This deflectable pneumatic spindle is capable of compensating part and positioning tolerances when machining. This means that it is possible to trace a part contour with constant pressure and achieve uniform removal, even under fluctuating conditions. An optimum application for this system is, e.g. the automated deburring of castings or machined components using an industrial robot. The deflection force is individually infinitely adjustable using air pressure (2-6 bar), even during processing.