Configuration design and redundancy optimization of a novel kinematically redundant parallel external fixator for interference avoidance in foot and ankle deformity correction

Abstract

During foot and ankle deformity correction via external fixators, successful implementation of the preplanned optimal correction strategy is crucial for achieving acceptable correction outcomes. However, interference phenomena can interrupt the correction process. Owing to the inherent non-redundant mechanism properties of existing external fixators, current interference avoidance methods inevitably necessitate adjustments of the pre-determined assembly relation and/or equally-spaced correction trajectories, thereby hindering the implementability of the optimal correction strategy. To address this issue, this paper introduces the concept of kinematic redundancy in external fixator design, and a novel 2(SPS-P-SPS)-SPR kinematically redundant external fixator with configuration optimization capabilities is proposed. Subsequently, based on the algebraic solution for forward kinematics while combining the cost functions for interference avoidance tasks, the inverse kinematics of the proposed external fixator is resolved using the gradient projection method with closed-loop feedback. Clinical case simulations demonstrate the effectiveness of the external fixator in avoiding multiple interference problems while maintaining the optimal correction strategy. Comparative analyses further reveal considerable improvements in the tracking accuracy of the correction trajectory compared with the conventional velocity-level method with open-loop solutions.