Device for shaping object with a profile of at least a partial sphere

1. 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)

2. The device of claim 1 , wherein

at least one of the corresponding cutting element cutting edge intersects the longitudinal axis at the common distance; wherein

the cutting depth of at least one of the corresponding cutting element is partially overlapped with the cutting depth of another cutting element.

3. The device of claim 1 , wherein the attachment frame further comprises:

a first attachment frame and a second attachment frame concentrically arranged;

each of the first attachment frame and the second attachment frame having at least two mounting sites arranged symmetrically apart from the longitudinal axis; wherein

the first attachment frame and the second attachment frame are independently driven by the drive shaft.

4. The device of claim 3 , wherein

the drive shaft has a main drive shaft and an auxiliary drive shaft concentrically arranged;

the first attachment frame is driven at a lower rotating speed by the main drive shaft; and

second attachment frame is driven at a higher rotating speed by the auxiliary drive shaft concentrically resided within the main drive shaft.

5. The device of claim 3 , wherein

the corresponding cutting elements of the first attachment frame having different cutting depth from the corresponding cutting elements of the second attachment frame; and

the cutting depths of the corresponding cutting elements of the first and second attachment frames, respectively, are adjacent to each other.

6. The device of claim 3 , wherein

the corresponding cutting elements of the first attachment frame and the second attachment frame having different tilt angles, respectively; and

the cutting depths of the corresponding cutting elements of the first and second attachment frames, respectively, are adjacent to each other.

7. The device of claim 6 , wherein

the first attachment frame is driven at a first rotating speed;

the second attachment frame is driven at a second rotating speed.

8. The device of claim 1 , wherein

the arm length, r orb , of each mounting site, and the cutting element radius, r ce , of each corresponding cutting element, are the same; and

the cutting edge of one of the corresponding cutting element intersects the longitudinal axis at the common distance.

9. The device of claim 8 , wherein

the tilt angles of the at least two mounting sites, respectively, are different from each other; and

the cutting depths of the corresponding cutting element of the at least two mounting sites, respectively, are partially overlapped to each other.

10. A device having an adjustable cutting profile for shaping at least a portion of a spherical surface comprising:

an attachment base having at least one guiding slot and rotating around a longitudinal axis;

an adjustment mechanism located on the attachment base;

a plurality of arms, each being moveable within the corresponding guiding slot, having mounting site connected to a circular cutting element at a distal end; and

a plurality of links connected to each corresponding arms to the adjustment mechanism; wherein

each cutting element having a cutting surface rotating around its own self-spinning axis, a radius, r ce , a tilt angle, α, defining an angle between the longitudinal axis and the self-spinning axis, a cutting depth, D, of a partial spherical surface to be shaped, an arm length, r orb , defining a distance between a common spherical center along the longitudinal axis and a circular center of the cutting surface, and forming a spherical radius, R sph , of a partial spherical surface to be shaped; wherein

the spherical radius, R sph , is determined by selecting the proper combination of the arm length, r orb , and the cutting element radius, r ce , of each cutting element; and

the cutting depth, D, of the partial spherical surface shaped is determined by selecting the proper combination of the cutting element radius, r ce , and the 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)

wherein

the portion of the spherical surface to be shaped by the device is a permutation of all the partial spherical surfaces shaped by each cutting element along a direction of the longitudinal axis.

11. The device of claim 10 , wherein

varying the spherical radius, R sph , is equivalent to varying the arm length, r orb , of the corresponding cutting element according to the formula 1).

12. The device of claim 10 , wherein

each cutting element mounted on the corresponding arms is referenced to the same common spherical center, forming the same spherical radius, R sph ; wherein

the cutting depth, D, of each of the cutting element is arranged to be partially overlapped, completely overlapped or adjacent with each other.

13. The device of claim 12 , wherein

the guiding slot is arc-shaped, having a track radius, r rack , and a track center thereof situated at an imaginary apex of the spherical surface to be shaped by the device.

14. The device of claim 13 , wherein

the plurality of arms comprising a pair of arc-shaped swing arms movable within the arc-shaped guiding slot;

each of the_swing arms has a swing angle, φ, defined by an angle between a horizontal plane of each cutting element and the longitudinal axis;

the adjustment mechanism continually varying the swing angle, φ, by moving the swing arms through the guiding slot referenced to the track center.

15. The device of claim 14 , wherein

the varying of the swing angle, φ, is equivalent to simultaneously varying both the spherical radius, R sph , and the cutting depth, D, of the cutting element.

16. The device of claim 14 , wherein

the adjustment mechanism having sliding members coupled with each of the corresponding plurality of links for continually varying at least the spherical radius, R sph , of each cutting element.

17. A device having a variable cutting profile for shaping a spherical surface comprising:

a hollow main drive shaft rotating about a longitudinal axis;

an auxiliary drive shaft concentrically arranged within the main drive shaft;

an attachment frame driven by the main drive shaft, having an angled passage with a predetermined tilt angle, α;

the angled passage has a frame length, r att , spaced away from a common spherical center of the spherical surface to be shaped on the longitudinal axis;

an one-piece angled soft shaft arranged within the angled passage, driven directly by the auxiliary drive shaft at one end;

an interchangeable circular cutting element with cutting edge at its circumference;

the cutting element having its own self-spinning axis referenced to the common spherical center;

the cutting edge circumference of the cutting element maintains a common distance defining a spherical radius, R sph , of the spherical surface to be shaped, referenced to the common spherical center;

the cutting edge of the cutting element intersects the longitudinal axis at the common distance;

the cutting element having an integral coupler with a specific coupler length, Δr orb , and a predetermined radius, r ce ; and

the integral coupler is connected to another end of the angled soft shaft;

the cutting edge of the cutting element maintains a common distance defining the spherical radius, R sph , referenced to the common spherical center; wherein

a total arm length, r orb , of the cutting element is determined by:

r orb =r att +Δr orb ;

the cutting element has a cutting depth, D, determined by an angle combination of the tilt angle, α, and the radius, r ce , according to a formula:

D= 2 r ce sin(180−α),  1)

and

the common_spherical radius, R sph , of the spherical surface to be shaped is determined by a combination of the radius, r ce , and the total arm length, r orb , of the corresponding cutting element, according to a formula:

R sph =√{square root over (( r orb ) 2 +( r ce ) 2 )}{square root over (( r orb ) 2 +( r ce ) 2 )}.  2)

18. The device of claim 17 , wherein

the cutting element is interchangeable with another cutting element having different cutting element radius and coupler length.

19. The device of claim 17 , wherein

the main drive shaft is rotating at a lower speed than the auxiliary drive shaft; and

the spherical radius, R sph , of the spherical surface to be shaped is variable by the arm length, r orb , according to formula 2).