The grasping instruments used in minimally invasive surgery reduce the ability of the surgeon to feel the forces applied on the tissue, thereby complicating the handling of the tissue and increasing the risk of tissue damage. Force sensors implemented in the forceps of the instruments enable accurate measurements of applied forces, but also complicate the design of the instrument. Alternatively, indirect estimations of tissue interaction forces from measurements of the forces applied on the handle are prone to errors due to friction in the linkages. Further, the force transmission from handle to forceps exhibits large nonlinearities, so that extensive calibration procedures are needed. The kinematic analysis of the grasping mechanism and experimental results presented in this paper show that an intermediate solution, force measurements at the shaft and rod of the grasper, enables accurate measurements of the pinch and pull forces on tissue with only a limited number of calibration measurements. We further show that the force propagation from the shaft and rod to the forceps can be approximated by a linear two-dimensional function of the opening angle of the grasper and the force on the rod.