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Multiport modeling of force and displacement in elastic transmissions for underactuated hands

An approach to construct an elastic transmission mechanism for a compliant underactuated robotic hand from the interconnection of smaller compliant mechanisms is proposed, and a mathematical model for the interaction between multiple actuators and multiple digits is developed. It is proven that any interconnection of compliant objects results in an elastic transmission element that has a positive definite stiffness matrix, which indicates that small perturbations to tendon excursion will yield a stable grasp. The branch and cable circuit connections of two-port modeled digits in a simple grasping mechanism are analyzed mathematically.