By Edward Y. L. Gu
This publication offers readers with an outstanding set of various and crucial instruments for the theoretical modeling and regulate of complicated robot platforms, in addition to for electronic human modeling and real looking movement iteration. Following a accomplished advent to the basics of robot kinematics, dynamics and keep an eye on structures layout, the writer extends robot modeling approaches and movement algorithms to a far higher-dimensional, higher scale and extra subtle examine zone, specifically electronic human modeling. many of the tools are illustrated by means of MATLAB codes and pattern graphical visualizations, delivering a distinct closed loop among conceptual realizing and visualization.
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Extra info for A Journey from Robot to Digital Human: Mathematical Principles and Applications with MATLAB Programming
Chapters 2 and 3 introduce all the useful and relevant mathematical fundamentals. Chapter 4 starts a robotic modeling procedure and kinematic formulation. Chapter 5 will study the robots with redundancy, as well as the forward and inverse kinematics for serial/parallel hybrid-chain robotic systems. Once the foundations of robotics are built up, Chapter 6 will describe 12 1 Introduction to Robotics and Digital Human Modeling and illustrate the major steps to create parts and assemble them to mock up a complete robotic system with 3D solid drawing in MATLABT M .
4! 8) where the well-known Taylor expansions have been applied: sin φ = φ − φ3 φ5 + − ··· 3! 5! and cos φ = 1 − φ2 φ4 + − ···. 2! 4! 8), commonly called the Rodrigues formula, provides a means as a forward direction to determine the equivalent rotation matrix R if a frame is to be rotated by a given angle φ about a given unit vector k. , tr(R) = 3 − 2(1 − cos φ) = 1 + 2 cos φ so that φ = arccos tr(R) − 1 2 . 8) yields R − RT = 2 sin φK, and ﬁnally we have K= R − RT . 11) oﬀer an inverse formula in a recursive order to determine φ and k in terms of a given rotation matrix R.
All the n by n real orthogonal matrices with multiplication form an orthogonal Lie group O(n), and by further imposing the determinant of each member of O(n) to be +1, it becomes a special orthogonal group SO(n). Every rotation matrix belongs to the SO(3) group. However, many useful sets under certain binary operations violate either one or more conditions of the group deﬁnition, and they cannot be a group, though they are quite useful. In order to keep them for further study and application, we have to relax the conditions.