Articulated-body dynamic equations

The development of the recursive articulated-body dynamic equations begins with the simple free-body dynamic equations of the two individual links. In the notation of this book, we may write the free-body equation for link 1 as follows ... 

We will now extend the recursive articulated-body dynamic equations for an open chain to describe the dynamics of a chain which is constrained at the tip. For this task, we will refer again to Figure 4.3. Now, however, we will assume that f, the spatial force exerted by the tip, is nonzero. 

Recursive dynamic equations fw a single c n chain are derived by Featherstone in [9] and later presented again by Brandi, et al. in [3]. The formulation of these equations is based on the concept of treating a chain of rigid bodies connected by joints as a single articulated body . The recursive equations allow the dynamics of the entire chain to be resolved to a single link called the handle of the articulated body. All interactions with the articulated body are assumed to... 

This is a simple recursive acceleration equation fw the unconstrained articulated body. Equation 4.37 may be combined with Equations 4.31 and 4.32 to give the following dynamic equation for link 1, the handle of the unconstrained articulated body ... 

The equations given above may be generalized for the case of an unconstrained articulated body with an arbitrary number of links. The dynamic equation for link i as the handle of the unconstrained articulated body, ignoring bias terms, is written in Equation 4.30, repeated here for convenience ... 

The ATB model is based on the rigid body dynamics which uses Euler s equations of motion with constraint relations of the type employed in the Lagrange method. The model has been successfully used to study the articulated human body motion under various types of body segment and joint loads. The technology of robotic telepresence will provide remote, closed-loop, human control of mobile robots. 

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