The Fractal Hand–I: A Non-anthropomorphic, but Synergistic, Adaptable Gripper

We introduce a novel Fractal Hand robotic gripper. The hand has only 1 actuator, but (2
ⁿ⁺¹
−1) joints, where a design parameter n defines the depth of the fingers’ tree structures. The hand is synergistic in its operation (because its joint movements are coupled through the hand’s interaction with the grasped object), but it is not anthropomorphic. The basic finger and hand geometry, governing kinematics, and quasi-statics mechanics of a rigid version of the hand are developed. These analyses remarkably show that under mild constraints, the grasped object is compliantly stable at an equilibrium grasp configuration. Thus, the Fractal Hand adapts to a very wide range of planar objects with a single design. Grasp planning is thus simplified. A companion paper [33] introduces a design methodology for this new class of robot hands, and multiple prototypes.