I had the requirement to control a device in 6 degrees of freedom (DOF). There were 3 motorized translation stages to control the position of the tool in 3D space and 3 rotary motorized stages to control its orientation. Although it could be thought as a robot arm having 3 prismatic joints and 3 revolute joints, I did not want to involve complex forward and inverse kinematics for this simple testing equipment.
Here is an example transformation. By arranging rotational axes of rotary motorized stages to intersect at the tool, a simple direct 6 DOF control could be achieved. The following figures show schematic diagram and 3D drawing for the equipment that I designed.