Current methods for singularity avoidance are analysed through study of the Jacobian minors. It is demonstrated that semi-singular positions, often defined as positions where dexterity decreases, occur as one minor becomes zero and that the only truly, uncontrollable, singular regions occur when all minors are zero. Existing singularity avoidance methods are analysed with attention to the way they deal with semi-singular regions. An 8-Degree Of Freedom (8-DOF) redundant autonomous articulated robot is used to demonstrate the effectiveness of the studied methods. Particular attention is made to the inherent limitations caused by a desire to maintain the aspect (sometimes referred to as configuration) in which the robot is operating. The use of the minors in manipulator analysis is shown to be useful in clarifying what truly occurs when dexterity is lost.