In-Hand Manipulative Synthesis Using Velocity Subspaces

The kinematic design of robots for tasks involving positions and its derivatives has been explored in the past in order to shape the trajectory of the robot at a given set of points. This approach has been successful for the synthesis of linkages for grasping applications; however defining a single velocity in the vicinity of a specified location might not be enough for a desired manipulation task. In the synthesis of multi-fingered robotic hands, it is interesting to ask whether a hand can be designed for a certain in-hand manipulation task that ensures contact and at the same time relative motion of the fingertips on the object surface in multiple desired directions. In this article we define a method for designing robotic hands that guide an object through a kinematic task with velocity specifications in the vicinity of key task positions. Given the mobility for a hand topology, the necessary velocities are derived at each task position to fully define a subspace of allowable directions for object manipulation. As an example, a multi-fingered robotic hand for an in-hand manipulation of a body with a known geometry has been designed. The proposed synthesis technique is the first step in creating tangent spaces in the vicinity of positions to successfully guide a body for desired manipulation tasks.