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Cosine Calculations: Solving Robotic Arm Reach with the Law of Cosines
Cosine Calculations: Solving Robotic Arm Reach with the Law of Cosines
How can we solve for unknown sides or angles in robotic arm designs, and what does the solution tell us about whether our robot can reach its target or operate within its mechanical limits?
Learning Intentions:
Recognize when the Law of Cosines is required (for SSS or SAS triangle situations), use the formula to solve for unknown sides or angles, and apply this method to robotic arm triangle setups to evaluate reach or angle constraints, interpreting what their solution means for the feasibility and limits of their robot’s design.
Today's Concept:
We've covered right triangles (SOHCAHTOA) and oblique triangles with a 'complete pair' (Law of Sines). But what about the most common problem in robotics?
Imagine you know how long your two robot arm links are, and you know exactly where you want the hand to end up. You know all three 'sides' of the triangle (Link 1, Link 2, and the distance to the target). You have SSS. No right angles. No complete pairs. This is where the 'heavy lifter' comes in: The Law of Cosines. This is the tool that solves the 'elbow problem', calculating the exact angle your robot needs to bend to reach a specific spot.
Station 1
Station 1
Explore It – Cosine Calculations: Solving Robotic Arm Reach with the Law of Cosines
Station 2
Station 2
Practice It – Law of Cosines Mini-Lesson & Guided Practice
Station 3
Station 3
Apply It – Hands-On Robot Reach Check & Independent Problem Solving
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