Expresión 13: "E" Subscript, 1 , Baseline equals 1 half left parenthesis, "x" Subscript, 1 , Baseline plus "x" Subscript, 2 , Baseline , right parenthesis plus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis Over 2 "R" squared , EndFraction left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis plus 1 half StartRoot, 2 StartFraction, left parenthesis, "r" squared plus "r" squared , right parenthesis Over "R" squared , EndFraction minus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis squared Over "R" to the 4th power , EndFraction minus 1 , EndRoot left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesisE1=12x1+x2+r21−r222R2x2−x1+122r21+r22R2−r21−r222R4−1y2−y1
equals=
0.4 6 1 2 3 7 4 5 6 5 2 50.461237456525
13
Expresión 14: "E" Subscript, 2 , Baseline equals 1 half left parenthesis, "y" Subscript, 1 , Baseline plus "y" Subscript, 2 , Baseline , right parenthesis plus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis Over 2 "R" squared , EndFraction left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis plus 1 half StartRoot, 2 StartFraction, left parenthesis, "r" squared plus "r" squared , right parenthesis Over "R" squared , EndFraction minus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis squared Over "R" to the 4th power , EndFraction minus 1 , EndRoot left parenthesis, "x" Subscript, 1 , Baseline minus "x" Subscript, 2 , Baseline , right parenthesisE2=12y1+y2+r21−r222R2y2−y1+122r21+r22R2−r21−r222R4−1x1−x2
equals=
1.4 2 7 3 2 6 1 7 4 61.4273261746
14
Expresión 15: "E" Subscript, 3 , Baseline equals 1 half left parenthesis, "x" Subscript, 1 , Baseline plus "x" Subscript, 2 , Baseline , right parenthesis plus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis Over 2 "R" squared , EndFraction left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis minus 1 half StartRoot, 2 StartFraction, left parenthesis, "r" squared plus "r" squared , right parenthesis Over "R" squared , EndFraction minus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis squared Over "R" to the 4th power , EndFraction minus 1 , EndRoot left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesisE3=12x1+x2+r21−r222R2x2−x1−122r21+r22R2−r21−r222R4−1y2−y1
equals=
negative 1.0 1 9 8 9 1 5 8 7 1−1.0198915871
15
Expresión 16: "E" Subscript, 4 , Baseline equals 1 half left parenthesis, "y" Subscript, 1 , Baseline plus "y" Subscript, 2 , Baseline , right parenthesis plus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis Over 2 "R" squared , EndFraction left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis minus 1 half StartRoot, 2 StartFraction, left parenthesis, "r" squared plus "r" squared , right parenthesis Over "R" squared , EndFraction minus StartFraction, left parenthesis, "r" squared minus "r" squared , right parenthesis squared Over "R" to the 4th power , EndFraction minus 1 , EndRoot left parenthesis, "x" Subscript, 1 , Baseline minus "x" Subscript, 2 , Baseline , right parenthesisE4=12y1+y2+r21−r222R2y2−y1−122r21+r22R2−r21−r222R4−1x1−x2
equals=
1.0 9 9 9 1 8 7 0 1 81.0999187018
16
"x" Subscript, 3 , Baselinex3
"y" Subscript, 3 , Baseliney3
"x" Subscript, 1 , Baselinex1
"y" Subscript, 1 , Baseliney1
r1c3:
"E" Subscript, 1 , BaselineE1
"E" Subscript, 2 , BaselineE2
r2c3:
"x" Subscript, 2 , Baselinex2
"y" Subscript, 2 , Baseliney2
r3c3:
r4c3:
17
"x" Subscript, 4 , Baselinex4
"y" Subscript, 4 , Baseliney4
"x" Subscript, 1 , Baselinex1
"y" Subscript, 1 , Baseliney1
r1c3:
"E" Subscript, 3 , BaselineE3
"E" Subscript, 4 , BaselineE4
r2c3:
"x" Subscript, 2 , Baselinex2
"y" Subscript, 2 , Baseliney2
r3c3:
r4c3:
18
Rótulo oculto: "a" Subscript, 1 , Baseline equals left parenthesis, "E" Subscript, 1 , Baseline , "E" Subscript, 2 , Baseline , right parenthesisa1=E1,E2
Expresión 21: arc tangent left parenthesis, "E" Subscript, 2 , Baseline , "E" Subscript, 1 , Baseline , right parenthesisarctanE2,E1
equals=
72.0 9 1 8 7 0 2 2 6 772.0918702267
21
this is the elbow angle (relative to robot frame, not shoulder)
22
Expresión 23: arc tangent left parenthesis, left parenthesis, "c" Subscript, 2 , Baseline . "y" minus "a" Subscript, 1 , Baseline . "y" , right parenthesis , left parenthesis, "c" Subscript, 2 , Baseline . "x" minus "a" Subscript, 1 , Baseline . "x" , right parenthesis , right parenthesisarctanc2.y−a1.y,c2.x−a1.x
equals=
151.7 9 1 9 9 9 2 2 2151.791999222
23
Rótulo oculto: "a" Subscript, 2 , Baseline equals left parenthesis, "E" Subscript, 3 , Baseline , "E" Subscript, 4 , Baseline , right parenthesisa2=E3,E4
Expresión 25: arc tangent left parenthesis, "E" Subscript, 4 , Baseline , "E" Subscript, 3 , Baseline , right parenthesisarctanE4,E3
equals=
132.8 3 7 9 9 5 4 5 7132.837995457
25
Expresión 26: arc tangent left parenthesis, left parenthesis, "c" Subscript, 2 , Baseline . "y" minus "a" Subscript, 2 , Baseline . "y" , right parenthesis , left parenthesis, "c" Subscript, 2 , Baseline . "x" minus "a" Subscript, 2 , Baseline . "x" , right parenthesis , right parenthesisarctanc2.y−a2.y,c2.x−a2.x
