A system, for planning a grasp for implementation by a grasping device having multiple grasping members, including a processor and a computer-readable storage device having stored thereon computer-executable instructions that, when executed by the processor, cause the processor to perform multiple operations. The operations include generating, for each of the multiple grasping members, multiple planar polygon representations of a three-dimensional object model. The operations also include transforming a planar polygon, of the multiple polygons generated, to a frame of a link of multiple links of a subject member of the multiple grasping members, forming a transformed polygon, being a cross-section of the object model taken along a member-curling plane of the subject member. The operations further include sweeping, in iterations associated respectively with each link of the subject member, the link from a fully-open position for the link to a point at which the link contacts the transformed planar polygon.