When a grasped object is in contact with the external environment, it is necessary to perform assembly tasks to identify contact conditions. In this paper a new algorithm for identifying unknown parameters using the data collected by a 6-axis force sensor is proposed. It explicitly expresses the contact conditions. We subdivide the constraint conditions and reduce the number of unknown parameters. The problems of identifying the contact conditions are nonlinear, but they can be transformed to linear problems. The necessary number of active sensing motions is clarified for identification of the unknown parameters. We establish an efficient algorithm for identification of the contact conditions.