DenavitHartenbergparametere

Denavit-Hartenberg parameters provide a standardized method for describing the kinematic structure of a robot arm or any articulated kinematic chain. This system assigns a unique coordinate frame to each link in the chain. The relationship between two successive coordinate frames, and thus between two successive links, is defined by four parameters: link length (a), link twist (alpha), link offset (d), and joint angle (theta).

Link length refers to the distance along the common normal between the z-axis of frame i and the z-axis of frame i+1. Link twist is the angle between the z-axis of frame i and the z-axis of frame i+1, measured along the common normal. Link offset is the distance along the z-axis of frame i from the origin of frame i to the common normal. Joint angle is the angle between the x-axis of frame i and the x-axis of frame i+1, measured along the common normal.

These four parameters, denoted as (a, alpha, d, theta), allow for the construction of a homogeneous transformation matrix that relates the coordinate frame of one link to the coordinate frame of the next. By multiplying these transformation matrices sequentially along the kinematic chain, one can determine the position and orientation of the end-effector relative to the base frame. This systematic approach is fundamental in robotics for modeling robot kinematics, path planning, and control.