T1707205-v1 BS PI Matrix Calc - Test Hang Version 6/29/2017

Current version of the calculation assumes the BS Test Hang assembly frame arrangement with L (longitudinal) = -X (global) = y (this calculation) and T (transverse) = -Y = -x.

Graphics/geometry stuff

vals = {
R->715/1000, (* PI radius *)
Sradius -> Sqrt[123.346^2+459.968^2]/1000, (* 3D CAD *)
Gradius -> 602.6/1000, (* 3D CAD *)
Lradius -> Sqrt[131.764^2+579.648^2]/1000, (* 3D CAD *)
l->200/1000, (* For graphics *)
origin -> 0°
};

Lradius/.vals

Angular locations of the various items

Sangles = {270°,(270+120)°,(270+240)°}

Gangles = {315°,(315+120)°,(315+240)°}

Langles = {330°,(330+120)°,(330+240)°}

Positions of the various items as vectors

Spositions =Sradius* Table[RotationMatrix[Sangles[[i]]].{1,0},{i,1,3}]

Gpositions =  Gradius*Table[RotationMatrix[Gangles[[i]]].{1,0},{i,1,3}]

Lpositions =  Lradius*Table[RotationMatrix[Langles[[i]]].{1,0},{i,1,3}]

Orientations of the various items as unit vectors

Svectors = Table[RotationMatrix[Sangles[[i]]].{0,1},{i,1,3}]

Gvectors =Table[RotationMatrix[Gangles[[i]]].{0,1},{i,1,3}]

Lvectors =Table[RotationMatrix[Langles[[i]]].{0,1},{i,1,3}]

Diagram

Graphics[{
Circle[{0,0},R],
Red,
Sequence[Table[Arrow[{Spositions[[i]]-Svectors[[i]]*l/2,Spositions[[i]]+Svectors[[i]]*l/2}],{i,1,3}
]],
Green,
Sequence[Table[Arrow[{Gpositions[[i]]-Gvectors[[i]]*l/2,Gpositions[[i]]+Gvectors[[i]]*l/2}],{i,1,3}
]],
Blue,
Sequence[Table[Arrow[{Lpositions[[i]]-Lvectors[[i]]*l/2,Lpositions[[i]]+Lvectors[[i]]*l/2}],{i,1,3}
]]
}]/.vals

(LVDTfromLTY = {
Table[Lvectors[[i]].{1,0},{i,1,3}],
Table[Lvectors[[i]].{0,1},{i,1,3}],
Table[Lvectors[[i]].Lvectors[[i]]*Lradius,{i,1,3}]
})//TableForm

LVDTfromLTY/.vals//N//TableForm

(LTYfromLVDT = Inverse[LVDTfromLTY])//TableForm

Transpose[LTYfromLVDT]/.vals//N//TableForm

LTYfromLVDT/.vals//N//TableForm