Design principles and kinematic analysis of a novel spherical 2-degree-of-freedom (DOF) parallel mechanism

Abstract. The spherical parallel mechanism (SPM) offers several advantages such as high stiffness, precision, a large workspace, immunity to interference, and simple kinematic calculations. Consequently, SPM finds extensive applications in fields like surgical robots, exoskeleton robots, and others. This paper proposes a design principle based on the virtual middle-plane constraint method, which integrates the branch constraint of the mechanism into the intermediate virtual constraint plane. On the one side, a symmetric spherical 3R branch consisting of two spherical links is provided to offer 3 rotational degrees of freedom (DOFs). On the other side, a constraint force located on the middle plane constrains 1 rotational DOF, enabling the end effector link to achieve 2 DOFs. Several symmetrical SPMs are synthesized based on the constraint force provided by the branches. The mechanism can achieve continuous motion from an initial position to a final position by undergoing a single equivalent rotation around an axis on the virtual symmetric plane passing through the center. The forward and inverse kinematic solutions and the velocity Jacobian matrix of the symmetrical SPM are determined. The workspace of the mechanism is obtained by considering inverse kinematics and link interference conditions. The dexterity and force/torque transfer performance of the mechanism within a certain range are analyzed. The correctness of the kinematics of the symmetrical SPM is demonstrated through simulation analysis and prototype experiment. This research lays a foundation for motion planning and dynamic analysis of this kind of mechanism by providing a variety of configurations for practical applications.