Joint Parameter Calculation in Robotic Arms Using the Denavit-Hartenberg Transformation Algorithm

Abstract

Getting the joint angles and lengths just right is a must if robotic arms are going to move smoothly and hit their marks, especially in busy factories or delicate hospital rooms. In this paper, we rely on the Denavit-Hartenberg (DH) method, a clear step-by-step way to show how each arm segment sits in relation to the next, for our calculations. Instead of wrestling with every curve and corner, the DH scheme shrinks the job to four numbers for each pair of links: how long the link is, how much it twists, where the joint pivots, and how far the link starts from that pivot. By stacking these numbers into tidy transformation tables, we can reliably work out where a multi-jointed arm ends up most of the time. Here, we run the standard DH process on a mix of robot setups, from a simple three-joint arm to a whole six-joint rig. Our method walks through forming each matrix, adding them up, and finally showing the tool's tip sits in space relative to the base. When we compare the numbers that come out of the simulation with what we recorded in the real world, they line up closely, proving that DH still delivers the precision many modern jobs demand. The system now works hand-in-hand with inverse-kinematics tools so that planners can steer a robot in real time. Engineers kicked the code around in MATLAB and Python, and both show that the setup moves easily from one platform to another. In short, the Denavit-Hartenberg rules still provide a fast, solid way to figure joint angles and study motion, opening the door to more brilliant, more flexible robot brains. Looking ahead, the team plans to stretch the model so it also fits robots with extra joints or joints that bend in tricky ways