Apparatus and method for forming three-dimensional objects using a curved build platform

Abstract

An apparatus and method for making a three-dimensional object from a solidifiable material using a linear solidification device is shown and described. In certain examples, the linear solidification device includes a laser diode that projects light onto a scanning device, such as a rotating polygonal mirror or a linear scanning micromirror, which then deflects the light onto a photohardenable resin. As a result, the linear solidification device scans a line of solidification energy in a direction that is substantially orthogonal to the direction of travel of the laser diode. In other examples, the linear solidification device is a laser device array or light emitting diode array that extends in a direction substantially orthogonal to the direction of travel of the array.

What is claimed is: 
     
         1 . An apparatus for making a three-dimensional object from a solidifiable material, comprising:
 a solidification energy source;   a source of the solidifiable material;   a build platform movable along a build axis, wherein the build platform has a cross-sectional profile when viewed along a cross-sectional axis direction perpendicular to the build axis, and the cross-sectional profile includes a curved surface.   
     
     
         2 . The apparatus of  claim 1 , wherein the curved surface has a substantially constant radius of curvature. 
     
     
         3 . The apparatus of  claim 1 , wherein the build platform has an upper surface and a lower surface, the lower surface is between the solidification energy source and the upper surface, and the lower surface is the curved surface. 
     
     
         4 . The apparatus of  claim 3 , wherein the lower surface is curved in a direction along a travel axis perpendicular to the build axis and the cross-sectional axis. 
     
     
         5 . The apparatus of  claim 3 , wherein the lower surface has direction of curvature and a mid-point along the direction of curvature, the lower surface includes a sagittal line extending along the cross-sectional axis at the of the mid-point along the direction of curvature, and during an object building operation, the sagittal line traverses a trochoidal path. 
     
     
         6 . The apparatus of  claim 5 , wherein during an object building operation, the solidifiable material is solidified into a plurality of layers, following the solidification of each layer a partially-solidified exposed object surface is formed, and during the object building operation solidification occurs exclusively at positions along the exposed object surface that lie at a constant distance along the build axis from the solidification energy source. 
     
     
         7 . The apparatus of  claim 5 , wherein an exposed surface of the object attached to the build platform defines a tangent plane perpendicular to the build axis and a tangent line defined by the intersection of the tangent plane and the exposed surface of the object, and during the object building operation the tangent line moves along the travel axis direction in coordination with the solidification energy source. 
     
     
         8 . The apparatus of  claim 7 , wherein during an object building operation the solidification energy source projects solidification energy to solidify the solidifiable material into a plurality of layers comprising the three-dimensional object, each layer has a layer thickness, and following the solidification of each layer the build platform moves along the build axis such that the sagittal line moves away from the solidification energy source along the build axis by a distance equal to the layer thickness. 
     
     
         9 . The apparatus of  claim 1 , wherein the build platform has a lower surface spaced apart from an upper surface along the build axis, the upper surface is between the solidification energy source and the lower surface, and the upper surface is the curved surface. 
     
     
         10 . The apparatus of  claim 9 , wherein the upper surface is curved in a direction along a travel axis direction perpendicular to the build axis and the cross-sectional axis direction. 
     
     
         11 . The apparatus of  claim 1 , wherein during an object building operation the solidification energy source moves along a travel axis as it projects solidification energy along the build axis. 
     
     
         12 . The apparatus of  claim 11 , wherein during a single layer solidification operation during which the solidification energy source projects solidification energy to solidify the solidifiable material, the build platform moves along the travel axis direction and along the build axis. 
     
     
         13 . The apparatus of  claim 12 , wherein during the single layer solidification operation the build platform moves simultaneously along the travel axis and along the build axis. 
     
     
         14 . The apparatus of  claim 11 , wherein during an object building operation, the solidification energy source moves along the travel axis and projects solidification energy along the build axis and in a scanning pattern along the cross-sectional axis direction. 
     
     
         15 . The apparatus of  claim 14 , wherein during an object building operation, the build platform rotates about an axis of rotation parallel to the cross-sectional axis direction as the solidification energy source projects solidification energy along the cross-sectional axis direction. 
     
     
         16 . The apparatus of  claim 1 , wherein the curved surface has a direction of curvature and a mid-point along the direction of curvature, the curved surface includes a sagittal plane defining a sagittal line extending along the cross-sectional axis at the of the mid-point along the direction of curvature, and during a single layer solidification operation, the build platform rotates about the axis of rotation from a first angular orientation to a second angular orientation as the sagittal line travels a distance Δx along the travel axis direction, and the distance Δx is related to the first and second angular positions as follows:
   Δ x=a[ø   R1 −ø R2   ]+b [sin(2π−ø R1 )−sin(2π−ø R2 )]
 
 wherein, 
 Δx=change in position of the sagittal line along the travel axis from a first position x 1  to a second position x 2 ; 
 ø R1 =the angle of rotation of the build platform when the sagittal line is at the first travel axis position x 1  relative to a reference angular orientation at which the sagittal plane is parallel to the build axis; 
 ø R2 =the angle of rotation of the build platform when the sagittal plane is at the second travel axis position x 2  relative to the reference angular orientation; 
 a=the length of the radius of curvature of the curved surface of the build platform; and 
 b=the distance between the sagittal line and the center of a circle of radius a defined by the curved surface along the radial direction of the circle. 
 
     
     
         17 . The apparatus of  claim 16 , wherein the during a single layer solidification operation, the sagittal line moves a distance Δz along the build axis as the build platform rotates about the axis of rotation from the first angular orientation to the second angular orientation, and the distance Δz is related to the first and second angular orientations as follows:
   Δ z=b [cos(2π−ø R1 )−cos(2π−ø R2 )]
 
 wherein,
 Δz=the distance traveled by the sagittal line along the build axis from a first position z 1  to a second position z 2 ; 
 ø R1 =the angle of rotation of the build platform when the sagittal line is at the first build axis position z 1  relative to a reference angular orientation at which the sagittal plane is parallel to the build axis; 
 ø R2 =the angle of rotation of the build platform when the sagittal line is at the second build axis position z 2  relative to the reference angular orientation; 
 a=the length of the radius of curvature of the curved surface of the build platform; and 
 b=the distance between the sagittal line and the center of a circle of radius a defined by the curved surface along the radial direction of the circle. 
 
 
     
     
         18 . The apparatus of  claim 15 , wherein during the single layer solidification operation, the build platform simultaneously rotates about the axis of rotation, moves along the build axis, and moves along the travel axis direction. 
     
     
         19 . The apparatus of  claim 1 , wherein the cross-sectional profile of the build platform perpendicular to the cross-sectional direction axis is a circular segment. 
     
     
         20 . The apparatus of  claim 1 , wherein during an object building operation, the solidification energy source projects solidification energy to the solidifiable material as the solidification energy source moves in a first direction along a travel axis and does not project solidification energy to the solidifiable material as it moves in a second direction along the travel axis, wherein the first direction along the travel axis is opposite the second direction along the travel axis. 
     
     
         21 . The apparatus of  claim 1 , further comprising a linear solidification device comprising the solidification energy source, wherein the linear solidification energy source projects energy along the cross-sectional axis direction. 
     
     
         22 . The apparatus of  claim 21 , wherein the linear solidification device comprises rotating energy deflector in optical communication with the solidification energy source. 
     
     
         23 . The apparatus of  claim 1 , further comprising a build platform travel axis translation motor, a build platform build axis translation motor, and a build platform rotation motor, wherein during a single layer solidification operation, the build platform travel axis translation motor, the build platform build axis translation motor, and the build platform rotation motor are each operated so that an axis of rotation of the build platform rotation motor traverses a trochoidal path. 
     
     
         24 . The apparatus of  claim 1 , wherein during the formation of a single object layer, the build platform is rotated at a constant angular speed about an axis of rotation. 
     
     
         25 . The apparatus of  claim 24 , wherein the curved surface has a direction of curvature and a mid-point along the direction of curvature, the curved surface includes a sagittal plane defining a sagittal line extending along the cross-sectional axis at the of the mid-point along the direction of curvature, and during the formation of a single object layer, the sagittal line moves along the travel axis at a speed that is related to the constant angular speed at which the build platform rotates about the axis of rotation in accordance with the following relationship:
     dx/dt =ω( a−b [cos(ω t )])
   wherein,
 dx/dt is the velocity of the sagittal line along the travel axis (mm/sec); 
 ω=angular rotational velocity of the build platform (radians/sec); 
 a=the length of the radius of curvature defined by curved build platform surface (mm); and 
 b=the distance between the center of a trochoidal circle defined by the radius of curvature of the curved build platform surface and the sagittal line along the radial direction of the circle (mm); and 
 t=time (sec) required for a trochoidal circle of radius a to rotate at the angular rotational velocity ω from a reference position at which the sagittal plane is parallel to the build axis to the current angular orientation of the sagittal plane. 
   
     
     
         26 . The apparatus of  claim 25 , wherein during the formation of a single object layer, the sagittal line moves along the build axis at a speed that is related to the constant angular speed at which the build platform rotates about the axis of rotation in accordance with the following relationship:
     dz/dt=b ω[sin(ω t )]
   wherein,
 dz/dt is the velocity of the sagittal line along the build axis (mm/sec); 
 ω=angular rotational velocity of the build platform (radians/sec); 
 b=the distance between the center of a trochoidal circle defined by the radius of curvature of the curved build platform surface and the sagittal line along the radial direction of the circle (mm); and 
 t=time (sec) required for a trochoidal circle of radius a to rotate at the angular rotational velocity ω from a reference position at which the sagittal plane is parallel to the build axis to the current angular orientation of the sagittal plane. 
   
     
     
         27 . An apparatus for making a three-dimensional object from a solidifiable material, comprising:
 a solidification energy source that moves along a travel axis;   a source of the solidifiable material;   a build platform that moves along the travel axis while rotating about an axis of rotation perpendicular to the travel axis during the formation of a single object layer.   
     
     
         28 . The apparatus of  claim 27 , wherein the solidification energy source moves along the travel axis as the build platform moves along the travel axis during the formation of a single object layer. 
     
     
         29 . The apparatus of  claim 27 , wherein during the formation of a single object layer, the build platform moves along a build axis perpendicular to the travel axis as the build platform moves along the travel axis and rotates about the axis of rotation. 
     
     
         30 . The apparatus of  claim 27 , wherein the build platform has a cross-sectional profile when viewed along a cross-sectional axis perpendicular to the build axis and the travel axis, and the cross-sectional profile includes a curved surface that is curved along the travel axis. 
     
     
         31 . The apparatus of  claim 30 , wherein the curved surface has a mid-point and a sagittal line extending along the cross-sectional axis direction at the mid-point, and during the formation of a single object layer, the sagittal line traverses a trochoidal path along the travel axis. 
     
     
         32 . The apparatus of  claim 27 , wherein during an object building operation, the solidifiable material is solidified into a plurality of layers, following the solidification of each layer an exposed object surface is formed, and the build platform is manipulated such that solidification energy is only transmitted to the solidifiable material when the exposed object surface at the travel axis position of the solidification energy source is at a fixed distance from the solidification energy source along the build axis. 
     
     
         33 . The apparatus of  claim 27 , wherein during an object building operation, the solidification energy source moves along the travel axis and projects solidification energy in a scanning pattern along a cross-sectional axis parallel to the axis of rotation of the build platform. 
     
     
         34 . The apparatus of  claim 27 , wherein during an object building operation the solidification energy source projects solidification energy to the solidifiable material as the solidification energy source moves in a first direction along the travel axis and does not project solidification energy to the solidifiable material as it moves in a second direction along the travel axis, wherein the first direction along the travel axis is opposite the second direction along the travel axis. 
     
     
         35 . The apparatus of  claim 27 , further comprising a build platform travel axis translation motor, a build platform rotation motor, and a build platform build axis translation motor, wherein during the formation of a single object layer, the build platform travel axis translation motor, the build platform rotation motor, and the build platform build axis translation motor are operated such that an axis of rotation of the build axis rotation motor traverses a trochoidal path. 
     
     
         36 . A method of making a layer of a three-dimensional object on a build platform from a solidifiable material, wherein the build platform has a curved surface and a sagittal line lying on the curved surface, the method comprising:
 providing a solidification energy source;   moving the solidification energy source along a travel axis;   moving the build platform along the travel axis and along a build axis;   rotating the build platform about an axis of rotation; and   selectively supplying solidification energy from the solidification energy source to the solidifiable material along a scanning axis direction.   
     
     
         37 . The method of  claim 36 , further comprising traversing the sagittal line in a trochoidal path. 
     
     
         38 . The method of  claim 36 , further comprising traversing the axis of rotation in a trochoidal path. 
     
     
         39 . The method of  claim 36 , wherein build platform has a curved surface with a radius of curvature of length a, the step of moving the solidification energy source along the travel axis comprises moving the solidification energy source along the travel axis at a velocity v x , and the step of rotating the build platform about the axis of rotation comprises rotating the build platform at an angular velocity ω in accordance with the following relationship:
   ω=(1 /a ) v   x  
 
 wherein, 
 ω=angular velocity (radians/sec); 
 a=the length of the radius of curvature (mm); and 
 v x =velocity of the solidification energy source along the travel axis (mm/sec). 
 
     
     
         40 . The method of  claim 39 , wherein the step of moving the build platform along the travel axis comprises moving the build platform along the travel axis at a travel axis velocity that varies with the angular velocity ω. 
     
     
         41 . The method of  claim 39 , wherein the step of moving the build platform along the build axis comprises moving the build platform along the build axis at a build axis velocity that varies with the angular velocity ω. 
     
     
         42 . The method of  claim 36 , wherein the step of rotating the build platform about an axis of rotation comprises rotating the build platform from a first angular orientation to a second angular orientation. 
     
     
         43 . The method of  claim 42 , wherein the step of moving the build platform along the travel axis comprises moving the build platform by a distance along the travel axis that varies with the first angular orientation and the second angular orientation. 
     
     
         44 . The method of  claim 42 , wherein the step of moving the build platform along the build axis comprises moving the build platform by a distance along the build axis that varies with the first angular orientation and the second angular orientation. 
     
     
         45 . A method of making a three-dimensional object comprising a removable support section and a finished object section from a solidifiable material, wherein the removable support section and the finished object section are at adjacent locations along a build axis, the method comprising:
 forming the removable support section on a curved surface of a build platform, wherein the curved surface defines a sagittal plane parallel to the build axis, the removable support section has a build platform contacting surface and a finished object contacting surface;   forming the finished object section such that the finished object section has a base connected to the finished object contacting surface of the removable support section, and the base of the finished object section is planar.   
     
     
         46 . The method of  claim 45 , wherein the base of the finished object section includes a surface that faces the curved surface of the build platform, and the spacing between the finished object base and the curved surface of the build platform varies along the width of the build platform. 
     
     
         47 . The method of  claim 45 , wherein the base of the removable support section is discontinuous. 
     
     
         48 . The method of  claim 45 , wherein the build platform is curved along a direction perpendicular to the build axis. 
     
     
         49 . The method of  claim 45 , further comprising removing the removable support section from the build platform. 
     
     
         50 . The method of  claim 45 , further comprising separating the finished object section from the removable support section.