2D Inverse Kinematics Implementation

Question

I am trying to implement Inverse Kinematics on a 2D arm(made up of three sticks with joints). I am able to rotate the lowest arm to the desired position. Now, I have some questi

Answer 1

The DH (Denavit-Hartenberg) notation is part of the solution. It helps you collect a succinct set of values that describe the mechanics of your robot such as link length and joint type.

From there it becomes easier to calculate forward kinematics. The first think you have to understand is how to translate a coordinate frame from one place to another coordinate frame. For example, given your robot (or the DH table of it), what is the set of rotations and translations you have to apply to one coordinate frame (the world for example) to know the location of a point (or vector) in the robot's wrist coordinate frame.

As you may already know, homogeneous transform matrices are very useful for such transformations. They are 4x4 matrices that encapsulate rotation and translation. Another very useful property of those matrices is that if you have two coordinate frames linked and defined by some rotation and translation, if you multiply the two matrices together, then you just need to multiply your transformation target by the product of that multiplication.

So the DH table will help you build that matrix.

Inverse kinematics is a bit more complicated though and depends on your application. The complication arises from having multiple solutions for the same problem. The greater the number of DOF, the greater the number of solutions.

Think about your arm. Pinch something solid around you. You can move your arm to several locations in the space and still keep your pinching vector unchanged. Solving the inverse kinematics problem involves deciding which solution to choose as well.