MR Second Printing

Overall

There are a few places in the book where we have an italic T instead of a roman T for transpose, often where they are preceded by a negative (inverse) sign. These should be corrected. The ones we're aware of are listed below:

• Equation (5.4) p149
• Fifth line of p163
• p168 third line of Eq (5.27)
• Last line of p216
• p239: eq (8.21) and equation just above.
• p254: Eqs (8.75), (8.76), (8.78), (8.79), 8.80)
• pp256-7: several instances in Ch 8.6. Just after eq (8.87) (two times), four times in eq (8.88), just after (8.88), and (8.90) and (8.91).
• p272, in each of the two displayed equations in the 2nd bullet
• p491, second-to-last bullet, in each of the two displayed equations and the in-line equation just after.

Chapter 1

• p3, middle: Change "convenient way to calculate a lower bound on the dof" to "convenient way to calculate the dof"

Chapter 2

• Proposition 2.2, p16: "This formula holds only if all joint constraints are independent. If they are not independent then the formula provides a lower bound on the number of degrees of freedom." should be "This formula holds in "generic" cases, but it fails under certain configurations of the links and joints, such as when the joint constraints are not independent."

• Chapter 2.2.2, Example 2.3, p16: "Substituting" is misspelled.

• Eliminate two sentences on p19: "Grubler's formula provides ... are discussed in Chapter 7."

• Fifth bullet of Chapter 2.6 p32: Eliminate the last sentence "If the constraints enforced ... degrees of freedom."

Chapter 3

• In the caption of Figure 3.3 p53, $(0.5,1/{\sqrt {2}})$ should read $(1/2,{\sqrt {3}}/2)$, and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (-1/{\sqrt {2}},0.5)} should read Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (-{\sqrt {3}}/2,1/2)} .

• Under "Representing a configuration" in Chapter 3.3.1.2 p78 near the bottom, the text says "Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle T_{bc}=(R_{bc},p_{bc})} represents {b} relative to {c}" but it should say "represents {c} relative to {b}".
• There is a typo in the final matrix, $T_{ce}$, of Example 3.19, p82. The term Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 130/{\sqrt {2}}} should be Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 160/{\sqrt {2}}} .
• In the displayed equation just after Equation (3.76) p85, the left-hand side should be $[{\mathcal {V}}_{s}]$ (the brackets are missing).
• Near the end of Chapter 3.6 Software p97, the function "AxisAng" should be written "AxisAng6."
• Exercise 3.16(i) p103 asks for "the" Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \{q,{\hat {s}},h\}} representation but it should say "a" $\{q,{\hat {s}},h\}$ representation (since $q$ is not unique). Replace "the" with "a".

Chapter 4

• Example 4.1, last row of the table (screw axis for joint 3), middle of p122: The linear component Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle v_{i}} should be Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (0,-L_{2},0)} (the $-$ sign is missing).

Chapter 5

• Equation (5.7) p153: The the first two terms on the right-hand side of the equation should be $J_{s1}{\dot {\theta }}_{1}+J_{s2}(\theta ){\dot {\theta }}_{2}$.

• Exercise 5.2(b) p173: Change (a) to "Suppose that the last link must apply a wrench corresponding to a force of ..." (then continue as current, "5 N in the..."). In (b), change "the tip" to "the last link".

• Figure 5.15(b) p174: The circular arrow indicating the rotation of joint 3 is slightly misplaced.

• Exercise 5.11(a) p178: Change "What are the..." to "Is this motion possible? If so, what are the ..."

• Exercise 5.16 p180: change "PRRRRR" to "PRPRRR". Similarly, caption of Figure 5.26, p181, change "PRRRRR" to "PRPRRR."

• Exercise 5.25(b) p186: At the end of part (b), add the sentence "Comment on why it is usually preferred to use the body Jacobian instead of the space Jacobian for the manipulability ellipsoid."

Chapter 6

• Chapter 6.3, first sentence after Eq (6.7), p199: the matrices $T_{sd}^{-1}{\dot {T}}_{sd}$ and ${\dot {T}}_{sd}T_{sd}^{-1}$ are referred to as twists, but these are the se(3) matrix representations of the twists. Change the beginning of this sentence to "The matrix form $[{\mathcal {V}}_{d}(t)]$ of the desired twist is either $T_{sd}^{-1}(t){\dot {T}}_{sd}(t)$ (the matrix form of the body twist of the desired trajectory at time $t$) or ${\dot {T}}_{sd}(t)T_{sd}^{-1}(t)$ (the matrix form of the spatial twist), depending ..." and then complete the sentence as is.

Chapter 7

• FRANK CHECK: p218 displayed equation after (7.12): suggest replacing $\phi _{5}$ with Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \psi _{5}} in $q_{p}$ to be consistent with definition of $q_{a}$.

• Just below caption for Figure 7.8 p222: There is an extraneous dot.

Chapter 8

• Description of constrained dynamics (see conversation with Zack).

• In Equation (8.14) p236, ${\mathcal {K}}(\theta )$ should be replaced by Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\mathcal {K}}(\theta ,{\dot {\theta }})} .

• Figure 8.5 p244 says the volume of the rectangular parallelepiped is $abc$ but it should be $hlw$.

• End of first sentence after Eq (8.26) in Section 8.2.1 p244 should read "... columns of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_{bc}} correspond to the eigenvectors of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{I}_b} ." (The word "eigenvalues" should be replaced by "eigenvectors.")

• FRANK CHECK: Possible derivation error between equations (8.46) and (8.47), pp 249-50.

• p258: In the parenthetical text a few lines before Equation (8.95): "...there is an equality constraint..." should instead be "...there is also an inequality constraint..."

• Caption of Figure 8.10 p264: The operating region is light gray and the continuous operating region is dark gray (swap the two parenthetical statements).

• Exercise 8.6(a) p276: The expression Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{ad}_{J_i}(J_j)} has the indices switched; the correct expression is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{ad}_{J_j}(J_i)} .

• Exercise 8.7 p276: The expression should be written:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dot{M} = -\mathcal{A}^{\rm T} \mathcal{L}^{\rm T} \mathcal{W}^{\rm T} [\mbox{ad}_{\mathcal{A} \dot{\theta}}]^{\rm T} \mathcal{L}^{\rm T} \mathcal{GLA} - \mathcal{A}^{\rm T} \mathcal{L}^{\rm T} \mathcal{GL} [\mbox{ad}_{\mathcal{A} \dot{\theta}}] \mathcal{WLA} }

Chapter 10

• Equation (10.4) p332 should read Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u = F(q) - B \dot{q}} (the plus sign in the book should be a minus sign).

• p335, first line of chapter 10.6.4: should be $u=F(q)-B{\dot {q}}$ (plus sign should be a minus sign). In the second-to-last line on the same page, the plus sign should be a minus sign.

Chapter 11

• In the displayed equation after Equation (11.18) p360, the vector Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X_e(t)} is a six-vector. The bottom three elements are written correctly, but the top three elements, an angular velocity, are written instead in their 3x3 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle so(3)} form. Also, the term written Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R^{\text{T}}(d)} should be written Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R^{\text{T}}(t)} . So, replace the top three elements in the vector by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \omega_e(t)} , make the period after the equation a comma, and insert a line immediately following saying "where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\omega_e(t)] = \log(R^{\text{T}}(t) R_d(t))} ."

• In Equation (11.33) p366, the right-hand side should be zero, not $c$.

• Figure 11.24 p384, the Robonaut 2 series elastic actuator, fourth sentence of the caption: The words "outer" and "inner" should be switched, so the new sentence reads "The inner ring of hole mounts connects to the harmonic gearhead output, and the outer ring of hole mounts is the output of the SEA, connecting to the next link."

Chapter 12

• In Example 12.4 p404, the elements of the wrenches Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{F}_1, \mathcal{F}_2, \mathcal{F}_3} are erroneously written in the order Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (f_x,f_y,m_z)} ; they should be written in the order Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (m_z,f_x,f_y)} . In other words, change these to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-2,0,1)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1,-1,0)} , and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1,1,0)} , respectively.

• Caption of Figure 12.14 p412, second-to-last sentence: "rotation if possible" should be "rotation is possible."

Chapter 13

• Equation (13.29) p467: $y_{p}$ should be Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y_P} (P is capitalized).

• p469, first line just below the figure: get rid of the absolute value signs, so should be $v_d \neq 0$.

Appendix C

• Section C.3, Equation (C.5) p507: All four instances of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi_{i-1}} should be replaced by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi_i} .

• In Equation (C.12) p510, two instances of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_{i-1}} should be replaced by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_i} .

A partial list of errata contributors

Thanks to the following people who provided corrections, starting from the preliminary version of the book posted in October, 2016:

H. Andy Nam, Eric Lee, Yuchen Rao, Chainatee Tanakulrongson, Mengjiao Hong, Kevin Cheng, Jens Lundell, Elton Cheng, Michael Young, Jarvis Schultz, Logan Springgate, Sofya Akhmametyeva, Aykut Onol, Josh Holcomb, Yue Chen, Mark Shi, AJ Ibraheem, Yalun Wen, Seongjae Jeong, Josh Mehling, Felix Wang, Drew Warren, Chris Miller, Clemens Eppner, Zack Woodruff, Jian Shi, Jixiang Zhang, Shachar Liberman, Will Wu, Dirk Boysen, Awe Wang, Ville Kyrki, John Troll, Andrew Taylor, Nikhil Bakshi