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Forward Kinematics

Forward kinematics computes the tool's position and orientation directly from the known joint angles. For a planar 2-link arm the contribution from each link is summed with simple trigonometry. This is always unambiguous: given the joint angles, there is only one possible tool position.

x=L1cos⁡θ1+L2cos⁡(θ1+θ2)x=L_1\cos\theta_1+L_2\cos(\theta_1+\theta_2)x-coordinate for a planar 2-link arm
y=L1sin⁡θ1+L2sin⁡(θ1+θ2)y=L_1\sin\theta_1+L_2\sin(\theta_1+\theta_2)y-coordinate for the same arm

Symbols

L1, L2L_1,\ L_2link lengthsm
θ1, θ2\theta_1,\ \theta_2joint angles°

Example

L1=L2=1L_1=L_2=1 m, θ1=0\theta_1=0, θ2=90°\theta_2=90°:

x=1+cos⁡90°=1x=1+\cos90°=1, y=0+sin⁡90°=1y=0+\sin90°=1.

Forward kinematics always has exactly one solution – it is inverse kinematics that can have several.
Practise kinematics for free →

← Euler Angles and Quaternions · Inverse Kinematics (2 Links) →

Part of Robotics: Kinematics.