Introduction¶

Inverse Kinematics is an important part of robotics. It allows us to position an end-effector (such as a gripper) at a specified co-ordinate in 3D space. Consider your hand on the end of your arm. When you wish to pick up a can of beer, you do not think "I must move my upper arm 30 degrees from my body, angle it 20 degrees forwards, bend my elbow at 120 degrees and open my hand". We simply move our hand to 3D co-ordinate of the beer can. However, robotic arms for instance, do not work like this. Each joint is usually a motor (typically a servo for hobbyist type projects) than we can accurately control the angle of. The previous example of setting the angle of each joint to position the end-effector is known as Forward Kinematics. Inverse Kinematics is the opposite in that we decide what X,Y,Z co-ordinate we want the end effector to be positioned at, and then calculate the required joint angles.

For simple robotic arms, this can be done analytically with some pretty basic trigonometry. More complicated robotic arms with more degrees of freedom require a more complex approach. This page will step through the derivations of the inverse kinematic equations of a fairly simple, low-cost robotic arm that is perfect for hobbyists, the #MeArm from phenoptix.com http://www.phenoptix.com/products/mearm-pocket-sized-robot-arm. Hopefully this will allow you to develop similar equations for your robotic arm (or leg).