# The synthesis of stable grasps in ..

In some cases, the task parameters—position, forces, and velocities—can define a desired region (in the parameter space) required to achieve the task. Several grasping points and hand configurations can be considered for solving the task, and for each grasp/hand configuration a feasible region for each task parameter can be computed. Let and be the distances from the origin to the feasible and required sets (of forces, velocities, positions) along a given direction in the corresponding space. A safety margin is defined as

## The Synthesis of Stable Grasps in the Plane.

### A main character of multi-finger stable grasp is force- closure, ..

is independent of the reference system used to compute torques, but it does not indicate whether the grasp has a poor capacity of compensating perturbation wrenches in some particular directions, i.e. with the same a given grasp could stand a much lower force than another one in a certain direction. As in the case of , it is necessary to establish a suitable metric in the wrench space to simultaneously consider pure forces and torques.

### The Synthesis of Stable Grasps in the Plane - CORE

has a clear and useful physical meaning for general purpose grasps, but depends on the reference system used to compute torques. Selecting the object’s center of mass as the origin of the reference system is coherent with the system dynamics, but as stated above for other measures, in some cases it may be difficult to know the center of mass accurately. Besides, it is necessary to establish a metric in the wrench space to simultaneously consider pure forces and torques, as defined by the factor introduced in Sect. (Roa and Suárez ). can be normalized with respect to the maximum value that it can reach for a given object, which indicates how far the grasp is from being optimum. However, this requires the computation of the maximum value, implying an additional computational cost. A recent attempt to overcome the dependence of on the reference frame was proposed by setting the moment origin at the centroid of contact positions so that the grasp wrench sets are frame independent (Zheng and Qian ). In that work, instead of dividing the torque component by a factor it is proposed to multiply the force components by the average distance from the contacts to their centroid, which makes that the grasp wrench sets have the same scale in all wrench directions, and sets the scale factor of the ball in the wrench space directly proportional to the same average distance.