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. Author manuscript; available in PMC: 2011 Feb 25.
Published in final edited form as: Int J Rob Res. 2009;57:535–549. doi: 10.1007/978-3-642-00312-7_33

Fig. 2.

Fig. 2

Choice of coordinates and reference frame Ψn at the needle tip. Control input ω generates a rotation around z, while control input v generates a circular motion around an axis parallel to x and passing through (0, −r, 0).