Modeling the Dynamics of a Collaborative Parallel Kinematic Robot with Elastic Actuators for Automated Periorbital Massage

Abstract

This paper presents the development of a dynamic model of a collaborative robotic system based on parallel kinematics with series elastic actuators (SEA) for automated periorbital massage. The proposed system is intended for rehabilitation and therapeutic applications, including meibomian gland dysfunction treatment and postoperative recovery. A mathematical model of the delta manipulator dynamics is developed, incorporating actuator dynamics, SEA elasticity, and contact interaction with soft tissues. Three control strategies are compared through computational simulation: rigid positioning (high-stiffness SEA), passive compliance (soft SEA without force feedback), and active compliance (hybrid position–force control with trajectory correction based on contact force measurement). The simulation results demonstrate that the hybrid controller significantly reduces peak contact force and force tracking error compared to both rigid and passive compliance modes, while maintaining acceptable position accuracy for periorbital massage. The proposed active compliance approach effectively limits interaction force to a specified safe level, ensuring patient safety even under large-amplitude motions. The developed model provides a foundation for designing SEA-based collaborative robots for delicate facial massage procedures.