Model for Simple Closed-Chain Mechanisms

Multiple chain robotic systems can take many forms, some of them quite complex. Simple closed-chain mechanisms are a subset of multiple chain systems with specific structural characteristics. In this section, a model for simple closed-chain mechanisms is described, and the nature of the simulation problem for these mechanisms is discussed. 

The structure of a simple closed-chain mechanism is characterized by m actuated chains which support a single common reference member [31]. The supporting chains are assumed to be serial-link chains, firee of intmial closed loops. Therefore, the removal of the reference membo breaks all closed Io( in the system. Each chain may have an arbitrary numbo of links and degrees of freedom. The 

As was mentioned biefly in Chapt 1, th arc two basic types of simple closed-chain mechanisms called Type 0 and lype 1, respectively [31]. These two types are defined based on the nature of the interactions which occur between the links of the chain and the reference member or support surface. For both types, the support surface acts as the base of each chain. We will refa to the link which interacts with the support surface as link 1, and the link which intmcts with the reference member will be called the last link or end effector (link N). The far end of link N is the tip of the chain. 

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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. 

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