Abrasive device that maintains normal line of contact with curved abrasive surface and method of using same

An abrasive method for abrading a curved surface of a workpiece by providing an abrading head including an abrading tip having a substantially spherical outer surface and a rotating shaft supporting the abrading tip, the abrading head being positioned to face the curved surface, the abrading head and the curved surface being vertically, laterally and pivotably movable relative to one another using a thrust moving mechanism, a lateral moving mechanism and a pivotable moving mechanism all controlled with a controller, said method comprising:

• performing a first abrading operation comprising:
• contacting the substantially spherical abrading tip to the curved surface while maintaining an angle other than zero between the pressing direction of the abrading tip and the curved surface;
• rotating the abrading tip;
• scanning the curved surface with the rotating tip;
• controlling the abrading head, the lateral moving mechanism and the pivotable moving mechanism synchronously so that the abrading tip contacts and presses the curved surface at any point thereon with a substantially constant pressure in a direction consistent with a normal line thereat;
• and
• performing a second abrading operation comprising:
• contacting the spherical abrading tip to the curved surface perpendicularly;
• rotating the abrading tip;
• scanning the curved surface with the rotating tip;
• and
• controlling the abrading head, the lateral moving mechanism and the pivotable moving mechanism synchronously so that the abrading tip contacts and presses the curved surface at any point thereon with the substantially constant pressure in a direction consistent with a normal line thereat.

An abrasive apparatus adapted to abrade a curved surface of a workpiece comprising:

• an abrading head including an abrading tip having a substantially spherical outer surface and a rotating shaft supporting the abrading tip, the abrading head being positioned to face the curved surface;
• a thrust moving mechanism for relatively moving the abrading head and the curved surface;
• a lateral moving mechanism for relatively moving the abrading head and the curved surface;
• a pivotable moving mechanism for relatively moving the abrading head and the curved surface pivotably around a center point;
• and
• a controller for controlling the abrading head, the lateral moving mechanism and the pivotable moving mechanism synchronously so that the abrading tip contacts and presses the curved surface at any point thereon with a substantially constant pressure in a direction consistent with a normal line thereat.