Design, Simulation and Implementation of a 3-PUU Parallel Mechanism for a Macro/mini Manipulator

Transcription

1 Desgn, Smulaton and Implementaton of a 3-PUU Parallel Mechansm for a Macro/mn Manpulator Zheng Ma, Aun-Neow Poo, Marcelo H. Ang Jr, Geok-Soon Hong, and Feng Huo, Abstract Parallel mechansms have the advantages of hgh rgdty, hgh precson and fast movement n ts workspace. It s a most sutable mechansm to serve as the mn manpulator n a macro/mn manpulator as the mn manpulator needs to have fast response and hgh resoluton n postonng. In ths paper, the desgn of a 3-PUU parallel mechansm to be used as such a mn s presented. Falures are encountered durng the process of smulaton and mplementaton of the parallel mechansm. Causes of the falures are analyzed and solutons are proposed to overcome these. Based on the lessons from buldng the frst prototype, mprovements were made to the second prototype whch effectvely removed the shortcomngs resultng n a mn whch met the requrements for ts ntended applcaton. I. INRODUCION he development and applcaton of robotcs has made much progress snce the frst programmable ndustral robotc arm, the Unmate, was nvented n Compared wth human operators, ndustral robots have the advantages of hgh precson, repeatablty and speed of moton, and hgh dexterty. hey can also work n envronments hazardous or unsutable for human bengs and, wth large robots, are capable of carryng and movng, wth hgher speeds and accuracy of moton, heavy workpeces. In addton, except for downtme for mantenance, they are 4/7 workers who do not need rest or holday leaves and can thus mprove productvty and speed of producton. When used approprately, ndustral robots can reduce the need, not only of unsklled labourers but also sklled workers, n ndustry. As a result, they have found wdespread applcatons n repettve operatons such as materal handlng and assembly, weldng and spray pantng. o date, most of the applcatons of ndustral robots are for non-contnuous contact type of operatons, operatons whch do not requre the robotc end-effector to be n contnuous contact, and wth a controlled level of contact force, wth the workpeces. Recent advances n robotcs technology have allowed the development of robotc arms wth ncreased speeds and precson of moton and wth greater buld-n ntellgence. here s now ncreasng nterest n developng and employng these devces for more challengng tasks, ncludng those labour-ntensve and low-productvty operatons whch *Research supported by SIMech-NUS Jont Laboratory and A*SAR. Zheng Ma s wth the Advanced Robotcs Center and the SIMech-NUS Jont Laboratory (Industral Robotcs), Natonal Unversty of Sngapore, Sngapore, (Correspondng author. Phone: ; Emal: mpemz@nus.edu.sg). Aun-Neow Poo, Marcelo H. Ang Jr, Geok-Soon Hong and Feng Huo are wth the Department of Mechancal Engneerng, Natonal Unversty of Sngapore, Sngapore, (Emals: mpepooan@nus.edu.sg, mpeangh@nus.edu.sg, mpehgs@nus.edu.sg and huofeng@nus.edu.sg). nvolved contnuous contact between the robot end-effector and the workpece, and the smultaneous control of the force at the pont of contact. Such force/poston controlled operatons nclude hgh-precson edge and surface fnshng operatons often encountered n the precson engneerng, aerospace, and marne ndustres. Snce an adequate workspace and a suffcent payload-carryng capacty are requred n the performance of ther tasks, ndustral robots are often desgned wth long and large arms. Wth ts large mass and nerta [1], t s thus dffcult to control such a sngle robotc arm n applcatons whch requre poston, force or force/poston control and acheve hgh accuracy wth a fast response smultaneously. A proposed soluton s to mplement a compact end-effector wth a small lmted workspace whch can have a hgh bandwdth and hgh accuracy n postonng and have ths carred by a larger but slower robotc arm. hs confguraton s commonly referred as a macro/mn manpulator, where the large robotc arm s referred to as the macro, and the smaller and faster end-effector referred to as the mn. he macro/mn manpulator has the advantages of a large workspace provded by the macro robotc arm, as well as a fast and hgh-accuracy response provded by the mn []. Consderatons whch need to be taken n the desgn of a mn manpulator depend on what tasks t s beng developed for. In ths paper, a mn manpulator desgned for polshng and deburrng tasks s dscussed. he normal forces that need to be appled by the polshng or deburrng tool on the workpece are estmated at up to 100 N and a few Newtons for polshng and deburrng respectvely. he optmum exerted force depends on the type of operaton, the materal of the workpece and the type of tool used. A rough sandng/polshng operaton usng a sandng/polshng pad whch has a large area of contact wth the workpece surface wll requre a large exerted force whereas a small exerted force wll be needed for a fne fnshng operaton wth a smaller polshng pad. he profle of the surface of the workpece that s to be operated on s assumed not to have sudden rapd changes such that a workspace n the form of a sphere wth a dameter of 40mm wll be suffcent for the mn end-effector. Durng a polshng or deburrng operaton, the macro manpulator carres the mn manpulator (end-effector) along a desred reference path parallel to and at a small dstance away from the surface to be polshed or from the edge of the workpece to be deburred. For optmum operaton, the orentaton of the end-effector should have a predefned orentaton wth respect to the surface, or edge, of the workpece. Whle beng moved along ths reference path by the macro, the mn moves n such FnE-R 015 he path to success: Falures n Real Robots Page 4 IROS 015, Hamburg - Germany October, 015

2 a way as to exert the desred normal force on the workpece. Snce the mn s always n contact wth the surface or edge of the workpece, and as long as there are no sudden and large change to the surface or edge of the workpece, the workspace of the mn wll not need to be large to perform the polshng or deburrng task. Based on the aforesad consderatons and usng feedback from users wth experence n polshng and deburrng operatons, a 3-DOF PUU(Prsmatc-Unversal-Unversal) parallel mechansm, nspred by the Delta robot was selected for the mn manpulator. hs 3-DOF translatonal parallel mechansm (PM) has only pure translatonal motons and was desgned to have a cylndrcal workspace wth a dameter of 40mm and a heght of 30mm. In the desgn process, sold models were frst created to smulate and to analyze the motons, and to evaluate the stresses and deformatons n the varous lnks and components when t s subjected to the maxmum desgn appled forces and torques. Durng the smulaton study of ts motons, unexpected motons wth extra degrees of freedom were observed whch caused the mn manpulator to take on postures n whch the platform on the mn end-effector was not purely translated but was rotated from ts startng poston. A knematc analyss based on the 3-DOF translatonal moton fals to explan these unexpected motons snce the assumptons made n the knematc analyss does not hold when the mechansm s not n parallel wth ts startng poston. o reduce the overall cost and tme, the unversal jont components are drectly ordered off the shelf for mplementaton. he parallel mechansm appears to have notable backlash. he resultng precson of the mechansm s poor and cannot serve as the mn manpulator whch supposed to have hgh accuracy n postonng. he mechansm s modfed eventually to overcome the backlash problem and retans the same knematcs as prevously desgned. As a result, the workng range and moblty of the mechansm meets the requrement. ogether wth a proper control algorthm, the mechansm can be used to serve as the mn manpulator whch has a fast response and hgh precesson n postonng. In ths paper, the 3-PUU parallel mechansm s frst descrbed and a standard knematc analyss s derved under assumptons. Unexpected motons n smulatons are shown, wth a bref analyss of the reason why t happens. Problems of backlash and postonng accuracy encountered n mplementaton s dscussed wth an analyss of an off-the-shelf unversal jont structure. Improvements of the mechansm archtecture and jont optons are presented whch overcomes the falure from the smulaton as well as the real mplementaton. prsmatc jonts move n a drecton perpendcular to the base platform and are attached symmetrcally at 10 degrees apart at A, where 1,, 3, to the base platform. As shown n Fg. 1, two unversal jonts (unversal jonts) connect the end of each prsmatc jont to the top platform. he axes of the two unversal jonts are parallel to each other and perpendcular to the prsmatc jont. Accordng to the Chebychev-Grübler Kutzbach crteron [3], the number of degrees-of-freedom s gven by: j M 3(N 1 j) f 1 where N s the total number of lnks, j the total number of jonts, and f, ( 1,, 3 ) the degrees of freedom of lnk. For the mechansm shown n Fg. 1, the total number of lnks (ncludng the base lnk) s N 8, the total number of jonts s j 9, and the degree of freedom s f 1 for the prsmatc jonts and f for the unversal jonts. hus M 3(8 1 9) and the mechansm shown n Fg. 1 has three degrees-of-freedom wth all beng translatonal motons as wll be elaborated on n the next secton. hs ensures that the top platform s always parallel to the base platform. P 3 A3 B 3 base platform top platform O O A 1 B 1 B U jont U jont Prsmatc jont Fgure 1. Structure of the 3-PUU parallel mechansm. P 1 P A II. MECHANISM DESCRIPION AND KINEMAIC ANALYSIS A. A 3-PUU Parallel Mechansm he structure of the 3-PUU parallel mechansm desgned s shown n Fg. 1 wth three dentcal lmbs connectng the base platform to the top platform. Fg. shows the structure for one of the lmbs. From the fgures, t can be noted that the three Fgure. One of the lmbs of the 3-PUU parallel mechansm. FnE-R 015 he path to success: Falures n Real Robots Page 43 IROS 015, Hamburg - Germany October, 015

3 B. Knematc Analyss of 3-DOF ranslatonal Moton Wth knowledge of the 3-DOF translatonal moblty, the knematc model of the parallel mechansm can be derved [4]. he top vew of the base and top platform s shown n Fg. 3, where A and B are the locatons where the prsmatc jonts and the unversal jonts are mounted to the base and the top platform respectvely. Coordnate Frame O and Frame O are respectvely attached at the centre of the base and the top platform. he dstance from the center of the platforms to A and B are R and r respectvely. Let the dsplacement of the th prsmatc jont attached at A be z. All the unversal jonts are passve. Snce the parallel mechansm are constraned to have only translatonal motons, the transformaton matrx for rotaton from frame O to frame O s an dentty matrx. Let the poston vector of Frame O n Frame O be [ c ] ( x y z) A 3 R O Fgure 3. op vew of base platform(left) and top platform(rght). A A 1 Accordng to the mechansm structure shown n Fg. 1 and the geometrc condtons shown n Fg. 3, the nverse and forward knematcs of the parallel mechansm can be obtaned. By assumng the top platform has only translatonal moton wth respect to the base platform, poston vector B n frame O s [ B ] O' ( r cos r sn 0), 1 30, 150, 3 90 herefore the poston vector B n frame O s [ B ] O ( r cos x r sn y z) and the poston vector P n frame O s [ P ] ( Rcos Rsn z ) O For all three lmbs, f the dstance between the two unversal jonts, B to P s L. he constrant equaton can then be wrtten as [ B P ] L O After substtutng B and P nto (7), we have ( x x ) ( y y ) ( z z) L, x ( R r)cos, y ( R r) sn he nverse knematcs thus can be obtaned as B 3 r B B 1 z L ( x x ) ( y y ) z In the same way, the forward knematcs can be obtaned by applyng the same constrant equaton. III. FAILURES IN SIMULAION AND IMPLEMENAION Wth the knematc model obtaned, the parameters R, r and L were chosen to meet the workspace crtera. Sold models were then establshed for moton and stress analyss, the former to confrm the translatonal motons of the top platform wthn the specfed workspace and the latter for szng the components for strength and stablty. Durng smulaton, some unexpected results were observed when the top platform moved away from beng parallel to the base platform. Unacceptable moton performance was also obtaned wth the frst prototype developed usng off-the-shelf unversal jonts. hese wll be dscussed n the followng sectons. A. Extra DOF observed n Smulaton Sold models of the parallel mechansm were created usng the software SoldWorks. Moton studes were done smulatng moton at the three prsmatc jonts. hs caused the three lower unversal jonts, P 1, P, and P 3 n Fg. 1, to move vertcally. Varous combnatons of lnear motons for the three prsmatc jonts were used to study the movement of the top platform relatve to the base platform, as well as to verfy the sze of workspace of the parallel mechansm. he top platform was expected to reman parallel to the base platform at all tmes snce the desgn of the mechansm constraned t to have only 3-DOF translatonal moton. However, t was noted that for some moton combnatons of the prsmatc jonts, the top platform does not always reman parallel to the base platform but moved nto a non-parallel mode of moton after remanng parallel for some tme. Fg. 4 shows an example of how the roll-ptch-yaw angles of Frame O wth respect to Frame O change wth tme for one such nstance. From the fgure, t can be seen that the top platform moves wth only translatonal moton for about 11s after whch t has rotatonal motons. Fgure 4. Roll-ptch-yaw angles oftop platform for non-paralle moton. FnE-R 015 he path to success: Falures n Real Robots Page 44 IROS 015, Hamburg - Germany October, 015

4 o explan the unexpected rotatonal moton, the assumpton of pure translatonal moton was revewed. A typcal drawng of a unversal jont s shown n Fg.5. Ux a hole to accommodate the external shaft and a dowel pn s used to hold the shaft to the jont as shown n the fgure. Uy UzP Platform sde Fgure 5. Rotatonal axs of a unversal jont. Lnk sde UzL Fgure 6. Unversal jont(double) [7]. Fgure 7 shows the frst prototype of the mn manpulator mechansm usng these unversal jonts. hree lnear actuators, labeled wth 0, 1 and, are used for the prsmatc jonts. Each lnk connectng the prsmatc jont to the top platform s made up of a crcular shaft wth a unversal jont at each end. he unversal jont at one end of each lnk s fxed to a lnear actuator and the other end to the top platform. Consder one of the three unversal jonts attached to the top platform as shown n Fg. 5. Wth the other end, P, of the lnk fxed, there wll be no rotaton about the axs UzL, he unversal jont can only rotate about the Ux and Uy axes, enabled by the cross component n the jont. Wth only two degrees-of-freedom, there wll not be any rotaton about the axs UzP, and thus no rotaton of the platform [5]. Snce there are three unversal jonts attached to the top platform, therefore no rotaton of the platform s allowed about three axes. When these three axes are lnearly ndependent n 3, the top platform wll lose all the rotatonal moton and ts 3-DOF motons wll be purely translatonal. Based on ths analyss, the rotatonal moton of the top platform durng smulaton as shown n Fg. 4 s thus unexpected. hs rotatonal moton observed n smulaton s suspected to be caused by the loss of ndependence among the three axes UzP. When two or more axes become lnearly dependent, the parallel mechansm wll be n a sngular poston. Unlke the sngulartes n seral-lnk robots, nstead of losng degrees of moblty, a parallel mechansm gans extra degrees of freedom at a sngular poston [6]. In Fg. 4, t s lkely that the parallel mechansm reached a sngular poston at about 11s, ganed an extra degree of rotatonal moblty and the top platform became non-parallel to the base platform. hereafter, the moton of the mechansm was no longer constraned to be purely translatonal. Referrng to the Chebychev-Grübler Kutzbach crteron, the mechansm should have three degrees-of-freedom when t s not n a sngular poston. It s lkely that the moton of the mechansm after passng through the sngular poston s a combnaton of three degrees of moton wth both rotaton and translaton. Further nvestgaton wll be needed explan and to understand ths unexpected smulaton result. B. Backlash n Implementaton he unversal jonts used n the constructon of the frst prototype were off-the-shelf good qualty jonts the schematc of whch s shown n Fg. 6. Each sde of the unversal jont has Fgure 7. ranslatonal parallel mechansm usng U-jonts. When the three lnear actuators are fxed n any poston,.e. not movng, the top platform should also reman n a fxed poston parallel to the base platform. However, t was found that wth the actuators fxed n ther postons, the horzontal slack of the top platform was 4 to 5 mm, whch s unacceptably large, together wth unacceptably large angular rotatons. Investgatons showed that these unacceptably large motons, or backlash, are due to the clearances used n the manufacture of the mechancal components used. Whle pure translaton moton of the top platform was observed n smulaton for whch perfect dmensons of the varous components are used n computaton, such perfectly formed parts are not avalable n practce, thereby resultng n the unacceptable results. A close examnaton of the frst prototype showed that the exhbted backlash phenomenon s due almost entrely to clearances n the off-the-shelf unversal jonts used. he unversal jont, also known as a Hooke's jont, s a jont or couplng whch s commonly used to transmt rotary moton from one rgd shaft to another rgd shaft when the axes of the two shafts are at a small angle to each other. he rotary moton transmtted s usually n one drecton only. Because there s no change n drecton of the transmtted rotary moton, the small clearances desgned nto them for ease of manufacture does not cause any backlash problem. he unversal jonts used n the PM mechansm n the work here serve a dfferent purpose. hey serve as jonts provdng two degrees of freedom (rotary moton) constranng FnE-R 015 he path to success: Falures n Real Robots Page 45 IROS 015, Hamburg - Germany October, 015

5 the moton of the parallel mechansm as requred from the structure shown n Fg. 1. Referrng to Fg. 5, the unversal jonts used should rotate only about axes Ux and Uy to cause the top platform of the PM mechansm to move. here should be no rotaton about axs UzL or UzP. However, when one sde of the U jont, say the lnk sde, s fxed and not allow to rotate about ts axs UzL, t s observed that the other sde has freedom to rotate, about axs UzP, to some sgnfcant degree. hs s due to manufacturng clearances desgned nto the jonts, n partcular at the four ends of the cross component n the jont. he resultng free-play or backlash s accentuated due to the short lengths of the two rods formng the cross component n the jont. he off-the-shelf U jonts thus dd not have suffcent stffness along the Uz axes and are not sutable for the PM mechansm. Another sgnfcant cause of the free-play or backlash problem n the moton of the PM mechansm s due to clearance appled durng the fabrcaton of the mechansm. As mentoned earler and wth reference to Fg. 6, dowel pns were used to connect the external shaft to each end of the U jonts. Ideally, the two holes n the U jont and the one n the shaft to accommodate the dowel pn should all be of exactly the same dameter, correspondng to the dameter of the dowel pn, wth ther centers perfectly algned. However, as the holes were drlled at dfferent tmes, f they were to be made of the same dameter wth very lttle clearance, the centers of the holes need to be perfectly algned n order for the dowel pn to be nserted. Algnment of the holes, when drlled separately, s not easly done. As such, the fabrcator ntroduce some clearance and made the hole n the shaft larger (Fg. 8) than that of the holes n the U jont, whch s of the same dameter as the dowel pn. Whle ths allowed for the nserton of the dowel pn even f there s some slght msalgnment of the holes durng manufacture, t caused sgnfcant rotatonal free-play or backlash between shaft and the unversal jont. Here agan, the rotatonal backlash s accentuated by the small dameter of the shaft, and thus the length of the hole n t. are used for ther typcal functons of transmttng rotary moton between two shafts. he frst prototype faled to meet the requrements for ts ntended applcaton and a revew of the desgn, and where t faled, was carred out to come up wth the second prototype. IV. LEARNING FROM HE FAILURES In the process of developng and buldng the frst prototype, two valuable lessons were learned. One s the unexpected results durng smulaton studes and the other s the poor performance n the fabrcated mechansm due to manufacturng clearances and backlash n the off-the-shelf unversal jonts used. It s noted that that the top platform of the mechansm does not reman parallel to the base platform under all crcumstances. Rather, when startng from a parallel poston, the top platform may move nto a mode, or regon of ts workspace, where t gans rotatonal motons after passng through a sngular poston. hs problem occurred durng smulaton when t s put all possble motons wthn ts total workspace. In practce, ths problem can easly be overcome by constranng the motons of the three actuators such that ts workspace clearly does not contan any sngular postons. he frst prototype has unacceptably poor accuracy n ts moton and postonng. he top platform has some degrees of moblty, of about 5 mm due to backlash when the actuators are fxed n ther postons. hs moblty s not acceptable as the mn manpulator s requred to have hgh stffness and precson. It s clear that ths problem s caused by the manufacturng clearances n the off-the-shelf unversal jonts used. o overcome ths problem, whle stll usng lower-cost off-the-shelf components, other type of jonts whch has the same moton propertes as unversal jonts but do not suffer from the same backlash problem was nvestgated as replacements. he mechancal structure to replace the lnk wth ts par of unversal jonts s shown n Fg. 9. It s composed of four ball jonts connected n a way to form a parallelogram. A B D C Fgure 8. Clearamce between dowel pn and the external shaft connected to the U-jont. he unsatsfactory moton of the frst prototype of the mechansm s largely due to the clearances n the off-the-shelf unversal jonts and the lmted machnng accuracy of the fabrcated parts. Informaton on clearances for off-the-shelf unversal jonts are not readly avalable from manufacturers as such nformaton may not have been mportant when they Fgure 9. Improved parallel mechansm wth ball jonts. Accordng to the property of an deal parallelogram, the opposte sdes of the parallelogram wll always be parallel. herefore, the sde AB wll always be parallel to the sde CD n Fg. 9. Snce the sde CD s mounted parallel and fxed to the base platform, the sde AB wll also always be parallel to the base platform. As there are three lmbs n the PM mechansm, FnE-R 015 he path to success: Falures n Real Robots Page 46 IROS 015, Hamburg - Germany October, 015

6 there are three parallelogram wth three sdes AB attached to the top platform. hese three parallelogram lmbs are attached to the top platform such that the three sdes AB all le n a plane and the top platform s parallel to ths plane. Snce all the three sdes AB are parallel to the base platform, the plane formed by them wll be parallel to the base platform. herefore, the top platform wll also always be parallel to the base platform. Wth the top platform constraned to be parallel to the base platform, and the base platform s fxed and mmoble, the moton of the top platform wll be constraned to be translatonal only. If there s free play or backlash n the ball jonts at A, B, C, or D n Fg. 9, then the parallelogram formed wll not be an deal parallelogram. In ths case, the sdes AB may become non-parallel to the sde CD. he amount of non-parallelsm depends on the amount of free play n the ball jonts and the length of the sdes AB and CD, the longer the sdes are, the smaller the degree of non-parallelsm. For the typcal applcatons they are ntended for, good qualty ball jonts have almost no free play or backlash. he length of the sdes AB and CD of the parallelogram are also much longer than the length of the cross component n the unversal jonts. As such, the use of ball jonts wth a parallelogram structure for the three lmbs of the PM mechansm effectvely elmnated the free play and backlash problem. he resultng second prototype s rgd and has hgh precson n postonng. Wth the actuator fxed n ther postons, there s no measurable backlash n the top platform. he backlash found n the frst prototype had been effectvely elmnated and ths second prototype wll be sutable as the mn n a macro-mn manpulator to be used for fnshng and deburrng applcatons for whch both poston and force/poston control are requred. Unlke a seral-lnk robot, the parallel structure of ths robotc devce gves t the hgh rgdty and thus the capablty of exertng large forces on the workpece n force-controlled polshng applcatons V. CONCLUSIONS A parallel mechansm, based on the structure of the Delta robot, was desgned and mplemented to serve as a mn manpulator, actng as an end-effector, n a macro-mn manpulator confguraton for polshng and deburrng applcatons. Knematc models of the mechansm were frst obtaned and appled to fulfl the gven crtera. Sold models were created to smulate and analyze the resultng motons and workspace of the mechansm whch was desgn. Unexpected and unacceptable motons of the top platform n the mechansm were observed durng the smulaton experments. he knematc models faled to explan the moton snce the assumpton of pure translatonal moton of the top platform dd not hold. It s lkely that the non-parallel motons of the top platform n the mechansm was due to t passng through a sngular poston at whch t ganed extra degrees of freedom. Wth the moton of the actuators n the mechansm constraned such that no sngular postons le wthn the workspace, the problem of non-parallel motons can be resolved. Further research wll be done to determne the exact cause of the rotatonal motons of the 3-PUU parallel mechansm durng smulaton. Unacceptable free play and backlash was exhbted by the frst prototype. hs was not evdent n the smulaton experments whch are based on perfectly manufactured components. Investgatons showed that ths problem was due to naccuraces n the dmensons of the components used. he man cause was the free play n the off-the-shelf unversal jonts used for the frst prototype. o overcome ths problem the unversal jonts were replaced by off-the-shelf ball jonts formng a parallelogram structure for the three lmbs of the mechansm. he knematc model of the mechansm remans the same but the free play problem was effectvely elmnated and the second prototype exhbts hgh stffness and postonng accuracy. Lessons were learned from unexpected outcomes and falures durng the smulaton experments and n mplementaton. Properly desgned smulaton experments may produce results not predcted by theoretcal studes as these studes are normally based on certan smplfcatons and assumptons, whch cannot be completely replcated n smulaton experments. Furthermore, straghtforward smulaton experments whch are based on perfect physcal propertes of the component parts may not show up possble nadequaces n the desgn. hese nadequaces may show up only n the prototypes bult due to unavodable mperfectons n the physcal components makng up the whole system. ACKNOWLEDGMEN he authors acknowledge the support from the Collaboratve Research Project under the SIMech-NUS Jont Laboratory (Industral Robotcs). hs work was also supported n part by the Scence and Engneerng Research Councl (SERC) A*SAR Industral Robotcs Program Grant REFERENCES [1] O. Khatb, "Inertal propertes n robotc manpulaton: an objectve-level framework," he Internatonal Journal of Robotcs Research, vol. 1, no. 13, pp , February [] Z. Ma, G. S. Hong, M. Ang and A. N. Poo, "Md-rangng control of a macro/mn manpulator," n IEEE Internatonal Conference on Advanced Intellgent Mechatroncs, Busan, 015. [3] J. Angeles and C. ruesdell, Ratonal Knematcs, Sprnger 1988, p. 78. [4] Y. L and Q. Xu, "Knematc Analyss and Dynamc Control of a 3-PUU Parallel Manpulator for Cardopulmonary Resusctaton," n 1th Internatonal Conference on Advanced Robotcs, Seattle, 005. [5] I. Bonev and D. Zatanov, "he Mystery of the Sngular SNU ranslatonal Parallel Robot," 1 June 001. [Onlne]. Avalable: [Accessed 11 March 014]. [6] G. Gogu, Structural Synthess of Parallel Robots, Dordrecht: Sprnger 008, p. 49. [7] Msum, "Unversal Jonts-Set Pn ype," Msum, [Onlne]. Avalable: [Accessed 17 July 015]. FnE-R 015 he path to success: Falures n Real Robots Page 47 IROS 015, Hamburg - Germany October, 015