Patent ID: 8771275

Claim:
A device for shaping a spherical surface comprising: a drive shaft rotating about a longitudinal axis; at least one attachment frame having at least two mounting sites referenced to a common spherical center located on the longitudinal axis; each mounting site having a corresponding circular cutting element with cutting edge at its circumference; each corresponding cutting element having its own self-spinning axis intersecting the longitudinal axis at the common spherical center, and a cutting depth, D, along the longitudinal axis; the cutting edge circumference of all the corresponding cutting elements maintains a common distance defining a common spherical radius, R sph , referenced to the common spherical center; at least one of the corresponding cutting elements having a different cutting depth from at least one other corresponding cutting element; and an overall cutting depth of the spherical surface to be shaped by the device is determined by a permutation of all the cutting depths of all the corresponding cutting elements along the longitudinal axis; wherein common spherical radius, R sph , is determined by selecting a proper combination of an arm length, r orb , of the attachment frame, and the cutting element radius, r ce , of each cutting element; and the cutting depth of each corresponding cutting element is determined by a proper combination of the cutting element radius, r ce , and a tilt angle, α, of each cutting element, according to the following expressions, respectively: R sph =√{square root over (( r orb ) 2 +( r ce ) 2 )}{square root over (( r orb ) 2 +( r ce ) 2 )}; 1) and D= 2 r ce sin(180−α). 2)