Forward kinematics

Forward kinematics computes an end effector's configuration from a mechanism's joint coordinates and geometric model. For a serial robot arm, each joint contributes a relative displacement or rotation, and composing these transformations gives the tool's position and orientation relative to the base. This is a geometric calculation; the forces needed to realize the motion belong to dynamics.^[ref]

For a two-link planar arm, with relative joint angles ${\theta }_1,{\theta }_2$ and lengths $l_1,l_2$,For $l_1=l_2=1\mathrm{m}$, ${\theta }_1=\pi /2$ and ${\theta }_2=0$, the tool is at $(0,2)\mathrm{m}$ and points at angle $\pi /2$. Using ${\theta }_2$ alone for the second link's absolute angle would give the wrong result. Comparing this predicted position with an external measurement tests the link lengths, zero-angle calibration and rigid-link approximation.