# How to derive the inverse kinematic equations for this simple 6-DOF robot?

For the simple 6-DOF shown, we have to solve for the inverse kinematic equations and its resulting figures.

What should I do to solve this? P.s. That's all the information our teacher gave us.

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– Ben
Mar 8 at 18:19

The first step is to create the model of the robot. I recommend you to model the robot using modified denavit hartenberg (There are plenty of book and youtube provide the information you need). Then you can simply use this robotic toolbox and use function like SerialLink.ikine to get the mathematical function of inverse kinematic.

Hope that help :)

As mentioned above, you first need to develop the kinematic model of the robot. Try formulating the forward kinematics of the robot. For the inverse kinematics, you can either use geometric or algebraic method. A very good source to learn would be this book: "Introduction to Robotics - Mechanics and Control". In fact, there is a complete solution for forward and inverse kinematics of a 6dof robotics arm. Specifically, the inverse kinematics is solved in the 4th chapter. Here's the Link to the book

Since you are solving an Inverse Kinematics (IK) problem, you should already have the pose (position and orientation) of the end effector (EE) relative to the fixed base of the robot (or the pose of both the base and the EE in one common frame). You should also already know how to generate the Forward Kinematics (FK), which can come in handy.

There are two ways that I generally recommend approaching an IK problem for a robot that you haven't seen before: one where you turn it into a simpler IK problem and one where you look carefully at the FK equations.

For the first one, see if you can find a reference point on the robot that you can locate using only the EE pose which will not move when you rotate the last 1-3 (or more) joints. Once you've found that reference point, you can solve a simpler IK problem to figure out how to use the remaining joints to place the reference point at the desired location.

For the second one, the FK equations will tell you which elements of the EE pose are affected by which of the joints: if the joint variable appears in the equation for the height of the EE, for example, then that joint affects the height. If you can find one element that only has 1 joint variable in it then you can solve that element using the reduced set of equations. This also works if there are 2 elements with only 2 joint variables, as long as they are the same 2 variables in both equations, and so on for more elements.

Hope that helps! As Ben said in his comment, without more details on what you've tried so far we won't be able to provide more than the first steps of a homework problem.

Cheers, Brandon