To wield an object means to hold and move it in a way that exploits its functions. When humans wield tools -- such as writing with a pen or cutting with scissors -- our hands would reach very specific poses, often drastically different from how we pick up the same objects just to transport them. In this work, we investigate the design of tool-wielding multi-finger robotic hand through a hypothesis: If a hand can kinematically reach a foundational pose (FP) with a tool, then it can wield the tool from that FP. We interpret FPs as snapshots that capture the workings of underlying parallel mechanisms formed by the tool and the hand, and one hand can form multiple mechanisms with the same tool. We tested our hypothesis in a hand design experiment, where we developed a sampling-based multi-objective design optimization framework that uses three FPs to computationally generate many different hand designs and evaluate them. The results show that 10,785 out of the 100,480 hand designs we sampled reached the FPs; more than 99\% of the 10,785 hands that reached the FPs successfully wielded tools, supporting our hypothesis. Meanwhile, our methods provide insights into the non-convex, multi-objective hand design optimization problem -- such as clustering and the Pareto front -- that could be hard to unveil with methods that return a single ``optimal" design. Lastly, we demonstrate our methods' real-world feasibility and potential with a hardware prototype equipped with rigid endoskeleton and soft skin.
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