Dynamic Modeling, Optimization, and Validation of a Handheld 3-PRS Compliant Robot with Coupled Bending-Torsion Deformation

The handheld 3-Prismatic-Revolute-Spherical parallel compliant robot offers a viable solution for suppressing hand tremor and assisting membrane peeling via vibration. Achieving these tasks requires a thorough understanding of the robot’s dynamic behavior, including the coupled bending-torsion deformation of the spherical joint, the bending of the revolute joint, and the coupled behaviors of joints in parallel mechanisms. To address this challenge, this paper introduces a pseudo-rigid-body-based dynamic model for the proposed compliant robot and conducts optimization studies. First, a pseudo-rigid-body model with two orthogonally arranged elements and an additional torsional energy term is developed to capture the coupled bending-torsion behavior of the spherical joint. A pseudo-rigid-body model is also introduced to model the deformation of the revolute joint. Then, by combining the joint models and the robot’s configuration, a dynamic model of the proposed robot is established using the Lagrangian method. Using the proposed dynamic model, the relationships among the coupled bending-torsion deformation of the spherical joint, the bending of the revolute joint, and the motor’s driving force are analyzed under specified vibration frequencies and amplitudes. Next, the design parameters corresponding to the peak driving force, which reflects maximum stiffness, are determined through optimization. Finally, the dynamic model and optimization results are validated through experiments. Experimental results show that the dynamic model achieves approximately 7.58% error. The vibration amplitude is approximately 935.7μm in both orthogonal and oblique directions at 15Hz, and a maximum driving force of 0.87N.