In this paper, we explore the idea of designing nonanthropomorphic, multi-fingered robotic hands for tasks that replicate the motion of the human hand. Taking as input data rigid-body trajectories for the five fingertips, we develop a method to perform dimensional synthesis for a kinematic chain with a tree structure, with three common joints and five branches. We state the forward kinematics equations of relative displacements for each serial chain expressed as dual quaternions, and solve for up to five chains simultaneously to reach a number of poses along the hand trajectory using a hybrid global numerical solver that integrates a genetic algorithm and a Levenberg- Marquardt local optimizer. Although the number of candidate solutions in this problem is very high, the use of the genetic algorithm lets us to perform an exhaustive exploration of the solution space and retain a subset of them. We then can choose some of the solutions based on the specific task to perform. Note that these designs could match the task exactly while having a finger design radically different from that of the human hand.

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