By Jorge Angeles
This ebook bargains with robots - corresponding to distant manipulators, multifingered palms, jogging machines, flight simulators, and desktop instruments - that depend on mechanical structures to accomplish their projects. It goals to set up the rules on which the layout, regulate and implementation of the underlying mechanical structures are established. The remedy assumes familiarity with a few calculus, linear algebra, and hassle-free mechanics; in spite of the fact that, the weather of rigid-body mechanics and of linear changes are reviewed within the first chapters, making the presentation self-contained. an intensive set of workouts is incorporated and this re-creation accommodates quite a few advances.
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Extra resources for Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms 3rd edition (Mechanical Engineering Series)
Sample text
9) Consequently, in order to represent the images of the m vectors of Bu, namely, the set { L u j } " , n x m real numbers lij, for i = l , . . , n and j — 1 , . . ,m, are necessary. 1 The jth column of the matrix representation of L with respect to the bases Bu and By is composed of the n real coefficients lij of the representation of the image of the jth vector of Bu in terms of By. 10) is rather cumbersome, for it involves one subscript and one superscript. Moreover, each of these is subscripted.
Two different bases are unavoidable when the two spaces under study are physically distinct, which is the case in velocity analysis of manipulators. As we will see in Chapter 4, in these analyses we distinguish between the velocity of the manipulator in Cartesian space and that in the joint-rate space. While the Cartesian-space velocity—or Cartesian velocity, for brevity—consists, in general, of a 6-dimensional vector containing the 3-dimensional angular velocity of the end-effector and the translational velocity of one of its points, the latter is an n-dimensional vector.
10) is rather cumbersome, for it involves one subscript and one superscript. Moreover, each of these is subscripted. In practice, the bases involved are self-evident, which makes an explicit mention of these unnecessary. In particular, when L is a mapping of U onto itself, a single basis suffices to represent L in matrix form. In this case, its bracket will bear only a subscript, and no superscript, namely, [Ljg. Moreover, we will use, henceforth, the concept of basis and coordinate frame interchangeably, since one implies the other.