Kinematic Analysis and Simulation of Workspace of a 6-DOF Positioning Platform

This manuscript presents the development of an HEX platform inverse kinematics model, its numerical implementation, and experimental validation. A complete inverse-kinematics formulation is established from the geometric definition of the base and mobile joint coordinates and a z–y–x Euler rotation sequence, allowing actuator-length computation for arbitrary 6-DOF poses. The model is implemented to map the operational workspace under actuator stroke and joint-angle constraints via a two-stage deterministic search, providing dense workspace point clouds, surfaces, and quantitative translational/rotational limits for multiple stroke ranges. Experimental validation is performed on a hexapod platform controlled through an embedded inverse-kinematics layer within a cascaded position–velocity–current architecture with dual-encoder actuator feedback. For a ±25 mm actuator travel range, the experiments confirm close agreement with translation simulations with differences of the order of 2% to 3% in x, y, and z, while larger discrepancies were observed in orientation limits, i.e., the model predicts γ ≈ ±32.5° and α, β ≈ ±10–11°, whereas measurements yield γ ≈ ±30° and α,β ≈ ±14–15°, evidencing higher sensitivity of rotational capability to real mechanical and control factors.