Forward kinematics accuracy enhancement of a force-torque decoupled spherical parallel manipulator near singular configurations within a tripodal robot

Abstract This article presents an extended mechanical design of the general spherical parallel manipulator to enhance the accuracy of the forward kinematics problem subject to measurement inaccuracies with a significant improvement upon the state-of-the-art close to singular configurations. This is achieved through integration of an internal serial structure occupying the unused space within the manipulator centre, which allows to attach a fourth joint sensor collecting partially redundant information. Although this alters the topological structure of the classical 3-RRR mechanism, we utilize a non-overconstrained design comprising an outer 3-CCC shell combined with an inner RRR chain, creating a dedicated force-torque separation which avoids interferences with the conceptual properties of the manipulator. Since the additional measurement axis coincides with the axis sensitive to singular configurations, this allows to salvage fundamentally ill-conditioned postures where the classical three-sensor method is prone to inaccuracies. The set-up is investigated analytically through derivation of the corresponding sensor Jacobian matrix, where the proposed method incorporates a dynamically adjusted attraction coefficient within an optimization problem to avoid overshooting. Verification is conducted through simulation with distorted measurement signals, evaluated by both the classical and proposed methods, illustrating improved reconstruction accuracy and robustness. With the mechanism being part of a serial-parallel, tripodal robot, validation with respect to feasibility, integration and real-time capability is performed on the built prototype. Special methods for inverse and forward kinematics suitable for high-speed applications using spherical trigonometry and spatial vector constructions are implemented and validated, simplifying classical 8th-order polynomial approaches to provide a unique solution through working and assembly mode continuity.