Denavit-Hartenberg Notation-Based Kinematic Constraint Equations for Forward Kinematics of the 3–6 Stewart Platform

Abstract

This paper presents a new forward kinematic approach for the 3–6 Stewart platform. In the 3–6 Stewart platform, the position and orientation of the moving platform can be determined through kinematic constraint equations that indicate the possible trajectories of the three joints on the platform from the base coordinates. In most previous studies, the constraint equations were obtained through vector equations, which involve many complicated steps and multiple variables. Based on Denavit–Hartenberg (D-H) notation, the proposed approach allows a constraint equation representation with only four parameters. In addition, to implement the forward kinematics with the fewest possible D-H parameters, the 3–6 Stewart platform is reconfigured into three virtual revolute joints sharing base coordinates. Consequently, the constraint equations can be intuitively derived, and the computation process becomes more concise. The feasibility of the proposed approach is verified through an iterative numerical analysis and a simulation comparison with the general inverse kinematics.