Introduction to Robotics
Exam drill
Find the end-effector position: exam drill
This one costs students marks every year: degrees versus radians
Quick check · tap an answer to continue
Lesson notes
Key points
- Use x = L1cosθ1 + L2cos(θ1+θ2) and y = L1sinθ1 + L2sin(θ1+θ2).
- θ1+θ2 = 0°, so the second link points along the positive x-axis.
- x = 1·cos90° + 1·cos0° = 0 + 1 = 1 m.
- y = 1·sin90° + 1·sin0° = 1 + 0 = 1 m, giving (1, 1).
Takeaway: Link two's direction is θ1+θ2, never θ2 alone.
Quick check: 2-link planar arm, L1 = L2 = 1 m, θ1 = 90°, θ2 = −90° (relative). Find end-effector (x, y).
- (1, 1)
- (0, 2)
- (1, 0)
Write the general FK equations first, then substitute; show the summed angle.
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