International Conference on Robotics and Automation c 1997 IEEEAlbuquerque

In this paper, we study the 66 Cartesian stiiness matrix. We show that the stiiness of a rigid body subjected to conservative forces and moments is described by a (0; 2) tensor which is the Hessian of the potential function. The key observation of the paper is that since the Hessian depends on the choice of an aane connection in the task space, so will the Carte-sian stiiness matrix. Further, the symmetry of the Hessian and thus of the stiiness matrix depends on the symmetry of the connection. The connection that is implicit in the deenition of the Cartesian stiiness matrix through the joint stiiness matrix 1] is made explicit and shown to be symmetric. In contrast, the direct deenition of the Cartesian stiiness matrix in 2, 3, 4] is shown to be derived from an asymmetric connection. A numerical example is provided to illustrate the main ideas of the paper.