FIELD OF THE INVENTION
The present invention relates to a process for Curved Layer Fused Deposition Modeling
(CLFDM) and a system for executing said CLFDM process for application in Rapid
Prototyping (RP) whereby prototypes comprising thin curved parts with improved strength,
lesser number of layers and better surface finish compared to those of the same part
made by flat layered Fused Deposition modeling (FDM) can be created from computer
generated (CAD) models so as to favor rapid manufacturing process. More particularly, the
present invention is directed to a method and system for CLFDM having at least 3 axes
and preferably having 5 axes configuration for the desired flexibility of the extruder nozzle
relative to the work table as well as its workability to facilitate depositing the filaments in
curved non-planar layers. More particularly, the present invention is directed to a method
and system for CLFDM having 5 axes configuration to deposit the filaments in curved
layers and to maintain the nozzle axis normal to the curved surface generated at any
instant and location such that the filament trajectory at the instant of touching the surface
(being built up) is normal to the surface at that point and time. Importantly, such manner
of deposition of the thermoplastic fused filament in curved layers, one atop the other to
build a pre-determined curved shape such as manufacturing of thin, curved parts is
adapted to favour the reduction of stair-step effect, as found in conventional flat-layered
FDM process. More advantageously, the CLFDM process according to the present invention
is adapted to produce parts by curved layer deposition of fused filament on a support
structure/pre-placed mandrel, conjugate of the lower surface of the part and favoring
bottom-up build direction which is found to decrease the number of layers for building up
the part on one hand and on the other hand ensure more continuity of fibers across any
planar cross section and thus ensuring enhanced strength of the part and productivity in
RP processes for thin curved contoured components. The invention would thus favour the
desired continuous mass manufacturing environment and is found to be adapted to

robust/concurrent engineering principles to meet customers' preferences or to attain
design modification of such parts directed to providing desired technical attributes in the
end product in shortest possible time and thus having wide prospects and economic
significance in industrial applications.
BACKGROUND ART
It is known in the art of manufacturing prototypes in CAD-CAM interfaced continuous mass
manufacturing set up wherein Rapid prototyping refers to a group of solid freeform
fabrication (SFF) processes that are capable of developing complex shapes without part-
specific tooling in a short span of time. Newer RP processes are being developed and
commercialized regularly to cater to the needs of various industry segments. Layered
Manufacturing (LM) technology is employed for most of the RP processes wherein a part is
produced by depositing fused materials layer-by-layer. Fused Deposition Modeling (FDM) is
one of the commercially exploited LM process wherein a filament of heated thermoplastic
material in fused/semisolid state is extruded through a deposition nozzle and applied over
a surface to form a layer. FDM is a widely applied process for RP technology whereby
prototypes can be created from computer-generated models for concept modeling,
assembly and functional operation.
Conventional FDM is the technology of applying fused plastic filaments in layers by means
of an extruder, such that layers are built one atop the other so as to obtain a pre-
determined shape. The fused material layers ultimately bond together and form a solid
part. The main advantage of the LM/FDM process over any other conventional
manufacturing process is that, complex shapes can be physically achieved without
requiring any elaborate/complex tooling.

Prior art FDM mentions the "contemplation" of developing "patterns" in free space like
"threads", "struts" and "strands" by assistance of ultrasonic energy or cooling agents and
without the application of any support system or pre-formed mandrel (see US patent
5121329, col 14 line 60 and US patent 5340433, col 20 line 32). Prior art US patent
5121329 posts a drawing accompanying said patent specification where a curved member
is shown to be built up by a process that suffered from a number of limitations as the
following:
1. No means provided for path generation criteria and path generation procedure for the
extruder nozzle with respect to the table (holding part being built up) in order to achieve
curved layer FDM.
2. No consideration for Shape of the bottom face of nozzle to avoid damage of built up
surface.
3. No consideration for maintaining the filament trajectory at the exit of the extruder
nozzle along the normal to the surface being built up at the point of deposition favoring
desired surface curvature.
4. No provision for 4 or 5 axis configuration of equipment for control of nozzle with respect
to table assembly holding the workpiece for the purpose of curved layer filament
deposition.
5. The processes and devices not adequate to ensure quality of thin curved parts in terms
of dimensional accuracy as well as precision of shapes in case of very thin curved parts.
6. Proper offset between layers in curved layer FDM is not addressed. Simple "Z" offset,
that is, shifting the "Z" axis position of the extruder relative to the table has been
suggested in prior art. "Z" offset is not necessarily appropriate in CLFDM.
It is however known in the prior art FDM process, "canting" of the extruder has been
suggested for making spatially curved members without laminations. Canting is a one-time

(fixed) tilting of the extruder nozzle axis with respect to the vertical and will not always
keep the trajectory of the filament aligned along the normal to the surface being built up
at the point of deposition.
Further to this, in the prior art FDM processes depositing flat layers of fused filament, it is
experienced that LM/FDM fails to meet the requirements of consistency with regard to
shape, structural homogeneity, strength and surface finish, particularly in generating some
specific part shapes like thin curved shell like structure such as shapes of skull bone/dome
or turbine blades. The LM or Flat-layered FDM process in such cases leads to lack of
strength of deposited layer and parts made therefrom, derived from inherent characteristic
process limitations like anisotropy [Lee CS, Kimb SG, Kimb HJ, Ahnb SH, Measurement of
anisotropic compressive strength of rapid prototyping parts, Journal of Materials
Processing Technology 2007, 187-188:627-30] and adhesive strength between layers (or
across adjacent filaments) that is appreciably lower than the strength of the continuous
filament (longitudinal strength). Zhong et al [Zhong W, Li F, Zhang Z, Song L, Li Z- 'Short
fibre reinforced composites for fused deposition modeling', Material Science and
Engineering 2001, A301:125-30] studied the mechanical properties of short fibre-
reinforced ABS (Acrylonitrile Butadiene Styrene) polymers for use as a FDM feed stock
material. Marked differences were observed between the longitudinal filament strength
and the adhesive strength, the former being substantially higher than the latter. Similar
studies on anisotropy of FDM parts due to differences in strength along and across
filaments have been reported by Bellini and Guceri (Bellini A and Gugeri S, Mechanical
characterization of parts fabricated using fused deposition modeling, Rapid Prototyping
Journal Volume 9 . Number 4 . 2003 . pp. 252-264).The flat layer LM/FDM process applied
to generate thin curved parts, further suffer from limitations like the stair-step effect
leading to poor surface finish of final part and large number of layers and associated
higher build up time. The reason behind such poor part quality is the nature and extent of

discontinuity of the filaments in flat-layered FDM while attempting to build up thin slightly
curved part. Apart from this, there is pronounced stair-step effect at the boundaries of
built up layers, when flat layer FDM is deployed to generate curved contour. It is obvious
that layer thickness would have to be appreciably reduced in order to achieve better
surface finish by compensating stair-step effect. This in turn as a consequence of larger
number of layers required, increase the build time.
There has therefore been a persistent need in the field of RP processes to develop a
curved layer fused deposition modeling technology in order to eliminate the limitations of
the prior art flat layer FDM process when a prototype having thin curved shape is required
to be built. The method and system for curved layer fused deposition modeling has been
attempted to find a viable alternative to solve problems associated with the prior art RP
process such as the flat layer LM/FDM. The curved layer fused deposition modeling
(CLFDM) wherein the extruder nozzle is adapted to depositing fused filaments in curved
layers one atop the other instead of flat layer, over a support material or pre-placed
mandrel on the work table such that the parts made of such curved layer filament
deposition are having higher strength, less stair-step effect, less number of layers and
consequently faster prototyping, maintaining more continuity of fibers across any planar
cross section. The method of fused deposition modeling to generate thin and curved parts
is further required to achieve greater adhesive bonding and strength avoiding anisotropy
or any considerable discontinuity in structure.

OBJECTS OF THE INVENTION
It is thus the basic object of the present invention to develop a method for Curved Layer
Fused Deposition Modeling (CLFDM) and a system for implementing the method for rapid
prototyping processes for thin and curved parts.
A further object of the present invention is directed to developing a method and system of
CLFDM for Rapid Prototype manufacturing of thin curved parts wherein the process would
be capable of depositing fused thermoplastic filament in a curved layers one atop the other
in a manner reducing the number of layers as compared to the conventional flat layer FDM
process if applied for the same part with equal filament diameter and thus making the
process faster.
A further object of the present invention is directed to developing a method and system of
of CLFDM for Rapid Prototype manufacturing of thin curved parts wherein the stair-step
effect experienced in conventional Fused Deposition Modeling (FDM) could be reduced and
thereby enabling attaining improved surface finish of parts.
A still further object of the present invention is directed to developing a method and a
system of CLFDM for Rapid Prototype manufacturing of thin curved parts wherein the
process would favour deposition of curved layers with long continuous filaments instead of
flat layers with short discontinuous filaments, thus replacing adhesive strength between
layers in case of flat-layered FDM by longitudinal strength of continuous filaments in
CLFDM, also replacing lesser number of layers in cross sections of thin curved parts in flat
layered FDM by more number of layers in same cross sections of same thin curved parts in
CLFDM and thereby ensure isotropy and consequent higher strength of the thin curved
part produced by CLFDM.

A further object of the present invention is directed to developing a method and a system
for CLFDM for Rapid Prototype manufacturing of thin curved parts wherein said method
would be adapted to generate thin shell-typed slightly curved parts by depositing fused
filament in curved layers directed to avoid the limitations and shortcomings of the
conventional FDM.
A further object of the present invention is directed to developing a method and a system
of CLFDM for Rapid Prototype manufacturing of thin curved parts wherein curved layers
could be effectively deposited with provision for maneuverability of both the extruder and
also the table, for generating the rapid prototype, such that verticality of the filament
trajectory and its normality to the surface being built up at the point of deposition, is
maintained.
A further object of the present invention is directed to developing a system of CLFDM for
Rapid Prototype manufacturing of thin curved parts wherein said system would be
advantageously adapted for executing the CLFDM process for Rapid Prototyping with
configuration for movement of the extruder nozzle and/or the worktable with support
structure favoring faster fused filament curved layer deposition to obtain desired thin
curved layered prototype having requisite strength.
SUMMARY OF THE INVENTION
Thus according to the basic aspect of the invention there is provided a method for curved
layer fused deposition modeling comprising:
providing a support structure having an upper surface which is the conjugate of the lower
surface of the shape to be developed by curved layer deposition thereon on a table;

applying the said fused material on top of the support structure in the form of curved
layers by selectively adjusting the extruder head and /or the table holding the support
structure.
According to a preferred aspect the method for curved layer fused deposition modeling
comprises:
(a) providing a support structure on a table, the upper surface of the support structure
having the conjugate shape of the lower surface of the part to be made by curved layer
fused deposition modeling;
(b) applying the said fused material on top of the support structure in the form of
filaments in curved layers one atop the other by extruding the fused material from an
extruder by relative and selective motion of the extruder with respect to the table holding
the support structure such that the filament trajectory is normal to the prototype surface
or any intermediate curved layer surface at any point of time.
Importantly, in the above method for curved layer fused deposition modeling of the
invention is adapted for changing the orientation of the filaments from one curved layer to
another. Importantly, the trajectory of the extruded filament is kept vertical using desired
machine configuration. In particular, the method for curved layer fused deposition
modeling provides for maintaining the trajectory of the extruded filament along the normal
to the surface of the curved layer being applied at the point of application of filament.
According to a preferred aspect the method for curved layer fused deposition modeling
includes:

determining the filament paths and ensuring proper lateral bonding between filaments ;
determining the filament location such as to have a constant superposition with the lower
surface as well as with the adjacent filament(s).
Advantageously, the above method for curved layer fused deposition modeling provides
for the filaments to be continuous for improved strength and good adhesive bonding.
Importantly, the above method for curved layer fused deposition modeling involves using
2C,L (x- and y- axes with continuous control, z-axis with linear interpolation control) for
deposition of curved layers.
Preferably, in accordance with another aspect of the invention, the adjacent filament
cross-sections are constrained by a prespecified superposition realized through a constant
common chord of contact between the superposed adjacent filament preferably circular
sections and also inter-layer preferably curved overlap throughout the path such as to
achieve uniform lateral bonding.
According to yet another aspect of the invention the method for curved layer fused
deposition modeling comprises:
forming the mandrel;
depositing the layers of materials extruded by FDM on said mandrel to build up the part
with the top surface of the mandrel corresponding to the lower surface of the thin curved

part to be prototyped thereby building curved layers from the bottom towards the top till
the part is fully reproduced.
In accordance with another aspect of the invention there is provided a system for carrying
out the method of curved layer fused deposition modeling comprising:
an extruding head adapted for said relative motion for selective extrusion of the fused
material;
a support table adapted for holding said support structure and adapted for executing
relative motion with respect to the extruder nozzle to facilitate maintaining the trajectory
of the fused extruded material from the nozzle along vertical and along normal to the
curved layer surface.
Preferably, in the above system for carrying out the method of curved layer fused
deposition modeling the extrusion head is adapted for three dimensional motion (x, y and
z) relative to the support table on which the prototype is built up and said support table is
adapted to be rotatable about the x- and y- axes to thereby provide for a 5 axes
configuration with translation along x,y and z axes.
Importantly also, the system for carrying out the method of curved layer fused deposition
modeling is adapted such that the trajectory of the fused extruded material from the
nozzle could be maintained vertical and normal to the curved layer surface.
Advantageously, the above discussed system for carrying out the method of curved layer
fused deposition modeling provides for facilitating the avoidance of gouging (undesirable
interference between nozzle tip and deposited material) and for the purpose the

deposition head shape is selectively adapted preferably convex shape with extruder
aperture at the tip.
The present invention and its objectives and advantages are described in greater detail
hereunder with reference to the accompanying non-limiting exemplary illustrations as per
the following :
BRIEF DESCRIPTION OF THE ACOMPANYING DRAWINGS
Figure 1: is the schematic illustration of the conventional FDM process for flat layer
deposition in RP process.
Figure 2: is the schematic illustration for developing curved part using conventional flat
layer FDM process and its limitations of the same in RP process.
Figure 3: is the schematic illustration of the curved layer fused deposition modeling
(CLFDM) using 3-axis control (e.g. x, y & z) over a support structure for developing thin
curved part according to the present invention.
Figure 3(a): is the illustration of comparative views to illustrate the structural homogeneity
and surface uniformity achieved in producing thin, curved, shell type parts by flat FDM
(conventional art) and CLFDM ( present invention);
Figure 4: is the illustration for choice of build direction to achieve smooth borders with
continuous filaments in thin curved sections with flat layered FDM.

Figure 5: is the illustration of a typical example of a thin curved part with bi-directional
curvature.
Figure 6: is the illustration of a prototyping of thin curved part in CLFDM using deposition
of filaments in alternate directions for isotropy.
Figure 7(a): is the illustration of the sectional view of the part produced by FDM wherein
the overlapped section of two adjacent layers in FDM is shown by shaded lines.
Figure 7(b): is the enlarged view of illustration of the adherence and overlap of the
adjacent filaments in curved layers of CLFDM.
Figure 8: is the illustration of geometric distortion effect of gantry tilt on a 3D surface
rendered skull and the same data after necessary correction.
Figure 9: is the illustration of the model development of different complex geometries
using CLFDM e.g.-(a) a hemispherical surface with a straight trim on one side, (b) trimmed
surface of a part in the interior, discontinuous filament deposition method, (c) trimmed
surface of a part in the interior, continuous filament deposition method, (d) surface made
of two patches, continuous filament method.
Figure 10: is the illustration of the CLFDM path generation for RP of the turbine blade
showing the FLCs (filament location curve) in a single layer only.
Figure 11: is the illustration of one embodiment of schematic configuration of 5-axes
machine for CLFDM showing the translation and rotation about the different axes either of
the extruder nozzle head or the worktable holding the part.

Figure 12: illustrate the various axis definitions used in different alternative embodiments
of the CLFDM machine according to the present invention.
Figure 13(a)-(s): are the illustrations of the different possible alternative axis description
of the embodiments of the CLFDM machine according to the present invention.(3-axis
configuration figure on page 2 of figure file may be retained if the three axes configuration
is capable of CLFDM on the laid down curved filament path generation principle of the
invention).
DETAILED DESCRIPTION OF THE INVENTION WITH REFERENCE TO THE
ACCOMPANYING FIGURES
As discussed hereinbefore the present invention is directed to a method of curved layer
fused deposition modeling (CLFDM) for Rapid Prototyping and a machine for CLFDM having
Atleast 3-axes or 4-axes or 5-axes configuration for relative movements between extruder
head and worktable for the part to be prototyped. The CLFDM is particularly applicable for
the generation of thin curved parts facilitating RP process and other manufacturing
industries especially including the impeller or turbine blades manufacturing or biomedical
industry where the conventional flat FDM process is unable to provide desired surface
finish due to stair-step effect or may consume more time by laying larger number of layers
of reduced thickness to compensate the stair-step effect and also do not provide enough
strength of the part due to discontinuity of layers in flat layered FDM leading to lower
number of layers in a section or resultant anisotropy due to appreciable difference
between longitudinal filament strength and adhesive bond strength between filaments.

Reference is first invited to the accompanying Figure 1 which is the schematic illustration
of the traditional flat multi layer FDM for RP process. The conventional FDM uses an
extruder nozzle that deposits consecutive layers of filaments generating flat surface one
over the other on a worktable on which the part is built, the filament material comprising
the thermoplastic materials comprising Acrylonitrile butadiene styrene (ABS) Polymer,
polycarbonates polycaprolactone, polyphenylsulfones, waxes and metals are used, usually
in the form of either pellets or wires, depending on requirements of shape volume or
strength requirements. It is observed that the deposition of flat layers suffer from the
limitations of stair-step effect and lack in strength particularly when the part is thin or
having small radius of curvature because of the inherent discontinuity in between layers or
anisotropy in character of deposits in such flat FDM process.
Reference is also invited to the accompanying Figure 2, wherein the Flat layer FDM
process for prototyping a thin curved part has been illustrated schematically. It is
moreover illustrated that while generating a curved profile by flat filament layer
deposition, by the extruder movement relative to table in horizontal plane x-y, with z
movement taking place relatively between extruder and table after completion of each
layer so as to increase their distance in order to start a fresh layer atop the last deposited
layer, thus creating the significant stair-step effect and hence poor surface finish of thin
curved part which will need to be finally finished by grinding or other means to attain
exact curved shape and acceptable surface finish. Further, it is noticed that if layers are
made of thin filament deposition to reduce the stair-step effect, the number of layers
required to generate desired curved shape would increase, consuming more time for
prototyping. The curved part so generated has less strength due to inherent defects of the
flat layer FDM process like the lack of strength due to discontinuity of flat layers in thin
curved part or anisotropy due to appreciable difference between adhesive bond strength of
adjacent filaments within a layer or across layers and the longitudinal strength of the

continuous filament. In flat-layered FDM, 3-axis CNC is sufficient for the deposition of
filaments in flat layers and for moving the extruder relative to table for offset. In
conventional FDM, the filaments in a layer are all in a single plane and hence the
maintenance of a constant extruder path interval ensures that the adjacent filaments
(roads) have uniform lateral overlap/superposition (negative gap) and hence uniform
lateral bonding along their respective lengths. It is not possible to maintain uniform
overlap between deposited adjacent filaments (throughout their respective lengths) in bi-
directionally curved thin members in CLFDM by employing a constant extruder path
interval.
However, it is experienced in the existing art, in some cases, proper choice of orientation
of the part or build direction in the FDM chamber may eliminate some of the drawbacks
observed in flat layer FDM. For example, in the case of a typical curved thin part under
consideration, continuity of filaments can be obtained in the concerned section part if it is
held upright, as illustrated in Figure 4, in the deposition chamber and the deposition
carried out as the "contour fill" scheme of FDM whereby a continuous filament is deposited
to define the border and the interior is filled out by subsequent deposition, thus yielding a
smooth border in that section. However, in spite of the choice of build direction by
preferred part orientation in FDM, discontinuity of filaments would still exist across the
sections shown by dotted lines. In fact, there would not be a single continuous fibres
across these sections. Hence the strength across the section would be defined completely
by adhesive bonding. Further, if the part has bi-directional curvature as shown in Figure
5, the selection of build direction orientation would not serve the purpose of reducing the
surface roughness as there would still be roughness obtained in the direction of build.
Adaptive slicing is the effective solution for such problems in flat layered FDM. Depositing
thinner layers in regions of low/near horizontal surface slope and high curvature would
certainly reduce the surface roughness. At the same time, build time is not expected to

increase substantially as higher layer thickness would be retained in places of high
(vertical or near vertical) surface slope and low curvature. However, the improvement in
strength of the part due to thinner layers would be marginal. Further, if thinner layers are
applied only at selected regions according to the underlying principles of adaptive slicing,
the part would remain as weak as the thick layered regions. A number of attempts for
adaptive slicing of parts have been made which include direct slicing and slicing of faceted
surfaces in the form of STL files.
Thus there had been a need to develop a curved layer fused deposition modeling process
and a system to execute such process to eliminate the limitations of the existing flat FDM
process. The present invention directed to developing CLFDM process favoring rapid
prototyping of thin curved parts by employing a system for such process, ensuring
improved isotropy, strength, surface finish and speed of prototyping.
Reference is now invited to accompanying Figure 3, that illustrate the principle of the
CLFDM process according to the present invention and its comparative advantageous
aspects over flat layer FDM applied for rapid prototyping or other like applications in
manufacturing. In CLFDM, the curved layers are deposited on an initial support structure
whose upper profile is the conjugate of the profile of the lower surface of the part,
developed either by flat-layer deposition of support material or by the use of a pre-placed
mandrel on the worktable. On top of this structure, fused filament is deposited in the form
of curved layers. The extruder path generation in this case is achieved by three
dimensional (x, y & z) control of motion of the nozzle head relative to the table on which
the prototype is built up. The extrusion axis is vertical so that gravity does not affect the
filament trajectory. In order that the filament trajectory is vertical as well as normal to the
prototype surface or any intermediate curved layer surface at the point of deposition, the
machine table should be additionally rotatable about the x- and y- axes. Hence the CLFDM

machine is ideally of 5-axes configuration, with translation along x, y and z and rotation of
worktable along x- and y-axes. However, a 3-axes or a 4-axes machine would also suffice
when this surface normal (n) does not appreciably deviate from the vertical as apparent
from Figure 3. This condition is valid only for slightly curved parts or if any intermediate
curved layer surface is not highly sloped with respect to the horizontal at any point with
the selected configuration.
Accompanying Figure 3a, is the illustration of the comparative aspects of thin curved
surface generation using conventional flat FDM and the structural consistency and
enhanced strength by producing the same part using CLFDM according to the present
invention. The thin curved shell-like part produced by the CLFDM process as illustrated in
the accompanying Figure 3a, is having advantageous aspect of reduced stair-step effect,
reduced number of layers, reduced time for deposition and increase in strength by
depositing continuous length of filaments providing higher strength across any transverse
section ensuring deposition of greater amount of fused material at: any cross-section/
across any planar cross section, without any discontinuity, compared to conventional FDM.
The objective of the present work is the investigation for the manufacturing of curved thin
parts by depositing material in curved non-horizontal layers using FDM. It is established
that substantial improvement in the mechanical properties of thin-section curved shell-
type parts is achieved when made by CLFDM in comparison to FDM. It is also aimed at
developing and implementing appropriate algorithm for generating 3D curved paths of the
extruder head relative to the table for filament deposition to achieve successful
reproduction of part shape and proper inter-filament bonding.
With the advent of bio-friendly materials, RP technology has been extended in the field of
biomedical engineering which requires precision and flexibility. Bio-compatible PMMA-resin

has been used for developing the part of a skull for replacement in the case of an accident
victim. The present method of CLFDM would be very appropriate for the manufacturing of
functional prototypes of skull bones and other thin shell type parts. Other potential
application areas are in the manufacturing of intricate and small sized turbine blades or
objects of thin cross-section, produced for actual use or for design verification and testing.
The advantages of the CLFDM according to the present method and system are lying with
the lesser numbers of layers for identical part, higher continuity of filament resulting in
more strength and more bonding between consecutive layers due to larger area of inter-
layer bonding.
Reference is now invited to the accompanying Figure 6, that illustrates the CLFDM process
implementation according to an embodiment of the invention to generate thin curved parts
by application of the present system laying filament alternate direction for isotropy. In
CLFDM, ideally choice a 5-axis configured CNC machine has been used, such that the
extruder axis always coincides with the normal (n) to the layer at the point of deposition,
although a 3-axis machine is sufficient for CLFDM when curve slope is not so steep and the
extruder axis is approximately normal to surface at the point of deposition. While the FDM
process for flat layer deposition uses 2C,P (x- and y- axes with contouring control and z-
axis with point-to-point control) control for the table and head movement, CLFDM
necessarily use 2C, L control which means x- and y- axes for contouring control and z-axis
with linear interpolation control because the table needs a 3D linear interpolator for the
deposition of curved layers. Contouring control is retained along x-and y-axes to permit
flat-layered FDM with contour fill option, if required.
The deposition of the filaments has to be done in alternate directions for successive curved
layers as illustrated in the accompanying Figure 6. This, first of all, ensures continuity of

filaments in any direction and thereby increase isotropy due to such alternate orientation
of continuous filaments in the part.
It is thus important to first determine the filament deposition path for proper reproduction
of part shape by CLFDM. Moreover, considering the fact that in the case of CLFDM,
adjacent filaments (roads) do not necessarily lie on the same plane, proper lateral bonding
between the filaments is also an important aspect in this process applied to rapid
prototyping. In the present invention, the filament location (position of the cross-section of
the filament at a point on the free form surface) is planned so as to have a constant
superposition with the lower surface or previous surface as well as the adjacent filaments.
This process of filament deposition ensures uniform bonding between adjacent filaments
and also between the adjacent layers. The filaments of thermoplastic material extruded in
CLFDM are approximately of circular cross-section with a constant diameter through out
the process. The adjacent filament cross-sections are constrained by a pre-specified
superposition realized through a constant common chord of contact (CC) between the
superposed adjacent filaments of circular section and also surveyed interlayer overlap
throughout the path to achieve uniform lateral and inter-layer bonding. Prior to starting
actual curved layered prototyping using CLFDM process of the invention, a support
structure or a mandrel is formed initially to act as support with matching surface same as
the conjugate of the bottom contour of the part to be built and thereafter layers of
material extruded by FDM would be laid on it to build up the part. Top surface of the
mandrel is conjugate of the lower surface of the thin curved part to be prototyped. The
strategy here is to build curved layers from the bottom towards the top i.e. a bottom-up
building direction, till the part is fully reproduced.
The filament cross-section locations are determined by two sequential steps - initial guess
point determination and correction of each point to satisfy the desired strength

requirement fulfilling the condition of constant common chord (CC). A given filament path
(FP) and the upper surface of the previous layer are used to identify the next FP. The
initial FP (say FP1) is chosen arbitrarily, preferably, along or very close to one of the edges
of the bottom surface of the part. Points along this isoparametric edge of the surface are
first selected to be contact points between filament and previous surface/mandrel as the
case may be.
As the longitudinal tensile strength of the filaments is higher than the bonding strength
between adjacent filaments, it results in anisotropy. For a flat-layered FDM generated part,
there remain no continuity of filament in many cross sections e.g. in the flat inter-layers.
Further, a tensile force across or a shear along the flat inter-layers of a FDM-generated
part, is resisted primarily by the inter-filament bonds between layers. In case of same part
made by CLFDM process, the inter-layers are not flat and they tend to span the whole
extent of the part. Hence, the inter-layer area per layer is considerably higher if CLFDM
process is applied as compared to the FDM. This makes the inter-layers of the CLFDM
generated part considerably stronger than those of the FDM-generated part.
Reference is now invited to the accompanying Figure 7(a) and 7(b), wherein the
comparison between the contact areas between layers of the two methods are shown.
Figure 7(a) shows that one layer is in contact with the layer above it through a thin
annular area, while the filaments are deposited in CLFDM ensuring sufficient overlap as is
shown in accompanying Figure 7(b) with selectively chosen chord of contact between the
filaments/tubes. As a result, the shear strength of the parts created from flat-layered FDM
is very low towards the top while in CLFDM a strong uniform bonding is maintained
through all interlayers. Moreover, CLFDM process creates a woven net like structure, which
provides the part produced more uniformity in strength. Conventional FDM process is

unable to provide the enhanced interlayer adhesion strength. Thus the CLFDM generated
parts have higher strength than identical part produced by flat layer FDM process.
Reference is now invited to the accompanying Figure 8 that illustrates the method of
compensating the gantry tilt effect in 3D Computer Tomography (CT) scan images used for
skull dome modeling. When a set of 2D slices is combined into an image volume for 3D
modeling, the gantry angle must be taken into account. Figure 8 illustrates the gantry tilt
effect in SLA prototyped part of skull dome showing the geometric distortion effect of
gantry tilt on a 3D surface rendered skull and the same data after necessary correction.
FDM is implemented after the paths have been transformed using the affine
transformations. The build direction does not pose a problem in CLFDM process. The 5-
axes control is easily utilized in CLFDM machine to take care of gantry tilts and hence can
fabricate such model easily and accurately.
Reference is now invited to the Figure 9(a), (b) & (c), wherein the various surface
generation examples have been illustrated applying CLFDM. In the case of surface with
trimming at one end, the FLP (Filament location point) do not alter and remain same as
the older FLPs with an additional truncation of the ends as shown in Figure 9(a). If
trimming of the part appears inside, the FLPs can be constructed in two different ways as
shown in Figures 9(b) and 9(c) respectively. In Figure 9(b), the filaments are deposited in
a discontinuous manner. The flow of the extruder is stopped at the trimmed region.
However, such a discontinuity of filaments may reduce the strength of the part produced.
An alternative approach has been shown in Figure 9(c) where the continuity of the
filaments is preserved.
A third kind of surface is considered where the surface is generated using two different
patches as illustrated in Figure 9(d). It is clearly apparent from the Figure 9(d) that the

surface patches are not treated in isolation and continuous filament paths are constructed
so as to obtain higher strength through continuous filaments or roads.
Reference is next invited to the accompanying Figure 10 that illustrates the generation of
Filament Location Curves corresponding to prototyping a typical turbine blade which is thin
and having curvatures in different directions for operating requirements. A typical turbine
blade surface is described by a parametric surface and the upper surface is considered for
the generation of the FLCs. Accompanying Figure 10 shows only one layer of FLCs for
clarity. It is observed that the FLCs produced are continuous and are capable of providing
higher strength compared to discontinuous filaments if made through the existing LM
processes.
Reference is now invited to the accompanying Figure 11 which schematically illustrates
an embodiment of the 5-axes machine for implementation of the CLFDM process according
to the present invention. The extruding head is mounted on the machine column and beam
support such that the extruder head is adapted to move in 3 dimensional directions along
x, y and z axes relative to the work table on which the proto type is built. Initially a
support structure is built either by flat-layer FDM or by the use of a pre-placed mandrel
that conforms the lower surface profile of the thin curved part to be built. On the top of
this support structure, the part is built in bottom-up direction by depositing successive
layers of fused thermoplastic filaments, applied following the pre-programmed trajectory
with selective superposition by the offset surface principle as explained in the filament
path generation method for CLFDM process, thus ensuring desired isotropy and strength,
avoiding discontinuity. In order that the filament trajectory is normal to the prototype
surface or any intermediate curved layer surface at any point of deposition, the machine
table is additionally adapted to orient the part rotatably about x and y axes, such that the
extrusion axis is vertical to the deposited surface at any instant ensuring that gravity does

not affect the filament trajectory. Hence, the CLFDM machine/system according to this
embodiment of the present invention having ideally 5-axes configuration with translation
of extruder head/nozzle along the x, y and z-axes directions and rotation of table about
the x and y axes. Thus the present invention is directed to developing Universal Fused
Deposition Modeling Machine capable of both flat layer and curved layer fused filament
deposition.
However, it has been studied and observed that 3-axes and 4 axes configuration of
machine to execute CLFDM process is also possible provided that the part surface or any
intermediate curved layer surface is not highly sloped with respect to the horizontal or
having high curvature at any point with the selected configuration.
For the operation of such 3/4/5-axes machine/system to generate thin curved part with
enhanced strength and desired isotropy, the system input requires a CAD model of part to
be prototyped along with software/algorithm for curved layer slicing and extruder path
generation, operatively interfaced with the drives and control units of the machine to
achieve desired sequenced motions of extruder or work table.
It is thus possible by way of the CLFDM machine and its method of operation to generate
filament path adapted to produce thin curved layered part for RP processes or
manufacturing components for real life production/automation environment. The method
and the system as described herein above is particularly suitable for generating thin walled
curved profile of shell type parts in various engineering applications from a wide range of
materials/metals e.g. the turbine blades, for the fabrication of cranial implants and
patterns for making implants. The machine and the process for CLFDM of the present
invention are capable of catering to the wide range of requirements of faster part

generation in the bio-medical industry, turbine blade and impeller manufacturers or
specific Rapid Manufacturing industry.
The accompanying Figure 12 illustrates the various axes definitions used to illustrate the
various configurations or alternative embodiments of the CLFDM machine or system
according to the present invention adapted to generate the desired filament path
generation by adaptive control on the motion of either extruder head/nozzle or the work
table along with the part which is built or both in combination, to favour rapid
reconstruction of the CAD modeling of any thin curved shell type parts to meet either RP
process or manufacturing objective. The figure illustrates the conventional positive axis
directions for either translation of the extruder nozzle or work table in x, y and z axes or,
for rotation of table about x , y or z axes.
The accompanying Figures 13 (a) to (s) illustrate the different possible alternative axes
configuration for translational/rotational motion of extruder and table in either of x, y or z
direction, in isolation or in combination of the Universal Fused Deposition Modeling
Machine according to the present invention, directed to rapid prototyping (RP) process or
manufacturing of thin curved shell type parts, by flat as well as curved layered fused
deposition, following the method of the extruder path generation and adaptive slicing of
curved surface interfaced with operating/application software/algorithm supported
computer system. It is apparent from the Figure that, such alternative embodiments are
adapted to enable generating the desired curved filament surface contour and at selective
offset surface. These alternative embodiments possess the capability of carrying out
CLFDM as already described.

It is thus possible by way of the present invention to develop a process for executing
curved layer fused deposition modeling in rapid prototype or manufacturing through
enabling desired extruder path generation such that the trajectory of fused filament is laid
in curved layers at selective superposition or offset surface and thereby ensuring desired
isotropy and enhanced interlayer adherence strength of part produced avoiding
discontinuity. The invention is further directed to a system/machine to implement the
process of curved layer fused deposition modeling, preferably having at least 3-axes and
ideally 5-axes configuration adapted to generate thin layered curved shell type part having
improved strength and surface finish avoiding undesired discontinuity of filament layers
and stair-step effect are essentially required to be generated with desired level of
accuracy. The higher strength of the part manufactured by the CLFDM process using the
system of the invention is achieved by way of employing longer stretches of continuous
filaments or roads, by implementing said extruder path generation algorithm/software so
that curved inter-layers of larger area per layer is ensured. The CLFDM method of the
invention has the potential to not only increase the strength of even thin curved layered
parts but to reduce stair-step effect and achieve better surface finish, reduced number of
layers of filament and consequent reduction of build time.

WE CLAIM:
1.A method for curved layer fused deposition modeling comprising:
providing a support structure having an upper surface which is the conjugate of the lower
surface of the shape to be developed by curved layer deposition thereon on a table;
applying the said fused material on top of the support structure in the form of curved
layers by selectively adjusting the extruder head and /or the table holding the support
structure.
2. A method for curved layer fused deposition modeling comprising:
(a) providing a support structure on a table, the upper surface of the support structure
having the conjugate shape of the lower surface of the part to be made by curved layer
fused deposition modeling;
(b) applying the said fused material on top of the support structure in the form of
filaments in curved layers one atop the other by extruding the fused material from an
extruder by relative and selective motion of the extruder with respect to the tabJe holding
the support structure such that the filament trajectory is normal to the prototype surface
or any intermediate curved layer surface at any point of time.
3. A method for curved layer fused deposition modeling as claimed in anyone of claims 1
or 2 comprising changing the orientation of the filaments from one curved layer to
another.

4. A method for curved layer fused deposition modeling as claimed in anyone of claims 1
to 3 wherein the trajectory of the extruded filament is kept vertical using desired machine
configuration.
5. A method for curved layer fused deposition modeling as claimed in anyone of claims 1
to 4 comprising maintaining the trajectory of the extruded filament along the normal to
the surface of the curved layer being applied at the point of application of filament.
6. A method for curved layer fused deposition modeling as claimed in anyone of claims 1
to 5 comprising :
determining the filament paths and ensuring proper lateral bonding between filaments ;
determining the filament location such as to have a constant superposition with the lower
surface as well as with the adjacent filament(s).
7. A method for curved layer fused deposition modeling as claimed in anyone of claims 1
to 6 wherein the filaments are continuous for improved strength and good adhesive
bonding.
8. A method for curved layer fused deposition modeling as claimed in anyone of claims 1
to 7 comprising using 2C,L (x- and y- axes with continuous control, z-axis with linear
interpolation control) for deposition of curved layers.
9. A method for curved layer fused deposition modeling as claimed in anyone of claims 1
to 8 wherein the adjacent filament cross-sections are constrained by a prespecified
superposition realized through a constant common chord of contact between the

superposed adjacent filament preferably circular sections and also inter-layer preferably
curved overlap throughout the path such as to achieve uniform lateral bonding.
10. A method for curved layer fused deposition modeling as claimed in anyone of claims
1 to 9 comprising:
forming the mandrel;
depositing the layers of materials extruded by FDM on said mandrel to build up the part
with the top surface of the mandrel corresponding to the lower surface of the thin curved
part to be prototyped thereby building curved layers from the bottom towards the top till
the part is fully reproduced.
11. A system for carrying out the method of curved layer fused deposition modeling as
claimed in anyone of claims 1 to 10 comprising:
an extruding head adapted for said relative motion for selective extrusion of the fused
material;
a support table adapted for holding said support structure and adapted for executing
relative motion with respect to the extruder nozzle to facilitate maintaining the trajectory
of the fused extruded material from the nozzle along vertical and along normal to the
curved layer surface.
12. A system for carrying out the method of curved layer fused deposition modeling as
claimed in claim 11 wherein the extrusion head is adapted for three dimensional motion
(x, y and z) relative to the support table on which the prototype is built up and said

support table is adapted to be rotatable about the x- and y- axes to thereby provide for a
5 axes configuration with translation along x, y and z axes.
13. A system for carrying out the method of curved layer fused deposition modeling as
claimed in anyone of claims 11 and 12 adapted such that the trajectory of the fused
extruded material from the nozzle could be maintained vertical and normal to the curved
layer surface.
14. A system for carrying out the method of curved layer fused deposition modeling as
claimed in anyone of claims 11 to 13 wherein to facilitate the avoidance of gouging
(undesirable interference between nozzle and part being built up), the deposition head
shape is selectively adapted preferably convex shape with extruder aperture at the tip.
15. A method and a system for carrying out the method of curved layer fused deposition
modeling having selective configuration substantially as herein described and illustrated
with reference to the accompanying figures.

A method for Curved Layer Fused Deposition Modeling (CLFDM) and a system for carrying
out such process in Rapid Prototyping (RP) especially thin curved parts with improved
isotropy, strength and better surface finish. Importantly, the CLFDM method would avoid
limitations of FDM in manufacturing thin, curved parts (shells) by reduction of stair-step
effect and increasing the strength and reduction in number of layers. The system for
CLFDM is provided such as to favour the CLFDM having at least 3 axes and preferably
having 5 axes for relative translation and/or rotation of the extruder nozzle and the
worktable so that thermoplastic fused filament is essentially deposited normal to the
curved surface generated at a point and the trajectory of the filament at the point of
ejection from extruder nozzle is preferably vertical. More advantageously, the system of
CLFDM includes a support structure/pre-placed mandrel, conjugate of the lower surface of
the part favouring the bottom-up build direction ensuring enhanced productivity in RP
processes.