  In this paper we present a potential energy map based approach that provides
a framework for the design and control of a robotic grasper. Unlike other
potential energy map approaches, our framework is able to consider friction for
a more realistic perspective on grasper performance. Our analysis establishes
the importance of including variable geometry in a grasper design, namely with
regards to palm width, link lengths, and transmission ratio. We demonstrate the
use of this method specifically for a two-phalanx tendon-pulley underactuated
grasper, and show how various design parameters - palm width, link lengths, and
transmission ratios - impact the grasping and manipulation performance of a
specific design across a range of object sizes and friction coefficients.
Optimal grasping designs have palms that scale with object size, and
transmission ratios that scale with the coefficient of friction. Using a custom
manipulation metric we compared a grasper that only dynamically varied its
geometry to a grasper with a variable palm and distinct actuation commands. The
analysis revealed the advantage of the compliant reconfiguration ability
intrinsic to underactuated mechanisms; by varying only the geometry of the
grasper, manipulation of a wide range of objects could be performed.
