A Journey from Robot to Digital Human: Mathematical by Edward Y. L. Gu

By Edward Y. L. Gu

This ebook presents readers with an exceptional set of varied and crucial instruments for the theoretical modeling and keep an eye on of complicated robot platforms, in addition to for electronic human modeling and reasonable movement iteration. Following a entire advent to the basics of robot kinematics, dynamics and regulate structures layout, the writer extends robot modeling tactics and movement algorithms to a miles higher-dimensional, better scale and extra refined examine region, specifically electronic human modeling. lots of the tools are illustrated by way of MATLAB codes and pattern graphical visualizations, providing a special closed loop among conceptual realizing and visualization.

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2 On the other hand, ⎞ ⎛ −4 0 v3T det ⎝ v1T ⎠ = det ⎝ 2 −1 v2T 0 1 ⎛ ⎞ 2 0 ⎠ = 16. 3 Thus, both approaches to evaluating the triple scalar product agree with each other. Furthermore, the triple vector product can be calculated by ⎛ ⎞⎛ ⎞ ⎛ ⎞ 0 −2 0 −3 12 v3 × (v1 × v2 ) = S(v3 )(v1 × v2 ) = ⎝ 2 0 4 ⎠ ⎝ −6 ⎠ = ⎝ 2 ⎠ . 0 −4 0 2 24 It can also be evaluated by ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ 2 0 12 v3 × (v1 × v2 ) = (v3T v2 )v1 − (v3T v1 )v2 = 6 ⎝ −1 ⎠ + 8 ⎝ 1 ⎠ = ⎝ 2 ⎠ . 0 3 24 Therefore, the two different ways for calculating the triple vector product match their answers with each other, too.

This has been recognized to be the most consistent, secure and unique approach. 2). Such a rotation approach is intuitively more natural, effective and easier for sampling in robotic path planning applications because the multiplication of matrices in a successive rotation process is not commutable ⎛ ⎞ in general. k1 Let a unit vector k = ⎝ k2 ⎠ be referred and projected onto a given k3 frame to be performed for a rotation. Clearly, k 2 = k12 + k22 + k32 = 1. Its corresponding skew-symmetric matrix is given by ⎞ ⎛ 0 −k3 k2 S(k) = K = ⎝ k3 0 −k1 ⎠ .

Springer (2008) 9. : Modeling and Control of Robot Manipulators. McGraw-Hill (1996) 10. , Husty, M. ): Advances in Robot Kinematics: Analysis and Control. Kluwer Academic Publishers, the Netherlands (1998) 11. Cubero, S. ): Industrial Robotics: Theory, Modelling and Control. Pro Literatur Verlag, Germany/ARS, Austria (2006) References 13 12. : Robotics, Modeling, Planning and Control. Springer (2009) 13. : Manufacturing Simulation with Plant Simulation and SimTalk Usage and Programming with Examples and Solutions.

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