Robot Modeling and Kinematics Errata R. Manseur. List of errors and typos reported as of 4/1/2007:

Transcription

1 Robot Modelng and Knematcs Errata R. Manseur. Lst of errors and typos reported as of 4//7:. Fle CF4.wrl mentoned on page 45 s not on the CD. Fle ZYZ_Sm.wrl mentoned on page 67 s not on the CD. 3. Pg. 43. End of frst paragraph below Eq..3, correct v = [4.767,.] T. 4. Pg. 46. Example., Use F = {O, x, y, z }. 5. Pg. 5. Lne below Eq..33. Z coordnate of Q s Page 57. Equatons.57 to.59 are wrong. Correct equatons are: R ( α) R ( β) R ( γ) F F F F. (.57) z y z 3 R= R = R R R = Rz Ry Rz 3 3 ( α) ( β) ( γ) cα sα c s β β cγ sγ = s c α α sγ cγ sβ c β (.58) c c c s s c c s s c c s R = s c c + c s s c s + c c s s sβ cγ sβ sγ cβ α β γ α γ α β γ α γ α β α β γ α γ α β γ α γ α β. (.59) 7. Page 59. Lne above Fgure.9. Correct φ = angle( x, ) and ψ = angle( z, u) r + r + r33 8. Page 6. Bottom of page: c θ =, u xy 9. Page 6: r + r + r33 θ = cos ( ). (.74). Page 69. Example.5. nd lne. Refer to Fgure.5.. Page 74. Exercse 7. Refer to Example.5.. Page 78. Last lne should be See fle: CHAPTERS\CHAPTER3\VRML3\C3F.wrl 3. Page 87. Second lne below Fgure 3.8. CHAPTERS\CHAPTER3\VRML3\C3F8.wrl 4. Page 9. Last paragraph, nd and thrd lnes. Correct (d, a, α, θ) = (,, -45, 6 ) for consstency wth Fg Page 9. Fgure 3.. Boxes 4 and 5 and ther captons should be swtched. 6. Page 9. Pont A s mssng n Fgure 3.. It should located at the center base of the robot.

2 Last part of tem. Correct α = 9. Table at the bottom of the page, d should be r3. 7. Page 93. In Fgure 3.3, Frames F and F 3 should have ther z-axs pontng down. 8. Page 95. End of top paragraph. θ 3 = -9. Second CD reference. Should be CHAPTERS\CHAPTER3\VRML3\C3F6.wrl. 9. Page 96. CD reference should be CHAPTERS\CHAPTER3\VRML3\C3F7.wrl. Page 97. Table 3.4. Should be θ = -θ 3 and θ 4 = π-θ.. Page 99. Table 3.6 has several errors. It should be: Table 3.6 DH Parameters of Converse Manpulator for Example 3.4 Lnk d a α θ Page. Sentence above Table 3.7. Should state d and d 3 are arbtrary, d must be zero. Parameters α and α must be 9 but α 3 s arbtrary. In Table 3.7. the value of α 3 may be set to zero. 3. Page. Fgure 3.3. Frame F should be moved up to the same orgn as F. 4. page 9. Change PUMAMod.exe to PUMAsm.exe. (Top of page and capton of Fg. 3.3) 5. Page 3. Exercse. Part b. Delete s drawn n ts home poston and ts 6. Pg.. Eq. 4.. Matrx A 3, Elements (,) = +c 3 and (,) = -s 3. Parameter d 3 s zero. c3 s3 a3c3 s3 c3 a3s 3 Matrx A3 should be A3 = Equatons 4. should be corrected to be ccc 3+ ss 3 cc s3+ sc 3 cs a3( ccc 3+ ss 3) + acc + ac + ds scc 3cs 3 sc s3cc 3 ss a3( scc 3 cs 3) + asc + as dc P= T3 = AAA3 = sc 3 ss 3 c asc as + d 7. Pg.. Equatons 4. to 4.4. Delete the term before last. Eqs. should be: p = a ( cc c + ss ) + a cc + ac + d s ; (4.) x p = a ( sc c cs ) + a sc + as d c ; (4.3) y z p = asc + as + d. (4.4) 3 3 a+ a + a3 Equaton 4.6 should be p = d. (4.6) d

3 8. Pg. 3. Eq. 4.9 needs mnus sgns n last column of matrx. Should be: c s a R R p γ s γc σ dσ A j = A = = σ s σc γ dγ Thrd lne above Eq Should refer to R -. (4.9) 9. Pg. 5. Eq. 4.4 should be p= R(...( Rn( Rn pn + pn ) + pn)...) + p Eq. 4.4: correct subscrpts and 3 on the poston vectors. Correct equaton s: p= R( R( R3( R4( R5p6 + p5) + p4) + p3) + p) + p 3. Pg. 6. Add parentheses n Eqs to In Eq. 4.5, replace x by z rght before closng paren. In Eq change t x to t z. 3. Pg. 3. Lne after Eq change end-effector frame to frame F Pg. 3. Eqs and Element (,3) should be s 4 s 5 n all relevant matrces. 8. Pg. 34. Secton 4.9, lne 4, Refer to Fgure Pg. 36. Eq A 4 (,) = s Pg. 43. nd lne above Eq Correct typo on product 3. Pg. 43. Eq Matrx has three sgn errors. Correct matrx s: cc + ss + γ+ cs + γ+ sc + σ+ cs + + σ+ sc + a+ cc + a+ ss + + ac sc + + cs + γ+ cc + γ+ ss + σ+ ss + σ+ cc + a+ sc + + a+ cs + + ac AA + = σ+ γ+ d+ + d 3. Pg. 48. Exercse 6. Part b. Should be Four A-matrces Part d: Second lne. Fourth jont value s mssng. It s -6 Next lne. Fourth jont value s 9. Exercse 7. Insert descrbed after the fourth word....robot s descrbed by Page 57. Md page. Left bracket s mssng for matrx R. 34. Pg. 59. Frst lne, mssng sgn: θ 3 = Pg. 67, Eq. 5.49, Frst element of vector should be σ 6 s 6. Second lne of secton , Refer to Fgure 5.7, not Fg Lne before last, bold vector p. 36. Pg. 68. Thrd lne below Eq. 5.58, bold vector t. 37. Pg. 7. Eq should be θ = atan( ± a + b d, d) atan( b, a). Eq Should be: = d =± d d θ = ± s c ( s ) atan[ (, ] b b b 38. pg. 73. Lne followng Eq Refer to Eq. D.36

4 Lne followng Eq. 5.75: ( p a a3 d3 d4) c = a 36. Pg. 74. Lne after Eq Refer to D.36, not D.35. Thrd lne after Eq. 5.78b, change 4.73j to 4.73g. Second lne after Eq change θ 4 + θ 5 to θ 4 + θ Pg. 75. Lne above Eq Correct b=d 4. Lne after Eq value of e must be changed to e = c 3 t x + c s 3 t z. 38. Pg. 76. Ffth lne below Eq refer to Example Pg. 8. Exercse. Matrx P element (,) should be s c Pg 87. Eq. 6.. Should be: Rp 3 z+ p z= Rp z-rp z Eq Should be Rzp R zp = R p z+ p z 3 4. Pg. 88. Eq. 6. Should be c γs σs ac ac R p z+ p z = s γc σc as as + = dγ+ d σ γ d d 4. Pg. 89. Eq Sgn error. Should be σ t x s - σ t y c + σ σ 3 c 3 = e Eq Change t z to p z n term between parentheses. 43. Pg. 9. Eq. 6.36: Sgn error. Should be: ( a+ a3c3) s ( σ d3 γa3s3) c= γpx s+ γpyc+ σ( pz d) 44. Pg. 9. Table 6. s ncorrect. The values of the a parameter are lsted under column d and vce versa. 45. Pg. 93. Eqs and 6.46 are ncomplete. The last w 4 n Eq dd not prnt and the second lne n Eq s mssng. Correct equatons are: d = σσ a[ a ( a w + σ w ) + σσ a d w ] + σ a [ σ ( a + σ d ) + σ a ] w (6.45) H or n expanded form: d = σσ aa a w + σσσ aa w + σσ σaa d w + σ σ a a w H σ3a3σσ d w4 + σ3σaa3 w4 46. Pg. 94. Table 6.. Entres 5 and 7 are ncomplete. A w 4 s mssng at the very end. 47. Pg. 96. Fgure 6.. Cases 4 and 6 are wrongly numbered 3 and 5 respectvely. 48. Pg. 97. Eq Second term of equaton starts wth e 4. Correct Equaton s: y x 3 4 y x 3 (6.46) {[ e ( at s + at c )]/ a σ } + {[ e ( a p s + a p c )]/ a a } =. (6.55) Eq should be: t y = σ 3 c 3 ; (6.57) 49. Pg. 98. Lne below Equaton 6.6. Should refer to Eq. D.43. (not D.39) 5. Pg.. Second lne after Eq Msprnt. Should be θ =-4.

5 Eqs and 6.74 : Second mnus sgn must be replaced by an arrow. Eqs. are: θ = and θ = 4 θ 3 = = (6.73) θ = 35 and θ = 4 θ 3 = = (6.74) 5. Pg.. Lne above Eq Should refer to D.4 (not D.39) 5. Pg. 3. Frst lne. Should be (θ, θ 3 ) Second lne below Equaton 6.89 should be: form of Equaton D.39 wth a = a, b = σ d 3, c = p x s + p y c, and d = p x c + p y s a. 5. Pg. 7. Exercse 5. Part b. Second lne. Change. m to. m 5. Pg.. Eq. 7.5 should be: Q= A P. (7.5) 5. Pg. 3. Secton 7., second lne. Refer to Eq. 7. or 7.4 (not 7.4 or 7.8). 53. Pg. 4. Eq Mssng mnus sgn n top rght expresson of matrx, should be: -R - p Eq. 7.9 should be q R p R p R = (p p ) = (Replace q by p ) 5. Pg. 5. Eq Frst and fourth terms n equaton need to be corrected. Correct equaton s ul ql= γ 4d4 + a3σ4 s4 d3σ3σ4c4 + d3γ3γ4 + σ4 s4( ac3+ σd s3) σ4c4( σdγ3c3 aγ3s3+ γdσ3) + γ4( aσ3s3 σdσ3c3+ γdγ3). Eq. 7.7: Bold vector t. 53. Pg. 6. Eq top vector value should be p x c +p y s -a. Eq Add +t z p z to the rght sde. Eq. s: u q= tx( px ac) + ty( py as) + tz pz Eq. 7.3 should be changed to q q= p p + a ( pxa c + pyas ). Eq Element (,3) of matrx should be a 3 σ 4 Element (3,3) should be -σ 3 a Pg. 7. Eq Second vector element should be γ 3 γ 4 -γ u z Item 3. Second lne. Refer to Equatons 6.35 and 6.36 (not 6.4 and 6.35) Equaton Rght vector. Second element. Sgn error. Change to γ q s + γ q c + σ ( q d ) x y z 55. Pg. 3. Eq has a sgn error. It should be e = ( σtx) s+ ( σty) c γtz + γ4 = 56. Pg. 8 Exercse 5, Part b. Change matrx P values to

6 P = Pg. 3. Lne below Eq. 8.. Insert be between can and manpulated. 58. Pg. 35. Eq. 8.8 has a sgn error. It should be: ( a4+ a5c5) s4 ( σ 4d5 γ4a5s5) c4= γ3qx s3+ γ3qyc3+ σ3( qz d3) 59. Pg. 37. Eq. 8.6 and Eq Second term s ncorrect. Eq. 8.6 should be ux = ( cc γss ) tx + ( sc + γcs ) ty + σstz Eq. 8.9 should be: qx = ( cc γss ) px + ( sc + γcs ) py + σspz ac a 6. Pg. 38. Eq Thrd lne, second mnus sgn s wrong. Change to +. Eq Frst lne. Fourth term on the rght. Insert γ 4 between d 4 and γ 5. Thrd lne, mddle term should be -σ 3 d 3 σ 4 c 4 6. Pg. 4. Eq Matrx has wrong ndexes. Correct Equaton s f f θ θ θ θ f ( θ, θ ) θ = θ new f f f ( θ, θ ) θ θ Second lne after Eq. 8.47, same matrx correcton s needed. Eq Rght sde numerator. Mssng ndex. Change θ to θ 6. Pg. 43. Eq Top element of vector, mddle term should be +s c t x Eq Top element of vector, second term should be +s c p y 63. Pg. 44. Eq Sgn error. Equaton should be ( a4+ a5c5) s4 d5 c4= qz d3 Eq Second lne, second term, delete σ Pg. 56. Bottom lne. Refer to equatons D.8 and D.9 (not D7 and D.8). 65. Pg. 6. Exercse 4. Change Matrx 3 P 6 to P6 = Exercse 6. Part b. Change matrx P to:

7 P = Exercse 7. Part a. Change pose matrx element. to. 66. Pg 66. Frst lne angles should be noted (α, β, γ). 67. Pg 67. Eqs., 9.6 and 9.8. Dots are mssng on q. 68. Pg. 7. Fgure 9.. Vector ω should have a subscrpt: ω Equaton 9.8. Last vector should be p -,n. Eq dot s mssng on θ. 69. Pg. 7. Eq. 9.. subscrpt on last vector element should be n (not 3). 7. Pg. 7. Second lne above Eq Refer to Fgure 9.3. Eqs. 9.7 and 9.8. A dot s needed on all the θ varables. 7. Pg. 77. Eq dot are mssng on all θ. 7. Pg. 78. Eq Decmal pont s mssng on second element of vector V (-.5) Mnus sgn s mssng on thrd element of vector ω. (-.4) Eqs. 9.5 and Dots are mssng on all q vectors and elements. 73. Pg. 8. Eq end of equaton s mssng 5 ω 6. Eq Dots are mssng on all θ. Eq Refer to Eq (not 4.35). 6. Pg. 8. Eq J vl (3,3) = a 3 c 3 +d 4 s Pg. 8. Eq Dots mssng on q vector 6. Pg. 87. Eq In second matrx, R x T (,) =. not. 63. Pg. 88. Eq Matrx elements Q(,) and Q(,) are ncorrect; They should be: ( s & βα & γ) ( s c & γ βα + c & γβ) ωz ω y Q = ( s & βα & γ) ( cγc & βα + s & γβ) = ωz ωx ( sc γ βα + cγβ) ( cc γ βα + sγβ) ωy ωx & & & & Eqs and Elements of vector ω should not be bold. Example 9.5. Second lne, The RPY angles should be (6, -3, ). 64. Pg. 89. Lne above Eq. 9.. Mssng dot on θ. 65. Pg. 9. Eq Element (,) of matrx should be s. Eq Last two vectors n cross product are duplcated and must be deleted. 66. Pg. 94. Exercse. Frst paragraph. Replace the two lnes rght before the matrx J by jonts are all movng at the same rate of.3 rd/s. Replace the lne mmedately after matrx J (last lne of exercse) by Compute the end-effector twst vector V. 67. Pg. 96. Exercse 7. Part a. θ, θ, θ3 must be dotted. Exercse 8. Part b. Begnnng of second lne. Mssng closng bracket.

8 Part e. Change the word speeds to rates. 68. Pg. 33. Lne before Eq..7. Refer to Example 9.4 (not 9.5). 69. Pg. 3. Eq..3. J(,) = (not -.7) 7. Pg. 3. Eq..3. Matrx has wrong numercal values. Should be: J + = Pg. 35. Exercse 7-d, nd lne, change ω to dq/dt 7. Pg. 34. Eq. D.4. Should be tan(α) = a / b and cot(α) = b / a. 73. Pg. 34. Eq. D.7 should be sn(α + β) = sn(α) cos(β) + cos(α) sn(β). 74. Pg Eq. D.37. Mddle value of α should be atan(-b, -a) f sn β < Eq. D.38. Result should be β (not α) Eq. D.4. Left sde of equaton should be a cos(α + β) + b cos(α) = c a sn(α + β) + b sn(α) = d