Introduction to Robotics
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Never forget 2-link forward kinematics again
Never forget how to find the end-effector position again
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Lesson notes
Calculate end-effector position of a planar 2-link arm from joint angles
Key points
- Clever / Cosine for x: Clever means cosine: x equals L1 cos θ1 plus L2 cos of the sum.
- Students / Sine for y: Students means sine: y equals L1 sin θ1 plus L2 sin of the sum.
- Add / Add link terms: Add the two link contributions; never just add raw link lengths together.
- Angles / Cumulative angle θ1+θ2: Angles reminds you link two uses θ1 plus θ2, measured from the base.
Takeaway: x uses cosines, y uses sines, link 2 uses θ1+θ2.
Quick check: For L1=1 m, L2=0.5 m, θ1=30°, θ2=45°, what angle sets link 2's x term?
- 45°
- 75°
- 15°
Link 2's direction is cumulative: θ1+θ2 = 30°+45° = 75°.
forward kinematicsDenavit-Hartenberg parametersend-effector
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