Two kinds of degree of freedom in constraint state and their application to assembly planning

In this paper, two kinds of the degree of freedom in constraint state (CSDOF) are defined for motion of an object in contact with an immobile environment, and then their application to planning of assembly tasks is discussed. The CSDOF of the first kind is defined as the number of independent directions in which the object can move, keeping the current constraint state. The CSDOF of the second kind is defined as the number of independent directions in which the object can move bilaterally when it is allowed to break the current constraint conditions and to go away from the current constraint state. We discuss the difficulty of state transition by considering the two kinds of CSDOF as well as the degree of constraint in constraint state (CS-DOC) and give a criterion function for state transitions. Based on this criterion function, we propose an algorithm for planning the optimal procedure for assembly tasks. Some numerical examples are given to show the validity of the proposed approach.