Automated error analysis of serial manipulators and servo heads

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, difŽ cult 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 in� uence 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 deŽ nition.