Object manipulation with the hand is a complex task. The task has redundancies at many levels, allowing many possibilities for the selection of grasp points, the orientation and posture of the hand, the forces to be applied at each fingertip and the impedance properties of the hand. Despite this inherent complexity, humans perform object manipulation nearly effortlessly. This article presents experimental findings of how humans grasp and manipulate objects, and examines the compatibility of grasps selected for specific tasks. This is accomplished by looking at the velocity transmission and force transmission ellipsoids, which represent the transmission ratios of the corresponding quantity from the joints to the object, as well as the stiffness ellipsoid which represents the directional stiffness of the grasp. These ellipsoids allow visualization of the grasp Jacobian and grasp stiffness matrices. The results show that the orientation of the ellipsoids can be related to salient task requirements.