Expression 25: "x" equals 0 left brace, "y" greater than or equal to 0 , right bracex=0y≥0
25
This an example lower boundary box
26
Expression 27: "y" equals "r" left brace, "x" greater than or equal to 0 , right brace left brace, "x" less than or equal to "l" Subscript, 2 , Baseline minus "l" Subscript, 1 , Baseline , right bracey=rx≥0x≤l2−l1
27
Expression 28: "x" equals "r" left brace, "y" greater than or equal to 0 , right brace left brace, "y" less than or equal to "l" Subscript, 2 , Baseline minus "l" Subscript, 1 , Baseline , right bracex=ry≥0y≤l2−l1
28
For even more simplicity, we will cut out the lower x range so that we don't have a cutout near the base. Alternatively, you can make the boundary horizontal matching the top of the above box if you need to go up to the origin
29
Expression 30: "x" Subscript, 1 , Baseline equals "r" left brace, "y" greater than or equal to 0 , right brace left brace, "y" less than or equal to StartRoot, left parenthesis, "l" Subscript, 2 , Baseline plus "l" Subscript, 1 , Baseline , right parenthesis squared minus left parenthesis, "l" Subscript, 2 , Baseline minus "l" Subscript, 1 , Baseline , right parenthesis squared , EndRoot , right bracex1=ry≥0y≤l2+l12−l2−l12
30
MOVE ME: left parenthesis, "a" , "f" left parenthesis, "a" , right parenthesis , right parenthesisa,fa
Label:
equals=
left parenthesis, 13.8 , 8.0 9 6 9 1 2 9 9 , right parenthesis13.8,8.09691299
Expression 33: "y" less than or equal to "f" left parenthesis, "a" , right parenthesis left brace, "x" greater than or equal to "l" Subscript, 2 , Baseline minus "l" Subscript, 1 , Baseline , right brace left brace, "x" less than or equal to "a" , right brace left brace, "y" greater than or equal to 0 , right bracey≤fax≥l2−l1x≤ay≥0
33
Expression 34: "x" less than or equal to "a" left brace, "y" greater than or equal to 0 , right brace left brace, "y" less than or equal to "f" left parenthesis, "a" , right parenthesis , right brace left brace, "x" greater than or equal to "r" , right bracex≤ay≥0y≤fax≥r
34
CALCULATING ARM ANGLES
35
GRIPPER POINT: left parenthesis, "p" Subscript, 1 , Baseline , "p" Subscript, 2 , Baseline , right parenthesisp1,p2
Label:
equals=
left parenthesis, 10 , 5.3 7 , right parenthesis10,5.37
Expression 41: "h" equals "p" squared plus "p" squaredh=p21+p22
equals=
128.8 3 6 9128.8369
41
Expression 42: "q" Subscript, 2 , Baseline equals cosine to the negative 1st power left parenthesis, StartFraction, left parenthesis, left parenthesis, "h" , right parenthesis minus "l" squared minus "l" squared , right parenthesis Over 2 times "l" Subscript, 1 , Baseline times "l" Subscript, 2 , Baseline , EndFraction , right parenthesisq2=cos−1h−l21−l222·l1·l2
equals=
1.6 3 0 5 2 4 3 3 3 0 91.63052433309
42
Expression 43: "q" Subscript, 1 , Baseline equals arc tangent left parenthesis, "p" Subscript, 2 , Baseline , "p" Subscript, 1 , Baseline , right parenthesis plus arc tangent left parenthesis, "l" Subscript, 2 , Baseline sin left parenthesis, "q" Subscript, 2 , Baseline , right parenthesis , "l" Subscript, 1 , Baseline plus "l" Subscript, 2 , Baseline cos left parenthesis, "q" Subscript, 2 , Baseline , right parenthesis , right parenthesisq1=arctanp2,p1+arctanl2sinq2,l1+l2cosq2
equals=
1.5 6 7 4 8 5 8 7 8 2 41.56748587824
43
"x" Subscript, 3 , Baselinex3
"y" Subscript, 3 , Baseliney3
00
00
r1c3:
"A" Subscript, "x" , BaselineAx
"A" Subscript, "y" , BaselineAy
r2c3:
r3c3:
44
"x" Subscript, 4 , Baselinex4
"y" Subscript, 4 , Baseliney4
"A" Subscript, "x" , Baseline plus 0Ax+0
"A" Subscript, "y" , Baseline plus 0Ay+0
r1c3:
"A" Subscript, "x" , Baseline plus "B" Subscript, "x" , BaselineAx+Bx
"A" Subscript, "y" , Baseline plus "B" Subscript, "y" , BaselineAy+By
r2c3:
r3c3:
45
Expression 46: "B" Subscript, "x" , Baseline equals "l" Subscript, 2 , Baseline cosine left parenthesis, "q" Subscript, 1 , Baseline minus "q" Subscript, 2 , Baseline , right parenthesisBx=l2cosq1−q2
equals=
9.9 8 0 1 3 7 3 4 4 9 59.98013734495
46
Expression 47: "B" Subscript, "y" , Baseline equals "l" Subscript, 2 , Baseline sine left parenthesis, "q" Subscript, 1 , Baseline minus "q" Subscript, 2 , Baseline , right parenthesisBy=l2sinq1−q2
equals=
negative 0.6 2 9 9 6 7 1 2 2 8 2 1−0.629967122821
47
Expression 48: "A" Subscript, "x" , Baseline equals "l" Subscript, 1 , Baseline cosine left parenthesis, "q" Subscript, 1 , Baseline , right parenthesisAx=l1cosq1
equals=
0.0 1 9 8 6 2 6 5 5 0 4 50.019862655045
48
Expression 49: "A" Subscript, "y" , Baseline equals "l" Subscript, 1 , Baseline sine left parenthesis, "q" Subscript, 1 , Baseline , right parenthesisAy=l1sinq1
