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HIGH TECHNOLOGY LEITERS IVol. 12 No. 1 1 Jan. 2α)6 63
Dynamics optimization of a novel high speed and high precision 3-DOF manipulator①
Lan Peng (蘭 朋悶,U Nianli , Sun Lining 鈴 ,Ding Qingyong 費
( School of Me.chatroni 臼 Engineering, Har也m Institute of Te<丁hnology, Harbin 15α刷 ,P . R .China) ( ? Robotics Institute, H缸bin Institute of Technolo町,Harbin 15僅見I , P.R.China)
Absti古董ct
After introducing a novel 3-DOF high speed and high precision manipulator which combines direct driven planar parallel mechanism and linear actuator, ways of increasing its stiffness a陀 studied through dynamics simulation in ADAMS softw缸它 environment . Design study is carried out by parametric analysis tools to analyze the approximate sensitivity of the design V缸iables , including the effects of p缸沮netens of each beam cross section and relative position of linear actuator on model performance. Conclusions a陀 drdwn on the appropriate way of dynamics optimization to get a lightweight and small deformation manipu- lator. A planar parallel mechanism wi出 different cross section is used to an improved manipulator. Re-
suits of dynamics simulation of the improved system and another unrefined one 缸e compa配d . η1e sti旺-
ness of them is almost equal , but the mass of 由e improved one decreas臼 greatly , which illustrates the ways efficient .
Key words: manipulator, ADAMS, optimization , dynamics simulation
0 Introduction
Parallel kinematic manipulatons ( PKM ) 耐 a class of promising machine for the manipulation and assemble of electronic device, because they have some advantages
over the serial manipulator, such as high load ca町ing capacity , g0<對 dynamic performance and precise position- ing[1l . A novel hybrid 3-DOF manipulator, which com-
bines the advantages of parallel manipulator and serial manipulator, is studied in this paper. As shown in Fig. 1, the manipulator is composed of planar parallel
mechanism ( PPM ) including parallelogram structure and linear actuator mounted on the end of PPM . Two A巳 di-
陀ct driven moto囚 integrated high 陀田lution em
selected as driven part of planar par茍Ilel mechanism . Lln- 回 actuator is driven by voice coil motor, which is con- sidered as ideal driven part for short travel . As a kind of non-commutated di陀ct 世ive , hysteresis-free, cog-free
device, voice coil motor can provide both high 歸sition sensitivity 阻d pert<叩force vensus stroke character. Hi班
precision linear encoder is used as feedback parts to 伊ar- ante悟 出e 陀陰暗tability in vertic況Idirection .
Compared with higher degree of freedom parallel ma-
nipulator, for example Steward platform or Tricept robot , kinematic and d嚴1amic m叫els of PPM ar吃 simple[ i-3] _
On the other hand , it has higher stiffness 由m 出e serial manipulator because of its close loop feature and low mo- ment of inertia . Meanwhile, the system can ove陀ome the mechanical elasticity introduced by flexible coupling, gear teeth, be白噸,bearing support , connecting shaft and other parts included by classical drive system . So this ma- nipulator is more easily to get well dynamics perfonnance and high p即ision .
Planar parallel mechanism
Motor
Fig.1 3-00F hyhrid structUJ它 manipulator
When the length of each link of pl四ar parallel mechanism is d配ided by kinematics analysis and syn出e- sis[4-7l , the primary task of optimal desi伊 should be in- creasing the stiffness and dee陀asing 由e mass. With re- gard to model wi由several par淚neters, it is important and
咀1at makes real time control possible and is mo陀 precise .
neees
ry to study the influence of each p
neter on
田 缸田
① Supported by 配 High Technology Research and Development Pr咱出nme of China ( No. 2003AA刷刷)) .
② To whom coπ呵lOndence 動 uld be addressed . E而 mail: l皿 p@ sma. 凹陽
Ri,cpjved on Sept. 29,刻Xl4
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64 1-DGH TECHNOLO(,Y LF.ITERSI Vol.12 No. I I Jan. 2(脅
model performance in order tu make fu出er optimization . This paper will carry out design study by parametric anal- ysis tools of ADAMS, and then p陀sent appropriate ways of optimization to get a lightweight and small deformation system .
1 Simulation model
ADAMS ( Automatic Dynamic Analy附 of Mechanical System) is a perfect software tool for dynamics simulation of mechanical system . It can deal with mechanism con- sisting of both rigid and flexible parts . Simulation model of the manipulator can be created in the ADAMS environ- ment as shown in Fig.2. OXYZ is the global reference
frame , and o.切:yz is local reference frame. Two AC direct
driven motors, expressed as 01A and Oi M , and linear actuator CH are t陀ated as rigid 以,dy . 幣1e rotor inertia of motor is 120kg · cm2 . 幣1e mass of linear actuator is 1.5kg. Links AB, DE, 03F and U are tr臼ted a,;; flexible
effector is used to characterize the dynamic stiffness, which is different at different configuration during the lin-
ear actuator moving fmward from initial position to the destination . 咀1e average vertical displacement of the end- effector is taken as the ob ective to study vertical stiff- n白白. The average difference of X-coordinate and Y『coor- dinate of point H between 由is model and a rigid model is 時cen as the objective to study level 叫iffness.
2 .1 Effect of er鴨 ”ction
。
Torsion defonnations of links will cause vertical dis- placement of the end-effector. So, torsional constants of cross section are studied first . Gravity is loaded on the system to study the vertical stiffness . Take torsional con- stant ι f section of each link and beam as design vari- able which varies from 0.1 x la5mm4 to 3 .5 x Ia5mm4 . Fig. 3 shows the average displacement of 由e end-effector
body. Beam『 GK , GM and KM , which form a triangle,
即e also treated as flexible body . The length of links a陀 decided in advance by kinematics design a,;; AB =的F """ 7cm, DE = IJ = 7cm , GK = 7cm , GM = 11.66cm, KM =
8.338cm . 響1e other dimensions in the figure a陀 01 A =
02 M = 7cm, CB = CD = HJ ::: 2.5cm , EF = EC = JK =
3cm.
Although the gross motion of planar parallel mecha- nism is in level, ho由 the vertical and level stiffness has to be considered . And the vertical stiffness is usually less than the level stiffness because of its cantilever character
in vertical plane. 咀1e cross section size of each beam of
-0.00相
r句Q士、 -0. 0013
。∞”
,,-0.00’4
?!匏?
-0.00咀
-0.00’7
。由17
?!尴?
0.0 0 $
,.-- 壺
’‘’
1-link 03F 2-link AB
3-link DE ←→且也日
5-beam GK 6一戰(zhàn)am GM
7 斗:,eam KM
,。 ’5 2.0 2.5 3.0 3.6
T惆ional cons陽ts (105mm勺
planar parallel mechanism and the relative position of lin- ear actuator 缸e two important factors that affect the stiff- ness of the system. Therefore, the following study is done in these respects .
Fig.2 Simulation mudd
2 Simulation r四時t
In this section , the average displacement of the end-
Fig. 3 Effect of torsional constant on vertial deformation
versus cross section torsional constant of each link and be卻n . According to it , the change rate of link AB is the biggest . Next is link DE ,日in tum res嚴ctively . B創(chuàng)ms GK and KM have the least eff白t on vertical stiffness. Other simulation shows that level displacement difference
of point H between this model and a rigid model changes little with respect to a change in the torsional constant when constant level inertia force is loaded on the linear actuator. But the level displacement of the end-effector changes in 出is simulation . η1at means vertical deforτna- tion of the system should produce level displacement of end回effector. Note that unevenness of the linear actuator is the main cause of level defonnation of end-effect肘,and the linear actuator is supported by two joints C and H. So we calculate the difference of Z -coordinate between 陽int C and H . As shown in Fig. 4, torsional constant of link DE affects the difference 出e most efficiently . Next is k田n GM and link U in order. Link 03F and beam GK have the leai;;t effect .
咀1erefore, links AB and DE should adopt se<;tion
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HIGH TECHNOLC見Y IEITERSI Vol.12 No. l lJan. 2α)6 65
with big torsional constant to enhance the vertical stiff- ness. Bigger torsional constant of link DE also caus臼less unevenness of the linear actuator . Decreasing the uneven- ness can reduce the level deformation .
2-link AB
stant ι .四e Irr of link AB , beam KM and link 03F are 出e three main factors that decide the vertical stiffness. Fig. 6 shows the Irr of link AB , beam KM and link 03F
缸它 also the three main facto陀 that decide the unevenness of the linear actuator. Di征erent analysis shows that I,, has the least effect on b 由 vertical and level stiffness . 幣iat
means this kind of structure has enough level stiffness. So
4一UnmkUGM
d asing I,, of links and increasing ”’ of link AB,
-be晦 配陀
beam KM and link 03F 缸它 the good ways to optimize the system .
2.2 Effect of the relative position of linear ac陽ator
3.7
3.6
QO 0.5 1.0 1.5 2.0 2.5 3.。 3.5
Torsional constants (1l?mm4)
η1e inertia of linear actuator is one of the main loads during the motion of manipulator . Different relative ve民i- cal position should produce different deformation . Fig. 7
Fig.4 Effect of torsional constant on unevenness
What Fig聲 .5 and 6 show are the effects of area
m
G
(EE一守LD己 言ωERE昏時唱g- 百多
.0.αJ05
shows the absolute average vertical displacement of end- effector when the driven motors rotate at a constant accel-
eration . We can see that too low or too hi班 時ative posi-
tion will cause bigger defonnation .咀1e best position is at a如ut Z = - 24mm where is approximate the midst from link AB to link 03F.
m
E
。
’6
m
A
.0.0025。。
4一link u
6 beam GM
0.5 1.0 1.5
Moments of iner由(llfmm‘}
J
d
O D41
l
AB
亞 刷
E
u
2.0 2.5 ]
Fig.5 Effect of moments of i陽rtia on vertial defo回國lion
。。
0.0
-?J.0
-40.0 .10.0
Z-coordinate (mm)
篇。 eoo
1 」ink 03F 3---link DE 5一悅am GK
2一link:AB
4--link 日
6--bE姐m GM
Fig.7 Effect of relative position of linear actuator
3
--5
"’
ι乙 』 回南.:::.-..乓芫叫
.. ·
、、
3 Analysis of an improved manipulator
According to above simulation result , an improved manipulator is designed as follows : cross s創(chuàng)ions of links
AB , DE ,日在附 hollow rectangle with 30mm b出e and
2.5 0.0 0.5 1.0
1.5
2.0 2.5
height , 10mm thickne制;link 向F and beam KM 町e I-
Moments of inertia (105mm‘)
Fig. 6 Effect of moments of inertia on unevenness
moment of inertia on the stiffness. 'lbe design variable is 臟a moment of inertia lyy and ι of each link and beam . Fig. 5 shows that inc陀兇e of Irr can 配duce the vertical deformation more rapidly than increase of torsional con-
beam with 30mm ba
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