A spherical bearing provides a passive apparatus that enables a contact sensor that needs to self-align to the surface of a test object. In some embodiments, the contact sensor is a transducer. This self-alignment apparatus may be used in a measurement system for aligning the face of a contact transducer to the surface of a material to be measured. The spherical bearing may be dry or may be lubricated with a liquid or with pressurized air to minimize the bearing friction and enable the transducer to self-align. The upper portion of the spherical bearing is preferably attached to a spring-loaded piston. The transducer is preferably attached to the lower portion of the spherical bearing. The spring-loaded piston holds the spherical bearing portions together and centers the floating lower bearing portion after each measurement operation. A cowling preferably retains the lower bearing portion between measurements.