Dynamics of Complex Robotic Mechanical Systems
The subject of this chapter is the dynamics of the class of robotic mechanical systems introduced in Chap. 10 under the generic name of complex. Notice that this class comprises serial manipulators not allowing a decoupling of the orientation from the pos
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Dynamics of Complex Robotic Mechanical Systems
12.1 Introduction The subject of this chapter is the dynamics of the class of robotic mechanical systems introduced in Chap. 10 under the generic name of complex. Notice that this class comprises serial manipulators not allowing a decoupling of the orientation from the positioning tasks. For purposes of dynamics, this decoupling is irrelevant and hence, was not a condition in the study of the dynamics of serial manipulators in Chap. 7. Thus, serial manipulators need not be further studied here, the focus being on parallel manipulators and rolling robots. The dynamics of walking machines and multifingered hands involves special features that render these systems more elaborate from the dynamics viewpoint, for they exhibit a time-varying topology. What this means is that these systems include kinematic loops that open when a leg takes off or when a finger releases an object and open chains that close when a leg touches ground or when a finger makes contact with an object. The implication here is that the degree of freedom of these systems is time-varying. The derivation of such a mathematical model is discussed in Pfeiffer et al. (1995), but is left out in this book. The degree of freedom (dof) of the mechanical systems studied here is thus constant. Now, the two kinds of systems studied here pertain to very different types, for parallel manipulators fall into the realm of holonomic, while rolling robots into that of nonholonomic, mechanical systems. In order to better understand this essential difference between these two types of systems, we give below a summary of the classification of mechanical systems at large.
12.2 Classification of Robotic Mechanical Systems with Regard to Dynamics Because robotic mechanical systems are a class of general mechanical systems, a classification of the latter will help us focus on the systems motivating this study. Mechanical systems can be classified according to various criteria, the most 507 J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Mechanical Engineering Series 124, DOI 10.1007/978-3-319-01851-5__12, © Springer International Publishing Switzerland 2014
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12 Dynamics of Complex Robotic Mechanical Systems
common one being based on the type of constraints to which these systems are subjected. In this context we find holonomic vs. nonholonomic and scleronomic vs. rheonomic constraints. Holonomic constraints are those that are expressed either as a system of algebraic equations in displacement variables, whether angular or translational, not involving any velocity variables, or as a system of equations in velocity variables that nevertheless can be integrated as a whole to produce a system of equations of the first type. Note that it is not necessary that every single scalar equation of velocity constraints be integrable; rather, the whole system must be integrable for the system of velocity constraints to lead to a system of displacement constraints. If the system of velocity con
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