Compliance analysis of an under-actuated robotic finger

Under-actuated robotic hands have multiple applications fields, like prosthetics and service robots. They are interesting for their versatility, simple control and minimal component usage. However, when external forces are applied on the finger-tip, the mechanical structure of the finger might not be able to resist them. In particular, only a subset of disturbance forces will meet finite compliance, while forces in other directions impose null-space motions (infinite compliance). Motivated by the observation that infinite compliance (i.e. zero stiffness) can occur due to under-actuation, this paper presents a geometric analysis of the finger-tip compliance of an under-actuated robotic finger. The analysis also provides an evaluation of the finger design, which determines the set of disturbances that is resisted by finite compliance. The analysis relies on the definition of proper metrics for the joint-configuration space. Trivially, without damping, the mass matrix is used as a metric. However, in the case of damping (power losses), the physical meaningful metric to be used is found to be the damping matrix. Simulation experiments confirm the theoretical results.