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By Fulton W.

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J. Physiol. Pharmacol. 60, 69–72 (2009) 4. E. Wall, A model of temporomandibular joint function in anthropoid primates based on condylar movements during mastication. Am. J. Phys. Anthropol. 109(1), 67–88 (1999) 5. J. Valero-Cuevas, H. U. J. A. Theodorou, Computational models for neuromuscular function. IEEE Rev. Biomed. Eng. 2, 110–135 (2009) 6. M. Murray, Z. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC, Boca Raton, 1994) 7. T. Yoshikawa, Foundations of Robotics: Analysis and Control (MIT Press, Cambridge, 1990) 8.

Murray, Z. S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC, Boca Raton, 1994) 7. T. Yoshikawa, Foundations of Robotics: Analysis and Control (MIT Press, Cambridge, 1990) 8. J. Valero-Cuevas, A mathematical approach to the mechanical capabilities of limbs and fingers. Adv. Exp. Med. Biol. 629, 619–633 (2009) 9. E. Zajac, Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17(4), 359–411 (1989) 10. J. J. Valero-Cuevas, Reported anatomical variability naturally leads to multimodal distributions of Denavit-Hartenberg parameters for the human thumb.

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.