A Note on Conceptual Models in Robotics: A Case Study of Modelling Mechanical Grippers Using Geometric and Topological Properties

Abstract

In this study, the geometric and topological aspects of mechanical grippers are investigated. The main focus is on their mechanical behaviour during a precision pinch. Precision pinch is one of the fundamental grasping mechanisms. It occurs when the thumb and index finger come together to grasp small objects, dynamically altering the gripper’s geometric and topological configuration. These localised geometric changes can affect force distribution, grip stability, and overall mechanical efficiency. A computer simulation was performed to quantify geometric and topological transformations during precision pinch and their impact on force trajectories. These trajectories were analysed in terms of geodesics on a torus, representing the shortest paths between two points on the fingers’ surface. It was demonstrated that variations in gripper geometry influence mechanical force distribution and structural connectivity. Incorporating geometric and topological modelling into gripper design may lead to adaptable bionic devices. Furthermore, this method may help identify stress-prone areas, optimising force trajectories and stress pathways while addressing the limitations of existing models that oversimplify grasping mechanics.