__Calculate a Robot Forward Kinematics in 5 easy steps:__

Kinematics can sometimes be a path. However, being told to ‘go and calculate the Forward Kinematics” is almost robotics research shorthand for “go and get familiar with this robot”. It’s the vital first step when using any new robot in research, particularly for manipulators.

**Step-1: Get a Pencil and Paper:** It can be tempting to jump straight for the computer when starting out with a new robot. However, even if the robot looks like a “standard” 6R manipulator, always sit down with a pencil and paper to draw out the kinematic diagram. This simple task forces you to carefully consider the actual physical configuration of the robot, avoiding false assumptions which can wreak havoc later on during coding.

There are various ways to draw a kinetic chain. Pick whichever style you prefer. Try to favor simple cylinders for the revolute joints and lines for the links. Do a Google Image Search for “kinematic Diagram” and see some of the different styles available. As you draw, work out which way each joint moves and draw this motion as double-ended arrows onto the diagram.

**Step-2: Figure out Your Axes:** The next key step is to draw the axes onto joint. The DH approach assigns a different axis to each movable joint. If you setup your axes correctly then working with the robot will be easy. Set them up incorrectly and you will suffer countless headaches. These axes will be required by simulators, inverse kinematic solvers and even other researchers.

The z-axis should lie on the axis of rotation for a revolute joint or axis of extension for a prismatic joint. The x-axis should lie along the “common normal” which is the shortest orthogonal line between the previous z-axis and the current z-axis.

**Step-3: Remember Your End Effector:** The goal of calculating the Forward Kinematics is to be able to calculate the end effector pose from the position of the joints. Most Forward Kinematics generates the end effector as a single distance from the final joint. This is fine for s simple “open-close” gripper. However, as modern grippers are often more complicated than this. It’s worth considering how the end effector operates.

**Step-4: Calculate the DH Parameters:** Denavit–Hartenberg parameters are often required to enter the robot model into a simulator and start performing any sort of analyzing on it. The DH parameters break down each joint of the robot into four parameters, each taken with reference to the previous joint. They are calculated in reference to the “common normal”.

**Note:** If the previous z-axis intersects the current z-axis, which is often the case, the common normal has a length of zero.

d – The distance between the previous x-axis and the current x-axis along the previous z-axis.

θ – The angle around the z-axis between the previous x-axis and current x-axis.

a (or r) – The length of the common normal, which is the distance between the previous z-axis and the current z-axis.

α – The angle around the common normal to between the previous z-axis and current z-axis.

**Step-5: Choose Your Library:** There are loads of kinematics software libraries and many of them do far more than just calculate Forward Kinematics. Most of them include Inverse Kinematic solvers, dynamics, visualization, motion planning and collision detection. These libraries will transform your DH parameters into matrices, which are then multiplied together to calculate the relationship between joint positions and end effector pose.