Composite Objective Optimization of Finger Length Under Performance Trade-Offs and Constraints

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Abstract
The inherent trade-off between structural compactness and functional versatility poses a fundamental challenge in biomimetic robotic hand design. This paper presents a multi-objective optimization framework for determining the optimal phalanx length allocation of a biomimetic finger under a fixed total-length constraint. Three performance criteria are formulated: grasp capability, measured by the area of a novel shared workspace (Region II) between power grasping and precision manipulation; kinematic dexterity, evaluated as the global average of the reciprocal condition number of the Jacobian matrix; and key-press range, defined as the maximum static fingertip span under perpendicularity and slope constraints. A full grid search reveals distinct optimal configurations for each objective. Pareto analysis of 117 non-dominated solutions shows that the key-press range is most sensitive to dimensional variations, with a 24.7% performance spread. A hierarchical selection strategy that prioritizes the key-press range while balancing the other two objectives yields a recommended compromise design. Experimental validation of the key-press reachability for the recommended compromise design achieves a 98.8% keystroke success rate over 1000 cross-row strikes without wrist movement. These results confirm its practical feasibility for fine manipulation tasks, while experimental characterization of the grasp capability and kinematic dexterity objectives remains as future work.

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