Automated error analysis of serial manipulators and servo heads

Abstract This paper presents a general mathematical treatment of serial manipulators, an important example of which is the servo head. The paper includes validation by application to the angle head via comparison with the previously known transformations and a new application to the error analysis of the angle head. The usual approach to the error analysis of a servo head is to develop a geometrical model by elementary geometrical considerations using trigonometric relationships and various simplifying assumptions. This approach is very error prone, difficult to verify and extremely time consuming. The techniques described here constitute matrix methods that have been programmed in a general way to derive automatically the analytical equations relating the angles of rotation of the head and alignment errors in the head to the position of the tool and errors in that position. The approach is to use rotation and transformation matrices to evaluate the influence of the various errors such as offsets and angular errors. A general approach to the sign convention and notation for angular errors is presented in an attempt to reduce the possibility of errors of definition.