Dynamic simulation of a single closed chain

EFFICIENT DYNAMIC SIMULATION OF A SINGLE CLOSED CHAIN... 

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... 

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 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. 

In this section, the computational requirements of the dynamic simulation algorithm for a single closed chain are summarized and discussed. The number of required scalar operations is tabulated for each step, with the exception of the integration step. The q)erations required for integration are usually not included in the overall computational complexity of a simulation algorithm. 

Like the dynamic simulation algorithm fw a single closed chain, the algorithm developed here for simple closed-chain mechanisms may also be presented as a series of steps. In this case, five computational steps are required, and they are as follows ... 

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. 

The purpose of this book is to present computationally efficient algorithms for the dynamic simulation of closed-chain robotic systems. In particular, the simulation of single closed chains and simple closed-chain mechanisms (such as multilegged vehicles or dexterous hands) is investi ted in detail. In conjunction with the simulation algorithms, efficient algorithms are also derived for the computation of the joint space and operational space inntia matrices of a manipulator. These two inertial quantities are important factors in a variety of robotics applications, including both simulation and control. 

The Monte Carlo simulation comprises three distinct moves (i) Canonical Monte Carlo moves update the molecular conformations in the Mr repUca. In this specific application, we employ a Smart Monte Carlo algorithm [119] that utilizes strong bonded forces to propose a trial displacement [43, 87]. The amplitude of the trial displacement has been optimized in order to maximize the mean-square displacement of molecules [91], and the single-chain dynamics closely resembles the Rouse-dynamics of unentangled macromolecules [120]. (ii) Since each replica is an... 

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