Parallel-distributed model of soft fingertips in three-dimensional grasping and manipulation

This paper focuses on fingertip model in three-dimensional grasping and manipulation. A mechanical model of fingertips, which is referred to as the parallel-distributed model, has been proposed to analyze grasping and manipulation process based on the proposed model. Unfortunately, the model and the analysis were two-dimensional; three-dimensional model has not been formulated. In this paper, we build fingertip model in three-dimensional grasping and manipulation. First, we review geometric constraints between a hemispherical soft fingertip and an object planar surface; one normal constraint and two tangential constraints. Second, we formulate the elastic potential energy stored in a soft fingertip due to the contact with the planar surface in three-dimensional grasping and manipulation, yielding the parallel-distributed model with 3D deformation. Finally, we sketch the Lagrangian of the system consisting of a rigid prism grasped by three fingers with soft fingertips to compare simulation and experimental results.