Dynamic simulation closed-chain

Using the first-principles molecular-dynamics simulation, Munejiri, Shimojo and Hoshino studied the structure of liquid sulfur at 400 K, below the polymerization temperature [79]. They found that some of the Ss ring molecules homolytically open up on excitation of one electron from the HOMO to the LUMO. The chain-like diradicals S " thus generated partly recombine intramolecularly with formation of a branched Sy=S species rather than cyclo-Ss- Furthermore, the authors showed that photo-induced polymerization occurs in liquid sulfur when the Ss chains or Sy=S species are close to each other at their end. The mechanism of polymerization of sulfur remains a challenging problem for further theoretical work. 

Previous research in the dynamic simulation of robotic mechanisms includes the examination of both open-chain mechanisms [2,3,12,42] and closed-chain configurations [4, 16, 22, 31, 33, 39]. Although many of these earli results are useful and impextant, further improvements in the computational efficiency of dynamic simulation algorithms are necessary for real-time implementation. 

Although the details may be quite different, every research effort in the area of dynamic simulation faces a common task — the efficient and accurate solution of the Direct Dynamics problem. In the development of algorithms for Direct Dynamics, two basic approaches have emerged for both open- and closed-chain systems. The first utilizes the inversion of the x manipulator joint space inertia matrix to solve for the joint accelerations. More accurately, the accelerations are found via the solution of a system of linear algebraic equations, but the... 

As mentioned above, more efficient algorithms are needed to make real-time dynamic simulation a reality. This need is particularly great fw robotic systems with multiple chains and closed kinematic loops. Thus, a fundamental goal of this book is the development of better and more efficient algorithms for the dynamic simulation of multiple chain robotic systems. In particular, solutions to the Direct Dynamics problem fw simple closed-chain mechanisms are investigated. 

This book is organized into two parts. The first part addresses the efficient computation of manipulator inertia matrices, both joint space and operational space. Grrresponding algorithms may be found in Chapters 3 and 4, respectively. Ibe second part of this book presents efficient dynamic simulation algorithms for closed-chain robotic systems and is comprised of Chapters S and 6. 

In the control domain, A may be used to decouple face and/a motion control about the workspace axes. Later in this boc, we will show that it is also useful in the development of dynamic simulation algoithms fa closed-chain robotic systems. 

EFFICIENT DYNAMIC SIMULATION OF A SINGLE CLOSED CHAIN... 

Although a single closed chain is a simple example of a closed-chain robotic mechanism, its real-time dynamic simulation is not trivial. The dynamics of the chain must be combined with the kinematic constraints which are imposed by the tip contact. In general, both the contact forces at the tip and the joint accelerations must be computed to completely solve the system. 

In this chapter, an efficient serial algorithm for the dynamic simulation of a single closed chain is developed. The algorithm is valid fw a manipulator with... 

A review of previous work related to the dynamic simulation of single closed chains is given in the second section of this chapter. The next three sections discuss several steps in the development of the simulation algorithm. In particular, in the third section, the equations of motion for a single chain are used to partition the joint acceleration vector into two terms, one known and one unknown. The unknown term is a function of the contact forces and moments at the tip. The end effector acceloation vector is partitioned in a similar way in the fourth section, making use of the operational space inertia matrix. In the fifth section, two classes of contacts are defined which may be used to model interactions between the end effector and other rigid bodies. Specific examples are provided. 

In the sixth section, the complete dynamic simulation algorithm for a single closed chain is presented as a series of four computational steps. Each step is explained in detail, particularly the step which computes the unknown contact forces and moments. The integration of the joint rates and accelerations to obtain the next state positions and rates is also briefly discussed. The computational requirements of both versions of the simulation algorithm are tabulated and compared in the seventh section of this chapter. 

Dynamic Simulation Algorithm for a Single Closed Chain... 

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