Calculate Inverse Kinematics


Robot kinematics (Kinematics is the study of motion without considering the cause of the motion, such as forces and torques.) involves deriving equations to describe an analytical relationship between the robot’s joint parameters and the end-effector. There are 2 ways to derive the equations of motion:

  • Forward kinematics. Given the joint angle values, forward kinematics equations calculate the robot’s end-effector location in the coordinate space.
  • Inverse kinematics. Given the robot’s end-effector location, inverse kinematics equations calculate the joint angles required to move the end-effector to that location.
Illustration showing a two-link robot arm with a desired end-effector location and the angles θ1 and θ2.



  • Analytical solution(in closed form)
  • Numerical solution((in iterative form)
From ETH, Robot Dynamics Lecture Notes, page 26,27

3-linked planar joints

[latexpage]From ETH, Robot Dynamics Lecture Notes, $l_0$ is fixed to the ground.
[latexpage]From ETH, Robot Dynamics Lecture Notes, page 34

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