developed. In  the  remaining  sections, the kinematic  and
dynamic  analysis  of  the  proposed  mobile robot  is
performed  and various  test results are  presented
demonstrate  the validity  and  feasibility  of  the proposed
mechanism.
2. Variable Wheel Arrangement Mechanism
In  this  section, the  structure and operational principle
of the proposed  variable wheel arrangement mechanism
(VWAM) will  be  presented. In  addition, comparison  of
this  mechanism  with  the  variable  footprint mechanism
(VFM) proposed by Wada is discussed  below. Fig. 1 Variable footprint mechanism for CVT [9].
Figure 1  shows  the variable  footprint mechanism  in
which  two  beams  can rotate  at  a  pivot  joint  P  in  the
middle  [9].  Note  that  the  two  beams  are constrained to
rotate in a symmetric fashion with a single DOF by means
of  differential  gears  at the  pivot.  The  ball  wheels and
motors are mounted at each end of the beams. Meanwhile,the variable wheel arrangement mechanism  (VWAM)
developed  in  this  research  is  illustrated in Fig.  2.  The
wheel module consists  of  the omnidirectional wheel
called  a  continuous altemate wheel developed  in  our
laboratory  [ll] (see  Fig.  6), an inpidual motor  and
steering  link. Notice  that  the four wheel modules can
rotate  about each pivot point  CI, .., C,  located  at  the
comers of the robot body, but they are constrained to have
a synchronized steering motion of  1 DOF by  the VWAM
comprising the connecting links and linear guide. In Figures 1 and 2, the steering angle 4  is defined as the
angle from the zero position  in which the beams (Fig. 1)
or the  lines (i.e.,  C,C3 or C2C4)  connecting the centers of
diagonally opposed wheels  (Fig.  2)  coincide  with  the
diagonal  lines  of  the robot  body.  The wheelbases, the
distances between the centers of two  adjacent wheels on
the x-  and y-axis, at the configuration 4 =  0 are denoted as
dxo  and dyo.  If the robot body is square, then dxo  =  dyo.
In  Fig.  1  the  rotation center of the wheel module  is
located  at  the  intersection P  of  the  two  beams. As  the
steering angle 4 becomes large, therefore, one side of the
rectangle whose vertices are wheel-ground contact points
may get excessively smaller than  the  other  side,  thus
leading  to  increased  instability. Hence the steering angle
was limited  to  the range between  -17.5'  and  +17.5'  ,
which  causes  the  range of velocity  ratio  (defined  in
Section 4) to be  limited. On the contrary, since the wheel
modules  in Fig. 2 rotate about each pivot joint C,,  .., C4
placed  at  the  comers  of  a  robot platform, the robot  is
structurally stable  even  for  a  large steering  angle. As  a
result  of  this feature,  the  steering angle can  be
substantially large,  and thus the range of velocity  ratio
increases accordingly. Figure  3  shows various wheel  .
arrangements  Using  the variable wheel arrangement 四轮全方位移动机器人英文文献和翻译(2):http://www.youerw.com/fanyi/lunwen_1818.html