䢳䣒䢳䢯䣈䢲䢵
Vibration Control and Mechanical Sway Stabilization of Flexible Link System     
Yusuke IMAI, Graduate School, Univ. of Tsukuba, s1220855@u.tsukuba.ac.jp
Daigoro ISOBE, Univ. of Tsukuba, isobe@kz.tsukuba.ac.jp

In this paper, we propose a mean of vibration control and mechanical sway stabilization of flexible link systems.
This system controls both the vibration generated in a link and the reaction moment generated by motion of anobject. Since the vibration is caused by the transition between strain energy and kinetic energy, the mean of vibration
control discussed in this paper aims to reduce the strain energy. The reaction moment is canceled by using a torquecanceling system (TCS) which is developed in the previous studies. The effect of this vibration control system isshown by carrying out finite element analysis of a simple flexible link system, and a calculated result of the reaction
moment generated at the location of a TCS.
Key Words : Flexible Manipulator, Trajectory Planning, Vibration Control, Mechanical Sway Stabilization

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1Fig.1 Vibration phenomena of a beam

[1][2]t + ∆t[M ]{üm }t+∆t + [M ]{üd }t+∆t + [C]{u̇d }t+∆t +[K]{∆ud } = {F }t+∆t − {R} (1)

[3]

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[K]
{R}

[C]
{F }

{üm }{üd }{u̇d }{∆ud }
Newmark

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TCS

{ud }t+∆t{um }t+∆t{u}t+∆t

TCS==={ud }t + {∆ud }{um }t + {∆um }{um }t+∆t + {ud }t+∆t䣐䣱䢰䢢䢳䢵䢯䢴䢢䣒䣴䣱䣥䣧䣧䣦䣫䣰䣩䣵䢢䣱䣨䢢䣶䣪䣧䢢䢴䢲䢳䢵䢢䣌䣕䣏䣇䢢䣅䣱䣰䣨䣧䣴䣧䣰䣥䣧䢢䣱䣰䢢䣔䣱䣤䣱䣶䣫䣥䣵䢢䣣䣰䣦䢢䣏䣧䣥䣪䣣䣶䣴䣱䣰䣫䣥䣵䢮䢢䣖䣵䣷䣭䣷䣤䣣䢮䢢䣌䣣䣲䣣䣰䢮䢢䣏䣣䣻䢢䢴䢴䢯䢴䢷䢮䢢䢴䢲䢳䢵䢳䣒䢳䢯䣈䢲䢵䢪䢳䢫

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TCSRigid link
Motion of link

ZPassive jointxYX

Flexible linkyz

Fig.3 Outline of a link system䣐䣱䢰䢢䢳䢵䢯䢴䢢䣒䣴䣱䣥䣧䣧䣦䣫䣰䣩䣵䢢䣱䣨䢢䣶䣪䣧䢢䢴䢲䢳䢵䢢䣌䣕䣏䣇䢢䣅䣱䣰䣨䣧䣴䣧䣰䣥䣧䢢䣱䣰䢢䣔䣱䣤䣱䣶䣫䣥䣵䢢䣣䣰䣦䢢䣏䣧䣥䣪䣣䣶䣴䣱䣰䣫䣥䣵䢮䢢䣖䣵䣷䣭䣷䣤䣣䢮䢢䣌䣣䣲䣣䣰䢮䢢䣏䣣䣻䢢䢴䢴䢯䢴䢷䢮䢢䢴䢲䢳䢵䢳䣒䢳䢯䣈䢲䢵䢪䢴䢫

Table1 Parameter of link members
34Aluminum
0.300
0.005
0.030
0.00
2.00

5
Stainless steel
0.100
0.040
0.040
0.00

 6.1

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9XRU=p9C[ P¡=>XX=\] TCS 6¢£9XR= (9Displacement of link head [m]12
Stainless steel
0.200
0.040
0.020
0.48
0.48

0.2
Strain energy [J]Link No.
Material
Length [m]Section size x [m]Section size y [m]Added mass [kg]0.10¤¥¦=> :\i9§69
R ¨©69ªO«¬­®Q6> SchemeA¯°3±R SchemeB²³3±
R [ 2 ´0µ­®Q¶· 2 ¸ ¹6º+,µ »¼[XR=m³
QC>»¼6j ½ ¾¿À TCS 6¢£Q69R 5 ¨©69P¡[ =Á9

Without vibration control
With vibration control

0.02
0.01
0-0.01
-0.02
-0.03

6.

7.

0.03

Without vibration control
With vibration control

0123
Time [s]40512345Time [s]Fig.4 Strain energy

Fig.5 Displacement of link head

0.8
Without vibration control
With vibration control

Without vibration control
With vibration control

20.6

Moment [N m]

X [m]

10.4

0.2

0-10-20123Time [s]450123Time [s]45Fig.6 X-coordinate of link head Fig.7 Generated moment at TCSÂ Ã[1] ÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕ: Ö3 ×ØÙÚÛÜªÝ&ÞßàáâÛNãäRåæÙçè éÖ, êëìíî
ïðVol.6,No.1,pp.42-51,1988.
[2] ñòóôõö÷øÉùú: ÖûÚÛÜªÝ&ßàáâÛNü Ö, êýþîïÿÊ
C Vol.66,No.645,pp.1574-1581,2000.
[3] Ì: Öº+,µ ý £îÖêëìíîïðVol.20,No.6,pp.647653,2002.
o£[4]  Ì, È , e  : Öîµ &ÜçäªO«¬Ö, êýþîïÿÊ C , Vol.77,No.775,pp.785798,2011.
[5] Ìå : ÖÚÛÜªÝ&Þã&OÞÚÚéÖ, êëìíîïðVol.25,No.4,pp.625-631,2007.

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