Dynamic simulation of simple closed-chain

EFFICIENT DYNAMIC SIMULATION OF SIMPLE CLOSED-CHAIN MECHANISMS... 

In this chapter, an efficient soial algorithm for the dynamic simulation of simple closed-chain mechanisms is derived. The development of this algorithm... 

A brief review of previous work related to the dynamic simulation of simple closed-chain mechanisms is given in the second section of this chapter. A model for simple closed-chain mechanisms is described in the third section, and the basic problem statement is also discussed. The dynamic equations of motion for the individual chains and the common reference member are summarized in the fourth section. 

In developing an efficient algwithm for the dynamic simulation of simple closed-chain mechanisms, we are naturally led to consider the relationship between the physical structure of the robotic system and the computational structure of the desired algorithm. Intuitively, it seems tqyparent that the structural parallelism present in a simple closed-chain mechanism should lead to computational parallelism in the solution of the Direct Dynamics problem for that mechanism. 

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. 

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. 

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. 

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 ... 

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