Appendix A: Primer on Linear Algebra and the Kinematics of Rigid Bodies (under construction)

Last updated Dec. 26 2015 by Francisco Valero-Cuevas

Abstract: _____

This brief primer provides basic concepts and reference material related to the critical concepts of linear algebra that are needed to work with rigid body kinematics. These concepts are critical to the intuition developed throughout the book. Readers with recent backgrounds in linear algebra may not need this, but others who have not seen linear algebra for some time would benefit from this review. I cannot overemphasize the benefits that come from having working knowledge of these fundamental con- cepts that are, in fact, within reach for anyone with even cursory exposure to high school algebra. There are multiple texts that cover this material in detail, but I would recommend [1, 2] as first texts, followed by [3] for those interested in a more detailed treatment of the subject in the context of robotics.

Forum, Exercises and Commentary: _________ Coming soon!

Additional references and suggested reading: ________________ Coming soon!

References in book: _______

G. Strang, Introduction to Linear Algebra (Wellesley Cambridge Press, Wellesley,2003)
T. Yoshikawa,Foundations of Robotics: Analysis and Control (MIT Press, Cambridge,1990)
R.M. Murray, Z. Li, S.S. Sastry, A Mathematical Introduction to Robotic Manipulation (CRC, Boca Raton, 1994)
Wikipedia contributors. Cartesian coordinate system. Wikipedia,The Free Encyclopedia. http://en.wikipedia.org/wiki/Cartesian_coordinate_system. Accessed 12 Feb 2015
F.J. Valero-Cuevas, A mathematical approach to the mechanical capabilities of limbs and fingers. Adv. Exp. Med./Biol. 629, 619–633 (2009)
F.J. Valero-Cuevas, B.A. Cohn, H.F. Yngvason, E.L. Lawrence, Exploring the high-dimensional structure of muscle redundancy via subject-specific and generic musculoskeletal models. J. Biomech. 48(11), 2887–2896 (2015)
Wikipedia contributors. Basisvectors. Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/wiki/Basis_(linear_algebra). Accessed 12 Feb 2015
Wikipedia contributors. Linear independence. Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Linear_independence. Accessed 23 May 2015
Wikipedia contributors. Right hand rule. Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Right-hand_rule. Accessed 23 May 2015
T.R. Kane, D.A. Levinson, Dynamics, Theory and Applications (McGraw Hill, New York, 1985)
J. Denavit, A kinematic notation for lower-pair mechanisms based on matrices. J.Appl.Mech. 22, 215–221 (1955)
V.J. Santos, F.J. Valero-Cuevas, Reported anatomical variability naturally leads t omultimodal distributions of Denavit-Hartenberg parameters for the human thumb. IEEE Trans. Biomed. Eng. 53, 155–163 (2006)
Wikipedia contributors. Denavit-hartenberg. Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Denavit-Hartenberg_parameters. Accessed 25 May 2015

Code: _____ Coming soon!