Research Article DEVELOPMENT OF A NEW LINEAR DELTA ROBOT FOR THE FUSED DEPOSITION MODELLING PROCESS

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1 Tansactions of the TSME (07) Vol. 5, No., 4 54 Jounal of eseach and Applications in Mechanical Engineeing Copight 07 b TSME ISSN 9-5 pint DOI: /jame.07.4 eseach Aticle DEVEOPMENT OF A NEW INEA DETA OBOT FO THE FUSED DEPOSITION MODEING POCESS J. Pattavanitch * S. Panau Depatment of Mechanical Engineeing, Facult of Engineeing, Buapha Univesit 69 ong-had Bangsaen d., Muang, Chonbui, 0 Thailand ABSTACT: This pape aims to eplain the design and constuction of a new linea delta obot fo the fused deposition modelling (FDM) pocess. The kinematics of the obot, including the invese and fowad kinematics, ae deived. These kinematics ae used to detemine the geometic paametes of the obot. The wokspace of the designed obot is pesented, and the obot pefomance is checked with the conditioning inde (CI). The obot is tested to evaluate obot accuac b epeatedl tavelling to the equied location. The actual tavel paths of the obot ae also investigated. The obot is equipped with a filament spool, etude nozzle to fabicate phsical objects b FDM pocess. The contol sstem is compute-based. The contol pogam is developed using a Visual Basic.NET famewok. The pogam allows the use to contol the obot and the pocess via a gaphical use inteface (GUI). The obot sstem is tested to ceate thin-wall objects with fou diffeent shapes which ae squae, clindical, squae-based pamid and ounded gea to illustate the capabilit of the developed additive manufactuing sstem. Kewods: inea delta obot, Fused deposition modelling, Additive manufactuing. INTODUCTION In poduct development, pototpes must be ceated to visualise aspects such as shape, to inspect dimensions o sometimes to do phsical testing befoe mass manufactuing. Man techniques ae used to ceate pototpes, one of which is additive manufactuing (AM) o D pinting. AM efes to a goup of pocesses fo fabicating phsical objects diectl fom D compute-aided design (D CAD) involving lae-b-lae stacking []. Thus, AM offes the oppotunit of fabicating components without elaboate tooling. Thee ae seveal diffeent methods of AM. The most widel used is a pocess known as fused deposition modelling (FDM), developed b Statass Inc. In the FDM pocess, filament-based mateial is fed into the heating element to melt the mateial and is then etuded though a nozzle. Afte deposition, the fused mateial solidifies and adhees to the peceding lae. Thus, a new lae is ceated. The nozzle keeps moving to deposit the subsequent laes until the pocess is completed. Because the laes ae fomed using a mobile nozzle, the objects can be fabicated not onl within a build chambe but also on an suface outside the confines of a build chambe, such as on a feefom suface [] o pe-machined component faces [, 4]. Anothe advantage of this pocess is that it is able to handle multiple pinting heads to fabicate a component with diffeent mateials [5]. * Coesponding autho: J. Pattavanitch addess: jitti@eng.buu.ac.th 4 /Volume 5(), 07 Tansactions of the TSME: JAME

2 The themal etusion pocess in the FDM pocess enables the use of vaious tpes of mateial, fom taditional themoplastic such as pollactic acid (PA) and aclonitile butadiene stene (ABS) to newe mateials such as bioesobable polme [6], ceamics [7], metal [8] and composite mateial [9,0]. FDM is used to build pats fo man applications anging fom lage-scale components in the automotive [0] and aeospace industies [] to mico-scale objects in medical applications []. Because the FDM pocess uses a mobile nozzle, it equies a mechanism to position the nozzle. Thee ae seveal tpes of mechanisms designed fo the FDM pocess, such as Catesian, linea delta, pola and SCAA mechanisms. Howeve, onl the fist two ae cuentl available on the D pinte maket. A Catesian mechanism consists of thee linea aes that ae pependicula to each othe. The movement of an ais will not affect the othe aes. With a Catesian aangement, the pint nozzle moves on the X-Y plane and a pint bed moves on the Z ais [, 4] o the nozzle tavels on the X-Z plane and a pint bed moves on the Y ais [5]. In compaison, the linea delta mechanism uses paallelogams to manoeuve the nozzle. Theefoe, the pint bed is stationa and the pint head is located in a D space [6, 7]. The Catesian mechanism is of a simple design, esulting in ease of contol. Howeve, the opeation speeds ae athe low. This is because some of the moving components have to ca the moto and the components of othe aes, esulting in inceased time to acceleate o deceleate the mechanism s inetia. In contast, the motos in a linea delta mechanism ae mounted to the fame of the pinte. Theefoe, the weight and inetia of the moving pats is low. Consequentl, the linea delta mechanism can opeate at high speeds and acceleations. Due to its high speed capabilit, a linea delta mechanism can be used not onl in the conventional FDM pocess but also in cuved lae fused deposition modelling (CFDM) [8] in which the nozzle tavels with vaious z- values athe than a fied value duing the ceation of a lae. The main advantages of CFDM ae the impovement in suface smoothness and the stength of completed objects [9]. At the pesent time, linea delta D pintes ae available in the maketplace. Howeve, the pefomance of the mechanism and how the accuac of the pinte is achieved ae not detailed. Theefoe, the aim of this pape is to descibe the design and constuction of a new linea delta obot that can be used to fabicate phsical objects using the FDM pocess and to analse the accuac of the mechanism. A compute pogam to contol and monito the pinte is also developed. Although the obots can be emploed to fabicate components using CFDM, the wok heein focuses on conventional FDM.. INEA DETA OBOT CONFIGUATION The configuation of the obot is illustated in Fig.. The obot has thee pais of columns that ae fied on the base. Each pai of columns has a caiage that attaches to the end effecto b two paallel ams of the same length via ball joints at each end. Consequentl, the motion of the end effecto is constained to thee tanslational degees of feedom and is paallel to the base. Theefoe, when caiages slide along the columns, the ams will tansmit the movement to the effecto, and the effecto moves. Column Ball joint Am Caiage End-effecto Fig.. Schematic of a delta obot. Tansactions of the TSME: JAME 07, Volume 5() / 4

3 . KINEMATIC ANAYSIS OF DETA OBOT The kinematic equations of the obot show the elationship between the position of the effecto and that of each caiage. To analse the kinematic equations, the obot configuation (Fig. ) is educed to a simple mechanism, as illustated in Figs. and. Thee pais of columns ae epesented b thee vetical clindes, with thei top ends denoted as A i ( i =,, ).The midpoint between two ball joints connecting on a caiage is denoted as Bi and the midpoint on the effecto is denoted as P i (see Fig. (a)). The ams have the length of ( P i B i = ) (Fig. (b)). A Y Z O X A O Z Y B A z A B B P B Z Y Z O / X O P P (a) (b) Fig.. a) Kinematic paametes of the delta obot; b) kinematic chain pojected on the Y-Z plane. Y Y Y A P P O X P O P X A (a) A Fig.. a) Top view of the obot; b) top view of the end-effecto. To deive the kinematic model of the obot, two efeence sstems ae defined in the analsis. The global efeence sstem ( O X Y Z ) is located at the cente of the tiangle ( A A A ) (Fig. (a)). The end effecto efeence ( O X Y Z ) is assigned to the cente of the tiangle ( P P P ). Assuming that the distance fom the global efeence ( O ) to A i is ( OA = OA = OA = ) (Fig. (a)) and the distance fom the effecto efeence ( O ) to Pi is ( O P = O P = O P = ) (Fig. (b)). Conside the loop O Bi Pi O in Fig. (b); the vecto-loop closue equation with espect to the global efeence ( O X Y Z ) can be epessed as: (b) Pi Bi = ( O Pi + OO ) OBi () 44 /Volume 5(), 07 Tansactions of the TSME: JAME

4 The position of point O and Bi with espect to the global efeence ( O ) is: T O O = [ z] () T OB i = [ cosθi sinθi zi ] () 4 whee θ = i i π, 6 and the position of point Pi in the platfom efeence ( O ) can be epesented as follows: T Pi = [ cosθi sinθi 0 (4) O ] B substituting the position vectos (Eqs. () - (4)) into the vecto-loop enclosue equation (Eq. ()) and using constain P i B i =, the kinematic equations of the obot can then be witten as: ( + ) + ( z z ) + (5) = ( ) + ( ) + ( z z ) (6) = ( ) + ( ) + ( z z) (7) =. Invese position kinematics Invese kinematics efes to the use of the kinematics equations to detemine the elationship between the positions of the thee caiages ( z i ) on thei columns and the location of the end effecto. B eaanging Eqs (5) - (7), the vaiable z i can be epessed as a function of the position (,, z ) of the effecto, as follows: ( ) z = z ± + (8) z = z ± ( ) ( ) (9) z = z ± ( ) ( ) (0) In this wok, the sign in the equations is assumed to be positive. Tansactions of the TSME: JAME 07, Volume 5() / 45

5 . Fowad position kinematics Fowad kinematics involve solving kinematic equations to detemine the position of the effecto (,, z ) when the positions of the thee caiages ( z i ) ae specified. The fowad kinematics equations ae obtained b calculating the oot of the following paametes: E z + F z + G = 0 () = Az + B () = Cz + D () whee A ( z z) ( ), ( z ) = z B = ( ), ( z z ) ( ) ( ) C = A, D = z z ( ) ( ) B, E = A + C +, F = AB + CD C ( ) z, and G = B + D D( ) + ( ) + z. Jacobian mati and conditioning inde The Jacobian mati is defined as the mati that maps the elationship between the velocit of the effecto and the vecto of actuated joint ates [0]. The velocit equation of the obot can be obtained b diffeentiating the kinematic equation (Eqs. (5) - (7)) with espect to time, which is witten into mati fom as: vɺ = Juɺ (4) whee vɺ and uɺ ae the vecto velocities of the effecto and caiages, which ae T v ɺ = [ ɺ ɺ zɺ ] (5) and T u ɺ = [ z ɺ zɺ zɺ ] (6) The Jacobian mati ( J ) of the obot can then be deived as follows:. 46 /Volume 5(), 07 Tansactions of the TSME: JAME

6 Tansactions of the TSME: JAME 07, Volume 5() / 47 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + + = J (7) The conditioning inde ( CI ) is used to evaluate the isotop of the obot, which can be calculated as []: J J = CI (8) whee J is calculated as: ( ); WJ J J T t = I W n = (9) whee n is the dimension of the Jacobian mati, and I is the n n identit mati. The CI has a value between 0 and. The obot is in its isotop configuation if CI equals. When the CI equals 0, the obot is in its singulait, whee the obot will be out of contol. 4. WOKSPACE ANAYSIS The values of the obot paametes that is,, and ae equied to constuct the obot. These paametes will affect not onl the volume of the wokspace but also the pefomance of the obot. In this wok, the conditions to detemine the obot paametes ae that the obot has a wokspace of mm and, to ensue that the obot is fa fom singulait, the value of the CI within the wokspace must not be less than 0.6. B using an iteation technique, the value of the paametes ae computed as =50 mm, =78 mm and =0 mm. With these paametes, the eachable wokspace of the obot is bigge than the equied wokspace (see Fig. 4(a)), and the minimum value of the CI within the wokspace (epesented in the ectangula aea in Figs 4(b) to (d)) is 0.6, which is geate than that of the constaint value (0.60). The computed obot paametes satisf the designed conditions. Theefoe, the obot will be built using these paametes.

7 CI (a) CI (b) CI (c) (d) Fig. 4. a) The wokspace of the obot; Distibution of CI: b) X-Y plane; c) X-Z plane; d) Y-Z plane. 5. HADWAE DEVEOPMENT AND CONTO SYSTEM The designed obot uses a tiangula fame to povide good balance and stabilit (see Fig. 5). The mateial fo the top plate is aluminium allo and that fo the bottom plate is steel. Si shafts ae fastened to the top and bottom plates. These shafts ae made fom steel to povide sufficient igidit and to potect against fame distotions. The ams of the obot ae made of hollow stainless tube. Each am has two paallel links connecting each caiage to the end effecto via od-end ball joints. The end effecto is made of aluminium allo and has a tiangula shape. A caiage is connected to a pai of shafts using linea beaings. Timing belts ae attached to the caiages to actuate the caiages along the shafts. The motos to dive the timing belts ae mounted at the bottom of the stuctue. All the dive motos ae NEMA steppe motos equipped with moto dives with a esolution of 0,000 step/ev. These motos can poduce high toques at high speeds. The filament of the mateial is stoed in a spool located on the top of the obot fame. A filament etusion, which is a mechanism made up of a moto to otate a toothed pinch wheel, is installed on the top of the obot fame. The etude motos is NEMA 7 steppe motos equipped with moto dives with a esolution of,600 step/ev. The etude pulls the filament fom its spool though a low-fiction Teflon tube to the pint head. The pint head consists of a nozzle, a filament heate and a cooling fan. These components ae fastened togethe at the cente of the effecto. When the filament is etuded though the heate and the nozzle, the molten filament is deposited on the build plate. The build plate is a heat plate coveed b a glass plate. The plate is suspended on fou adjustable sping bolts used to adjust the tilt of the bed to ensue the build suface is pefectl flat. A limit switch is mounted at the uppe end of a pai of columns to povide a setting point fo the home position of the caiages and to pevent the caiages tanslate out of the obot. 48 /Volume 5(), 07 Tansactions of the TSME: JAME

8 Etude moto Filament imit switch Caiage End-effecto Dive moto Pulle Build platfom Nozzle Fig. 5. The developed delta obot sstem. Filament heate A pogammable logic contolle (PC) is used fo the main contolle of the obot because it has seveal digital inputs and outputs and is highl accuate in tems of timing the steps fo the steppe motos. In addition, a PC can pocess multiple tasks at the same time. A diagam of the obot contol sstem, which is compute-based, is shown in Fig. 6. The contol pogam is witten using a Visual Basic.NET famewok. The pogam allows the use to contol the obot via a GUI. To opeate the obot sstem, the use inputs the paths of the nozzle as in the fom of G-code, feed ate and the tempeatue of the build platfom and filament heate. The pogam detemines the numbe of pulse steps and the pulse fequenc equied to otate the dive motos and the etude moto, and it also convets the tempeatue values to headecimal fomat. These paametes ae sent to the PC via a seial communication pot. The PC then geneates electical signals to tun all motos snchonousl and ceates a setting point fo the tempeatue contolles so that the tempeatues of the heat plate and the filament heate ae at the equied values duing the building of objects. Two themocouples, one at the filament heate and the othe at the build plate, ae used to send signals fo each tempeatue contolle. As the obot is opeating, the PC sends the cuent values of the steps of the motos and of the cuent tempeatues (in headecimal fomat) to the contol pogam so that those paametes ae conveted to the cuent position of the nozzle and the cuent tempeatue of the building platfom and the filament heate. Tansactions of the TSME: JAME 07, Volume 5() / 49

9 Moto: Ais- Moto: Ais- PC Pogammab le ogic Contolle Moto: Ais- Moto: Tempeatue Heat-plate Themocouple PID Tempeatue PID Filament Heate Themocouple Fig. 6. Diagam of contol sstem. 6. MOTION ANAYSIS To investigate the accuac of the obot, epeiments in obot positioning wee pefomed. The end effecto of the obot was moved in the, and z diections, with linea tavel paths at diffeent distances and feed ates. The distances epeimentall measued wee compaed with the equied distances to find the eo of the effecto positions. The epeimental setup is shown in Fig. 7. The distances in the and diections wee measued using the digital dial gauge with a measuing ange of 0 80 mm and accuac of ±0.00 mm. The distance in the z diection was measued b a lase displacement senso with a esolution of µm that was installed on the effecto. In the epeiments, the effecto was tavelled at thee diffeent feed ates 50 mm/s, 00 mm/s and 00 mm/s and diffeent distances ±0 mm, ±0 mm and ±60 mm. The tests wee pefomed 50 times in each moving diection. The aveage values of the measued distances and the eos ae shown in Table.. ase displacement senso Digital dial gauge Fig. 7. Distance measuement setup. 50 /Volume 5(), 07 Tansactions of the TSME: JAME

10 The esults show that the eo of the obot position inceases with inceasing tavel distance and feed ate. Fo eample, conside the movement in the diection at a feed ate of 50 mm/s; when the distance is inceased fom 0 mm to 60 mm, the eo inceases fom 0.0 mm to mm. Also conside the movement in the - diection at the distance of 0 mm; when the feed ate is inceased fom 50 mm/s to 00 mm/s, the eo inceases fom 0.05 mm to mm. This is to be epected because an inceased distance and feed ate esults in an inceasing quantisation eo of the pulse ate computed fo each moto. The aveage value of the eo at the feed ates of 50 mm/s, 00 mm/s and 00 mm/s is 0.07 mm, mm and 0.50 mm, espectivel. Table : Measued distances at diffeent tavel paametes Feed 50 mm/s Feed 00 mm/s Feed 00 mm/s Diection Distance (mm) Distance (mm) Distance (mm) ±0 ±0 ±60 ±0 ±0 ±60 ±0 ±0 ±60 X Y Z In addition, based on obsevation, the tavel paths detemined in the epeiments show that although the effecto was equied to tavel on the - plane with a fied z-value; the z-value of the effecto was not constant but vaied acoss the tavel path. Fo eample, conside the actual tavel path of the effecto, which tavelled a distance of 60 mm in the diection. At the beginning of tavelling, the z-value was 0 mm but deceased to -.94 mm (see Fig. 8) when the effecto was located at the middle of the tavel path. Afte that, it inceased back to 0 mm when the effecto eached the end position. This is because the kinematics of the mechanism ae nonlinea in natue; that is, the kinematics ae in sphee equation with the adius of, as epesented in Eqs. (5) - (7). Consequentl, the actual tavel path of the end effecto was not staight but concavel cuved. Distance (mm) Z (mm) Fig. 8. The actual tavel path of the end-effecto at diffeent distances. Howeve, in the FDM pocess, the z-value of the nozzle has to be constant to poduce a staight lae. Theefoe, it is necessa to investigate the technique of contolling the obot to educe the vaiation in the z-value of the effecto as it is tavelling. Tansactions of the TSME: JAME 07, Volume 5() / 5

11 Based on the tests, when the effecto tavels a shote distance, the vaiation of the z-value becomes smalle. Fo eample, the deviation in the z-value deceased fom -.94 mm to -0.0 mm when the tavel distance was educed fom 60 mm to 5 mm (Fig. 8). Theefoe, to educe the vaiation in the z-value, the effecto has to tavel within a shote distance. This can be done b dividing the tavel path into small segments. The length of each segment depends on the allowable vaiation in the z-value. The eample of tavel paths epeimentall obtained using diffeent lengths of segment is illustated in Fig. 9. Distance (mm) ength of a segment Z (mm) Fig. 9. The actual path of the effecto tavelling a distance of 60 mm in the -diection on diffeent segment lengths. 7. EXPEIMENTA TESTS To demonstate that the developed obot sstem can poduce eal objects, fou thin-wall objects having diffeent shapes squae, clindical, squae-based pamid and ounded gea shapes (Fig. 0.) wee fabicated. The CAD models and dimensions of the models ae shown in Figs. 0(a) to 0(d). (a) (b) (c) (d) Fig. 0. D model of (a) squae, (b) clindical, (c) squae-based pamid and (d) ounded gea. The conditions of fabicating ae that a lae thickness is 0. mm and a feed ate is 50 mm/min. In the tests, the vaiation in z-value was set to not be geate than the lae thickness. Theefoe, the length of segment was selected to be 5 mm, which esults in a maimum vaiation in the z-value of 0.0 mm. 5 /Volume 5(), 07 Tansactions of the TSME: JAME

12 To fabicate the pats pecisel, the CAD models must be offset b a distance of a half of a lae width into the model. Based on pelimina tests, at the fabicating condition, the aveage width of a lae is about 0.9 mm. Theefoe, the value of 0.08 mm (0.9/=0.08 mm) was used as the offset distance. The tool paths wee ceated fom the offset pofiles. The final pats of each shape ae shown in Figs. (a) - (d). The dimensions of the actual pats wee measued and compaed with nominal values fom CAD models to assess the fabicating accuac. These wee the width (A and B) and the height (H) of the pats (see Figs. 0(a) -0(d)). The wee measued using digital Venie callipe with accuac of ±0.00 mm. All measuements wee pefomed five times. The nominal and aveage actual values of the dimensions as well as standad deviation (SD) of the measuements ae shown in Table.. The value of dimensions of the actual pats and CAD models ae close. The aveage eos of fabication objects with the squae, clindical, squae pamid and ounded gea shapes ae 0.04 mm, mm, mm and mm, espectivel. Although the actual pats wee built fom tool paths that wee offset fom the CAD models, thee ae eos in the dimensions between the pats and CAD models. This is because in the FDM pocess, thee ae othe factos that affect the dimensional pecision, such as nozzle and etusion feed ate, lae thickness, tempeatue of the building platfom and the filament heate. Theefoe, to incease the accuac of fabication pats b the FDM pocess, these factos have to be investigated. (a) (b) (c) (d) Fig.. Final pats of the (a) squae, (b) clindical, (c) squae-based pamid and (d) ounded gea. Table : CAD and measued values of dimensions of thin-wall objects A (mm) H (mm) B (mm) Nominal Actual SD Eo Nominal Actual SD Eo Nominal Actual SD Eo Squae Clindical Squae pamid ounded gea CONCUSION In the pape, the design and constuction of a new linea delta obot fo use in fuse filament additive manufactuing wee detailed. The invese and fowad kinematics of the manipulato wee deived. The paametes of the obot wee optimised based on the kinematic equations and condition numbe in the equied wokspace. epeatabilit tests wee pefomed to evaluate the accuac of the obot sstem. The investigation of the tavel path of the effecto showed that the effecto should tavel within a shot distance so that the vaiation in z-value will be educed. To demonstate the capabilities of the developed obot sstem, components with fou diffeent shapes wee poduced. The esults eveal that the obot can complete fabication objects using the FDM pocess. Tansactions of the TSME: JAME 07, Volume 5() / 5

13 9. ACKNOWEDGEMENT The authos gatefull acknowledge the financial suppot fo this wok fom the facult of Engineeing, Buapha Univesit, Thailand via Contact no. &D /558. EFEENCES [] Chua, C.K., eong, K.F. and im, C.S. apid Pototping: Pinciples and Applications, 00, Wold Scientific Publishing, Singapoe. [] Choia, J.W., Medinaa, F., Kim, C., Espalin, D., odiguez, D., Stucke, B. and Wicke,. Development of a mobile fused deposition modeling sstem with enhanced manufactuing fleibilit, Jounal of Mateials Pocessing Technolog, Vol. (), 0, pp [] ee, W.C., Wei, C.C. and Chung, S.H. Development of a hbid apid pototping sstem using low-cost fused deposition modeling and five-ais machining, Jounal of Mateials Pocessing Technolog, Vol. 4 (), 04, pp [4] Song, X., Pan, Y. and Chen, Y. Development of a low-cost paallel kinematic machine fo multidiectional additive manufactuing, Jounal of Manufactuing Science and Engineeing, Vol. 7(), 05, pp [5] David Espalin. Development of a multi-mateial, multi-technolog FDM sstem fo pocess impovement epeimentation, Dissetations, Univesit of Teas, El Paso, 0. [6] Iwan, Z., Dietma, W.H., Kim, C.T. and Swee, H.T. Fused deposition modeling of novel scaffold achitectues fo tissue engineeing applications, Biomateials, Vol. (4), 00, pp [7] Allahvedi, M., Danfoth, S. C., Jafai, M. and Safai, A. Pocessing of advanced electoceamic components b fused deposition technique, Jounal of the Euopean Ceamic Societ, Vol. (0-), 00, pp [8] Mieles, J., Kim, H.C., ee, I.H., Espalin, D., Medina, F., MacDonald, E. and Wicke,. Development of a fused deposition modeling sstem fo low melting tempeatue metal allos, Jounal of Electonic Packaging Tansactions of the ASME, Vol. 5(), 0, [0008]. [9] Dudek, P. FDM D pinting technolog in manufactuing composite elements, Achives of Metallug and Mateials, Vol. 58(4), 0, pp [0] Ilado,. and Williams C.B. Design and manufactue of a fomula SAE intake sstem using fused deposition modeling and fibe-einfoced composite mateials, apid Pototping Jounal, Vol. 6(), 00, pp [] Vashishtha, V.K., Makade,. and Mehla, N. Advancement of apid pototping in aeospace indust - a eview, Intenational Jounal of Engineeing Science and Technolog, Vol. (), 0, pp [] Tellisa, B.C., Sziveka, J.A., Blissa C.., Magolisa, D.S., Vaidanathanb,.K. and Calvetc, P. Tabecula scaffolds ceated using mico CT guided fused deposition modeling, Mateials Science and Engineeing: C, Vol. 8(), 009, pp [] Ultimake D pinte, U: accessed on 5/04/07. [4] Makebot D pinte, U: accessed on 5/04/07. [5] Pusa D pinte, U: accessed on 5/04/07. [6] Seemecnc D pinte, U: accessed on 5/04/07. [7] Deltamake D pinte, U: accessed on 5/04/07. [8] Allen,. and Task,. An epeimental demonstation of effective Cuved ae Fused Filament Fabication utilising a paallel deposition obot, Additive Manufactuing, Vol. 8, 05, pp [9] Huang, B. and Singamneni, S. Altenate slicing and deposition stategies fo fused deposition modeling of light cuved pats, Jounal of Achievements in Mateials and Manufactuing Engineeing, Vol. 55(), 0, pp [0] iu, X.J., Wang, J.S., OH, K.K. and Kim, J.W. A New Appoach to the Design of a DETA obot with a Desied Wokspace, Jounal of Intelligent and obotic Sstems, Vol. 9(), 004, pp [] iu, X.J. Optimal kinematic design of a thee tanslational DoFs paallel manipulato, obotica, Vol. 4(), 006, pp /Volume 5(), 07 Tansactions of the TSME: JAME