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1 Research Mechancal Engneerng Artcle Engneerng 05, (): 9 98 DOI 0.50/J-ENG-0506 A Precson-Postonng Method for a Hgh-Acceleraton Low-Load Mechansm Based on Optmal Spatal and Temporal Dstrbuton of Inertal Energy Xn Chen, Youdun Ba, Zhjun Yang*, Jan Gao, Gongfa Chen ABSTRACT Hgh-speed and precson postonng are fund a mental requrements for hgh-acceleraton low-load mechansms n ntegrated crcut (IC) packagng equpment. In ths paper, we derve the transent nonlnear dynamcresponse equatons of hgh-acceleraton mechansms, whch reveal that stffness, frequency, dampng, and drvng frequency are the prmary factors. Therefore, we propose a new structural optmzaton and velocty-plannng method for the precson postonng of a hgh-acceleraton mechansm based on optmal spatal and temporal dstrbuton of nertal energy. For structural optmzaton, we frst revewed the commonly flexble multbody dynamc optmzaton usng equvalent statc loads method (ESLM), and then we selected the modfed ESLM for optmal spatal dstrbuton of nertal energy; hence, not only the stffness but also the nerta and frequency of the real modal shapes are consdered. For velocty plannng, we developed a new velocty-plannng method based on nonlnear dynamc-response optmzaton wth varyng moton condtons. Our method was verfed on a hgh-acceleraton de bonder. The ampltude of resdual vbraton could be decreased by more than 0% va structural optmzaton and the postonng tme could be reduced by more than 40% va asymmetrc varable veloc ty plannng. Ths method provdes an effectve theoretcal support for the precson postonng of hgh-acceleraton low-load mechansms. KEYWORDS hgh-acceleraton low-load mechansm, precs on postonng, spatal and temporal dstrbuton, nertal energy, equvalent statc loads method (ESLM), velocty plannng Introducton Wth the rapd development of electronc manufacturng technology and the electronc market, the demand for hghacceleraton and hgh-precson mechansms are ncreasng. For example, some manpulators n packagng equpment run at the speed of cycle tmes per hour, wth peak acceleraton of g 5g and a postonng precson of 5 µm. Hgh-acceleraton and short-cyclng-tme mechansms are nevtably subjected to elastc deformaton and vbratons caused by the nertal force. It s very dffcult to acheve hgh postonng accuracy n a very short deceleraton phase. Frequent but short acceleraton-deceleraton cycles could result n abrason or even falure of the mechansms []. Hence, t s necessary to fnd a new approach to optmze ths type of mechansm. When a mechansm moves at hgh speed, ts components should be regarded as flexble bodes, so the whole mechansm becomes a flexble multbody dynamc system, n whch the rgd-body moton s coupled wth the elastc deformaton. Therefore, the resultng dynamc model s a set of hghdmensonal dfferental equatons wth tme-varyng coeffcents and non-smooth nonlnear terms, whch s dffcult to model, analyze, and optmze []. For the last two decades, though tremendous progress has been acheved n the analyss of knematcs and the dynamcs of flexble multbody dynamc systems [], the optmzaton of flexble multbody dynamc systems s not completely solved. The equvalent statc loads method (ESLM) [4 0] proposed by Park et al. s the most effectve method for the dynamc optmzaton of flexble multbody dynamc systems. It has been mplemented nto the commercal software HyperWorks. The ESLM has been successfully used n the optmzaton of automotve collson dynamcs, Boeng arcraft wng structure [9], and so forth. The man dea of ths method s to convert the nonlnear dynamc response, by dscretzng the tme varable, nto response equatons of a seres of equvalent statc loads [4 0]. As the current dynamc topology optmzaton methods only consder some natural frequences, but the correspondng mode shapes may not reflect the real deforma- The Key Laboratory of Mechancal Equpment Manufacturng & Control Technology of Mnstry of Educaton, Guangdong Unversty of Technology, Guangzhou 50006, Chna * Correspondence author. E-mal: yangzj@gdut.edu.cn Receved 4 January 05; receved n revsed form 6 June 05; accepted 0 June 05 The Author(s) 05. Publshed by Engneerng Scences Press. Ths s an open access artcle under the CC BY lcense ( Volume Issue September 05 Engneerng 9

2 Research Mechancal Engneerng Artcle ton. Another mportant factor s the moton profle. At present, velocty-plannng methods manly consder geometrc smoothng whle gnorng the nfluence of curve parameters on the dynamc response. The S curve has a smoother varaton n acceleraton compared to the trapezodal profle, so t can reduce the resdual vbraton to some extent [, ]. Input shapng, such as a dgtal flter, not only causes tme delay, but also s dffcult to apply to the nonlnear dynamc system, where both stffness and frequences vary wth poston []. Therefore, a dynamc-response optmzaton for the velocty plannng s necessary. Some scholars have an equvalent moton stage system as a sngle-degree-of-freedom system to obtan optmal parameters of the S-type moton curve to reduce resdual vbraton [4]. However, because of hgh-acceleraton low-load mechansm s three dmensonal and frequently starts and stops, ts velocty plannng s a much more complcated problem. In ths paper, the nonlnear dynamc response of a hghacceleraton low-load mechansm s dscussed. We derve the transent nonlnear dynamc-response equatons of hgh acceleraton mechansms, whch reveal that stffness, frequences, and dampng (related to the layout of materal,.e., the spatal dstrbuton of nertal energy), as well as the drvng frequency (related to the moton profle,.e., the temporal dstrbuton of nertal energy), are the prmary factors. Therefore, we propose a new structural optmzaton and velocty-plannng method for the precson postonng of a hgh acceleraton mechansm based on optmal spatal and temporal dstrbuton of nertal energy. For structural optmzaton, the ESLM-based flexble multbody dynamc optmzaton s revewed and modfed for hgh-acceleraton low-load mechansms by means of the Raylegh-Rtz method, whch has been done n our prevous work [5, 6]. For velocty plannng, a new asymmetrc velocty profle s proposed based on nonlnear dynamc optmzaton wth varyng boundary condtons. Fnally, a practcal example of a hgh-speed de bonder s studed, whch shows that the resdual vbraton can be reduced by more than 0% by structural optmzaton and the postonng tme can be reduced by more than 40% by asymmetrc varable velocty plannng. Numercal tests show that the proposed method s effcent for structural desgn and velocty plannng for a hgh-acceleraton low-load mechansm. Techncal background For mechansms operatng at very hgh speed, the vbraton of the structures must be consdered. When the deformaton s large, the absolute nodal coordnate formulaton (ANCF) s more effcent [6]. Wthn the ANCF for hghly flexble bodes, the absolute coordnates are represented by a vector y, characterzng the materal ponts of the bodes by an approprate shape functon. The moton equaton s M t y + C t y + K t y = q t () where M(t), C(t) and K(t) are mass, dampng, and stffness matrces at tme t, respectvely. The moton equaton for flexble bodes has the same format as that of structural vbraton. The dsplacement y conssts of rgd moton y R and elastc modes y E. If we consder when the mechansm moves at a poston, the mechansm can be regarded as a structure wth knetc degrees of freedom. Let u R and u E be the dsplacements of the rgd modes and elastc modes, respectvely. Therefore, the total dsplacement of the flexble multbody s u t = u t + u t = Φ η t + Φ η t () R E R R E E where Φ R and Φ E are the matrces of the modal shapes of the rgd modes and elastc modes; and η R and η E are the correspondng coordnates. The modal shape of the whole system s the combnaton of Φ R and Φ E : [ ] Φ = Φ Φ () R E For the rgd modes, there exsts M η = Φ q (4) T R R R t And for the elastc modes, the followng equaton s satsf e d : M η + C η + K η = Φ q (5) T E E E E E E E t where M R = Φ T RMΦ R denotes the modal mass of the rgd modes; M E = Φ T EMΦ E, C E = Φ T ECΦ E, K E = Φ T EKΦ E = M E Λ E are the modal mass, modal dampng, and modal stffness of the elastc modes, respectvely; and Φ T Rq(t) s the modal load. Assumng that C E = Φ T ECΦ E = M E Γ E, the egenvalues of the damped elastc modes are Γ E = ξ ω E E For each degree of freedom: ξ ω E E ξ ω n n E E E E E E E E E E (6) + + = q t (7) m η ξ ω η ω η ce where ξe =, Eq. (7) s smlar to the dynamc resp onse of a one-degree-of-freedom system. me ωe Assume that the nput force s a harmonc exctaton: q t = F Ω t (8) E E cos Usng modal superposton and assumng that n modes are consdered, the modal velocty s where F K η t = Ω sn Ωt + φ + n E E E H = E E E tan ω ξ ω =, E E E φ H E ξ ω ω ω ω E (9) = Ω (0) Usually, f we transfer the hgh-speed moton profle to the frequency doman usng a fast Fourer transformaton (Fgure ), the nput force can be regarded as a seres of harmonc exctatons: m q t = F cos Ω t () E Ej j j= So the correspondng modal velocty should be 9 Engneerng Volume Issue September 05

3 Mechancal Engneerng Artcle Research Acceleraton (mm. s ) E+7 8E+6 6E+6 4E+6 E+6 Ω Ω Ω Ω Frequency (Hz) Fgure. The seres of harmonc motons n the frequency doman. Response Tme step t 0 t t t t q Load case f 0 f f f f q eq eq eq eq eq Fgure. Equvalent statc loads n the number of tme ponts. F K η t = Ω sn( Ω t + φ ) () + m n Ej E E j j H j= = E E E ω ξ ω Eq. () shows that the vbraton response of the hghspeed mechansm s affected by the stffness, dampng, and frequences of elastc modes, and also by the exctaton frequences. The former s related to the structural desgn and the latter s related to the moton profle, so the optmal spatal and temporal dstrbuton of nertal energy would be an effcent way to mnmze the vbraton at the end of the manpulator and the fnal stage of the moton. However, as the vbraton response s dffcult to obtan due to the varaton n stffness, nerta, and moton condtons, numercal methods such as the nonlnear fnte element method of flexble multbody dynamcs are needed to solve the dynamc-response analyss and optmzaton. Optmal structural desgn usng ESLM The moton equaton for an equvalent structural response under a dynamc load at poston y R can be wrtten as M y y + K y y = q y () R E R E R, t where vectors y R and y E represent the dsplacement of the rgd body and elastc deformaton, respectvely, and the dampng effect s gnored. Wth the ESLM [0], we can derve the equvalent statc loads usng the fnte element method. Rearrangng Eq. () leads to or K y y = q y, t M y y (4) R E E R E K y y = f (5) R E eq f = q y, t M y y (6) eq R R E where Eq. (6) represents the equvalent statc loads at tme t [0]. For optmzaton, the number of the equvalent statc loads (Fgure ) can be treated as multple loadng condtons. Thus, the equvalent load set can regenerate dynamc propertes such as tme-dependent dsplacement or stress. In fact, the ESLM s an nterface between nonlnear response analyss and lnear statc optmzaton (Fgure ), and analyss s performed n the analyss doman, where equvalent loads are calculated. Lnear-response optmzaton s performed usng the equvalent statc loads n the desgn doman. The process proceeds n a cyclc manner. Analyss doman Not a lnear response analyss Dsp. feld Updated desgn Equvalent statc loads Multple loadng condtons Fgure. The analyss and desgn doman usng the ESLM. Desgn doman Lnear statc optmzaton In hgh-acceleraton low-load mechansms, the prncpal loads are the nertal forces nduced by acceleratons. Hence, mechancal desgn should consder lght-weght structures to mnmze such loads. However, the lnear statc optmzaton cannot handle dynamc features such as nertal property and dynamc stffness, even wthn the ESLM. Lnear statc optmzaton needs to be modfed wth only one teraton n lnear statc optmzaton, so that the change of materal can be reflected on the nertal forces. Moreover, we have to modfy the senstvty analyss of the ESLM to meet the requrements of a hgh-acceleraton low-load mechansm. 4 A new structural-desgn method based on optmal spatal dstrbuton of nertal energy In the orgnal ESLM, only the stffness changes are consdered when removng an element, so the element senstvty s defned by the element stran energy [0, 5]. However, the modfcaton of elements also changes the nertal force, resultng n a change to the stran energy [6]. Assumng that the th element s removed from the reference structure at the jth poston, the change n stran energy s E = f y = y K K K y + M y = y K y + y M y = y K y + y M y S T T T, j j, j j j j, j j, j j T T j, j j j, j j T e T e j, j j j, j j (7) where superscrpts T, e, and S refer to transposton, element, and stran, respectvely; Δ s the ncrement; and E s energy. In addton, n a hgh-acceleraton low-load mechansm, the nertal force s the man load, so the nertal property should be consdered. Lke the stran energy, the nertal property can be measured by the knetc energy. Accordngly, when an Volume Issue September 05 Engneerng 9

4 Research Mechancal Engneerng Artcle element s removed from the reference structure at poston j, the change n knematc energy s E = m r = m y (8) ω K, j, j j, j where the superscrpt K means knematc; m s the mass of the th element; ω j s the rotatonal velocty at the jth poston; and r, j and ẏ, j are the gyro radus and velocty of the center of the th element n the jth poston, respectvely. For hgh-acceleraton mechansms, we need to maxmze the stffness whle mnmzng the nerta. As wth the to Raylegh-Rtz analyss, we can dvde the stran energy by the knematc energy to quantfy the senstvty of an element: curve. As we can see n Secton, the moton profle can be transformed to a seres of harmonc exctatons n the frequency doman, whch causes dffculty n calculatons of the nonlnear dynamc response. However, f we can parameterze the moton profle as varable moton boundary condtons, we can acheve optmum parameters for the moton profle usng nonlnear dynamc-response optmzaton. In partcular, when the machne moves at very hgh speed, such as durng de bondng and wre bondng, the nput sgnal conssts of pulses or jumps wth sudden changes. Snce the S curve s wdely used n ndustral stuatons, we take the asymmetrc S curve as an example. The parameters are four jerks for each secton (Fgure 4), namely G G 4. E y K y + y M y S = = E m y S, j, j K, j T e T e j, j j j, j j j (9) Assumng that the number of dscreet postons s m, and that ΔS max, j s the maxmum senstvty at the jth poston, the comprehensve senstvty s defned by S S = m S m j (0) j = max, j Evoluton structural optmzaton (ESO) s employed to perform the modfcaton. If the ΔS s less than a gven threshold, the materal property s set as a deleted materal densty, the elastc modulus of whch s very low, only % 0% of that of the normal materal. If we normalze the total E S by the scalar product of dsplacement and the total E K by the scalar product of velocty, we form the S and K, respectvely. Then the rato of S to K should reach a maxmum regardless of the deformaton and speed: E / / E y y y Ky y y S = = = E E /( y y ) y My /( y y ) S K S K, T T T T T T () The optmzaton problem of hgh-acceleraton low-load mechansms becomes Max S s.t. U U * () where U s the resdual vbraton ampltude wthn a requred statonary tme and U* s the postonng precson requrement. We made a stand-alone program for senstvty analyss and generated the command to modfy the model. It can be ntegrated wth the commercal software I-DEAS and AD- AMS to perform an optmzaton desgn for a hgh acceleraton mechansm. G G G The optmzaton model can be descrbed as. Fnd G, G, G, G 4 Objectve: Mn T T = T + T + T + T + T 4 s Subject to: abs s s + abs v < * T G = T G T G = T G 4 ε T G T + T = T G T + T 4 () The followng equaton s used to determne when the postonng accuracy s reached: * (4) abs s s +abs v < ε Let the objectve poston s * be Q. Then the tme segment for each moton s T = 6 E F + G + H + I + J G A + B + C + D Jerk Acceleraton Velocty Dsplacement T T T T 4 t Fgure 4. The parameters of the asymmetrc S curve. G 4 (5) 5 Moton profle based on temporal optmal dstrbuton of nertal energy As hgh-acceleraton low-load mechansms start and stop frequently, the prmary moton-control polcy s open-loop control wth a prescrbed moton profle, and the performance s manly dependent on the parameter of the gven moton T = T G T T = (6) G G G ( + G ) G G ( + G ) 4 (7) 94 Engneerng Volume Issue September 05

5 Mechancal Engneerng Artcle Research where T G T = (8) G 4 A = G G G + G G G + G G G G G G G G + G G G + G G G B = G G G G G + G G G G+ G G G G G G + G G G G + G C = G G G G G + G G G G + G 4 4 D = G G G G G + G G G G + G E = QG G G G + G G 4 4 F = G G G + G G G + G G G G G G G G + G G G + G G G od can also be appled to any other parameterzed moton curves, as well as to the parameter optmzaton of control systems. 6 Numercal examples Consder the structural optmzaton and velocty plannng of a hgh-acceleraton low-load de bonder for an ntegrated crcut (IC) packagng devce, wth a producton rate of des per hour. The moton tme for the bonder to move from the wafer to the lead frame (Fgure 5) s only 50 ms. The external load s the nertal force of the de, whch s neglgble when compared wth that of the de bonder. Motor shaft Poston Poston Capllary Capllary G = G G G G G + G G G G + G 4 4 H = G G G G G + G G G G + G I = G G G G G + G G G G + G 4 4 J = G G G G G + G G G G + G Usng the varable moton boundary condton nonlnear dynamc-optmzaton method, the procedure s shown as follows: () Defne the desgn varables, G, G, G, G 4, and the poston objectve Q. Defne the tme varables T, T, T, T 4, and evaluate them usng Eqs. (5) (8), respectvely. Defne the tme nterval T = T + T, T = T + T, and T 4 = T + T 4. () Buld the geometry of the mechansm, assgn materals, buld jonts, and apply moton, usng the followng functon: IF(T < T : G, G, IF(T < T : G, G, IF(T < T : G, G 4, IF(T < T 4 : G 4, 0, 0)))) () Mesh the key parts, assgn element propertes, and create the degrees of freedom of the connecton; defne the soluton type as super element creaton, and solve and output the modal neutral fle. (4) Replace the rgd body wth the correspondng flexble multbody, and defne the measurement of dsplacement and the velocty of the postonng pont. (5) Defne the measurement of tme and the sensor to trgger the event when the poston accuracy s met. (6) Select G, G, G, and G 4 as desgn varables, defne the total postonng tme as the objectve functon, and use the global optmzaton method to get the optmal result. By usng the above varable moton boundary condton nonlnear dynamc-response optmzaton, the parameters lkely to cause resonance wll be excluded from the optmzaton of feasble solutons; thus, velocty plannng s obtaned n whch the temporal dstrbuton of nertal energy s optmal. Moreover, the presented velocty-plannng meth- De Bonder arm Wafer Bonder arm Fgure 5. The workng prncple of the de bonder. Leadframe The materal used s alumnum alloy 7075, wth elastc modulus, mass densty, and Posson rato of 79.9 GPa, 700 kg.m, and 0.5, respectvely. The radus of gyraton s 80 mm, and the requred postonng accuracy s ± 0.5 µm (after vbraton attenuaton). The sze of the base structure s 05 mm 0 mm 5 mm, whle the total mass s 0. kg, and the nerta property s 0.97 kg.mm. The loads are the nertal force and the unt force appled to the tp of the capllary. 6. Optmal structural desgn We have compared the structural optmzaton wth three dfferent methods, namely the tradtonal structural optmzaton, the ESLM wth only one teraton n each cycle, and the modfed ESLM. The nonlnear dynamc smulatons of the optmal structures from the above methods are performed under the same moton profle wth dfferent parameters, where the moton perod of the bonder s 00 ms (normal acceleraton), 0 ms (hgh acceleraton), and ms (very hgh acceleraton). The maxmum ampltude of the resdual vbratons s lsted n Table. For the sake of comparson, the optmal structure usng tradtonal structural optmzaton s set as the reference, and the vbraton ampltude of the other two are compared wth t. The results show that when the de bonder moves wth a normal acceleraton, the ESLM s nearly the same as the structural optmzaton (wth a reducton of only.66%), and the data of the modfed ESLM also gves smlar results (wth a decrease of only.09%). When the bonder arm moves wth hgh acceleraton, the ESLM s more effcent (droppng by.4%), and the modfed ESLM wth the vbraton ampltude s reduced by.66%. It can be seen that the nfluence of nertal force s sgnfcant. When the bonder moves wth very hgh acceleraton, both the vbraton ampltudes are very large, whlst the modfed ESLM (.%) s stll more effcent than the ESLM (less than 0.00%). De Volume Issue September 05 Engneerng 95

6 Research Mechancal Engneerng Artcle Table. Resdual vbraton of the capllary for dfferent angular veloctes [6]. Optmzaton method Tradtonal structural optmzaton Normal acceleraton (moton tme 00 ms) Vbraton ampltude (mm) Improvement (%) Hgh acceleraton (moton tme 0 ms) Vbraton ampltude (mm) Improvement (%) Very hgh acceleraton (moton tme ms) Vbraton ampltude (mm) Improvement (%) ESLM( teraton) Modfed ESLM Table. The teraton of nonlnear response optmzaton of the parameterzed moton profle. Iteraton T 4 (ms) T s (ms) G ( s ) G ( s ) G ( s ) G 4 ( s ) E E E E E E E+8.880E E E+8.770E E E+9.95E E+9.9E eE+9.406E+0.809E+9.047E+9 Angular acceleraton (. s ) Tme (s) Iter_0 Iter_ Iter_ Iter_ Iter_ Engneerng applcaton In order to show ts practcal sgnfcance n engneerng, the presented method s appled to the development of a de bonder. The bonder s a swng arm that s drectly drven by a servo moto. The orgnal desgn s shown n Fgure 8(a). Fgure 6. The angular acceleraton durng optmzaton. 6. Moton profle plannng Furthermore, the parameters of the moton profle have been optmzed usng the nonlnear response optmzaton (Fgure 6), and after four teratons (Table ), convergence was acheved. In order to show the effcency of the asymmetrc S curve, the vbraton response s compared wth the symmetrc S curve. If the let G = G = G = G 4 = G n Eqs. (5) (8), then the jerk of the symmetrc S curve wth an equvalent drve s the same, and both S curves beng compared have the same drven tme (Fgure 7). We can see that the postonng tme changes from 9.40 ms to.5 ms at postonng accuracy ± 0.5 µm, a reducton of 4.5%. Dsplacement (mm) Asymmetrc Symmetrc Tme (s) Fgure 7. The resdual vbraton of asymmetrc and symmetrc S curves wth the same drven tme. (a) (c) Fgure 8. The structure of a de bonder. (a) Base structure; (b) desgn area; (c) optmal desgn; (d) f nal desgn. 7. Optmal structural desgn The presented method s based on the fnte element model, wth 46 elements (6046 elements n the desgn doman). The materal used s alumnum, wth a Young s modulus of 79 GPa, Posson rato of 0., and mass densty of 700 kg.m. After four teratons, the optmal result was found by deletng 000 elements (Fgure 8(c)). The fnal desgn s shown n Fgure 8(d). The vbraton ampltude dropped by 94.00%, and the power consumpton was also reduced by 8.46% (Table ). The fnal desgn was selected as the engneerng desgn (Fgure 9). 7. Moton profle plannng In order to show the effcency of the proposed moton profle based on the temporal optmal dstrbuton of nertal energy, the same procedure s appled to the parameter optmzaton of a proporton-ntegraton-dfferentaton (PID) control system (Fgure 0). (b) (d) 96 Engneerng Volume Issue September 05

7 Mechancal Engneerng Artcle Research Table. Comparson of the vbraton and power consumpton. Base Mass (g) Vbraton ampltude (mm) Improvement (%) Power (W) Improvement (%) Optmal Fnal Kd y z Sum x + Theta Kp K Velocty Saturaton s Integrator Poston Adams_sub Fgure 9. The engneerng desgn. Fgure 0. The control model. The ntal values of the three varables Kp, K, and Kd are set as.00. The orgnal postonng tme s 6.5 s. Usng parameter optmzaton based on nonlnear dynamc smulaton usng finte element analyss, after four teratons (Table 4), the optmal results are found wth Kp, K, and Kd at the values of 694.0, 4.5, and 40.4, respectvely. Ths procedure also shows the effcency of the two presented methods. acceleraton low-load mechansms and reduces the resdual vbraton by 0%; whle the nonlnear dynamc response for the asymmetrc S curve s decreased by more than 40%. The presented method was also appled to a desgn of a de bonder and to an optmal desgn of the PID parameters of a control system; both procedures showed the efficency of the metnod. The method has also been tested on a varety of hgh-acceleraton low-load mechansms n IC packagng equpment desgn (such as de bonders, wre bonders, surface mount technology (SMT), and hgh-acceleraton robotcs, etc.), and a sgnficant achevement has been accomplshed. Table 4. The optmzaton process of PID. Iteraton Postonng number tme (s) Kp K Kd Acknowledgements Ths work s supported by the Natonal Key Basc Research Program of Chna (0CB004), Natonal Natural Scence Foundaton of Chna (U4004), Guangdong Provncal Natural Scence Foundaton (05A00008), Scence and Technology Program of Guangzhou (050008), and Guangdong Provncal Scence and Technology Plan (0B004004). Complance wth ethcs gudelnes Xn Chen, Youdun Ba, Zhjun Yang, Jan Gao, and Gongfa Chen declare that they have no conflct of nterest or financal conflcts to dsclose. 8 Conclusons References In ths paper, the optmzaton problem of the nonlnear dynamc response of a hgh-acceleraton low-load mechansm was dscussed. Systematc methods were proposed to solve the problem from the optmal dstrbuton of nertal energy n space and tme domans. A modfed ESLM was selected for optmal structural desgn n order to mprove the dynamc response of hghacceleraton low-load mechansms. A new velocty profile based on nonlnear dynamc response was proposed n order to reduce postonng tme. The numercal example showed that the modfed ESLM s effcent for hgh-. H. Dng, L. M. Zhu, Z. Q. Ln. Accurate postonng and operaton of hgh acceleraton and hgh precson stage for IC packagng. Prog. Nat. Sc., 00, (6): (n Chnese). Z. H. Feng, H. Y. Hu. Advances n dynamcs of hgh-speed mechansms. Adv. Mech., 00, (): (n Chnese). O. Wallrapp. Revew of past developments n multbody system dynamcs at DLR From FADYNA to SIMPACK. Vehcle Syst. Dyn., 004, 4(5): W. S. Cho, G. J. Park. Structural optmzaton usng equvalent statc loads at all the tme ntervals. Comput. Method. Appl. M., 00, 9(9 0): G. J. Park, B. S. Kang. Valdaton of a structural optmzaton algorthm transformng dynamc loads nto equvalent statc loads. J. Optmz. Theory App., 00, 8(): W. S. Cho, G. J. Park. Structural optmzaton usng equvalent statc loads at all tme ntervals. Comput. Method. Appl. M., 00, 9(9 0): Y. I. Km, G. J. Park. Nonlnear dynamc response structural optmzaton usng equvalent statc loads. Comput. Method. Appl. M., 00, 99(9 ): M. K. Shn, K. J. Park, G. J. Park. Optmzaton of structures wth nonlnear behavor usng equvalent loads. Comput. Method. Appl. M., 007, 96(4 6): Volume Issue September 05 Engneerng 97

8 Research Mechancal Engneerng Artcle 9. H. A. Lee, Y. I. Km, G. J. Park, R. M. Kolonay, M. Blar, R. A. Canfeld. Structural optmzaton of a joned wng usng equvalent statc loads. J. Arcraft, 007, 44(4): B. S. Kang, G. J. Park, J. S. Arora. Optmzaton of flexble multbody dynamc systems usng the equvalent statc load method. AIAA J., 005, 4(4): K. D. Nguyen, T. C. Ng, I. M. Chen. On algorthms for plannng S-curve moton profles. Int. J. Adv. Robot. Syst., 008, 5(): K. Zheng, L. Cheng. Adaptve s-curve acceleraton/deceleraton control method. In: Proceedngs of the 7th World Congress on Intellgent Control and Automaton. Chongqng, Chna, 008: P. H. Meckl. Optmzed s-curve moton profles for mnmum resdual vbraton. In: Proceedngs of the 998 Amercan Control Conference. Phladelpha, PA, USA, 998: H. Z. L, Z. Gong, W. Ln, T. Lppa. A new moton control approach for jerk and transent vbraton suppresson. In: Proceedngs of 006 IEEE Internatonal Conference on Industral Informatcs. Sngapore, 006: Z. J. Yang. Topologcal optmzaton approach for structure desgn of hgh acceleraton mechansms usng equvalent statc loads method. J. Mech. Eng., 0, 47(7): 9 6 (n Chnese) 6. Z. J. Yang, X. Chen, R. Kelly. A topologcal optmzaton approach for structural desgn of a hgh-speed low-load mechansm usng the equvalent statc loads method. Int. J. Numer. Meth. Eng., 0, 89(5): H. L, M. D. Le, Z. M. Gong, W. Ln. Moton profle desgn to reduce resdual vbraton of hgh-speed postonng stages. IEEE/ASME T. Mech., 009, 4(): Engneerng Volume Issue September 05