🤖 Trigonometry in Robotics

Robotic systems depend on trigonometric calculations for precise movement, positioning, and environmental interaction.

Inverse Kinematics

Calculating joint angles to reach target positions:

θ₂ = arccos[(x² + y² - L₁² - L₂²)/(2L₁L₂)]
θ₁ = arctan(y/x) - arctan[(L₂sinθ₂)/(L₁ + L₂cosθ₂)]

Applications

SCARA Robot Example

2-link arm (L₁=0.5m, L₂=0.3m) reaching for (0.6,0.4):
1. Calculate θ₂ using Law of Cosines
2. Determine θ₁ using tangent relationships
3. Verify solution reaches target

Sensor Systems

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