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Erratum to ‘A Robust Forward-Displacement Analysis of Spherical Parallel Robots’ [Mech. Mach. Theory, 2009, 44(12), pp. 2204–2216]
Mechanism and Machine Theory 55 (2012) 122
Contents lists available at SciVerse ScienceDirect
Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt
Erratum
Erratum to ‘A Robust Forward-Displacement Analysis of Spherical Parallel Robots’ [Mech. Mach. Theory, 2009, 44(12), pp. 2204–2216] Shaoping Bai a, Michael R. Hansen b, Jorge Angeles c,⁎ a b c
Department of Mechanical and Manufacturing Engineering, Aalborg University, 9200 Aalborg, Denmark Department of Engineering, University of Agder, Norway Department of Mechanical Engineering, McGill University, Montreal, Canada
The authors would like to point out some typographical errors in the paper Bai, S., Hansen, M.R. and Angeles, J., “A Robust Forward-Displacement Analysis of Spherical Parallel Robots,” Mechanism and Machine Theory, 44(12), pp. 2204–2216, 2009. 1. In Eq. (12) a minus sign is missing. The equation should thus read: sin ψ ¼ −
1 ðA C −A2 C 1 Þ Δ 1 2
2. Eq. (18) should read: Q ¼ R x ðγ−π ÞRz ðθ1 ÞRx ðα 1 ÞRz ðϕ1 −π ÞRx ðα 2 ÞRz ðψÞ 3. In Eq. (21) a subscript ‘3’ appears where subscript ‘2’ should have been typed. The equation should thus read: na ¼
w 2 w1 jjw2 w1 jj
4. In Example 1, the correct values of α4 and α5 are 2.204 rad and 1.476 rad, respectively. Likewise, the numerical values of the three angles ∠C1OC2, ∠C2OC3 and ∠C1OC3 are 2.204 rad, 1.514 rad, and 1.476 rad, respectively. The value 1.514 was mistakenly attributed to α5. These errors notwithstanding, the algorithm remains valid and the numerical results are otherwise correct. The authors are grateful to Mr. Arjan Westerhuis, University of Twente, The Netherlands, who read thoroughly the paper, implemented our algorithm, and pointed out these errors. Moreover, he reportedly obtained the same numerical results recorded in the paper, with the provision of those cited in entry 4 above.
DOI of original article: http://dx.doi.org/10.1016/j.mechmachtheory.2009.07.005. ⁎ Corresponding author. E-mail addresses: [email protected] (S. Bai), [email protected] (M.R. Hansen), [email protected] (J. Angeles). 0094-114X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2012.05.001
Contents lists available at SciVerse ScienceDirect
Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt
Erratum
Erratum to ‘A Robust Forward-Displacement Analysis of Spherical Parallel Robots’ [Mech. Mach. Theory, 2009, 44(12), pp. 2204–2216] Shaoping Bai a, Michael R. Hansen b, Jorge Angeles c,⁎ a b c
Department of Mechanical and Manufacturing Engineering, Aalborg University, 9200 Aalborg, Denmark Department of Engineering, University of Agder, Norway Department of Mechanical Engineering, McGill University, Montreal, Canada
The authors would like to point out some typographical errors in the paper Bai, S., Hansen, M.R. and Angeles, J., “A Robust Forward-Displacement Analysis of Spherical Parallel Robots,” Mechanism and Machine Theory, 44(12), pp. 2204–2216, 2009. 1. In Eq. (12) a minus sign is missing. The equation should thus read: sin ψ ¼ −
1 ðA C −A2 C 1 Þ Δ 1 2
2. Eq. (18) should read: Q ¼ R x ðγ−π ÞRz ðθ1 ÞRx ðα 1 ÞRz ðϕ1 −π ÞRx ðα 2 ÞRz ðψÞ 3. In Eq. (21) a subscript ‘3’ appears where subscript ‘2’ should have been typed. The equation should thus read: na ¼
w 2 w1 jjw2 w1 jj
4. In Example 1, the correct values of α4 and α5 are 2.204 rad and 1.476 rad, respectively. Likewise, the numerical values of the three angles ∠C1OC2, ∠C2OC3 and ∠C1OC3 are 2.204 rad, 1.514 rad, and 1.476 rad, respectively. The value 1.514 was mistakenly attributed to α5. These errors notwithstanding, the algorithm remains valid and the numerical results are otherwise correct. The authors are grateful to Mr. Arjan Westerhuis, University of Twente, The Netherlands, who read thoroughly the paper, implemented our algorithm, and pointed out these errors. Moreover, he reportedly obtained the same numerical results recorded in the paper, with the provision of those cited in entry 4 above.
DOI of original article: http://dx.doi.org/10.1016/j.mechmachtheory.2009.07.005. ⁎ Corresponding author. E-mail addresses: [email protected] (S. Bai), [email protected] (M.R. Hansen), [email protected] (J. Angeles). 0094-114X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2012.05.001