Transforming feedback variables into a different co-ordinate system is a practical and effective way of simplifying controller design for multi-axis motion systems. A general transformation framework is presented in this paper for parallel-actuator systems, including those with overconstraint (i.e. with more actuators than rigid body degrees-of-freedom). Force control for the extra axes is considered, and appropriate transformations from measured actuator positions and forces to position and force variables used for control are given, although solutions are not unique. A number of heuristic techniques which are already used in the structural testing industry can be formalised as part of the new framework; examples are given in the paper. The framework also allows these techniques to be extended to new applications, particularly those with overconstraint.