90°).
Program Joint 1 (shoulder) through a series of angles (e.g., 20°, 30°, 60°, ... up to the robot’s safe maximum-150°).
For each new angle of θ₁.
Move the robot arm; mark the end effector’s location on the paper.
Record the programmed angles of each dot with the angles (e.g., θ₁, 90°)
Program Joint 2, Hold Joint 1 Fixed (3 min)
Choose a specific value for Joint 1 (e.g., 45°).
Program Joint 2 through its range (e.g., 10°, 30°, 60°, ...).
For each, set the new angles, move the arm, and mark the pen’s tip on the paper.
Label each spot with the angle pair (45°, θ₂).
Repeat with at least one more value for θ₁. Determine the min and max for θ₂.
Connect the Dots and Observe (3 min)
Use lines to connect the points made when varying one joint at a time.
Use different colors or dashed lines to show different motion paths.
Step back and look at the shape being formed.
Are there gaps or unreachable zones?
What shape is the full reachable space?
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