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In this study, we present an efficient mathematical representation of soft robotic fingers based on screw theory. Then, we show how the model and its main properties can be exploited in the design phase, and we present an application for an underactuated tendon-driven gripper with a modular structure, in which the joint stiffness values are defined to obtain the desired equivalent stiffness and kinematics manipulability at the fingertips. A distribution of stiffness through the flexible parts of the gripper is fundamental to characterize its overall behavior: The introduced mathematical model enables the gripper designer to analyze how a specific property, e.g., a desired trajectory of the fingertips, a desired overall stiffness, a distribution of contact force, etc., is influenced by the stiffness of its passive joints, and vice-versa evaluating the joint stiffness values allowing to get a desired properties. Joints with different stiffness values can be obtained by regulating three-dimensional-printing parameters and material properties in the manufacturing process. It is possible to design modular grippers with the same mechanical structure, but different behaviours, i.e., different fingertip trajectories, equivalent fingertip stiffness ellipsoids etc. Gripper modules can be easily assembled and disassembled, maintaining the same base, to adapt them to different tasks. The presented model and design guidelines are a first step in the direction of soft grippers that can be optimized for a specific problem.
Hussain et al. (Mon,) studied this question.