Stiffness characterization of delta parallel robots: Linear VJM modeling and experimental identification

This paper proposes a computationally efficient framework for elastostatic stiffness identification of a Delta parallel robot using the Virtual Joint Method (VJM). A linear VJM-based model is developed, enabling structural parameter identification via a least-squares approach. The kinematic structure is defined using Denavit–Hartenberg conventions, while elastic parameters are identified from experimental deflection data under varied loading conditions. Experimental validation demonstrates high model fidelity, with average end-effector position errors below 4% across the operational workspace. In addition, stiffness maps are generated to quantify translational and rotational stiffness indices, providing a scalar characterization of configuration-dependent behavior. Compared to conventional FEA- or MSA-based stiffness models, the proposed methodology offers a robust and computationally efficient solution for modeling elastic behavior in high-precision and force-control applications. The results confirm that linearized lumped-parameter VJM models can effectively capture as-built stiffness characteristics of laboratory prototypes that are often neglected in idealized models.