— This paper provides that an elastic force and an elastic potential energy due to the deformation of soft fingers, which are previously derived, can be calculated into straightforward equations in an analytical way. These formulae lead to the fact that the potential energy of a soft fingertip is a function of two variables, and has a local minimum through the elastic rolling of a contacting object. We formulate four geometric constraints in grasping motions of a rigid object by means of two degrees of freedom robotic hand that has two rotational joints. We define a basic motion including translational and rolling motions when two fingers rotate by infinitesimal angle, and propose a quasi-static manipulation and its algorithm by using the local minimum of elastic potential energy (LMEE) of soft fingers with geometric constraints. In this theory, we define an energy function included in the LMEE algorithm. By solving that function we simulate the path of the center of gravity a...