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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