Avshalom Sheffer- Seminar

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Transcript of Avshalom Sheffer- Seminar

Examination of stability for tensegrity structures through the theory of machines

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3/6 Stewart Platform-Spatial Triad6/6 Stewart PlatformSpatial Double TriadSpatial Tetrad . . , . . (1965) 3/6 Stewart Platform .

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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 - .

() () - (-).

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-, (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 . . .

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Dual KennedyKennedy

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Relative instant center of bodiesRelative instant center of bodies

Relative equimomental line of faces

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, .

( ). ,

, " ( ) ., eqml ( ) ., " ( ) ., eqml ( ) . :

, (Twist vector)., (Wrench vector).

- Assur Graphs (AG)

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-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

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Common Normal

Common Normal

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- (3/6 SP)

Common Normal

: -eqml (0,2), (0,4) ,(2,4), , ( ).

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Common Normal

: eqml eqms (0,4).

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6/6 SP18 : .

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6/6 SP

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- SP - SP

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6/6 SP. -SP. (Slavutin M., Sheffer A., Shai O.): (AG) , (Cylindroid) , -ISA .

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- SP - SP .

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