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By Fulton W.

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It is important to first get a sense of what each of these forms of the Jacobian convey. This raises a question that is addressed in the remainder of this chapter: When is the Jacobian invertible, and why? But for now, I will consider a truncated version of the Jacobian in Sect. 7 that is both square and invertible. In the planar limb in Fig. 14) In this case, J ∈ R2×2 , and is a full rank invertible matrix (more on this in Sect. 5). 0 Draw such a limb and let us calculate some examples, such as applying a positive angular velocity at q1 to find the resulting instantaneous endpoint velocity vector x˙ using Eq.

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