A type of manipulator configuration with four-fingers is put forward, for grasping fragile hollow workpieces, with adjustable finger length and finger pad shape. Within a certain range, the manipulator can be used to grasp the internal cross section of fragile objects with different size of circular and oval shape. The design idea and structure of the manipulator are introduced, while the join positions between the finger pad and the finger body, as determined by uniform interpolation or Chebyshev interpolation, are comparatively analyzed and researched regarding forming force contact with workpiece. During the process of grasping, the internal forces and deformations between finger pad and workpiece are analyzed, based on a constructed finite element analysis model. The calculation example shows that, under the same grasping parameters, the maximum impact force on the workpiece is reduced by 63%, when the curvature adjustment points for the finger pad are distributed according to the Chebyshev interpolation, compared to their equal spacing distribution. Research has provided a theoretical basis for the design optimization of the finger pad structure and the connection point positions. For using manipulator to grasp objects with different size of circular and oval shape, the working space of the proposed manipulator is studied. The experiments show that, the manipulator structure, as presented in this article, can meet the requirements of relevant tasks.