By Constantinos A. Balafoutis, Rajnikant V. Patel

The goal of this monograph is to provide computationally effective algorithms for fixing uncomplicated difficulties in robotic manipulator dynamics. In par­ ticular, the subsequent difficulties of rigid-link open-chain manipulator dynam­ ics are thought of : i) computation of inverse dynamics, ii) computation of ahead dynamics, and iii) iteration of linearized dynamic types. Com­ putationally effective strategies of those difficulties are necessities for genuine­ time robotic functions and simulations. Cartesian tensor research is the mathematical beginning on which the above pointed out computational algorithms are established. particularly, it really is proven during this monograph that by means of exploiting the relationships among moment order Cartesian tensors and their vector invariants, a couple of new tensor­ vector identities could be acquired. those identities enhance the idea of Carte­ sian tensors and make allowance us to control complicated Cartesian tensor equations effuctively. additionally, in keeping with those identities the classical vector descrip­ tion for the Newton-Euler equations of inflexible physique movement are rewritten in an an identical tensor formula that is proven to have computational advan­ tages over the classical vector formula. hence, in accordance with Cartesian tensor research, a conceptually uncomplicated, effortless to enforce and computationally effective tensor technique is gifted during this monograph for learning classical inflexible physique dynamics. XlI program of this tensor method to the dynamic research of rigid-link open-chain robotic manipulators is straightforward and results in an effective fonnulation of the dynamic equations of motion.

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We shall rely on the context to distinguish between the two representations. 1)) in homogeneous coordinates as follows. 2. 4). From the foregoing, we have two ways of analyzing a general rigid body displacement transformation. 1) can be used. 11 a), is suitable for kinematic analysis of rigid body motion when computational issues are of main concern. 10), leads to compact representations, but with significantly higher computational complexity. 11) provide the bridge between them. , relative configurations of rigid bodies.

However, in the actual kinematic and dynamic analyses of a robot manipulator, we consider the configuration of its last link as the configuration of the robot manipulator. This is acceptable for two reasons: First, the end-effuctor is always attached rigidly to the last link, and thus has a constant configuration relative to that of the last link; and second, we want the analysis to be general and not specific to a particular end-effuctor. Moreover, to make the analysis independent of a particular environment where the robot may be used, we choose the inertial or reference coordinate system to be attached to the base of the robot.

Thus for n even there are, in general, no fixed points different from o. ), we always have at least one line of fixed points, the axis of the rotation. Therefore, a consequence of the general theory of rotations in odd dimensional Euclidean spaces is the following Theorem. 1 (Euler): If a rigid body undergoes a displacement, leaving fixed one of its points 0, then a set of points of the body lying on a line that passes through 0 remains fixed as well. A corollary to Euler's theorem, sometimes called Chasles' theorem, states the following result.

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