screws-overview.ps

关于旋量理论的Matlab描述和相应的源码实例

00FFF0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF000
0000FFF0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF0000000FFF0
000000FFF0000000FFF0000000FFF0000000FFF0000000FFF001F000FFF001F000FFF001F000FF
F001F000FFF001F000FFF001F000FFF001F000FFF001F000FFF001F000FFF003F0007FF803E000
7FF807E0003FFC07C0001FFE1F80000FFFFF800007FFFF000001FFFC0000003FF00024427EC12E
>I<007FE000003FF000FFFFE0007FFFF000FFFFE0007FFFF000FFFFE0007FFFF000FFFFE0007F
FFF000FFFFE0007FFFF00003FFE00001FFF00001FFE00000FFF00001FFE00000FFF00001FFE000
00FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE0
0000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FF
E00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001
FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF000
01FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00000FFF00001FFE00001FFF0
0001FFE00001FFF00001FFE00001FFF00001FFE00003FFF00001FFE00007FFF00000FFE0000F7F
F00000FFF0001F7FF000007FF0003E7FF800003FFE01FC7FFFE0001FFFFFF87FFFE0000FFFFFF0
7FFFE00003FFFFC07FFFE000003FFE007FFFE03B2E7CAD42>I<FFFFFF07FFFFE007FFFEFFFFFF
07FFFFE007FFFEFFFFFF07FFFFE007FFFEFFFFFF07FFFFE007FFFEFFFFFF07FFFFE007FFFE03FF
C0001FFC00003FC003FFE0000FFC00001F8001FFE0000FFC00001F0001FFE0000FFE00001F0001
FFF00007FE00003F0000FFF0000FFF00003E0000FFF8000FFF00007E00007FF8000FFF00007C00
007FF8001FFF80007C00003FFC001FFF8000F800003FFC003FFFC000F800003FFE003EFFC001F8
00001FFE003EFFC001F000001FFE007EFFE003F000000FFF007C7FE003E000000FFF00FC7FF003
E000000FFF80F83FF007E0000007FF80F83FF007C0000007FF81F83FF80FC0000003FFC1F01FF8
0F80000003FFC3F01FFC0F80000003FFE3E00FFC1F80000001FFE3E00FFC1F00000001FFE7E00F
FE3F00000000FFF7C007FE3E00000000FFFFC007FF3E00000000FFFF8003FF7E000000007FFF80
03FF7C000000007FFF8003FFFC000000003FFF0001FFF8000000003FFF0001FFF8000000003FFE
0000FFF8000000001FFE0000FFF0000000001FFE0000FFF0000000000FFC00007FE0000000000F
FC00007FE0000000000FF800003FE00000000007F800003FC00000000007F800003FC000000000
03F000001F800000000001E000000F0000004F2E7DAD56>119 D E /Fl
8 121 df<00000001F80000000000000001F80000000000000003FC0000000000000003FC0000
000000000007FE0000000000000007FE0000000000000007FE000000000000000FFF0000000000
00000FFF000000000000001FFF800000000000001FFF800000000000001FFF800000000000003F
FFC00000000000003FFFC00000000000007FFFE00000000000007FFFE00000000000007FFFE000
0000000000FFFFF0000000000000F9FFF0000000000001F9FFF8000000000001F0FFF800000000
0001F0FFF8000000000003F0FFFC000000000003E07FFC000000000007E07FFE000000000007C0
3FFE00000000000FC03FFF00000000000F803FFF00000000000F801FFF00000000001F801FFF80
000000001F000FFF80000000003F000FFFC0000000003E000FFFC0000000003E0007FFC0000000
007E0007FFE0000000007C0003FFE000000000FC0003FFF000000000F80003FFF000000000F800
01FFF000000001FFFFFFFFF800000001FFFFFFFFF800000003FFFFFFFFFC00000003FFFFFFFFFC
00000003E000007FFC00000007E000007FFE00000007C000003FFE0000000FC000003FFF000000
0F8000001FFF0000001F8000001FFF8000001F0000001FFF8000001F0000000FFF8000003F0000
000FFFC000003E00000007FFC000007E00000007FFE00000FF00000007FFE000FFFFFC0007FFFF
FFF0FFFFFC0007FFFFFFF0FFFFFC0007FFFFFFF0FFFFFC0007FFFFFFF0443B7DBA4B>65
D<FFFFFFFFFFC00000FFFFFFFFFFFC0000FFFFFFFFFFFF8000FFFFFFFFFFFFC000007FF80001FF
F000007FF80000FFF800007FF800007FFC00007FF800003FFE00007FF800001FFE00007FF80000
1FFF00007FF800001FFF00007FF800000FFF80007FF800000FFF80007FF800000FFF80007FF800
000FFF80007FF800000FFF80007FF800000FFF80007FF800000FFF80007FF800000FFF00007FF8
00001FFF00007FF800001FFF00007FF800003FFE00007FF800003FFC00007FF800007FF800007F
F80001FFF000007FF80003FFE000007FFFFFFFFF8000007FFFFFFFFE0000007FFFFFFFFE000000
7FFFFFFFFFC000007FF80001FFF000007FF800007FFC00007FF800001FFE00007FF800000FFF00
007FF800000FFF80007FF8000007FFC0007FF8000007FFC0007FF8000003FFE0007FF8000003FF
E0007FF8000003FFF0007FF8000003FFF0007FF8000003FFF0007FF8000003FFF0007FF8000003
FFF0007FF8000003FFF0007FF8000003FFF0007FF8000003FFF0007FF8000003FFE0007FF80000
03FFE0007FF8000007FFC0007FF800000FFFC0007FF800000FFF80007FF800001FFF00007FF800
007FFE00007FF80001FFFC00FFFFFFFFFFFFF800FFFFFFFFFFFFE000FFFFFFFFFFFF8000FFFFFF
FFFFF800003C3B7CBA46>I<000000003FC00000003FFFC00000003FFFC00000003FFFC0000000
3FFFC000000001FFC000000000FFC000000000FFC000000000FFC000000000FFC000000000FFC0
00000000FFC000000000FFC000000000FFC000000000FFC000000000FFC000000000FFC0000000
00FFC000000000FFC000000000FFC000000000FFC000000000FFC00001FF80FFC0000FFFF0FFC0
003FFFFCFFC000FFFFFFFFC003FFC03FFFC007FF0007FFC00FFE0003FFC01FFC0001FFC01FF800
00FFC03FF00000FFC03FF00000FFC07FF00000FFC07FE00000FFC07FE00000FFC0FFE00000FFC0
FFE00000FFC0FFE00000FFC0FFE00000FFC0FFE00000FFC0FFE00000FFC0FFE00000FFC0FFE000
00FFC0FFE00000FFC0FFE00000FFC07FE00000FFC07FE00000FFC07FF00000FFC03FF00000FFC0
3FF00000FFC01FF80001FFC01FF80003FFC00FFC0007FFC007FE001FFFC003FFC07FFFE001FFFF
FEFFFF007FFFF8FFFF001FFFE0FFFF0003FF00FFFF303C7DBB37>100 D<0001FFC000001FFFF8
00007FFFFE0000FFFFFF0003FFC1FF8007FE003FC00FFC001FE00FF8000FF01FF8000FF03FF000
07F83FF00007F87FF00007F87FE00007FC7FE00003FCFFE00003FCFFFFFFFFFCFFFFFFFFFCFFFF
FFFFFCFFFFFFFFFCFFE0000000FFE0000000FFE0000000FFE0000000FFE00000007FE00000007F
F00000007FF00000003FF000003C3FF800003C1FF800007C0FFC00007807FE0001F803FF8003F0
01FFF01FE000FFFFFFC0003FFFFF00000FFFFC000000FFE00026267DA52D>I<01F80003FC0007
FE000FFF001FFF801FFF801FFF801FFF801FFF801FFF800FFF0007FE0003FC0001F80000000000
000000000000000000000000000000000000000000000000FF00FFFF00FFFF00FFFF00FFFF0007
FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003
FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003FF0003
FF0003FF0003FF00FFFFF8FFFFF8FFFFF8FFFFF8153D7DBC1B>105 D<00FE007FC000FFFE03FF
F800FFFE0FFFFE00FFFE1FFFFF00FFFE3F03FF0007FE7C01FF8003FEF001FF8003FFE000FFC003
FFC000FFC003FFC000FFC003FF8000FFC003FF8000FFC003FF0000FFC003FF0000FFC003FF0000
FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003
FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000
FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC003FF0000FFC0FF
FFFC3FFFFFFFFFFC3FFFFFFFFFFC3FFFFFFFFFFC3FFFFF30267CA537>110
D<00FF00FFC000FFFF07FFF800FFFF3FFFFE00FFFFFFFFFF80FFFFFE03FFC007FFF000FFE003FF
C0007FF003FF80003FF803FF00003FF803FF00001FFC03FF00001FFC03FF00000FFE03FF00000F
FE03FF00000FFE03FF000007FF03FF000007FF03FF000007FF03FF000007FF03FF000007FF03FF
000007FF03FF000007FF03FF000007FF03FF000007FF03FF000007FF03FF00000FFE03FF00000F
FE03FF00000FFE03FF00001FFC03FF00001FFC03FF80003FF803FFC0007FF803FFE000FFF003FF
F001FFE003FFFC07FFC003FF7FFFFF0003FF3FFFFC0003FF0FFFF00003FF01FF800003FF000000
0003FF0000000003FF0000000003FF0000000003FF0000000003FF0000000003FF0000000003FF
0000000003FF0000000003FF0000000003FF0000000003FF0000000003FF00000000FFFFFC0000
00FFFFFC000000FFFFFC000000FFFFFC00000030377DA537>112 D<FFFFF007FFFCFFFFF007FF
FCFFFFF007FFFCFFFFF007FFFC01FF8000FE0000FFC000F80000FFE001F000007FF003E000003F
F007C000001FF80FC000000FFC1F8000000FFE1F00000007FF3E00000003FFFC00000001FFF800
000000FFF0000000007FE0000000007FF0000000003FF8000000001FF8000000001FFC00000000
3FFE000000007FFF00000000FBFF80000001F9FF80000003F0FFC0000003E07FE0000007C07FF0
00000F803FF800001F001FFC00003E000FFC00007C0007FE0000FC0003FF0001FC0003FF80FFFF
801FFFFEFFFF801FFFFEFFFF801FFFFEFFFF801FFFFE2F267EA534>120
D E end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 300
TeXDict begin
%%PaperSize: Letter

%%EndSetup
%%Page: 435 1
bop 319 629 a Fl(App)s(endix)34 b(B)319 839 y Fk(A)39 b(Mathematica)h(P)m(ac)
m(k)-7 b(age)319 963 y(for)40 b(Screw)f(Calculus)319 1181 y
Fj(This)19 b(app)q(endix)g(con)o(tains)f(a)h(brief)g(description)g(of)g(a)f
(Mathematica)g(pac)o(k)n(age,)319 1231 y Fi(Screws.m)p Fj(,)e(whic)o(h)h
(facilitates)f(the)i(use)g(of)f(screws,)i(t)o(wists,)f(and)f(wrenc)o(hes)j
(for)319 1280 y(analyzing)15 b(rob)q(ot)h(kinematics.)23 b(The)17
b Fi(Screws)e Fj(pac)o(k)n(age)g(implemen)o(ts)f(all)h(of)h(the)319
1330 y(functions)g(describ)q(ed)i(in)e(Chapter)h(2)e(and,)i(when)f(com)o
(bined)f(with)h(the)h(supple-)319 1380 y(men)o(tary)d(pac)o(k)n(age)g
Fi(RobotLinks.m)p Fj(,)e(allo)o(ws)i(sym)o(b)q(olic)f(and)h(n)o(umerical)f
(compu-)319 1430 y(tation)c(of)h(the)h(kinematics)d(of)i(op)q(en-c)o(hain)g
(rob)q(ot)g(manipulators)e(as)i(w)o(ell)g(as)g(man)o(y)319
1480 y(other)k(functions.)k(The)d(Mathematica)d(program)g(itself)i(is)g
(describ)q(ed)h(in)f([121)o(].)381 1531 y(The)20 b Fi(Screws)e
Fj(pac)o(k)n(age)h(is)h(a)o(v)n(ailable)d(via)i(anon)o(ymous)f(ftp)h(from)f
(the)i(host)319 1581 y Fi(avalon.caltech.e)o(du)14 b Fj(and)j(ma)o(y)e(b)q(e)
j(used)g(free)g(of)e(c)o(harge.)29 b(Do)q(cumen)o(tation)319
1631 y(and)18 b(installation)e(instructions)j(are)f(included)h(with)f(the)g
(source)i(co)q(de)f(for)f(the)319 1681 y(pac)o(k)n(age.)23
b(The)17 b Fi(Screws)d Fj(pac)o(k)n(age)i(w)o(as)f(written)i(b)o(y)e(R.)g
(Murra)o(y)h(and)g(S.)f(Sur)h(at)319 1730 y(the)11 b(California)e(Institute)i
(of)g(T)m(ec)o(hnology)m(.)k(All)10 b(corresp)q(ondence)k(concerning)e(the)
319 1780 y(soft)o(w)o(are)17 b(should)f(b)q(e)i(sen)o(t)g(to)e(via)h(e-mail)d
(to)j Fi([e-mail])o(tech.)o(edu)p Fj(.)319 1830 y(The)c(authors)h
(assume)f(no)g(resp)q(onsibilit)o(y)g(for)g(the)h(correctness)i(or)d(main)o
(tenance)319 1880 y(of)j(the)h Fi(Screws)f Fj(pac)o(k)n(age.)26
b(The)17 b(source)h(co)q(de)f(is)g(curren)o(tly)h(a)o(v)n(ailable)c
Fh(only)j Fj(via)319 1930 y(anon)o(ymous)12 b(ftp.)381 1981
y(The)19 b(remainder)g(of)f(this)h(app)q(endix)g(con)o(tains)f(a)h(brief)g
(description)g(of)g(the)319 2031 y Fi(Screws)d Fj(pac)o(k)n(age,)h
(describing)g(the)h(functions)f(whic)o(h)g(are)h(a)o(v)n(ailable)d(and)i
(their)319 2081 y(syn)o(tax.)30 b(Although)17 b(not)h(strictly)g(necessary)m
(,)i(some)d(familiarit)o(y)d(with)k(Mathe-)319 2131 y(matica)d(is)i(assumed.)
27 b(This)17 b(app)q(endix)g(can)g(also)f(b)q(e)i(used)g(as)f(a)g(guide)g
(for)f(im-)319 2181 y(plemen)o(ting)i(a)i(screw)h(calculus)f(pac)o(k)n(age)f
(in)h(other)g(sym)o(b)q(olic)e(and)i(n)o(umerical)319 2230
y(programmi)o(ng)11 b(languages.)319 2356 y Fg(Using)19 b(the)g(Screws)h(pac)
n(k)m(age)319 2436 y Fj(The)11 b Fi(Screws)e Fj(pac)o(k)n(age)h(implemen)o
(ts)f(screw)j(theory)f(in)f(3-dimensional)e(Euclidean)319 2485
y(space,)14 b Ff(R)474 2470 y Fe(3)490 2485 y Fj(.)k(It)13
b(uses)i(homogeneous)e(co)q(ordinates)i(to)e(represen)o(t)j(p)q(oin)o(ts,)e
(v)o(ectors,)944 2631 y(435)p eop
%%Page: 436 2
bop 319 200 a Fd(436)112 b(App)q(endix)15 b(B.)25 b(A)13 b(Mathematica)i(P)o
(ac)o(k)n(age)e(for)g(Screw)g(Calculus)319 316 y Fj(and)j(rigid)g(motions,)g
(making)e(it)j(easy)g(to)g(in)o(tegrate)g(in)o(to)f(other)i(Mathematica)319
366 y(pac)o(k)n(ages.)381 416 y(The)h Fi(Screws)e Fj(pac)o(k)n(age)h
(consists)h(of)f(t)o(w)o(o)g(groups)g(of)g(functions.)32 b(The)18
b(\014rst)319 466 y(group)g(op)q(erates)h(on)f(rotation)f(matrices)h(and)g
(implemen)o(ts)d(all)i(of)h(the)g(mathe-)319 516 y(matical)d(op)q(erations)j
(describ)q(ed)h(in)e(Section)h(2)g(of)f(Chapter)h(2.)29 b(The)18
b(follo)o(wing)319 565 y(functions)c(are)g(de\014ned)h(for)f(computing)e(in)h
Fc(S)r(O)q Fj(\(3\):)381 646 y Fb(\017)21 b Fi(AxisToSkew[w])423
696 y Fj(Generate)15 b(a)e(sk)o(ew-symmetric)g(matrix)f(giv)o(e)h(a)h(v)o
(ector)g Fi(w)e Fb(2)f Ff(R)1422 680 y Fe(3)1437 696 y Fj(.)381
777 y Fb(\017)21 b Fi(RotationAxis[R])423 827 y Fj(Calculate)13
b(the)i(axis)e(of)g(rotation)g(for)h(a)g(matrix)e Fi(R)f Fb(2)g
Fc(S)r(O)q Fj(\(3\).)381 909 y Fb(\017)21 b Fi(SkewExp[S,)e(theta])423
959 y Fj(Calculate)13 b(the)i(exp)q(onen)o(tial)f(of)g(a)f(sk)o(ew-symmetric)
g(matrix.)k(If)d Fi(theta)f Fj(is)423 1008 y(not)i(sp)q(eci\014ed,)j(it)d
(defaults)h(to)g(1.)23 b(If)16 b(the)g(\014rst)h(argumen)o(t)d(to)i
Fi(SkewExp)e Fj(is)423 1058 y(a)e(v)o(ector,)i Fi(SkewExp)e
Fj(\014rst)i(con)o(v)o(erts)g(it)e(to)h(a)g(sk)o(ew-symmetric)f(matrix)f(and)
423 1108 y(then)j(tak)o(es)g(its)g(exp)q(onen)o(tial.)381 1190
y Fb(\017)21 b Fi(SkewToAxis[S])423 1240 y Fj(Generates)15
b(a)e(v)o(ector)i(giv)o(en)f(a)f(sk)o(ew-symmetric)g(matrix.)319
1320 y(Limited)f(error)j(c)o(hec)o(king)f(is)g(used)h(to)f(insure)h(that)f
(the)g(argumen)o(ts)g(to)g(the)g(func-)319 1370 y(tions)f(are)i(in)e(the)i
(pr