Contents

• Motivation
• Example: Some-Sample-Task
• Past Work
• Methodology (etc.)
• Sample Input-Output
• Bibliography

Rapid Prototyping by layered manufacturing is an important technique in reducing the "time to market" for a part. This radically expedites the prototyping process and this is achieved through layered material addition directly through CAD model as compared to time consuming material removal or forming processes. This removes many of the traditional manufacturing constraints that result from the complexity of the surfaces of the part.
    In order to make such layered manufacturing possible a number of new issues have to be addressed. One such issue is the selection and evaluation of candidate bases. The selection should be such that there should be minimal instability as the model is built up from the candidate base. Another important criteria is the quality of the generated surfaces in terms of the surface roughness. Thus there is a strong need to develop the necessary and sufficient conditions for manufacturability of a part by layered Rapid Prototyping. 
    Depending on the method of deposition of material the RP family can be divided into a number of processes:

• Stereolithography
• Fludised mareial deposition
• Solid Ground curing
• Selective laser sintering etc

    Since slice generation of a CAD model is computation intensive it would be better if such selection of candidate bases could be done before such slice generation. Thus a method of extracting relevant information about stability roughness and build time will be a valuable, resource saving tool
    For a family of RP it is possible to obtain such optimal choices without the computation intensive slice generation operation.The RP processes for which this is valid are all Slope limited Rapid Prototyping processes like:

• Stereolithography
• Fluidised material Deposition

     EXAMPLE  & SAMPLE APPLICATION

  The domain of the current project would be to evaluate and then select the based possible base and direction of build given a part like:
 

    Input shape considered:

 
 

PREVIOUS METHODOLGY:
    The methodology that is usually adopted to ensure stability of the model is the following:
 

•     Finding the convex hull of the part and considering the faces of the convex hull as the candidate bases
• Starting with an arbitrary candidate base.
• Slicing the part after it has been oriented to rest on the selected candidate base;and identifying the loops.
• Seting up a tree like hierarchy of a solid loop with its directly lower hollow loop ;thus generating doublets.The first layer of doublets are labelled as supported.
• Generating the next sliced layer and identify the doublets of this layer.
• Solving the correspondence(connectivity) problem.
• Using polygon membership function on each doubet to find :                                                       (It intersects a solid loop of previous slice)||(Is totally included by a solid loop and totally excluded by its corresponding loop)
• If the above condition is satisfied then the current doublet inherits the support of the previous solid loop.
• For each supported doublet find the cg  & check if within the convex hull of the support.This ensures local stability.
• Find the CG of the stacked assembly & check idf within the convex hull of the union of all the bases of the ground layer.This ensures global stability.
• 
• Repeat for all candidate base.

         METHODOLOGY USED:
 

For all rapid prototyping processes where models are built up in layers without support, one can define a maximum slope of the surface which the process can handle. Thus it is easy to define a necessary condition for rapid prototypability of a model,on the basis of this maximum possible slope.

    A tool of much greater utility would be a form of sufficient condition. Such that given a model satisfies that particular condition it will not be necessary to make further checks for feasibility. Here an attempt will be made to derive such a necessary and a sufficient condition on the basis of some decision variable that can be evaluated without slicing of the part.In particular it will be established that if the maximum slope that the process can replicate makes a positive angle with the vertical in the anticlockwise sense then it is sufficient to check for the necessary condition that the upper bound of the slope has not been crossed.

     Here the criteria of surface roughness will also be considered to evaluate the possible bases. The surface roughness measure can be obtained by the magnitude of the projected step height along the direction normal to the surface. Thus the total surface roughness measure can be found by taking the dot product of the facet's area vectors and the outward pointing normal and integrating over the entire area.Since the nature of the process is such that both horizontal and verical surfaces are represented accurately it is necessary to take the minimum of the projection of normal to the surface on the direction of build as well as its orthogonal direction.

Another parameter to be taken into account is the build time. The factor which determines the difference between the time taken to build along different direction is not the sum of area of the layers as that will be constant and equal to the volume of the model. The determining factor is the number of layers necessary to produce the model as for each such layer there are idle times to allow reasonable curing of the current layer and the time for the next layer of the viscous resin to submerge it. Assuming constant layer thickness the number of layers become proportional to the height and becomes a reasonable indicator of the degree of time taken. Thus in this case if there are multiple candidate bases which have passed the constraints of stability one will have to choose the configuration with minimum build time. For constant layer thickness this simplifies to selecting the configuration with the minimum height.
    A much improved result is obtained if an adaptive slicing procedure is adopted.In such a strategy the step height is adaptively modulated so that a minimum roughness norm is maintained.However there is usually some minimum step height  constraint  for the process.Thus for this strategy it is necessary to find  for evry hieght that surface which has the maximum potential roughness.The slice hieght has to be calculated on the basis of this pessimistic criteria.
    The number of slices thus calculated  can serve as an useful guide of the amount of time for making the part.
 
 

The sample input will contain the tessellated solid model as a series of 3d triangles specified by their vertices and their outward pointing normal. In this context using .stl files as input will also be tried. The output of the code will be the base and direction  which is the best possible case found on the basis of considerations of stability, surface roughness &build time.A typical stl format is included.

An  STL File
Sample  summary out put
Detailed output
Prog for generating Candidate bases
program for evaluation of Candidate bases
Program for extracting geometry from stl files
Output of candidate bases
Top view of tesellated convex hull

Annotated Bibliography

@Article{jager,Broeck,Vergeest:1997,
author=         {P.J.de Jagger,J.J.Broeck,J.S.M.Vergeest},
year=           {1997},
keywords=       {Rapid prototyping,layered manufacturing,approximation algorithms},
title=          {A Comparison Between Zero and First Order Approximation Algorithms for Layered Manufacturing},
number=         {4},
volume=         {3},
Year=           {1997},
page=           {144-149},
annote=         {This paper makes a comparative study of the common 2.5D slicing which the authors call as '0'order approximation and a linear interpolated slicing procedure developed by them and called first order approximation.Both the algorithms were evaluated for nonconstant thickness slicing based on maximum permissible cusp hieght.
The performance of their algorithm is much better as it results in considerably
minimised staircasing and lower number of slices.This advantage stems from the
imposition of C0 continuity between the succesive layers}


@Article{Kulkarni,Dutta:1996,
  author=       {Prashant Kulkarni,Debashis Dutta },
  year  =       { 1996},
  keywords =    { rapid protyping,layered manufacturing,adaptive slicing}
  institution=  {versity of Michigan,Ann Arbor},
  title =       { An Accurate Slicing Procedure For Layered manufacturing}
  number =      {9 },
  year  =       { 1996},
  pages =       { 683-697 },
  annote=       {
{ This paper deals with a technique of improving the accuracy ,especially reduction of the surface roughness by means of adaptive slicing as compared to the prevalent mode of constant thickness slicing.The paper not only deals with the stair case effect but also considers the containment issue.The authors have developed an algorithm for determining the variable thickness of the slices taking special care that none of the tangential points on the surface are missed -a criteria not taken into consideration in mot of the earlier works}
}

@Article{Fadel,Kirschman:1996,
Author={Georges M Fadel,Chuck Kirschman},
Year={1996},
Keywords={CAD,rapid protyping,layered manufacturing,adaptive slicing}
Title={Accuracy issues in CAD to RP translation}
Vol={2}
Number={2}
Pages={4-17}
Annote={This paper studies the various sources and nature of error that affect the RP process. The paper considers errors in representation resulting from the peculiarities of the format used. Highliting the merits and demerits of different formats like stl cli,cfl etc. The authors also study the software generated errors in tesselation of these models and translating the data from the storage format to the format used by the RP apparatus.Appart from these "soft" errors hardware errors ie those involving dimensional and geometric accuracy are also modeled. Cases considered include errors due finite size of the laser beam,non circularity of the beam, staircasing, overcuring, errors dependant on orientation etc.}