Why Robotics Needs a Standardized Convention for Link Frames
Describing a multi-joint robot arm's geometry could technically be done many different ad-hoc ways, but the Denavit-Hartenberg (DH) convention exists specifically to standardize it — assigning exactly four parameters (joint angle theta, link offset d, link length a, and link twist alpha) to describe the transformation between each consecutive pair of link coordinate frames, rather than requiring a full, unconstrained 6-parameter description for every joint.
This reduction from six degrees of freedom to four is possible because of specific geometric constraints the DH convention deliberately imposes on how coordinate frames are attached to each link — constraints that, once followed consistently, let any two consecutive frames be related by exactly these four numbers, forming a standard 4x4 homogeneous transformation matrix that combines rotation and translation into a single matrix multiplication.
Chaining these per-joint transformation matrices together (multiplying them in sequence from the base frame outward) is exactly how forward kinematics for a full multi-joint arm gets computed in practice — each joint's individual DH matrix composes with the next, ultimately producing the complete transformation from the robot's base to its end-effector.