This paper presents a new method for identifying conditions governing all singular configurations of simple six-link manipulators whose inverse kinematic position problems have closed-form solutions. The method is developed based on the concepts of service sphere, free service region, and dextrous wrist. For a simple six-link manipulator, we identify its singular state with finite internal degrees of freedom by using the conditions that cause the manipulator's inverse solutions to be indeterminate. Meanwhile its singular state with infinitesimal internal degrees of freedom can be identified by examining the determinant of the Jacobion of the first three links. This simple and straightforward method is illustrated by three examples.

This paper presents a theoretical study on the dexterity problem of 6R manipulators. Particularly, it deals with the manipulator’s service angle around a reachable point in space. The first part conceptualizes the ideas of service region, free service region and polarities of robots, and shows that the entire service angle can be categorized into a number of free service regions. The remainder of the paper deals with the investigation of basic properties of free service regions. The relationship between free service regions and service angle is subsequently formulated into a set of theorems and criteria. Specific examples are given for illustration.

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