Examination of stability for tensegrity structures through the
theory of machines
'
" "
1
2
2
3
3/6 Stewart Platform-Spatial Triad6/6 Stewart PlatformSpatial
Double TriadSpatial Tetrad . . , . . (1965) 3/6 Stewart Platform
.
3
Hunts Singular Configuration (1978)
- SP
Stewart Platform
3C4D5A5B4BMerlet (1989) 3/6-SP Grassmann line geometry -3C, 4B,
4D, 5A -5B.
Hunt et al. (2002) (2006) GrassmannCayley algebra 144 .
3/6 SP - .
-3D- . - .
Self-stress is createdSelf-stress is createdTwo linesintersect
at a point
Self-stress is created -2D- .
3/6 SP- 3D Triad3D Double Triad3D Tetrad3D Pentad - .
() () - (-).
/?
-, (equimomental lines- eqml), (Shai and Pennock, 2005).Shai O.
and Pennock G. R, "The Duality Between Planar Kinematics and
Statics", ASME Design ngineering Technical Conferences, September,
24-28, 2005, in Long Beach, California, USA. Awarded the A.T. Yang
Memorial Award in Theoretical Kinematics.
-, (equimomental screws - eqms), -ISA (Instantaneous screw axis)
.
StaticsKinematics
. eqml . . .
12 :
Dual KennedyKennedy
4123
Relative instant center of bodiesRelative instant center of
bodies
Relative equimomental line of faces
41
23
, .
( ). ,
, " ( ) ., eqml ( ) ., " ( ) ., eqml ( ) . :
, (Twist vector)., (Wrench vector).
- Assur Graphs (AG)
15
-AG (Servatius et al, 2010). AG : .self-stress, , ., -AG
.Servatius B., Shai O., and Whiteley W., 2010, Geometric Properties
of Assur Graphs, European Journal of Combinatoric, 31(4), pp.
1105-1120
15
Common Normal
Common Normal
20
4
- (3/6 SP)
Common Normal
: -eqml (0,2), (0,4) ,(2,4), , ( ).
02
4
6
Common Normal
: eqml eqms (0,4).
563124
6/6 SP18 : .
18
6/6 SP
563124
- SP - SP
563124
5 - 6 5 - 6
:
563124
:
563124
3124
6/6 SP. -SP. (Slavutin M., Sheffer A., Shai O.): (AG) ,
(Cylindroid) , -ISA .
124
3
- SP - SP .
124
3
124
3
124
3
124
3
124
3
124
3
124
3
124356
33
. . . .34
34
!
